Rational chemical design of Triarylmethyl-based devices and 2D materials

Rational chemical design of Triarylmethyl-based devices and 2D materials Isaac Alcón Rovira Aquesta tesi doctoral està subjecta a la llicència Reconeixement 3.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento 3.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution 3.0. Spain License. Secció de Química Física Departament de Ciència de Materials i Química Física Facultat de Química Universitat de Barcelona Programa de doctorat de Química Teòrica i Modelització Computacional Rational chemical design of Triarylmethyl-based devices and 2D materials Memòria presentada per: Isaac Alcón Rovira per a optar al grau de Doctor per la Universitat de Barcelona Dirigida per: Dr. Stefan T. Bromley Dr. Francesc Illas i Riera (Universitat de Barcelona) (Universitat de Barcelona) Tutor: Dr. Iberio De Pinho Ribeiro Moreira (Universitat de Barcelona) UNIVERSITAT DE BARCELONA FACULTAD DE QUÍMICA DEPARTAMENT DE CIÈNCIA DE MATERIALS I QUÍMICA FÍSICA INTITUT DE QUÍMICA TEÒRICA I COMPUTACIONAL Rational chemical design of Triarylmethyl-based devices and 2D materials Isaac Alcón Rovira Barcelona, 2018 a l’Avi i la Iaia The work presented in this doctoral thesis has been carried out at the Materials Science and Physical Chemistry Department of the Chemistry Faculty at the University of Barcelona (UB) and within the Institute of Theoretical and Computational Chemistry (IQTC-UB) and the Reference Network of Theoretical and Computational Chemistry of Catalunya (XRQTC). This project has been possible in virtue of the financial support provided by the Spanish (MAT2012-30924 project) and the Catalan Government (2014SGR97 and XRQTC grants). Computer resources were partly provided by the Red Española de Supercomputación (RES) and the Centre de Supercomputació de Catalunya (CESCA). Isaac Alcón Rovira is also grateful for the pre-doctoral grants from the Catalan (FI-DGR) and Spanish Government (FPU14/01470), as well as for the grant-in-aid that covered the research stay at Imperial College London given by the Spanish Government (FPU). I Agraïments First of all I would like to thank Stefan Bromley, main supervisor of this PhD thesis, for his supervision and help during all these four years. I believe the success of this work has enormously relied on the intellectual freedom that Stefan gave me since the first day, promoting my own creativity and accepting new ideas, as well as being patient at the time of clarifying concepts and theories every time I needed. His accessibility has been of great value for me: I have had access to his time 80% of the occasions I pop up by his office, always open for discussion. I believe this is not that common within science. From a scientific perspective, I must recognise there are few more people with whom I connect more. That passion to seek for truth, even at the most fundamental level, is something I noticed even before starting this PhD thesis, and greatly appreciate. Again, unfortunately, this is a fundamental aptitude I fear is not that general in science today. All in all, I think we both have strongly believed in the work performed during time which, probably, is the result of the shared desire to do original, excellent and useful science. So... Thanks Stefan!! També vull expressar el meu agraïment al Francesc Illas, co-director d’aquest treball. La seva actitud oberta i ganes de donar un cop de mà en el que fes falta han estat claus durant tot aquest temps, en molts aspectes. De nou, la accessibilitat al seu coneixement i consell és quelcom que em va sobtar des d’un començament: el seu despatx sempre ha estat obert per discutir de qualsevol qüestió laboral, científica o, fins i tot, d’actualitat política. La seva actitud pro-activa constant és una de les qualitats pel que li estic més agraït. Estic convençut que no hauria estat capaç de portar a terme els seminaris Interns del IQTC (conjuntament amb el Manel Mondelo) si no hagués estat pel suport i ànim que el Francesc em va donar amb aquesta qüestió des del mateix matí que va sorgir la idea discutint al cafè. Aquesta visió de voler provar noves iniciatives “bottop-up” la comparteixo totalment. I també li vull agrair els coffee-breaks del CMSL on he aprés més de com funciona el món científic que en uns quants congressos als que he assistit: de nou una mostra més de la gran accessibilitat que s’ofereix al grup del Francesc i el Stefan, on sembla que la única barrera personal entre estudiants i professors és la distancia que hi ha entre oficines. Un gust! I per tancar el pack de direcció/tutoria, vull agrair al Iberio les seves classes particulars sobre mecànica quàntica i, en concret, els mètodes computacionals d’estructura electrònica. Al arribar a la UB el meu coneixement de tota aquesta branca de la ciència era completament nul·la, ha estat una sort per a mi poder nodrir-me del coneixement tan profund sobre els diferents models, aproximacions i “pegues” de cadascun d’ells que el Iberio m’ha aportat. Gràcies a ell tinc una idea aproximada (amb DFT... no podia ser d’un altre manera) del camp dels mètodes d’estructura electrònica la qual desitjo poder aprofundir en un futur amb més temps al meu abast. En termes més generals, vull agrair a tots els membres del IQTC i de la Secció de Química Física de la UB tota l’ajuda rebuda i moments compartits durant aquest temps. En especial, moltes gràcies Jordi, Carme, Paniagua, Konstantin, Gabor, Federico, Ángel, Viñes, Rosendo i a tots els companys de oficines varies: Ilker, Sergey, Dani, Vera, Maria, Marçal, Alberto, Julia, Almu, Tommy, Andy, Toni, Lorena, Cristina, Raul, Sergi, Oriol (salvador de portades), Hèctor, Gerard, Manel, etc etc etc... Tot i que ha estat un període de treball força elevat, sempre us he tingut a un o a l’altre per xerrar una estona, fer una de bolos, o discutir sobre qualsevol tema, el qual m’ha ajudat enormement en aquesta difícil empresa que és el doctorat. Moltíssimes gràcies nanus/es! També vull agrair al Manel la co-organització dels Seminaris Interns del IQTC. Organitzar-los no ha estat II una empresa fàcil, però crec que finalment hem fet una feina prou ben feta amb, sembla, recorregut! Moltes gràcies també al Ramón, tècnic del Departament per la seva ajuda en repetides ocasions amb els varis pòsters que li he anat donant durant aquest temps. I abans de tancar el bloc IQTC/Departament no em puc oblidar dels Srs. Administradors de sistema; Jordi i Teresa. Ha estat un plaer poder resoldre els meus dubtes sobre el Linux i els ordinadors en general amb la vostra constant ajuda. Sempre que ho he necessitat, m’heu facilitat tot el temps necessari, sense la mínima mostra de cansament (i mira que he pujat vegades a la planta 7a eh...). Dóna gust aprendre coses tan interessants com la command-line amb gent tan disposada a ensenyar com vosaltres, així que moltíssimes gràcies companys! Dedicaré una part d’aquests agraïments a la Dr. Marta Mas, ja no només per la qualitat com a persona i com d’agust es col·labora/treballa amb ella, si no també en particular per la vista que va tenir durant la meva tesis de Màster al proposar-me fer el doctorat dins la branca de la Química Computacional... Mai havia pensat en aquest camp, ni per descartar-lo. En canvi tu Marta vas veure que podia encaixar-hi i, 4 anys després, tinc clar que vull construir la meva carrera professional en aquesta direcció. Gràcies per veure en els teus estudiants quelcom més que eines per produir articles i preocupar-te pels seus camins personals, dins o fora de la teva línea de recerca. En el meu cas particular, ha estat clau. En un terreny més personal vull agrair en general a tota la família per la paciència que han tingut durant aquests últims anys amb el escàs temps que he tingut per ells. Papa, Mama, Gerard, sorry per tots aquests no-possibles dinars, o dinars mirant el rellotge per temes de treball, i gràcies per comprendre-ho i adaptar-vos sense dir ni “mu”. En la mateixa línea, gràcies Avi, Iaia, per entendre les meves visites cada cop més espaiades a mesura que ha anat avançant aquesta tesis doctoral. M’agradaria també agrair al Víctor, company de converses durant tots aquests anys, per la teva saviesa i guia en moments difícils. Que important és poder rebre un bon consell de tant en tant. Ha estat fantàstic. And last but not least, com se sol dir, et vull donar les gràcies, Jèssica, per ser-hi. El suport i estima que m’has donat tot aquest temps no es pot descriure en una frase o paràgraf. Simplement espero poder continuar el meu camí al teu costat per molts més anys. Avi, Iaia, gràcies per ser casa meva. Aquest treball va per vosaltres. 1 Chapter 1 INTRODUCTION 2 Chapter 1 Introduction 3 As may be deduced from the title of this work, this PhD thesis has been mainly focused on the study, by means of first principles density functional theory (DFT) calculations, of triarylmethyl-based (TAM) devices and 2D materials. Some of the works in this thesis in collaboration with the experimental group of Prof Jaume Veciana and Dr Marta Mas-Torrent study different physic-chemical properties of TAMs that could be exploited within different type of devices for nano-electronics applications such as molecules wires, molecular switches and spintronic components. Hence, my contribution in those works has mainly been a support to the experimental findings where, by means of computational chemistry, I have been able to provide a more detailed insight into the studied TAM systems. Such a collaboration has proven to be very successful during these last four years, producing interesting works such as those presented in publications #1, 2, 3 and #7. The proposition of TAM-based 2D covalent organic frameworks (TAM 2D-COFs) has arose using first principles DFT calculations as a tool to predict new molecular systems not experimentally realized yet (2nd part of this thesis). Despite the fact TAMs have been already used to construct different sorts of devices and materials, TAM 2D-COFs represent a class of materials which has not been experimentally realized yet. During this PhD project I have found such materials of primary interest, especially as future platforms for nano-electronics, and hence, by means of this work and key publications resulting from it, I propose such platforms to be applied in such direction in the future. The studies on different TAM 2D-COFs are described in publications #5, #6 and #8. Contribution #4 is a study of single-molecule TAMs that, later, lead to the design of TAM 2D-COFs and hence it may be considered as the starting point of such a research line. Consistently, in this chapter I will first introduce TAM molecules and their role as building blocks to prepare different sorts of multi-functional materials and devices. In the second part I will briefly introduce the relatively new field of 2D covalent organic frameworks (2D-COFs) to provide a basic idea about the type of molecular arrays that are being generated in this branch of chemistry and a few studies highlighting their potential for future nano-electronics. 1.1 Triarylmethyls: A bit of history 1.1.1 The discovery The start of the family of TAMs represents the start of organic radical chemistry, due to the fact the synthesis of the triphenylmethyl by Moses Gomberg in 1900 (see Fig. 1.1) is the first instance of a trivalent carbon atom;1 i.e. an organic radical. Gomberg was trying to synthesize the tetra-phenyl methyl, but the resulting synthesized product showed to be an unsaturated hydrocarbon which easily reacted with both atmospheric oxygen or even in contact with diluted solution of iodine, not fitting with the expected behaviour for saturated hydrocarbons such as the pursued tetraphenylmethyl or the potential dimer, the hexaphenyl-ethyl. After a long number of experiments Gomberg concluded he was dealing with the first 4 Chapter 1 instance of a trivalent carbon atom: i.e. the first instance of an organic radical, the triphenylmethyl1 (Fig. 1b). Fig. 1.1 a) Moses Gomberg working in his laboratory in Michigan. b) Chemical structure of the triphenylmethyl where the unpaired electron (dot) sits on the central methyl carbon atom. As showed by Gomberg, the triphenylmethyl was not an isolated case, but actually just the first example of a new family of compounds bearing a trivalent carbon atom.2 Indeed, his discovery opened the family of TAMs but, more importantly, the field of organic radicals. After his investigation, many more TAM compounds were synthesized during the 20th century. Moreover, some works showed that it was possible to have not only one trivalent carbon atom, but two,3 three,4 or multiple5 radical centres in the same purely organic compound, which was the start of organic poly-radicals.6,7 The importance of Gomberg’s synthesis of the triphenylmethyl is also highlighted by the interest of important chemists who synthesized some triphenylmehyl derivatives, such as Wilhelm Schlenk,8 or studied the optical properties of such a new family of compounds, such as Gilbert Newton Lewis.9 1.1.2 Towards chemical persistence: the PTM sub-family Triphenylmethyl-derivatives are not persistent organic radicals (i.e. they last no longer than some days in solution2) and hence, besides being of great fundamental significance, their discovery lacks any applicability for any chemical technology. This dramatically changed in 1971 thanks to the work pioneered by an organic chemist from the University of Barcelona, Manuel Ballester, who started synthesizing a new family of TAMs where the three aryl rings were substituted with chlorine atoms.10 These compounds were named perchlorotriarylmethyls or, in short, PTMs. As described by Ballester himself, PTMs showed a remarkable persistence not reacting with highly aggressive chemical species such as concentrated sulphuric and nitric acids, sodium hydroxide or halogens, not decomposing up to Introduction 5 300°C and having half-lives of decades in air.10 As pointed out in that first contribution, the principal reason for the inertness of the PTM series of radicals relied on the sterical protection, or shielding effect, provided by Clatoms of aryl rings on the central radical carbon (see Fig. 1.2a). Fig. 1.2 a) PTM structure using Van-der-Waals radius to illustrate the important sterical shielding effect of chlorine atoms on the central radical carbon (dashed central point). b) PTM-based self-assembled monolayer exploited as a robust memory device. With such outstanding chemical persistence, Ballester showed the chemical versatility of PTMs, where different chemical groups could be attached on the outer positions of the perchlorated aryl rings12 or where hetero-aromatic rings (such as pyridine) could also substitute one of the aryl rings.13 1.1.3 Towards application Again, as pioneered by Ballester, the outstanding chemical persistence of the new series of inert organic radicals made them very attractive for applications. Ballester exploited PTMs for the spin labelling of biomolecules (such as amino acids and peptides) which could be detected by EPR.14 However, it was two of Ballester’s followers, Profs Jaume Veciana and Concepció Rovira established at the Institute of Materials Science of Barcelona (ICMAB), who took the lead on the exploitation of PTMs for different applications mainly focused in materials science and electronics (see Fig. 1.2b). It turns out that the unpaired electron in TAMs (and, consequently, in PTMs) gives rise to a series of interesting properties such as a spin moment, enhanced electrical conduction, absorption and emission of UV-vis. light (i.e. colour and fluorescence) and redox activity. Upon acquiring the chemical persistence provided by PTMs, all these characteristics become suddenly available, which obviously has made the use of PTMs very attractive as appealing molecular monomers to construct different multi-functional materials and devices. In the following section I will describe most important instances where TAMs (but mainly PTMs) have been exploited as building blocks in the field of materials science for applications in electronics and magnetism. It is worth remembering that some TAMs have been highly used in the field of oxygen detection,15–19 spin labelling of bio-molecules15,20–22 (as previously mentioned) and also as 6 Chapter 1 dynamic nuclear polarization agents23,24 (to improve NMR signal/noise ratio). However, given the focus of this thesis toward applications in the field of materials science and devices for electronics and spintronics, those different applications will not be explained with further detail in this work. 1.2 TAM-based applications 1.2.1 TAM-based polymer magnets The first major applicability of TAMs in the field of materials science was, for obvious reasons, for the preparation of organic magnets. The basic rational was to covalently bond as many TAM units as possible so that the final oligomer or polymer could retain a magnetic moment by the interaction of all individual spin moments. Without going too much in details, the first stage in this research line was the synthesis of magnetic clusters where two TAM units, or more, were covalently bonded together in different ways and their magnetic properties assessed through electron paramagnetic resonance (EPR) measurements. A very instructive review was written by Nicolai M. Shishlov, where most of the synthesized TAM-based oligomers are reported.7 There, it is also possible to see the use of PTMs to synthesize such magnetic clusters, as pioneered by Veciana’s group. This race eventually culminated in a series of promising works,5,25,26 by Suchada and Andrzej Rajca who in 2001 reported the synthesis of the first magnetic plastic based in a triphenylmethyl polymer6 (Fig. 1.3). Fig. 1.3 Chemical structure of the highly cross-linked triphenylmethyl (or TPM) based polymer, where an effective magnetic moment corresponding to an average S equal to 5000 was measured at 10K by susceptibility SQUID measurements. Rajca and co-workers were able to synthesize the magnetic plastic shown in Fig. 1.3 by previously preparing the polymer based on methoxy-triphenylmethyl (i.e. non-radical species) which upon deprotection of methoxy groups by Na/K reduction and following mild oxidation with I2 generated the multi-radical disordered mesh. Such synthesis gave rise to the highest recorded spin moment for an organic polymer, with an average S equal to 5000 below 10 K, as found with susceptibility SQUID measurements.6 Introduction 7 1.2.2 TAM-based supra-molecular frameworks The important sterical hindrance provided by Cl atoms in PTMs prevented the successful synthesis of large PTM-based oligomers in a similar way as was done with the hydrogenated TAM (the triphenylmethyl).7 Oligomers with three27 or four28 covalently bonded PTM units already exhibit very crowded and highly constrained structures, even influencing the resulting magnetic behaviour,28 and hence those represent the furthest attempts of synthesizing PTM radical polymers. However, Veciana and co-workers found another very successful manner to generate PTM-based molecular frameworks through H-bonding. They found that PTM derivatives with carboxylate groups in parapositions bear an outstanding tendency to self-assemble.29 Changing the number of carboxyl groups, PTMs self-assemble in 1D, 2D and 3D supra-molecular orderings, where the H-bonding between carboxyl groups of adjacent PTM molecules is the driving force defining the topology of the different frameworks.29 As a culmination of such approach they reported a PTM-Cu(II) metal organic framework with large ordered pores (3 nm of diameter) with bulk magnetic ordering (see Fig. 1.4).30 Fig. 1.4 Different structural representations of the metal-organic framework based on a tri-carboxylated PTM radical and Cu2+. As reported by Maspoch et al.,30 the PTM-Cu-MOF showed the ability to change its pore size depending on the solvent that was absorbed while maintaining the main hexagonal porous skeleton. Such structural distortions lead to important changes in the magnetic interactions between radical PTM units within the material, which could be tracked by SQUID magnetometry observing different magnetic ordering depending on the swallowed solvent.30 As mentioned in that contribution, these materials could be used as highly selective solvent sensors. 1.2.3 TAM-based data-memory devices The spin moment in TAMs is not the only characteristic which makes them potential candidates for different applications in magnetism and electronics. Another appealing property of TAMs (and PTMs) is that they are easily reduced to the corresponding anion species; i.e. they are redox active.31,32 Moreover, the radical and anion species present distinct optical and magnetic properties. For instance the anion is not 8 Chapter 1 magnetically active, contrary to the neutral state due to the existence of the unpaired electron. Based on that and thanks to the persistence of PTMs on different substrates33 Concepció Rovira and co-workers were able to prepare a PTM-based data memory device34 (see Fig. 1.5). Fig. 1.5 Molecular switch based on a PTM self-assembled monolayer on ITO. As shown, the neutral and anion states of the PTM monolayer can be switched by means of positive and negative applied electrical bias. Both optical and magnetic properties of the monolayer change with the redox state, which then may be used as output signals of the device. Hence, PTMs were chemically bonded on a transparent and conductive substrate (Indium-Tin oxide, or ITO) and, by applying a negative (positive) voltage on the substrate, it was possible to switch the PTM SAM from the neutral to the -1 redox state (and viceversa) in a highly reversible manner. Because of the different magnetic and optical properties of the molecular monolayer in each state Rovira and co-workers were able to track the state of the switch by EPR and by UV-vis. spectroscopies (see Fig. 1.5 for details). As reported, the device was switched more than 60 times without showing any signal loss. 1.2.4 TAM-based molecular wires Having an unpaired electron which is π-conjugated through the entire molecular skeleton brings another interesting characteristic for molecular electronics and spintronics, which is the existence of a πconjugated singly-unoccupied molecular orbital (SUMO) through which incoming unpaired electrons may flow. Again, Veciana’s group took the lead in exploring such characteristic to build different types of electronic devices. One of the first demonstrations of such increased electrical conductivity was reported by the work of Nuria Crivillers et.al that compared the electrical conductivity of a radical PTM SAM and its hydrogenated version35 (where the H atom is bonded to the central carbon atom, and hence the PTM molecule becomes closed-shell, i.e. with all electrons paired), as schematically shown in Fig 1.6. Introduction 9 Fig. 1.6 a) Open-shell and b) closed-shell PTM-based SAMs on gold. c) Calculated orbital energies for each PTM monolayer compared with the Fermi energy levels of the utilized Au substrate and diamond tip (grey bars). By means of STM measurements, Crivillers et al. found that the single-molecule electronic conductivity through the open-shell PTM monolayer was an order of magnitude larger than the corresponding hydrogenated closed-shell counterpart. As highlighted in that work,35 such large differences in the conductivity could not be assigned to different molecular structures due to the fact both cases showed almost the same molecular conformation but, actually, an electronic effect due the π-conjugated SUMO in the radical PTM SAM in very close energy with the incoming electrons from the diamond tip (see Fig. 1.6c).35 A more recent work comparing such two systems using a GaIn electrode has determined a difference of two orders of magnitude between the radical and the hydrogenated closed-shell PTM SAMs.36 1.2.5 TAMs as spintronic devices Ultimately, the fact that, as demonstrated in the work presented above, electrical conduction takes place through the SUMO associated to the π-conjugated unpaired electron in TAMs, these organic radicals may present some potential for spintronics.37 The field of spintronics relies on the fact that conductive electrons may feel a resistance upon moving through magnetic defects. A signature of such phenomena is the so-called Kondo effect,38 which is translated in the appearance of the so-called Kondo peak in electrical current measurements through magnetic centres, such as radical centres. Such a peak was first reported for organic radical compounds for a physisorbed layer of a verdazyl radical derivative39 by means of scanning tunnelling spectroscopy (STS) measurements. The great difficulties in measuring such phenomena is due the fact that it is highly sensitive to other phenomena such as temperature. Because of this, very low temperature experiments are required, which imposes the necessity of using state-of-the-art equipment capable of running such type of electrical measurements at temperatures as low as 1K or below. Such measurements were able to measure the electrical conduction in a two and three terminal solid-state devices having a single PTM radical molecule as the central component of the molecular break-junction,40 as depicted in Fig. 1.7. Prof Bromley and myself participated in this work with specific DFT calculations (not included in this thesis). 10 Chapter 1 Fig. 1.7 a) Single-molecule break junction based on a specifically designed PTM organic radical. b) Detected Kondo peak in the corresponding dI/dV vs. V curves between both Au electrodes, indicative of the interaction between the unpaired electron in the radical centre and conductive electrons. The changes of the detected peak with an applied magnetic field demonstrate the magnetic nature of such feature. Testing twoand threeterminal devices, dI/dV vs. V STS (Scanning Tunneling Spectroscopy) curves showed the appearance of a Kondo peak at 0V.40 As it was reported, and shown in Fig. 1.7b, such a Kondo resonance was highly sensitive to temperature (already not detectable at 6K) and, very importantly, to the application of local magnetic fields (from 0 to 8T) where a Zeeman splitting may be observed (Fig. 1.7b). The latter demonstrates the paramagnetic nature of the Kondo resonance and, hence, its origin in the unpaired electron within the PTM core, demonstrating the potential of PTM (and TAMs) as organic spintronics components. As explained in the beginning of this chapter, the predictive part of this PhD thesis has been focused on the design of a new class of as yet unexplored 2D materials: TAM-based 2D covalent organic frameworks (TAM 2D-COFs). At the following section I will briefly introduce 2D-COFs, their potential for nanoelectronic applications and provide some relevant examples. 1.3 2D covalent organic frameworks (2D-COFs) 1.3.1 Preparation and structure of 2D-COFs 2D covalent organic frameworks are 2D materials made through a bottom-up approach41,42. Specifically designed discrete molecules are first deposited, normally by chemical vapour deposition (CVD), on a solid substrate (normally metals) at a certain temperature that allows the molecules to re-organize on the surface and form ordered physisorbed molecular arrays (see Fig. 1.8a). Application of higher temperatures leads to the 2D-COF formation, normally, as isolated islands over the substrate (see Fig. 1.8b and zoomed image in 1.8c). Introduction 17 Müllen and R. Fasel, Chem. Commun. (Camb)., 2009, 6919–21. 51 X.-H. Liu, Y.-P. Mo, J.-Y. Yue, Q.-N. Zheng, H.-J. Yan, D. Wang and L.-J. Wan, Small, 2014, 10, 4934–9. 52 C. Steiner, J. Gebhardt, M. Ammon, Z. Yang, A. Heidenreich, N. Hammer, A. Görling, M. Kivala and S. Maier, Nat. Commun., 2017, 8, 14765. 53 W. Liu, X. Luo, Y. Bao, Y. P. Liu, G.-H. Ning, I. Abdelwahab, L. Li, C. T. Nai, Z. G. Hu, D. Zhao, B. Liu, S. Y. Quek and K. P. Loh, Nat. Chem., 2017, 9, 563–570. 54 A. Basagni, F. Sedona, C. A. Pignedoli, M. Cattelan, L. Nicolas, M. Casarin and M. Sambi, J. Am. Chem. Soc., 2015. 55 A. Basagni, G. Vasseur, C. A. Pignedoli, M. Vilas-Varela, D. Peña, L. Nicolas, L. Vitali, J. Lobo-Checa, D. G. de Oteyza, F. Sedona, M. Casarin, J. E. Ortega and M. Sambi, ACS Nano, 2016, 10, 2644–2651. 56 W. Dong, L. Wang, H. Ding, L. Zhao, D. Wang, C. Wang and L.-J. Wan, Langmuir, 2015, 31, 11755–11759. 57 Q. Sun, C. Zhang, L. Cai, L. Xie, Q. Tan and W. Xu, Chem. Commun., 2015, 51, 2836–2839. 58 G. Gu, N. Li, L. Liu, X. Zhang, Q. Wu, D. Nieckarz, P. Szabelski, L. Peng, B. K. Teo, S. Hou, Y. Wang, R. Bhosale, A. Mateo-Alonso, J. V. Barth, K. Wu and Y. F. Wang, RSC Adv., 2016, 6, 66548–66552. 59 L. Lafferentz, V. Eberhardt, C. Dri, C. Africh, G. Comelli, F. Esch, S. Hecht and L. Grill, Nat. Chem., 2012, 4, 215– 20. 60 D. F. Perepichka and F. Rosei, Science (80-. )., 2009, 323, 216–217. 61 C. Nacci, F. Ample, D. Bleger, S. Hecht, C. Joachim and L. Grill, Nat. Commun., 2015, 6, 7397. 62 J. P. Llinas, A. Fairbrother, G. Borin Barin, W. Shi, K. Lee, S. Wu, B. Yong Choi, R. Braganza, J. Lear, N. Kau, W. Choi, C. Chen, Z. Pedramrazi, T. Dumslaff, A. Narita, X. Feng, K. Müllen, F. Fischer, A. Zettl, P. Ruffieux, E. Yablonovitch, M. Crommie, R. Fasel and J. Bokor, Nat. Commun., 2017, 8, 633. 63 J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp and W. A. de Heer, Nature, 2014, 506, 349–354. 64 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science (80-. )., 2004, 306, 666–669. 65 A. Narita, X.-Y. Wang, X. Feng and K. Müllen, Chem. Soc. Rev., 2015, 44, 6616–6643. 66 P. Ruffieux, S. Wang, B. Yang, C. Sanchez, J. Liu, T. Dienel, L. Talirz, P. Shinde, C. A. Pignedoli, D. Passerone, T. Dumslaff, X. Feng, K. Muellen and R. Fasel, Nature, 2015, 531, 15. 67 S. Kawai, S. Saito, S. Osumi, S. Yamaguchi, A. S. Foster, P. Spijker and E. Meyer, Nat. Commun., 2015, 6, 8098. 68 C. Bronner, S. Stremlau, M. Gille, F. Brauße, A. Haase, S. Hecht and P. Tegeder, Angew. Chemie Int. Ed., 2013, 52, 4422–4425. 18 Chapter 1 19 Chapter 2 Methodology 20 Chapter 2 Methodology 21 This PhD thesis has involved the computational modelling of different organic systems, mainly singlemolecules, self-assembled monolayers on metal surfaces (i.e. hybrid systems) and 2D covalent networks constructed by specific molecular building blocks. Each system has required its particular computational methodology and specific models. Such particularities are explained in detail on the methodology section within each publication presented in this work. However, throughout this PhD thesis I have used two different types of computational based methods, namely, force-fields (FFs) and density functional theory (DFT). FFs have been mainly utilized to optimize the atomic structure of molecules or periodic moleculebased 2D networks. DFT calculations have been used to further refine the pre-optimized structures by FFs and to obtain reliable information about the electronic structure and related properties (something not accessible just with FFs). In this section, I will briefly introduce FFs and devote most of it to a general introduction to electronic-structure modelling, placing special attention to DFT. Specific modelling tools and schemes used in this work such as molecular dynamics and periodic calculations will also be briefly introduced at the end of this chapter. 2.1 Force field calculations Force field (FF) calculations are the most computationally efficient way to optimize the atomic structure of molecules and materials. In such methods atoms are described as point masses interacting under classical potentials based on a number of structural parameters (like distances, angles, dihedrals) which determine the total energy of the system. The mathematical form of such classical potentials with respect to those structural parameters is often constructed by fitting analytical expressions to values from experimental data or higher-level theory calculations such as wave-function methods. The total energy of a molecular system can be separated as follows: (1.1) where is the total energy of the system, includes interactions between covalently bonded atoms, such as those within a molecule, and includes those interactions that do not require a covalent bond to take place, such as electrostatic interactions, H-bonds, etc. and can be further split into its different components: (1.2) (1.3) . 22 Chapter 2 In eq. 1.2 , and are equilibrium values for bond distances, bond angles and dihedral angles, respectively. represents the energy dependence on the distance between two bonded atoms, and the energy of the system upon varying the angle between two atoms bonded with the same connecting atom (i.e. bending). Both contributions are represented by simple harmonic potentials. completes the part and describes the energy associated to dihedral angles; i.e. those involving two molecular planes, such as the two phenyl rings twisting one respect each other in the biphenyl molecule. As it may be seen in eq. 1.2 presents a periodic form based in a cosine function with respect to the dihedral angle ( ), where is a non-negative number indicating periodicity. The term includes forces occurring between atoms which are non bonded. represents coulombic repulsion and attraction interactions between partial charges ( and ) associated to different atom types with separation , having the Coulombic form. This term will be positive (i.e. repulsive) or negative (i.e. attractive) depending on the sign of both involved charges. describes weakly attractive interactions between atoms such as dipole-dipole interactions, induced dipole-dipole interactions and dispersive interactions, all being collected in the term in eq. 1.3. is the equilibrium distance between atoms and and is a weighting parameter determining the energetic contribution of such interaction to . Finally, the last term in (see eq. 1.3) comes due to the Pauli exclusion principle, which is accounted for with a repulsive (i.e. positive) term which repels two atoms at short separation. These last two terms (i.e. and ) compose the so-called Lennard-Jones potential,1 describing the interaction between two atoms not taking into account coulombic interactions. Sometimes for some force-fields a Morse potential2 of the form , where , is used instead of the Lennard-Jones potential. All these different energy terms will allow us to compute the total energy of our system ( in eq. 1.1) in a particular conformation and to optimize the atomic structure by minimizing through methods such as the conjugate gradient3 or Newton-Raphson. Hence, the positions of all atoms will vary upon minimizing the total contribution of all terms in equations 1.2 and 1.3 and we will get the structural minima leading to the lowest value of . These methods are the same used in electronic structure calculations to optimize the atomic structure of the system. However, in those cases the atoms will move through a potential energy surface defined by the electrons,4 contrary to FFs where the energy is expressed through eq. 1.1 – 1.3. Methodology 23 Notice that from FF methods no electronic information is obtained at all. Through these calculations only an approximate atomic structure may be obtained and its accuracy will entirely rely on the particular FF utilized (determining all predesigned constant parameters appearing in equations 1.2 and 1.3). Hence, we may use FF calculations to get appropriate initial molecular structures which later we may use to obtain refined conformations and the associated electronic information by electronic structure methods, introduced in the following sections. 2.2 The Schrödinger equation The non-relativistic time-independent Schrödinger equation is normally used to describe the electronic structure of molecular systems: (2.1) Where is the wave function of a system described by the position of all nuclei ( ) and electrons ( ), is the Hamiltonian operator and is the associated energy of the system. The Hamiltonian is thus the operator which, upon being applied to a certain wave function (fully describing our system of nucleus and electrons) provides the associated energy of that system. The Hamiltonian has the following form: (2.2) . Note that here we have made use of atomic units for simplification, where the electron mass and charge, the reduced Planck’s constant and the Coulomb’s constant are all unity by definition.5 Therefore, in eq. 2.2 is the mass of a nucleus in multiples of the mass of an electron, is the atomic charge of nucleus in multiples of the charge of an electron (in absolute value) and and are the Laplacian operators (where ) applied to the spatial coordinates of the -th electron and the -th nucleus, respectively. , and are the distances between an electron and a nucleus ( ), between two electrons ( ) and between two nucleus ( ), respectively. The first two terms in eq. 2.2 define the kinetic energy for electrons and nucleus, respectively. The third, fourth and fifth terms define the electrostatic interaction energy between electrons and nucleus, between electrons with each other and between nucleus with each other, respectively. Because of their smaller mass, electrons move much faster than nuclei. The Born-Oppenheimer approximation assumes that, because of this, one may separate both movements, and consider the nuclei at fixed positions and the electrons as moving particles in such a nuclei-fixed structure. In such a situation, the previous equation can be simplified as such: (2.3) 24 Chapter 2 where (2.4) and is the remaining Coulomb interaction term between nuclei ( ). Hence, the total Hamiltonian, , is defined as the sum of a constant potential ( ) and the so-called electronic Hamiltonian that, as it may be seen in eq. 2.4, is only composed of those terms related to electrons: namely the electronic kinetic term ( ) and the electrostatic interaction of electrons with fixed nuclei ( ) and with themselves ( ). Now, solving the Schrödinger equation using such electronic Hamiltonian: (2.5) we get the electronic wave function ( ) which only depends on the electron coordinates, (note that the atomic coordinates, , enter as parameters, not variables) and the electronic energy ( ). If now we include the repulsion between fixed nuclei we may define the total energy of the system as: (2.6) . Therefore, with these equations one should be able to calculate both the electronic wave function ( ) and the total associated energy for any given system composed of electrons moving in a potential generated by fixed nuclei. From now on we will focus on the electronic Schrödinger equation (eq. 2.5) and, hence, the elec label (i.e. , , ) will be dropped out. Also it will be assumed that the nuclei coordinates are used as parameters in without the necessity to specify it anymore (i.e.  ). 2.2.1 The Variational Principle The problem upon solving the eq. 2.5 is finding the wave function corresponding to the ground state of our system, , which, when introduced in eq. 2.5 will deliver the true ground state energy, . It turns out that the exact form of is only available for the so-called hydrogen-like atoms, which are atoms with only one electron, like the hydrogen atom (i.e. H, He+, Li2+, Be3+…). For those cases we may know the exact analytical form of . However, for any more complex system, like any atom composed of more than one electron, there is no possible way of knowing the exact mathematical form of . Fortunately, there is a method to approach , and this is the variational principle, which states the following: (2.7) Methodology 25 in other words, any trial wave function ( ) introduced in the Hamilton operator will provide an associated trial energy which will always be an upper bound of the true ground state energy associated to the true ground state wave function of the system. Therefore, the obvious strategy is minimizing the functional (eq. 2.7) searching through all acceptable N-electron wave functions (i.e. wave functions which are continuous everywhere and quadratic integrable). Upon doing so, the function providing the lowest energy will be the true ground state wave function and the associated energy the true ground state energy, : (2.8) . Hence, through eq. 2.8 we have an strategy to find the true wave function of the ground state of our system and its corresponding energy, . As previously mentioned, for any relevant chemical system composed of several electrons and nuclei (like for instance, an organic compound) it is impossible to try all acceptable N-electron wave functions and test which one presents the lowest energy upon applying the electronic Hamiltonian through eq. 2.5. Because of this we need to use approximated ways to construct a subset of acceptable N-electron trial wave functions which, upon minimization following eq. 2.8, will provide our best approximation to the true wave function and ground state energy. Below I will describe the most popular approximate methods which, ultimately, led to the most utilized of them all: density functional theory. 2.3 The Hartree-Fock Approximation From basic quantum mechanics we know that the representation of the wave function describing our system of electrons (i.e. fermions) must be anti-symmetric. This means that upon interchanging the position of two electrons, the sign of the wave function must change. In the HF scheme we make an approximation to the N-electron wave function represented by an anti-symmetrised product of N oneelectron wave functions in the form of the so-called Slater determinant:6 (3.1) . The Slater determinant is composed of one-electron wave functions, , which are called spinorbitals, due to the fact they are composed of a spatial (orbital) part, , and a spin function , where may be α or β (i.e. spin up or down): (3.2) . 26 Chapter 2 Spin orbitals are orthonormal by construction (i.e. and ). For closed-shell systems, electrons will be paired in spatial orbitals, , having opposite spin components, . For open-shell systems (i.e. with unpaired electrons) other representations are considered, like unrestricted HF (see below), where and spin-orbitals do not share the same spatial part ( ). For now we will consider only closed-shell systems for simplicity. The Slater determinant accomplishes the anti-symmetry principle because interchanging the position of two electrons, which is equivalent to interchanging the position of two rows (each row in the Slater determinant is associated to one electron, ) it may be easily demonstrated that this leads to a change of sign of the determinant.6 Because of the anti-symmetry property, it may also be demonstrated that having two electrons occupying the same spin orbital (i.e. having two columns equal to each other) makes the Slater determinant equal to 0. In other words, two electrons cannot occupy the same spin orbital, which fulfils the Pauli exclusion principle, also arising from the anti-symmetry principle. Developing the Slater determinant in terms of orbital products (so called Hartree products) and applying the Hamiltonian operator we get the energy functional of the system of electrons with the following form: (3.3) where (3.4) is the mono-electronic operator defining the kinetic energy of electron and its attractive interaction energy with the nucleus, and (3.5) (3.6) define the energy terms related to the Coulomb and exchange interactions between two electrons ( and ). The first represents the electrostatic repulsive interaction between electrons (due to their negative charge) and the second, the exchange term, originates from quantum mechanics and only applies for electrons ( and ) of equal spin (i.e. with or with ). According to the variational principle (see section 2.2.1), the energy obtained from provided a trial will always be an upper bound of the energy associated to the best possible wave function representation within the HF approximation of the system: Methodology 33 Now, if we sum up equations 5.4 and 5.5 we get to the mathematical contradiction: (5.6) or This demonstrates that there cannot be two different external potentials ( and ) giving rise to the same electronic density ( ) or, in other words, that the ground-state-density uniquely determines the external potential and, consequently, the Hamiltonian of our system and, thus, the ground state wave function and energy and all related properties: (5.7) . Because the ground state energy is a functional of the electronic density, it is assumed that all its components must, also, be functionals of such simple variable, thus we end up with: (5.8) where the terms in the equation are the kinetic energy of the system, the electron-electron interaction (both coulombic and exchange included in ) and the electron-nuclei attraction term. Summarizing, the 1964 publication18 by Hohenberg and Kohn provided a mathematical simple demonstration that it is physically sound to use the electronic density of your system as the only variable determining the ground state energy and all other properties, by virtue of determining the corresponding Hamiltonian. However, nothing was known as to what mathematical form the energy terms of eq. 5.8 had to present with respect to that density, or even the density itself. 2.5.2 Second theorem: The variational principle In the 1964 contribution by Hohenberg and Kohn18 they also proposed a simple recipe to get the ground state electronic density, ; i.e. the quantity which then leads to the ground state energy and all other properties. Taking into account that eq. 5.8 is equivalent to applying the Hamiltonian to the ground state wave function: (5.9) It should be possible to take advantage of the variational principle which, applied to the density functional shown in eq. 5.8, states that the ground-state energy ( ) will be obtained if, and only if, the ground-state density ( ) is input in the equation. This, as already explained in the wave-function case, means that for any given trial electronic density, , the calculated corresponding energy given by eq. 5.8 will always be an upper bound to the true ground state energy. Mathematically: (5.10) 34 Chapter 2 This, as previously done for the wave function, gives rise to a minimization process (Levy constrainedsearch19) of the type: (5.11) where the first term within the minimization is the kinetic energy, the second is the coulomb electronic repulsion term, the third includes all non-classical electronic interaction effects (such as exchange, correlation, etc) and the last term is the interaction with the external potential, i.e. electrostatic interaction of electrons with nuclei. The first three terms normally compose what is called the universal functional , because they are system-independent, unlike the external potential that depends on the position and charge of the nuclei of our system. This method is called the constrained search because, as noted in the first minimization symbol ( ), the input trial densities must integrate to the total number of N electrons, hence . Upon carrying out the minimization of eq. 5.11 we should obtain the ground state density ( ) and ground state energy ( ). Of course, applying eq. 5.11 presents a fundamental problem which prevents any practical application of the constrained-search approach: we have not clue at all about the actual form of the first three terms within the minimization with respect to the density. However, this problem was, also, solved back in the 60s’, just a year later after the Hohenberg-Kohn theorems when Kohn and Sham presented a method to circumvent the fact that the universal functional ( ) exact form was unknown.20 This would, finally, make density functional theory ready to work. 2.6 The Kohn-Sham approach The Hohenberg-Kohn theorems represent the theoretical basis, fundamental demonstration that using the electronic density as the only variable to determine the total energy of our system was in fact a physically sound assumption. The variational principle also provided a hypothetical method through which it should be possible to find the ground state density ( ) of our system and, hence, the ground state energy ( ). However, from a practical perspective, such demonstrations were completely useless because they did not provide any clue about the form of the and components of the universal functional : (6.1) . As known from the Thomas-Fermi model13,14,16 where all components of the energy were explicitly established as functional of the electronic density , the major reason of total failure of this method to correctly describe realistic systems (e.g. according to calculations using this methodology, bond formation is not energetically favourable) is the over-simplified expression of the kinetic energy as Methodology 35 . As the rest of the terms presented in equations 4.4 and 4.6, the kinetic energy of our system should be defined following a more complex equation with respect to the electronic density. Going back to the HF method, we know that it uses an approximate representation of the true wave function; i.e. a Slater determinant. Also, we know that such representation is actually the true wave function of a system of N non-interacting electrons under the effect of an average effective potential. We know that the exact kinetic energy of such model is: (6.2) which, without being the exact kinetic energy of the true wave function, it is the exact kinetic energy of a system of N non-interacting fermions. Kohn and Sham suggested20 that instead of trying to find the exact functional connecting the kinetic energy and the electronic density (as done in the Thomas-Fermi model13,14,16) a better idea would be to compute a fraction of the kinetic energy exactly and to try to approximate the remaining part. The terms calculated exactly would be that of a reference system of non-interacting electrons under an external applied potential (i.e. that one calculated following equation 6.2, as in the HF model) whose associated electronic density would correspond to the true ground-state electronic density in the real interacting system, so: (6.3) where are the spin-orbitals of our reference N-electron non-interacting system composing the Slater determinant and, following the analogy with the Hartree-Fock approximation, are determined by: (6.4) . Defining the one-electron Kohn-Shan operator as: (6.5) where the first term is the mono-electronic exact kinetic energy operator (remember that ) and is the mono-electronic local effective potential (recall HF equations in section 2.3). Now, we need to find those orbitals of the reference non-interacting system which upon integration according to eq. 6.3 will give rise to the true ground state density of the real interacting sytem. Writing down the energy expression of the real interacting system of N-electrons, but now introducing the exact kinetic energy term of our reference non-interacting system we get: 36 Chapter 2 (6.6) where is the exact kinetic energy of our N-electrons non-interacting system, is the exact coulomb energy and represents the external potential due to nuclei. is the functional which contains all the unknown terms; i.e. the self-interaction error correction, exchange contribution and correlation effects and the residual part of kinetic energy which is not accounted by . Similarly as we did in the HF approximation, we may now apply the variational principle to eq. 6.6 and find the conditions that the orbitals must fulfil in order to minimize (remember that, through eq. 6.2 and 6.3 all terms, except the big unknown , in eq. 6.6 may be expressed as functionals of ). Upon doing so, as previously done for the HF approach, we now arrive to the Kohn-Sham monoelectronic equations which provide a means to get the spin-orbitals which will minimize the energy in eq. 6.6: (6.7) . Now, comparing this equation with the one-electron equations for our reference non-interacting Nelectron system, as previously introduced in eq. 6.5, we easily see that the external potential of our non-interacting N-electron system equals an effective potential composed by all energy terms within the brackets in eq. 6.7, i.e.: (6.8) . Because of the fact that the electronic density appears in the definition of the effective local potential through the coulombic term ( ), as the Hartree-Fock method, we will have to solve eq. 6.7 iteratively through the self-consistent field, getting the mono-electronic KS orbitals that deliver the true ground state electronic density of our real interacting system (through eq. 6.3) which, in turn, provides the associated ground state energy through eq. 6.6. It is worth noting that, if we knew exactly the form of in eq. 6.8, the big unknown, we would have access to the exact ground state energy of the system, (under the Born-Openheirmer approximation and neglecting relativistic effects). However, unfortunately, nor the Hohenberg-Kohn neither Kohn-Sham contributions give a clue about the exact form of . Giving, better and better approximate forms to such unknown functional is the holy grail of state-of-the-art density functional Methodology 37 theory and in the following section most common approaches developed since the late 80s up to the most popular ones today are reviewed. 2.7 Approximate exchange-correlation functionals After the Kohn and Sham constribution20 it was clear that the main goal in density functional theory was to come up with approximated explicit forms to , i.e., the universal functional containing the exchange and correlation contributions about the inter-electronic interactions and the remaining kinetic energy not accounted within (i.e. the exact kinetic energy of the non-interacting reference system; see section 2.6). Without entering into technical details, the different most popular approximations to and their main features and drawbacks are now described. 2.7.1 The Local Density Approximation (LDA) The first approximation to was based on considering the system of electrons as a uniform electron gas; i.e. a cloud of electrons under the influence of a positive uniform background charge, resembling pretty well simple metals such as sodium. This scheme, already proposed in the 1965 contribution by Kohn and Sham20, utilized as exchange density functional the one previously proposed by Dirac16 and Block17 in 1930 (included in the Thomas-Fermi-Dirac equation, eq. 4.6). In the local density approximation the universal functional presents the following form: (7.1) where is split in: (7.2) The exchange part presents the same form as that proposed by Dirac16 and Block17 in the 20s’: (7.3) Introducing eq. 7.3 into eq. 7.1 we get, again, the exponential factor, as derived by Slater within the HF scheme in 1951.15 No explicit formula exists for the term in eq. 7.2, but different authors have presented different analytical expressions for based on highly accurate numerical quatum MonteCarlo simulations based on the homogeneous electron gas.21 Despite the fact that considering our system as a uniform electron gas with a constant electron density is quite a drastic approximation (most chemical systems present largely varying densities within their structures), it turns out that LDA (and its spin unrestricted version; i.e. that one which works with the α and β parts of the total density: ) provides results that are comparable to those 38 Chapter 2 obtained within the Hartree-Fock approximation, or even better (comparing with experimental atomization energies from the G2 data set of molecules as reference, the average error of LDA is about 36 kcal/mol, whereas HF averages to 78 kcal/mol).22 In this line, LDA provides good estimates of equilibrium structures, harmonic frequencies or dipole moments, however, it usually fails with respect to bonding energies, where it tends to provide too high binding energies (contrary to HF that underestimates them). 2.7.2 The Generalized Gradient Approximation (GGA) Despite the fact LDA (and hence DFT) performed much better than expected and it was popular in some fields of solid-state physics, its accuracy for molecular systems was too poor to become popular among chemists, and hence DFT could not be considered for chemical applications yet. This situation started to change in the eighties were the first developments on top of LDA began to emerge. The first extension came up from the idea that, to improve LDA, one should not only consider the electronic density at a given position in space but also its gradient; i.e. . This was done with the purpose of taking into account the non-homogeneity of the true electron density. The series of new functionals which appeared in this realm are collected to which is known as the generalized gradient approximation (or GGA) and present the following general form: (7.4) where, as previously done in the LDA scheme, the is normally separated in its two basic contributions: (7.5) . It is worth noting that the form of and is no longer determined by the physics behind the concept of the exchange and correlation effects described for wave function theory but just adjusted to provide the best results as compared to standard reference data sets. Therefore, it can be seen how in DFT a formal rigorous approach is substituted by a pragmatic necessity of constructing a method which, at an affordable computational cost, provides good enough accurate results. The term usually takes the following form: (7.6) where , the reduced density gradient is defined as: (7.7) Methodology 39 where in eq. 7.6 is summed for both spin channels, i.e. and . There are different forms for in eq. 7.6 proposed over the years. A typical one is that proposed by Becke in 198823: (7.8) but much more complex forms of the function with respect to exist such as that proposed by Perdew in 1986.24 Regarding the correlation part they present even more complicated analytical expressions which cannot be understood by any physical interpretation but, as previously stated, they are obtained by fitting the outcome results to established reference data sets. Different GGA functionals have been proposed over the years, combining different forms of and . The most popular GGA functionals are PBE,25 BLYP,26,27 or BP86,28 which have become the workhorses of current density functional theory for chemical applications (errors with respect to the G2 reference data go down to about 5-7 kcal/mol). 2.7.3 Hybrid functionals As explained before, the Kohn-Sham scheme proposes to calculate the exact kinetic energy of a Nelectron non-interacting system (i.e. represented by a Slater determinant, as in the HF scheme), , and to approximate the remaining part to the exact kinetic energy of the real, interacting system, . It was realized that the same could be done with the exchange contribution to . Within the Kohn-Sham approach, the N-electron non-interacting electron system, whose wave function is represented by a Slater determinant (just as the Hartree-Fock method), the exchange can be exactly calculated as follows: (7.9) where is the exchange hole function determining the negative probability density of finding an electron at position once we know another reference electron is sitting at position . Hence, as previously done for the kinetic energy in the Kohn-Sham approach, now we could calculate a part of our term exactly (for the non-interacting reference system) and another part approximately (for our real, interacting system). The simplest model based on such ideas was introduced by Becke in 1993 proposing the half-and-half combination29: (7.10) where λ is a term that connects the non-interacting system (for λ=0; i.e. HF model) and the fully interacting real system (for λ=1). For the former we know, exactly, the exchange contribution to , but correlation effects are completely neglected, and for the second case both the exchange and correlation must be approximated, as done within the previously explained LDA and GGA flavours of 40 Chapter 2 DFT. The functional in eq. 7.10 represents the simplest form of what are known as DFT/HF hybrid functionals. More elaborated versions have been presented over the years, where the different contributions of correlation and exchange are normally combined through parameters that have been calculated semi-empirically (i.e. optimizing them to get the best fit with reference data such as the G2 set). Of this type we have a second functional also proposed by Becke in 199330: (7.11) . Parameters a, b and c were fitted to optimize the resulting ionization energies and proton affinities with respect to the G2 data set, getting values of a = 0.20, b = 0.72 and c = 0.81. This semi-empirically formulated equation results in an average error of only 2-3 kcal/mol with respect to the G2 data set, representing the best approximate DFT models. Some of the most commonly used hybrid DFT functionals are B3LYP31 and PBE032 (by Perdew, Burke and Ernzerhof) possessing 20% and 25% of exact exchange, respectively. PBE0 has been the main DFT functional utilized through this thesis, previously found to properly represent the electronic structure of π-conjugated radicals.33 It is worth mentioning that over the last few years an effort has been made to continue with the improvement of hybrid functionals beyond the most commonly used B3LYP and PBE0. In this direction some new hybrid functionals have been developed including empirical dispersion terms, such as APFD34 and X3LYP,35 to improve long-range weak interactions such as London interactions, hydrogen bonds and polarizabilities. Another successful approach has been the range-corrected exchange-correlation functionals, such as the so-called HSE06 functional,36 where the exact HF exchange varies with an adjustable distance parameter (ω). This approach has been especially helpful for using the hybrid scheme in inorganic solids.37 Other proposed functionals are the LC-ωPBE38 (improves the asymptotic limit) or the range separated corrected versions of the Minnesota functionals such as M1139 or MN12-SX,40 that improve the accuracy of the results but are heavily parameterized density functionals (22 and 80 parameters, respectively). 2.8 DFT at work: Introduction to basis sets 2.8.1 The Linear Combination of Atomic Orbitals (LCAO) As in the HF approximation, in the core of KS approach we have to calculate the one electron KS equations: (8.1) having the more compact expression: (8.2) . Methodology 41 Upon minimization of these equations we should get the set of one-electron orbitals which, if using the exact exchange-correlation functional , should provide the ground state density and the corresponding ground state energy . These equations, though, are very complicated coupled integrodifferential equations and numerical approaches are needed to solve them,41 these being too expensive for common chemical applications where larger systems than just single atoms or small molecules are studied.41 To circumvent this problem KS DFT applications make use of a scheme introduced by Roothaan in 195142 which defines each one-electron orbital as a linear combination of atomic orbitals (or LCAOs): (8.3) where are specific simple functions of different forms (originally they were constructed mimicking the hydrogen atomic orbitals, hence the name) which, upon being added through the weight parameters provide an estimation for the particular orbital . The larger the number of basis functions utilized (L) the better the representation of the particular orbital, ; or, in other words, if L = ∞ the orbital could be represented exactly. Now, thanks to the orbital representation according to eq. 8.3, the complicated integro-differential KS equation (eq. 8.1) is transformed in a much more affordable linear problem, where are the only variables to be calculated in our equations (remember is a pre-established fixed set of basis functions): (8.4) which is equivalent to: (8.5) where is the so-called Kohn-Sham matrix (equivalent to the Fock matrix in the HF scheme), is the overlap matrix, is a matrix containing the coefficient values of each orbital mapped on all basis functions and is a matrix whose diagonal terms are the orbital energies. Hence, the complicated coupled integro-differential equations (eq. 8.1) has transformed into a standard linear algebra problem which may be resolved working with matrices. As expressed in eq. 8.1, the KS operator (or Fock operator if working within the HF approximation) must be split in its individual parts and, each of them, calculated using the LCAO. Without going into much detail, it is worth mentioning that normally the term which requires more computational time due to its relatively complex mathematical structure is the Coulomb electronelectron repulsion term: (8.6) 42 Chapter 2 which is a four centre two electron integral. Hence, even after defining our set of orbitals as a linear combination of pre-established simple basis functions (eq. 8.3), the calculation of the Coulomb term (eq. 8.6) is the most computationally demanding one. 2.8.2 Types of basis sets There are different basis sets which have been introduced since the early days of wave function methods (such as HF), each presenting its own advantages and disadvantages. One of the most utilized types are the so-called cartesian Gaussian-type orbitals (or GTOs), which have the following form: (8.7) where N is the normalization factor and α determines how compact or diffuse the Gaussian function is. The additional l, m, and n terms determine whether the functions are of s type (l + n + m = 0), p type (l + n + m = 1), d type (l + n + m = 2), etc. GTO functions are the preferred basis sets because there are efficient ways to analytically calculate the complicated four-centre two-electron equations needed to calculate the coulomb contribution in KS (eq. 8.6) or the coulomb and exchange terms in HF (eq. 3.5 and 3.6, respectively). Another type of basis sets are the so-called Slater-type orbitals (or STOs). STOs are more physically sound due to the fact they ressemble very well the hydrogen atomic orbitals, with the following general form: (8.8) . Here n is the principal quantum number and are spherical harmonics describing the angular part of the function. However, there is no analytical treatment to solve the complex equations for the coulomb energy in KS nor the exchange in HF when using STOs as the basis set, which then imply solving those equations using numerical methods (see below), which are more computationally demanding and present their own particular difficulties. For such reasons the use of STOs is not that popular as compared to GTOs. As a way to have physically sensible basis sets while being computationally accessible, contracted Gaussian functions (CGF) were proposed.43,44 CGFs are functions where several primitive GTOs are linearly combined to resemble more physically sound functions (such as STOs). CGFs present the following general form: (8.9) Methodology 49 which implies: (10.7-a) (10.7-b) (10.7-c) where V is the volume in the real space defined as . Hence, a particular lattice of points in the real space defined by periodical vectors will be associated to a corresponding lattice in the reciprocal space whose translational vectors, , will obey equations 10.6 and 10.7.56 For the electronic wavefunction (or crystal orbitals) this is equivalent to apply the Fourier transformation to obtain the equivalent wave-function in the reciprocal lattice. Recall quantum number that defines our crystal orbitals in the real space, . is a vector in the reciprocal space which, without going into details, may take the following values: (10.8) Being the vector defining the unit cell in the real space. These limited values of define what is called the first Brillouin zone which may be understood as the unit cell in the reciprocal space. For instance, for the rectangular unit cell of a 2D arrangement of atoms defined by vectors and (see Fig. 2.2a) we will get the associated reciprocal vectors and (Fig. 2.2b).57 Fig. 2.2 a) Two dimensional unit cell of a 2D crystal defined with and vectors and b) associated reciprocal-space unit cell defined by reciprocal vectors and . The dotted squared area shown in Fig. 2.2 represents the first Brillouin zone defined by through eq. 10.8. Of course, more complex solids presenting more complex unit cells in three dimensions will have 50 Chapter 2 correspondingly more complex Brillouin zones. Fig. 2.3 shows one of such cases corresponding to the first Brillouin zone of the fcc Bravais lattice of bulk silicon indicating high-symmetry k-points (see below). Fig. 2.3 first Brillouin zone of the fcc Bravais lattice of bulk silicon showing high-symmetry directions and points. 2.10.4 High symmetry points, band structure and density of states The limited values of in eq. 10.8 define the first Brillouin zone, as previously explained, is used to define the crystal orbitals through equation 10.3 may take any value in the reciprocal space. Each particular will define a particular wave propagation direction in the reciprocal space with its particular modulus ( ). Hence, for each we will be able to construct a based in the atomic orbitals . Because there are infinite values of in the reciprocal space (in the same way there are infinite vectors in real space) we should strictly speaking calculate infinite values to properly represent the electronic structure of our solid. Likewise for each of these infinite crystal orbitals (each defined with a particular value of ) we should apply the Hamiltonian for each of them (i.e. infinitely) to obtain the total energy of our solid. Of course, this is completely unfeasible and what is done in practise is representing the crystal orbitals of the system and calculating the corresponding energy at particular high-symmetry points in the reciprocal space within the first Brillouin zone that will capture the most important contribution of to the total energy. In Fig. 2.4 it may be seen the unit cell of the 2D hexagonal structure of graphene and the corresponding first Brillouin zone indicating the highsymmetry points. Depending on the symmetry of the unit cell (Fig. 2.4a), the first Brillouin zone in the reciprocal space will present also a particular symmetry (Fig. 2.4b). The irreducible first Brillouin zone is that which by application of the symmetry operators of the particular symmetry group, may construct the entire first Brillouin zone. For graphene such irreducible first Brillouin zone is that defined by the high-symmetry points Γ, K and M. Methodology 51 Fig. 2.4 a) 2D hexagonal structure of graphene where the unit cell constructed with and vectors and b) Brillouin zone defined with the reciprocal vectors and highlighting the high-symmetry points Γ, K and M. Due to the fact these high-symmetry points, by symmetry operations, may construct the entire Brillouin zone, normally the vector used to construct the crystal orbitals of the solid takes discrete values connecting those point. Hence, for graphene, would take a finite set of values in the linear path from Γ to K, from K to M and from M to Γ. With these set of values we would then construct our set of crystal orbitals through: (10.9) and for each crystal orbital we could calculate the corresponding energy by applying the Hamiltonian: (10.10) . As we may see the energy is expressed as a function of which, in turn, will take discrete values (as many we may efficiently calculate) between the high-symmetry points in the reciprocal space as shown in Fig. 2.4 for graphene. In this way we will get the so-called band structure of our material where the energy of our set of crystal orbitals will be expressed as a function of . Fig. 2.5a shows the band structure for graphene where takes values between high-symmetry points Γ, K and M. As we may see in Fig. 2.5a upon doing so with graphene we get the very characteristic linear-dispersion crossing of bands at the Fermi level (dotted line) at the high-symmetry K point; the so-called Dirac cone. As it will be found in later chapters this electronic feature (i.e. the Dirac cone) plays a significant role in the latest works presented in this thesis. Normally, the band structure of any material is properly characterized plotting the crystal orbitals’ energy versus , as shown in Fig. 2.5a for graphene. However, if required a more complete representation of the first Brillouin zone may also be obtained upon plotting 52 Chapter 2 the variation of the energy of crystal orbitals against two reciprocal vectors and , as shown also for graphene in Fig. 2.5b. Fig. 2.5 a) Band structure of graphene versus which takes the values between high-symmetry points Γ, K and M. b) Band structure of graphene versus and which allow to represent the crystal orbitals’ energy in the entire first Brillouin zone. Graphene unit cell is an example of a very simple unit cell (it is composed by two atoms) due to the highsymmetry that this 2D material presents. Accordingly, its band structure sampling the different highsymmetry points is rather simple (Fig. 2.5a). However, most of the times this is not the case, and very complex band structures may be obtained depending on the modelled solid and the chosen units cell in real space and associated Brillouin zone (in the reciprocal space). This is for instance the case for the fcc Bravais lattice of bulk silicon, as shown in Fig. 2.6. Fig. 2.6 Band structure of fcc Bravais lattice of bulk silicon through the high-symmetry points (see Fig. 2.3). The red horizontal line indicates the Fermi level energy. Methodology 53 In such cases it is convenient to calculate the so-called density of states (or DOS). The DOS, as the name indicates, provides a measure about the density of states at a particular energy, as shown in the right panel in Fig. 2.6. The DOS is inversely proportion to the slope (also called dispersion) of bands against .58 Hence, the flatter a band (i.e. the more invariant its energy versus ) the larger the DOS will be for in the corresponding energy values. Contrary, the higher the energy variation of a particular band (or crystal orbital) the lower the DOS for that range of energies will be. If a number of crystal orbitals appear at a given range of energies, the sum of their contributions will define the DOS in that energetic range. As it may be understood, DOS does not provide information about the symmetry of bands (there is no dependency with ) but rather it is a simplified representation of the electronic structure of our solid facilitating important information like the energetic position of the valence and conduction bands of the material below and above the Fermi level, respectively. 2.11 Bibliography 1 J. E. Lennard-Jones, Proc. R. Soc. Lond. A, 1924, 106, 463–477. 2 J. P. Dahl and M. Springborg, J. Chem. Phys., 1988, 88, 4535–4547. 3 T. A. Straeter, NASA Tech. Reports Serv., 2011. 4 R. P. Feynman, Phys. Rev., 1939, 56, 340–343. 5 H. Shull and G. G. Hall, Nature, 1959, 184, 1559–1560. 6 A. Szabo and N. S. Ostlund, Modern quantum chemistry : introduction to advanced electronic structure theory, Macmillan, 1982. 7 T. A. Koopmans, Physica, 1934, 1, 104. 8 P. O. Löwdin, Adv. Chem. Phys., 1959, 2, 207. 9 R. J. Bartlett and J. F. Stanton, Rev. Comput. Chem., 1995, 5, 65. 10 C. Moller and M. S. Plesset, Phys. Rev., 1934, 46, 618. 11 K. Andemson, P.-A. Malmqvist, B. O. Roos, A. J. Sadlej and K. Wolinskit, J. Chem. Phys., 1990, 94, 5483. 12 K. Andersson, P.-A. Malmqvist and B. O. Roos, J. Chem. Phys., 1992, 96, 1218. 13 L. H. Thomas, Proc. Camb. Phil. Soc., 1927, 23, 542. 14 E. Fermi, Rend. Accad. Lincei, 1927, 6, 602. 15 J. C. Slater, Phys. Rev., 1951, 81, 385. 16 P. A. M. Dirac, Proc. Camb. Phil. Soc., 1930, 26, 376. 17 F. Bloch, Z. Phys., 1929, 57, 545. 18 P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864. 19 M. Levy, Proc. Natl. Acad. Sci., 1979, 76, 6062. 54 Chapter 2 20 W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133. 21 D. M. Ceperley and B. J. Alder, Phys. Rev. Lett., 1980, 45, 566. 22 W. Koch and M. C. Holthausen, A Chemist’s Guide to Density Functional Theory, Wiley-VCH Verlag GmbH, 2001. 23 A. D. Becke, Phys. Rev. A, 1988, 38, 3098. 24 J. P. Perdew, Phys. Rev. B, 1986, 33, 8822. 25 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 26 C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785–789. 27 A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100. 28 A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100. 29 A. D. Becke, J. Chem. Phys., 1993, 98, 1372. 30 A. D. Becke, J Chem Phys, 1993, 98, 5648. 31 P. J. Stephens, J. F. Devlin, C. F. Chabalowski and M. J. Frisch, J. Phys. Chem., 1994, 98, 11623. 32 C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158. 33 R. Improta and V. Barone, Chem. Rev., 2004, 104, 1231–54. 34 A. Austin, G. A. Petersson, M. J. Frisch, F. J. Dobek, G. Scalmani and K. J. Throssell, Chem. Theory Comput., 2012, 8, 4989–5007. 35 X. Xu and W. A. Goddard III, Proc. Natl. Acad. Sci., 2004, 101, 2673–77. 36 J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207. 37 B. G. Janesko, T. M. Henderson and G. E. Scuseria, Phys. Chem. Chem. Phys., 2009, 11, 443–454. 38 O. A. Vydrov and G. E. Scuseria, J. Chem. Phys., 2006, 125, 234109. 39 R. Peverati and D. G. Truhlar, J. Phys. Chem. Lett., 2011, 2, 2810–2817. 40 R. Peverati and D. G. Truhlar, Phys. Chem. Chem. Phys., 2012, 14, 16187. 41 A. D. Becke, Int. J. Quant. Chem. Symp., 1989, 23, 599. 42 C. C. J. Roothaan, Rev. Mod. Phys., 1951, 23, 69. 43 D. Feller and E. R. Davidson, Rev. Comput. Chem., 1990, 1, 1. 44 T. Helgaker and P. R. Taylor, in Modern Electronic Structure Theory, Part II, ed. D. R. Yarkony, World Scientific Publishing, Singapore, 1995. 45 P. E. Blöchl, P. Margl and K. Schwarz, in Chemical Applications of Density Functional Theory, eds. B. B. Laird, R. B. Ross and T. Ziegler, American Chemical Society, Washington DC, 1996. 46 W. J. Hehre, R. Ditchfield and J. A. Pople, J. Chem. Phys., 1972, 56, 2257. 47 P. C. Hariharan and J. A. Pople, Theor. Chim. Acta., 1973, 28, 213. 48 A. Schäfer, H. Horn and R. Ahlrichs, J. Chem. Phys., 1992, 97, 2571. 49 T. H. Dunning, J. Chem. Phys., 1989, 90, 1007. 50 A. D. Becke, J. Chem. Phys., 1988, 88, 2547. 51 P. M. W. Gill, B. G. Johnson and J. A. Pople, Chem. Phys. Lett., 1993, 209, 506. 52 V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter and M. Scheffler, Comp. Phys. Comm., 2009, Methodology 55 180, 2175–2196. 53 R. Car and M. Parrinello, Phys. Rev. Lett., 1985, 55, 2471. 54 G. Bussi, D. Donadio and M. Parrinello, J. Chem. Phys., 2007, 126, 14101. 55 F. Bloch, Z. Phys., 1928, 52, 555. 56 R. Dronskowski, Computational Chemistry of Solid State Materials, Wiley-VCH, 2005. 57 E. Canadell, M. L. Doublet and C. Iung, Orbital Approach to the Electronic Structure of Solids, Oxford University Press, 2012. 58 R. Hoffmann, Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures, VCH Publishers, Inc., 1988. 56 Chapter 2 57 Chapter 3 Modelling TAMs as potential devices 58 Chapter 3 Modelling TAMs as potential devices 65 did the cis- (Z) conformers reverse back to the most thermodynamically stable trans- (E) isomers. This could not be explained by energetic reasons, due to the fact the transisomer is the most stable one. In the experimental/theoretical collaborative Publication #3 we aimed, by DFT calculations and molecular dynamics simulations, to understand the fundamental reasons why the E  Z process in both PTM-ethylene derivatives was completely shifted to the cisisomer and irreversible (Fig. 3.7). Taking a close look at the dynamic fluctuations of both studied molecules in both conformations and comparing with the simplier stilbene case (Fig. 3.6) I came up with an original hypothesis to explain the unexpected experimental results. The core idea of my proposition is based on a sterical blockade of the torsion dynamics of the ethylene unit by the PTM bulky group. 3.2. Bibliography 1 F. Rissner, Z. Ma, O. T. Hofmann, C. Slugovc, Z. Shuai and E. Zojer, J. Mater. Chem., 2012, 22, 4269. 2 M. Mas-Torrent, N. Crivillers, V. Mugnaini, I. Ratera, C. Rovira and J. Veciana, J. Mater. Chem., 2009, 19, 1691. 3 M. Mas-Torrent, N. Crivillers, C. Rovira and J. Veciana, Chem. Rev., 2012, 112, 2506–27. 4 M. Ballester and J. Riera-Figueras, J. Am. Chem. Soc., 1971, 4254, 2215–2225. 5 C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158. 6 V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter and M. Scheffler, Comp. Phys. Comm., 2009, 180, 2175–2196. 7 J. Guasch, X. Fontrodona, I. Ratera, C. Rovira and J. Veciana, Acta Crystallogr., 2013, C69, 255–7. 8 N. Crivillers, M. Mas-Torrent, J. Vidal-Gancedo, J. Veciana and C. Rovira, J. Am. Chem. Soc., 2008, 130, 5499–5506. 9 R. Frisenda, R. Gaudenzi, C. Franco, M. Mas-Torrent, C. Rovira, J. Veciana, I. Alcon, S. T. Bromley, E. Burzurí and H. S. J. van der Zant, Nano Lett., 2015, 15, 3109–3114. 10 W.-G. Han, T. Lovell, T. Liu and L. Noodleman, ChemPhysChem, 2002, 3, 167–178. 11 C. Dugave and L. Demange, Chem. Rev., 2003, 103, 2475–2532. 12 D. Gegiou, K. A. Muszjat and E. Fischer, J. Am. Chem. Soc., 1968, 90, 3907–3918. 66 Chapter 3 3.3. Results Modelling TAMs as potential devices 67 Publication-draft #1 Realization of an open-shell self-assembled monolayer using closed-shell quinoidal molecular building blocks In preparation M. R. Ajayakumar, C. Moreno, I. Alcón, S. T. Bromley,* F. Illas, J. Veciana, A. Mugarza* and M. Mas-Torrent* 68 Chapter 3 Modelling TAMs as potential devices 69 70 Chapter 3 Modelling TAMs as potential devices 71 72 Chapter 3 Modelling TAMs as potential devices 73 74 Chapter 3 Modelling TAMs as potential devices 81 82 Chapter 3 Modelling TAMs as potential devices 83 84 Chapter 3 Modelling TAMs as potential devices 85 Publication #2 Direct covalent grafting of an organic radical core on gold and silver RSC Adv., 2017,7, 20076-20083 M. R. Ajayakumar, I. Alcón, S. T. Bromley, J. Veciana*, C. Rovira and M. Mas-Torrent* 86 Chapter 3 Modelling TAMs as potential devices 87 88 Chapter 3 Modelling TAMs as potential devices 89 90 Chapter 3 Modelling TAMs as potential devices 97 98 Chapter 3 Modelling TAMs as potential devices 99 100 Chapter 3 Modelling TAMs as potential devices 101 102 Chapter 3 Modelling TAMs as potential devices 103 Supporting Information of Publication #3 Study of the E–Z stilbene isomerisation in perchlorotriphenyl-methane (PTM) derivatives RSC Adv., 2017,7, 15278-15283 F. Bejarano, I. Alcón, N. Crivillers, M. Mas-Torrent*, S. T. Bromley, J. Veciana*, C. Rovira* 104 Chapter 3 Modelling TAMs as potential devices 105 106 Chapter 3 113 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 114 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 115 4.1 Introduction 4.1.1 What “controls” the unpaired electron in TAMs? As explained in the introduction of this PhD thesis, the use of TAMs in materials science and electronics has greatly increased during the last decades.1 Indeed, TAMs have been used to prepare different sorts of materials and devices such as metal-organic frameworks with solvent sensitive magnetic behaviour (Fig. 4.1a),2 self-assembled monolayers with redox switchable optical and magnetic properties (Fig. 4.1b),3 single-molecule devices with magnetoresistance phenomena4 (Fig. 4.1c) and magnetic plastics5 (Fig. 4.1d). Fig. 4.1 Utilization of TAMs to prepare different sorts of materials and devices such as magnetic MOFs (a), redox-switchable SAMs (b), magnetoresistance single-molecule junctions (c) and magnetic plastics (d). e) In TAMs, the unpaired electron giving rise to all these interesting characteristics resides on the central carbon atom but it is spread over the entire π-conjugated system. It is very interesting to realize that, for all such cases, the main target properties in each case are directly related with the existence of the unpaired electron in these open-shell molecules. For instance, magnetism (in Fig. 4.1a,d) is related with the spin moment of unpaired electrons, the colour and fluorescence (Fig. 4.1b) are associated with electronic transitions involving the electronic levels of the unpaired electron (i.e. the singly occupied/unoccupied molecular orbitals; SOMO/SUMO), the redox activity of TAMs (being easily reduced to the anion) is also because of the existence of the unpaired electron and, finally, the enhanced electrical conduction through TAMs (Fig. 4.1c) takes place through the SUMO, as demonstrated in ref 4. Therefore, at the start of this PhD thesis it was a primary objective for us to 116 Chapter 4 understand the nature of the unpaired electron in TAMs and, more importantly, if there was any chemical or structural way to control its spatial distribution and energy. If there was a simple manner to manipulate such unpaired electrons, this would lead to fine control over all the above mentioned properties for materials science applications. As shown in Fig. 4.2a, optimizing the structure of the simplest TAM within the DFT scheme (using the PBE functional6 in Gaussian097), the triphenylmethyl (or TPM, where all aryl rings are hydrogenated), one may take a look at the α-spin distribution (in green, associated to the unpaired electron) which permits one to see how the unpaired electron in TAMs is distributed. Here it can be seen that the unpaired electron is not completely localized on the central carbon atom (herein called αC) but it is actually spread over the entire molecule through the π-conjugated system. This is because the SOMO (and SUMO) associated to the unpaired electron are p orbitals, and hence are π-conjugated through the three aromatic aryl rings directly bonded to αC. Lewis resonance forms of π-conjugated electrons in organic systems normally provide a reasonable estimation about how these electrons behave. If we write down the different resonance forms that the unpaired electron (black dot in Fig. 4.2b) may follow through a particular aryl ring, we may see that besides being in the upper carbon atom, it may also reside in the orthoand parapositions of a particular aryl ring. Very clearly, this is confirmed upon looking at the computed α-spin density in Fig. 4.2a (in green), where we may see it distributes only through those three positions, i.e. in αC and in orthoand parapositions of each aryl ring. This π-conjugation of the unpaired electron is responsible for most of the interesting properties previously mentioned: electrical conduction through TAMs4 takes advantage of the fully delocalized SUMO orbital (i.e. a delocalized open channel for electrons to conduct); magnetism in TAM-based framework materials2,5 is also promoted through delocalized spin distributions enhancing magnetic interactions; the peculiar optical properties of TAMs, such as the reported non-linear optical response,8 are also found to arise due to the π-conjugated unpaired electron. If we take a closer look at the Lewis resonance forms in Fig. 4.2b, we may realize that those where the unpaired electron (black dot) resides in a position in the aryl ring require the formation of a double-bond between such an aryl ring and the upper carbon atom (red rectangles in Fig. 4.2b). Double-bonds are formed through overlap of p orbitals (perpendicular to the bonding direction) of the involved carbon atoms. Due to the fact that the overlap between those p orbitals forming the double bond depends on the twist angle between them (the less coplanar, the lower the overlap), it turns out that the degree of delocalization of the unpaired electron depending on the formation of such double-bond (see Fig. 4.2b) will entirely depend on the twist angle between the sp2 αC plane and the aryl ring plane (Fig. 4.2c). Different theoretical works from the 50s’ and 60s’, comparing their results with hyperfine coupling constants extracted from EPR measurements, pointed out that the spin delocalization and twist angle From aryl rings’ twist to TAM 2D-COFs 117 follow a correlation,9–12 where is the twist angle between both planes as represented in Fig. 4.2c. Fig. 4.2 a) Structure of the triphenylmethyl (or TPM), the simplest TAM, with the α-spin density associated to the unpaired electron, in green. b) Lewis resonance forms explaining the delocalization mechanism of the unpaired electron through each aryl rings bonded to αC. c) Molecular planes defining the twist angle that determines the localization/delocalization of the unpaired electron in the simplified phenyl-methyl radical (so-called benzyl radical). Having such a simple structural parameter to control the localization/delocalization of the unpaired electron in TAMs would represent a powerful tool to tune all related characteristics with potential for materials science applications (see above). However, in TAMs there are three aryl rings bonded to αC and no study has evaluated whether the chemical functionalization of these aryl rings also influences the spatial distribution of the unpaired electron. In Publication #4 presented in this chapter our core goal was to clarify the actual correlation between the localization of the unpaired electron in TAMs (represented by the corresponding spin localization) and the three aryl ring twist angles. Moreover we also assess the effect of different chemical functional groups of aryl rings with different electro-negativities and test the effect of finite temperatures on the electronicstructural correlation, where both bond vibrations and aryl ring rotations take place. Overall, as it is explained in detail in this contribution and later summarized, in Publication #4 we have been able to unambiguously demonstrate for the first time that in TAMs the spin localization (and hence the unpaired electron) is fully determined by the three aryl ring twist angles, following a linear correlation with the average of the cosines squared of the three dihedrals ( ). We also show that the chemical functionalization of aryl rings only affects the spin localization as much as it determines each of the three values via steric hindrance, and also demonstrate that such electronic-structural correlation is robust at finite temperatures. Consequently, our results show that if it was possible to manipulate aryl ring twist angles in a TAM-based material or device, the localization/delocalization of the unpaired electrons of the system could be controlled and, with it, any related property such as light-absorption bands,3 electrical conduction4 or magnetic interactions.2 118 Chapter 4 4.1.2 Towards external manipulation of aryl ring twist angles Aryl ring twist angles, as shown in Publication #4 (and previously demonstrated for TAMs by Lewis13) are determined by the particular chemical functionalization of aryl rings, mainly due to steric hindrance effects. Such a correlation was utilized by Venkataraman and co-workers14 to tune the twist angle in biphenyl single-molecule break junctions to demonstrate that the electrical conduction through such singlemolecule device entirely depends on this conformational parameter, also following a correlation (see Fig. 4.3). Fig. 4.3 a) Bi-phenyl series of compounds studied by Venkataraman and coworkers in 2006 as molecular wires in singlemolecule break junctions. The different aryl ring functionalizations force different dihedral angles between the two rings (green arrow) and, correspondingly, different degrees of electronic π-conjugation (blue arrow). b) Measured electrical conductivity versus , where is the dihedral angle between both phenyl rings in each single-molecule break junction. Hence, chemical functionalization is a powerful manner to tailor aryl ring twist angles and, in turn, determine certain properties of our molecular material or device such as electrical conductance14 or spin localization (Publication #4). However, chemical functionalization does not allow for externally manipulating aryl ring twist angles; in other words, given a chemical design of our molecules, the twist angle becomes a fixed parameter of our system. Hence, we need another way to manipulate aryl ring twist angles in order to design multi-functional TAM-based materials with externally controllable properties. As it will be explained in Publication #5, it turns out that there are no experimentally realized TAMbased materials that accomplish all structural requirements in order to allow for an efficient external manipulation of aryl ring twist angles of TAM monomers. We find that most appropriate type of materials are 2D-covalent organic frameworks (2D-COFs; for more information about this type of novel materials see Section 1.2 in the Introduction of this thesis – Chapter 1). Having such periodically ordered networks composed of TAM units covalently bonded with each other would permit one to apply strong enough external forces to overcome steric hindrance (which determines aryl ring twist angles) without breaking From aryl rings’ twist to TAM 2D-COFs 119 the basic skeleton of the 2D material. Moreover, the ordered structure of the material should ensure a homogeneous structural response to any external stimulus, hence facilitating the interpretation of the electronic outcome and its reproducibility. As explained in Publication #5, we found that stretching our designed TAM 2D-COFs in one direction parallel to the materials’ plane is an efficient manner to externally manipulate aryl ring twist angles of all TAM units composing it. Studying the effect of such mechanical distortion on the electronic structure of the material, we demonstrate the success of our approach to design TAM-based materials with externally controllable properties. Additionally, we also assess how the chemical functionalization of the network affects such external controllability and what is the effect of finite temperatures. 4.1.3 Searching for structural flexibility and chemical persistence As previously stated, perchlorotriarylmethyls (or PTMs) are the most persistent (i.e. chemically stable) class of TAMs because chlorine atoms provide a steric shielding effect on the central carbon atom (i.e. αC) where the unpaired electron mainly resides. The triphenylmethyl, or TPM, (i.e. fully hydrogenated TAM) only lasts in solution for few days15 due to its reaction with atmospheric O2.16,17 Conversely, PTMs are expected to last for tens of years under normal conditions,18,19 which highlights the tremendous steric protection effect of chlorine atoms on the αC central position. As a consequence, PTMs are by far the most utilized type of TAM building blocks for materials science and electronics,1 as explained in detail in Chapter 1. As demonstrated in Publication #5, chemical functionalization of aryl rings in TAM units within the 2DCOF (see Fig. 4.4) determine the ease by which aryl rings may be externally twisted by uniaxial strain. For the TPM-based 2D-COF (Fig. 4.4a), due to the small sterical hindrance imposed by Hatoms, a significant twisting of aryl rings is caused upon strain application, which then leads to a detectable variation of the properties of the 2D material. However, for the most experimentally relevant PTM 2DCOF (Fig. 4.4b), the huge steric hindrance of bulky Clatoms prevents an effective manipulation of the aryl ring twist angles. Consequenly, as showed in Publication #5 by running AIMD simulations at 300K, even upon stretching the PTM 2D-COF by a 20% of its length, no detectable changes of the material’s electronic properties take place at room temperature. This raises the problem that bulky perchlorated aryl rings needed for chemical persistence prevent the structural flexibility required to design multi-functional TAM 2D-COFs with externally controllable properties. To resolve such a dilemma in Publication #6 we made use of force-field calculations (using the universal force-field, UFF20) to screen over a number of different chemical functionalizations of TAM monomers composing the 2D material, focusing on the halogen series of atoms and studying different degrees and distributions of halogenation. 120 Chapter 4 Fig. 4.4 TPM (a) and PTM (b) based 2D-COFs from the y and z-views, also plotting the associated spin density in the bottom panels (green: α spin; purple: β spin). For each designed TAM 2D-COF based on a particularly functionalized TAM monomer, we smoothly stretch its structure uniaxially as done in Publication #5 and measure the resulting aryl ring twisting by calculating the average twist angle within the unit cell at each stretching point. As shown in Publication #6, considering 50 different TAM 2D-COFs each composed of a distinct TAM monomer and performing over 1700 FF calculations to obtain the stretching profile for each of them, we conclude that there are experimentally available TAM monomers which could be used to construct TAM 2D-COFs where chemical persistence and structural flexibility would co-exist. 4.2 Bibliography 1 J. Veciana and I. Ratera, in Stable Radicals: Fundamentals and Applied Aspects of Odd-Electron Compounds, ed. R. G. Hicks, John Wiley & Sons, Inc., 2010, pp. 33–80. 2 D. Maspoch, D. Ruiz-Molina, K. Wurst, N. Domingo, M. Cavallini, F. Biscarini, J. Tejada, C. Rovira and J. Veciana, Nat. Mater., 2003, 2, 190–5. 3 C. Simão, M. Mas-Torrent, N. Crivillers, V. Lloveras, J. M. Artés, P. Gorostiza, J. Veciana and C. Rovira, Nat. Chem., 2011, 3, 359–64. 4 R. Frisenda, R. Gaudenzi, C. Franco, M. Mas-Torrent, C. Rovira, J. Veciana, I. Alcon, S. T. Bromley, E. Burzurí and From aryl rings’ twist to TAM 2D-COFs 121 H. S. J. van der Zant, Nano Lett., 2015, 15, 3109–3114. 5 A. Rajca, J. Wongsriratanakul and S. Rajca, Science, 2001, 294, 1503–1505. 6 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 7 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Had and D. J. Fox, 2009. 8 I. Ratera, D. Ruiz-Molina, C. Sporer, S. Marcen, S. Montant, J.-F. Létard, E. Freysz, C. Rovira and J. Veciana, Polyhedron, 2003, 22, 1851–1856. 9 F. C. Adam and S. I. Weissman, J. Am. Chem. Soc., 1958, 80, 2057–2059. 10 M. Karplus and G. K. Fraenkel, J. Chem. Phys., 1961, 35, 1312–1323. 11 J. A. Pople and D. L. Beveridge, J.Chem.Phys., 1968, 49, 4725–4726. 12 M. J. S. Dewar, J. Am. Chem. Soc., 1952, 74, 3345–3350. 13 G. N. Lewis, D. Lipkin and T. T. Magel, J. Am. Chem. Soc., 1944, 66, 1579–1583. 14 L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen and M. L. Steigerwald, Nature, 2006, 442, 904–907. 15 M. Gomberg, J. Am. Chem. Soc., 1903, 25, 1274–1277. 16 M. Gomberg, J. Am. Chem. Soc., 1900, 22, 757–771. 17 M. Gomberg, J. Am. Chem. Soc., 1901, 23, 496–502. 18 M. Ballester, J. Riera, J. Castañer, C. Badía and J. M. Monsó, J. Am. Chem. Soc., 1971, 93, 2215–2225. 19 J. Guasch, X. Fontrodona, I. Ratera, C. Rovira and J. Veciana, Acta Crystallogr., 2013, C69, 255–7. 20 A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard III and W. M. Skiff, J. Am. Chem. Soc., 1992, 114, 10024– 10035. 21 X. H. Liu, C. Z. Guan, D. Wang and L. J. Wan, Adv. Mater., 2014, 26, 6912–20. 22 Q. Fan, J. M. Gottfried and J. Zhu, Acc. Chem. Res., 2015, 48, 2484–2494. 122 Chapter 4 4.3 Results From aryl rings’ twist to TAM 2D-COFs 129 130 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 131 132 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 133 Supporting Information of Publication #4 Structural control over spin localization in triarylmethyls RSC Adv., 2015, 5, 98593-98599 Isaac Alcon and Stefan T. Bromley* 134 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 135 136 Chapter 4 From aryl rings’ twist to TAM 2D-COFs 137 138 Chapter 4 Resum en Català 241 Fig. 8.2. a) Estructura del PTM utilitzant radis Van der Waals per il·lustrar l’important efecte estèric dels àtoms de clor sobre el carboni radical central (esfera ratllada). b) Mono-capa auto muntada de PTMs sobre una superfície d’or. Com es pot veure en la Fig. 8.2a, l’estructura dels PTMs està molt impedida estèricament per l’important volum dels àtoms de clor. Aquest impediment estèric protegeix el carboni radicalari central (petita esfera ratllada en el centre de la molècula, Fig. 8.2a) de manera que és molt difícil que cap reactiu orgànic pugui accedir-hi i reaccionar-hi. Aquesta protecció estèrica és, per tant, la principal raó per la qual els PTMs són una de les famílies de compostos orgànics radicals més estables. 8.1.2 TAMs com a maons per materials i dispositius. L’estabilitat química adquirida en els PTMs gràcies l’impediment estèric ofert pels anells perclorats, ha permès utilitzar aquest tipus de molècules radicals per a diferents aplicacions en el camp de la ciència de materials o el magnetisme i l’electrònica moleculars. Pel que fa a aplicacions, tot i que hi ha alguns exemples basats en el TPM,5 la família dels PTMs són el tipus de TAMs més utilitzats,9 per les raons ja esmentades. La principal causa de l’atractiu d’aquests radicals orgànics per a aplicacions en magnetisme o electrònica és l’existència de l’electró desaparellat, localitzat en el carboni central de les molècules TAM. Aquest electró desaparellat és el que genera totes i cadascuna de les propietats d’interès per a diferents aplicacions en els camps esmentats. Per exemple, l’electró desaparellat en els TAMs els proporciona l’espín magnètic que posteriorment fa que certs materials basats en unitats TAM es comportin com a imants,4,5,10–12 com per exemple els materials mostrats en la Fig. 8.3a, d. Altrament, els orbitals associats l’electró desaparellat, els anomenats orbitals moleculars individualment ocupats/desocupats (SOMO/SUMO respectivament, de l’anglès: singly occupied/unoccupied molecular orbitals) intervenen en l’absorció de llum en l’espectre visible, la qual proporciona a les molècules TAM color (absorció de llum) i fluorescència (emissió de llum) a certes longituds d’ona segons l’estructura de cada TAM particular. A més, aquestes propietats òptiques depenen de l’estat redox de la molècula TAM (és a dir, per l’estat neutre i l’anió corresponent), els quals es poden electro-generar per mitjà de potencials elèctrics. 242 Chapter 8 Fig. 8.3. Exemples de materials i dispositius basats en molècules TAM. a) Xarxa metall-orgànica amb comportament magnètic sensible al dissolvent absorbit, b) mono-capa auto muntada proposada com a dispositiu d’emmagatzematge d’informació, c) Unió uni-molecular mostrant interacció entre els electrons conductors i l’electró desaparellat de la unitat TAM i d) plàstic magnètic. Al centre de la figura es mostra l’estructura del TPM optimitzada dins de l’esquema del DFT, també mostrant la densitat d’espín en el canal α (en verd), associada a l’electró desaparellat. Això va permetre preparar al laboratori una mono-capa auto muntada (SAM, de l’anglès) basada en PTMs químicament enllaçats a una superfície d’òxid d’indi-estany (indium-tin-oxide o ITO, de l’anglès) en la qual es va poder canviar entre els dos estats redox per mitjà d’un potencial elèctric (Fig. 8.3b).13 Aleshores, a causa de les diferents propietats de cada estat (per exemple diferents colors absorbits, resposta magnètica diferent) es va poder llegir l’estat de la mono-capa amb diferents tècniques espectroscòpiques tal com la ressonància paramagnètica electrònica (EPR de l’anglès) o l’absorbància en el UV-visible. Per això, aquest dispositiu presentava molt potencial per aplicacions d’emmagatzematge d’informació.13 Finalment, una altra de les propietats d’interès per a aplicacions, relacionada amb l’electró desaparellat en els TAMs, és l’alta conducció electrònica que es dóna a través d’aquestes molècules. Com es mostra en la Fig. 8.3c, s’ha demostrat que aquesta conducció té lloc a través de l’orbital SOMO associat l’electró desaparellat, donant lloc a propietats magneto-resistents.14 En resum, l’electró desaparellat en les molècules TAM és el que les fa molt interessants per a diferents aplicacions tant en el camp del magnetisme com l’electrònica i, recentment, espintrònica moleculars. Com s’explicarà més endavant, donada la gran rellevància de l’electró desaparellat en aquestes molècules, Resum en Català 243 un dels principals objectius d’aquesta tesi ha estat entendre la naturalesa i comportant d’aquest electró i buscar possibles maneres de controlar la seva distribució espacial i energia en sistemes basats en TAMs. 8.1.3 Xarxes covalents 2D, o 2D-COFs Sense entrar molt en detall, les xarxes covalents 2D (o 2D-COFs de l’anglès) són materials estesos en dues dimensions que es preparen a sobre d’un substrat determinat. Els 2D-COF estan compostos per una unitat molecular que es diposita sobre un suport sòlid (normalment superfícies metàl·liques) i, a una certa temperatura, el conjunt de molècules s’auto ordenaran de manera periòdica en les dues dimensions. La Fig. 8.4a mostra aquest tipus d’ordenament 2D per a una molècula del tipus ftalocianina.15 Fig. 8.4 Imatges STM de a) una capa ordenada d’unitats de ftalocianina-Fe(II) i b-c) xarxa covalent 2D quadrada. Com es pot veure en la Fig. 8.4b-c, en augmentar la temperatura es dóna una reacció periòdica en les dues dimensions dins de les mono-capes moleculars, la qual cosa dóna lloc a les xarxes covalents 2D, les quals generen freqüentement en forma d’illes sobre la superfície metàl·lica (Fig. 8.4b). Com es pot apreciar a la Fig. 8.4c el 2D-COF hereta la topologia de les unitats moleculars corresponents. En aquest cas, la ftalocianina, d’estructura quadrada, dóna lloc a una xarxa quadricular. Així doncs, utilitzant unitats moleculars amb diferents topologies, es poden obtenir 2D-COFs amb topologies hexagonal,16–19 quadrada,15,20 rectangular,21 lineal22,23 i romboèdrica,24,25 entre d’altres.26 Donada la gran versatilitat estructural i química dels 2D-COFs, i la possibilitat de generar xarxes 2D amb precisió atòmica, aquest tipus de xarxes es comença a estudiar per a aplicacions en nano-electrònica. El cas més evident és el de les nano-cintes de grafè27 (GNRs de l’anglès), com es mostra a la Fig. 8.5: veiem com, depenent de la molècula utilitzada, s’obté un tipus de GNR o un altre. Així es pot generar GNR on els límits de la cinta presenten topologia zig-zag28,29 (Fig. 8.5a) o GNR amb un dopatge amb precisió atòmica amb àtoms de B.30 244 Chapter 8 Fig. 8.5 Imatges de Microscopia de forces atòmiques (AFM de l’anglès) de GNRs preparades a partir de precursors moleculars amb (a) límits amb topologia zig-zag i (b) dopatge amb àtoms de B amb precisió atòmica. És molt interessant veure que el STM (scanning tunnelling microscopy, de l’anglès) pot detectar la deficiència electrònica que els àtoms de B generen dins la xarxa covalent com esferes fosques en la imatge STM (Fig. 8.5b). Estudis preliminars indiquen el potencial d’aquestes GNRs com a portes lògiques27 (és a dir, com a nano-transistors). 8.2 Metodología: La teoría del funcional de la densitat electrònica (DFT) Aquesta tesi doctoral ha utilitzat principalment càlculs electrònics basats en la teoria del funcional de la densitat (o DFT, de l’anglès). El mètodes computacionals basats en l’esquema DFT són els més utilitzats dins de la comunitat de químics computacionals ja que genera resultats prou acurats en un temps relativament baix (és a dir, sense necessitar molt temps de càlcul en super-ordinadors). En aquesta secció introduiré breument l’enfocament DFT i les aproximacions corresponents utilitzades en aquesta tesi. La idea fonamental del DFT és la utilització de la densitat de la probabilitat electrònica com a única variable per definir el Hamiltonià del nostre sistema d’electrons (dins d’un camp generat per una xarxa d’àtoms) i, per tant, la funció d’ona corresponent i qualsevol altra propietat mesurable d’aquesta (com l’espín total, per exemple). La densitat de probabilitat electrònica s’abreuja generalment com a densitat electrònica i té la següent forma matemàtica: (1) on són les posicions de cada electró , i es la funció de probabilitat de trobar cadascun d’aquests electrons a les posicions , respectivament. La funció densitat ha de complir unes condicions de contorn tal com que ha de valdre zero a una distància infinita del Resum en Català 245 sistema nuclear i que la seva integració a tot l’espai ha de ser igual al nombre total d’electrons del sistema, . Els primers intents per construir un funcional que connectés l’energia del nostre sistema amb la densitat electrònica, , data del 1927 i va ser proposada per Thomas i Fermi.31,32 En la seva proposta, els autors proposaven tres termes energètics (tots ells en funció de la densitat electrònica) relacionats amb l’energia cinètica dels electrons del sistema, l’energia d’interacció atractiva d’aquests amb els nuclis del sistema, i l’energia d’interacció repulsiva entre electrons. Més tard, aquesta proposta es va complementar amb un altre terme, que relacionava la densitat electrònica amb el terme energètic degut a la interacció d’intercanvi entre electrons (anomenat exchange en anglès).33,34 Un pas molt important per l’èxit posterior de l’esquema DFT va ser l’estudi de Hohenberg i Kohn35 on van demostrar per mitjà d’un raonament força senzill ad absurdum que la densitat electrònica de l’estat fonamental d’un sistema d’electrons determina de manera exclusiva el Hamiltonià del sistema i, en conseqüència, la funció d’ona corresponent, l’energia fonamental i totes les altres propietats. Això ho van poder demostrar provant que la densitat electrònica determina el potencial extern (és a dir, el potencial creat pels nuclis) el qual, al seu torn, determina el Hamiltonià. Matemàticament: (2) . on és la densitat de l’estat fonamental del sistema, el potencial extern creat pels nuclis atòmics, és el Hamiltonià del sistema i i son la funció d’ona i energia de l’estat fonamental, respectivament. En el mateix treball publicat per Hohenberg i Kohn35 els autors també van proposar una manera de trobar la densitat electrònica de l’estat fonamental del sistema, . La seva proposta estava basada en el mètode variacional, mètode matemàtic fonamental de la mecànica quàntica que diu que qualsevol funció d’ona que no sigui la funció d’ona exacta de l’estat fonamental del nostre sistema, en aplicar-li el Hamiltonià mitjançant l’equació de Schrödinger resultarà en una energia per sobre de l’energia fonamental exacta, . Hohenberg i Kohn van demostrar que el principi variacional també s’aplica al funcional de la densitat electrònica: és a dir, l’energia que obtindrem del funcional només serà l’energia fonamental exacta, , si la densitat utilitzada és la densitat fonamental exacta, , altrament l’energia resultant serà per sobre de . Matemàticament, (3) on és el funcional de densitat electrònica compost del terme cinètic, , el terme d’interacció electrònica, , i el terme d’interacció entre electrons i nuclis, . D’aquesta manera, el que hauríem de fer seria minimitzar el funcional de densitat electrònica en funció de la densitat electrònica per trobar i . 246 Chapter 8 Tot i que pot semblar que l’estudi de Hohenberg i Kohn ofereix una ruta completa per poder utilitzar la densitat electrònica de manera exclusiva per trobar la funció d’ona de l’estat fonamental i totes les propietats associades, a la pràctica no és el cas. Això és així perquè el seu estudi no donava cap pista, o manera de trobar, la forma dels funcionals i en l’equació 3. Sense saber la forma d’aquests funcionals respecte la densitat electrònica no es pot utilitzar el principi variacional per trobar i . Això va canviar amb la contribució de Kohn i Sham36 al 1965 on, sense entrar molt en detall, van demostrat que el funcional de l’energia cinètica es podia calcular de manera exacta per un sistema d’electrons no interactius (és a dir, un sistema on els electrons no interaccionen entre ells com, per exemple, dins de l’esquema de Hartree-Fock) i la part romanent de l’energia cinètica exacta del nostre sistema d’electrons interactius es podria aproximar. D’aquesta manera, Kohn i Sham van definir el funcional universal, , on contenia tots aquells paràmetres energètics dels quals no es coneix la seva dependència vers la densitat electrònica, , tal com la part que no hem considerat de l’energia cinètica real del nostre sistema, el terme d’interacció d’intercanvi entre electrons i l’anomenada energia de correlació electrònica. Sense entrar molt en detalls, s’ha d’esmentar que un dels objectius principals del DFT modern ha estat trobar millors i millors aproximacions del terme . Per a tal empresa diferents enfocaments han estat aplicats al llarg del temps. Els més importants han estat l’aproximació de la densitat local (LDA de l’anglès),33,34 l’aproximació general del gradient37,38 (o GGA, de l’anglès) o els anomenats funcionals híbrids, on una part del terme energètic degut a l’intercanvi electrònic, , es calcula de manera exacta dins de l’esquema Hartree-Fock.39 Aquest últim tipus de funcionals (els híbrids), han estat força utilitzats en aquesta tesi doctoral. És el cas, per exemple, de l’anomenat PBE0,40 el qual conté un 25% d’ intercanvi exacte i com s’ha vist, és força apropiat per estudiar radicals orgànics amb sistemes π-conjugats.41 8.3 Simulació de dispositius basats en TAMs Aquest capítol està relacionat amb els primers tres treballs d’aquesta tesi doctoral, els tres en col·laboració amb els grups experimentals dels Profs. Jaume Veciana i Concepció Rovira i de la Dr. Marta Mas-Torrent, de l’Institut de Ciència dels Materials de Barcelona (ICMAB). En els tres treballs s’estudia sistemes basats en molècules TAM amb propietats potencials per diferents tipus de dispositius electrònics. Els dos primer treballs, molt relacionats entre ells, estan centrats en la preparació de mono-capes automuntades sobre diferents superfícies metàl·liques on el centre radicalari dins dels TAMs es troba particularment a prop de la superfície metàl·lica, el qual podria donar lloc a propietats magnetoresistents (és a dir, interacció entre els electrons conductors del metall i el centre radicalari). El tercer treball es centra en l’estudi d’uns compostos de capa tancada (és a dir, no radicals) basats en TAMs hidrogenats units a una unitat d’etilè (és a dir: C=C) on s’observa un bloqueig de l’isòmer cisno vist anteriorment. En aquest capítol introduiré de manera breu els tres treballs, explicant la rellevància de cadascun i, Resum en Català 247 posteriorment, resumiré els principals resultats. Informació detallada de cada treball es pot trobar al Capítol 3 d’aquesta tesi doctoral on els tres treballs són inclosos (dos publicats i un en format esborrany). 8.3.1 Síntesi de mono-capes auto-muntades radicals mitjançant molècules TAM de capa tancada. Aquest primer treball es basa en un treball computacional publicat al 201242 on es va proposar el mecanisme electrònic representat en la Fig. 8.6. Com es pot veure, de manera computacional, mitjançant càlculs DFT, es va demostrar que enllaçant molècules de capa tancada quinoides amb una superfície metàl·lica, com or, genera una mono-capa radical42 (r-SAM, de l’anglès) i, per tant, amb spín magnètic, com es mostra a la Fig. 8.6b. Fig. 8.6 a) Esquema general on, per mitjà d’una molècula de capa tancada quinoide es genera una mono-capa radical. b) Densitat d’espín electrònic de la mono-capa resultant en una superfície d’or, calculada dins de l’esquema DFT. c) Mecanisme electrònic que explica la generació de l’electró desaparellat en formar un enllaç covalent amb la superfície metàl·lica. El mecanisme que explica la generació de l’electró desaparellat en formar l’enllaç covalent entre les molècules i la superfície es mostra en la Fig. 8.6c. Aquest mecanisme és molt interessant perquè, si es demostrés experimentalment, ofereix una manera de generar SAMs radicals, de força interès per aplicacions en electrònica i espintrònica,43,44 utilitzant molècules de capa tancada (és a dir, no radicals) i per tant, a priori, menys reactives que les espècies radicals. Tot i que la predicció de Rissner et al.42 és de gran interès a nivell fonamental, manca potencial a nivell pràctic, donat que la mono-capa proposada en el seu treball no seria estable i, per tant, rarament aplicable en cap tipus de dispositiu. La principal raó és l’alta exposició de l’electró desaparellat generat en el mecanisme proposat en la Fig. 8.6, el qual podria reaccionar fàcilment amb espècies reactives del medi (com l’oxigen) o, fins i tot, amb la pròpia superfície metàl·lica. En aquest treball hem testejat la utilització de les molècules TAM de capa tancada que es mostren en la Fig. 8.7 com a candidates per formar una SAM radical mitjançant el mecanisme mostrat en la Fig. 8.6. 248 Chapter 8 Fig. 8.7. Candidats moleculars proposats en aquest treball. Com es veu en la figura, aquests candidats moleculars són TAMs modificats de manera que en l’anell aril inferior hi ha una configuració quinoide que, en cas de reaccionar el grup inferior amb una superfície metàl·lica, donaria lloc a la generació d’una SAM radical formada per molècules molt semblants a la família de compostos PTMs45 (o perclorotriarilmetils). Els PTMs, com s’explicarà més endavant són radicals TAM persistents a causa de la protecció estèrica que els clors ofereixen al carboni central, on es troba l’electró desaparellat. En el cas dels compostos radicals que es generarien a partir de la utilització dels candidats moleculars mostrats a la Fig. 8.7, aquests també serien estables perquè els àtoms de clor de la molècula (en verd en la Fig. 8.7) protegirien de manera estèrica l’electró desaparellat. Al treball Publication-draft #1 presentat en aquesta tesi es mostra els resultats d’aquesta investigació fruit d’una col·laboració estreta entre els grups experimentals del ICMAB i del ICN2 (Institut Català de Nano-ciència i Nano-tecnologia) i la nostra contribució computacional. Aquest treball es troba en el format d’un esborrany on es mostren les conclusions de les diferents contribucions teòriques i experimentals. Inicialment es va veure que dels tres candidats moleculars mostrats a la Fig. 8.7 només el candidat basat en el grup oxo-carbonil (anomenat TTM-O) era suficientment estable com per ser aïllat. Els altres dos compostos dimeritzaven o es descomponien en condicions normals. Així doncs el TTM-O es va sublimar en condicions d’ultra-buit sobre una superfície d’Au, de Ag i de Cu. Abans i després de cada sublimació les superfícies es van determinar amb diferents tècniques de caracterització superficial tal com X-ray photo-electron spectroscopy (XPS) i angle-resolved ultraviolet photoemission spectroscopy (ARUPS). En paral·lel, càlculs periòdics basats en DFT (utilitzant el funcional PBE38) es van portar a terme per cada sistema molècula-superfície. Les mesures experimentals en superfície demostraven la formació d’electrons desaparellats en la SAM construïda sobre la superfície de Ag, i no en les superfícies d’Au i de Cu. Els nostres càlculs periòdics mostraven l’aparició de densitat d’espín per les SAMs sobre Ag i Cu on les molècules presenten una conformació vertical respecte el pla superficial. Pel cas del Cu, però, els càlculs també mostren una forta interacció amb les molècules adsorbides quan aquestes mostren una conformació plana respecte la superfície. Això està en acord amb les mesures experimentals de la SAM sobre Cu, que indicaven la pèrdua d’àtoms de clor sobre aquesta superfície i la posterior polimerització de molècules TTM, però no la formació d’una SAM radical (és a dir, amb electrons Resum en Català 249 desaparellats). Per tant, la conclusió general del treball Publication-draft #1 és la demostració experimental de la predicció teòrica proposada per Rissner et al. al 2012: és a dir, es pot utilitzar molècules de capa tancada basades en TAM quinoides per formar la corresponent SAM radical. Tot i això, el nostre estudi també demostra que no totes les molècules TAM quinoides són viables, ja que no totes són estables experimentalment. A més, també demostrem que no totes les superfícies metàl·liques poden ser utilitzades per donar lloc al mecanisme electrònic mostrat a la Fig. 8.6 a partir del qual es genera l’electró desaparellat. Un cert grau de reactivitat per part de la superfície és necessari i, en el nostre cas particular, sembla que la superfície de Ag és la més adequada. 8.3.2 Enllaç directe entre un radical orgànic sobre or i plata El compost thio-carbonil mostrat a la Fig. 8.7 (compost central en la figura, TTM-S) es va trobar que dimeritza en solució donant lloc al corresponent compost bi-radical com es mostra en la Fig. 8.8. Fig. 8.8 Procés de dimerització del compost quinoide TTM-S en solució generant el corresponent bi-radical. Aquest tipus de compostos amb enllaços di-thiol es poden utilitzar per formar les SAMs corresponents sobre superfícies d’or, ja que l’enllaç S-S es trenca per formar dos enllaços S-Au. Mitjançant aquesta ruta, prèviament es va sintetitzar SAMs basades en radicals PTMs utilitzats com a interruptors electro-actius.46 Per tant, el bi-radical mostrat a la Fig. 8.8 es podria utilitzar per formar la SAM dels monòmers corresponents. Aquestes SAMs però, tindrien la particularitat que la unitat TTM estaria directament enllaçada amb la superfície metàl·lica. Normalment, com es representa en la Fig. 8.9 (part esquerra), les SAMs basades en PTMs tenen una cadena alquílica o aromàtica que separa el cor radical del grup que reacciona amb la superfície, aconseguint així separar físicament el cor radical dels electrons metàl·lics (evitant així possibles reaccions amb l’electró desaparellat). En el cas d’utilitzar el bi-radical representat en la Fig. 8.8, com es pot entendre, la unitat radical TTM serà directament enllaçada amb la superfície metàl·lica, com es representa a la part dreta de la Fig. 8.9. En aquest cas es podria esperar una reacció entre l’electró desaparellat de la unitat TTM i els electrons metàl·lics, per la gran proximitat entre ells. Malgrat això, en el cas que tal reacció no tingués lloc i la SAM radical fos estable, es podrien esperar fenòmens interessants com, per exemple, la interacció magnètica entre l’electró desaparellat de la monocapa TTM i els electrons conductors metàl·lics.43 Tal interacció ja s’ha demostrat per corrents 250 Chapter 8 elèctrics a través de molècules TAM situades entre dos elèctrodes d’or, donant lloc al conegut efecte de Kondo.14 Fig. 8.9 Diferents possibles SAMs en superfícies metàl·liques. En l’esquema de l’ esquerra es mostra la formació de SAMs on el radical (esfera blava) es troba separat físicament de la superfície per mitjà d’un grup linker (rosa). En el nostre cas, el cap radical està directament enllaçat a la superfície metàl·lica (esquema de la dreta). En el treball Publication #2, la molècula bi-radical TTM-S-S-TTM (veure estructura a la Fig. 8.8) va ser utilitzada per funcionalitzar una superfície d’ Au i d’ Ag mitjançant processos de formació de SAMs en solució (veure Publication #2 per detalls). Les superfícies es van caracteritzar mitjançant XPS, UPS i EPR. Les tres tècniques van corroborar la formació de la SAM i de la presència d’electrons desaparellats en la mono-capa orgànica. Mesures de voltametria cíclica (CV de l’anglès) també van corroborar la naturalesa electro-activa de la SAM, típica dels TAMs radicals.13 Els nostres càlculs periòdics DFT també van corroborar la persistència de densitat d’espín a la SAM de TTM-S. La densitat d’espín es trobava localitzada a la unitat TTM, però vam observar una certa polarització d’espín a la superfície metàl·lica, que podria ser indicatiu d’efectes magnetoresistents. Concloent, al treball Publication #2 hem demostrat la possibilitat de formar SAMs radicals on el cor radical es troba directament enllaçat a la superfície metàl·lica. Això, com els nostres resultats indiquen, no comporta la reacció entre l’electró desaparellat i els electrons conductors del metall. Aquests sistemes, com s’ha explicat anteriorment, mostren un cert potencial per aplicacions en espintrònica molecular.43 8.3.3 Estudi de la isomerització E-Z en compostos de H-PTM amb unitats d’etilè Els compostos basats en la unitat molecular etilè (C=C) poden mostrar la coneguda isomerització E-Z, com es mostra a la Fig. 8.10 per l’estilbè. Aquest tipus d’isomerització s’ha d’activar amb llum o amb productes químics,47 com el iode, ja que no té lloc de manera espontània, fins i tot a temperatures elevades. Això és així perquè per tenir lloc la isomerització la molècula ha de passar a través d’un estat de transició on el doble-enllaç C=C es trenca donant lloc a l’estat bi-radical, com es mostra a la Fig. 8.10b. Aquest mecanisme que involucra el gir sobre l’eix de l’enllaç C=C ha estat proposat teòricament com el mecanisme més probable connectant ambdós confòrmers.48 Resum en Català 257 funcionalitzats amb aquesta sèrie d’àtoms són els més estables químicament.45,56 En l’estudi Publication #6 hem considerat tant funcionalitzacions completes dels tres anells aril amb un únic tipus d’àtom, com funcionalitzacions parcials combinant dos tipus d’elements (Hi Clor Cli F-, per exemple). Així, dissenyant 50 TAM 2D-COFs diferents i estirant cada estructura mono-direccionalment en 35 punts diferents d’estirament, hem hagut de realitzar un total de 1750 càlculs periòdics en aquest estudi. Òbviament aquest nombre de càlculs no es podia realitzar dins de l’esquema DFT i llavors hem utilitzat camps de forces (o FFs, de l’anglés) que, per estudiar la estructura atòmica d’aquests materials aporten una bona relació entre exactitud i cost computacional. D’aquesta manera hem pogut trobar tota una sèrie de xarxes formades per TAMs que han estat sintetitzats al laboratori mostrant una certa persistència química on es pot causar un gir dels anells aril important en estirar el material en una direcció. A més, amb càlculs DFT realitzats en les xarxes més prometedores, hem comprovat que aquest gir dóna lloc a canvis electrònics detectables. Per tant, la conclusió general del Publication #6 és que hi ha molècules TAM informades a la literatura que es podrien utilitzar per construir xarxes covalents 2D amb propietats molt controlables per mitjans externs (com un estirant mono-direccional). 8.5 TAMs connectats en para-: Cap a semimetalls 2D 8.5.1 Connectant radicals orgànics π-conjugats: metavs. paraCom sabem gràcies a la química bàsica de sistemes orgànics π-conjugats, múltiples centres radicals πconjugats es poden connectar essencialment de dues maneres: en metao en para-. Aquestes dues opcions estan representades a la Fig. 8.16. Fig. 8.16 Connectivitats meta- (a) i para- (b) entre carbonis radicals (en color púrpura) en sistemes orgànics π-conjugats. c) i d) mostren l’estructura de tri-/bi-radicals experimentalment sintetitzats basats en unitats TAM amb connexions metai paraentre els centres radicalaris, respectivament. Per als casos para- (columna dreta) dues formes ressonants de Lewis són possibles. 258 Chapter 8 Com es representa en la Fig. 8.16, s’ha comprovat experimentalment que connectant centre radicalaris a través d’un sistema π-conjugats en metaun respecte de l’altre, els electrons desaparellats corresponents es mantenen localitzats i mostren una interacció lleugerament ferro-magnètica,3,57 com és representat a la Fig. 8.16a,c. En canvi, quan els centres radicalaris es connecten en paraun respecte l’altre, com en el cas del bi-radical anomenat hidrocarbur de Chichibabin58 (Fig. 8.16d), els electrons desaparellats es troben anti-ferromagnèticament acoblats però, a més, també es poden aparellar donant lloc a una configuració de capa tancada quinoidal59 (Fig. 8.16b,d). 8.5.2 Compostos de valència mixta: cap a l’electrònica orgànica. Què passa amb cadascun dels exemples mostrats anteriorment quan es redueix un dels centres radicals a l’estat redox -1 (és a dir, l’anió). En tal situació, el bi-radical esdevé un compost mono-radical on cada extrem de la molècula conté un nombre diferent d’electrons de valència. Per aquesta raó, aquest tipus de sistemes s’anomenen compostos de valència mixta (o MVC, de l’anglès). MVC s’han preparat basats en dos unitats PTM unides per diferents ponts π-conjugats60–62 on s’ha detectat la transferència de la càrrega negativa entre les dues unitats PTM (veure Fig. 8.17). És a dir, la càrrega negativa no està localitzada en una unitat PTM, sinó que pot “saltar” entre les dues unitats. Fig. 8.17 MVC basats en unitats PTM connectats en a) parai b) metaon una de les unitats PTM conté un electró desaparellat i l’altre un parell d’electrons associats a la càrrega negativa del compost. És força interessant el fet que depenent de com les dues unitats de PTM estiguin connectades, la càrrega negativa tindrà, o no, la capacitat de “saltar” entre les dues unitats, el que s’anomena transferència de càrrega dins del compost MVC. Així doncs, s’ha vist experimentalment que MVC-PTM connectats en meta- (Fig. 8.17b) mostren la càrrega negativa localitzada en un dels PTMs i, en canvi, MVC-PTM connectats en para- (Fig. 8.17a) mostren la transferència de càrrega, demostrat amb diferents tècniques espectroscòpiques tal com absorció en el UV-visible o ressonància electrònica paramagnètica (EPR, de l’anglès).60,61 Resum en Català 259 8.5.3 Quin és el mecanisme de transferència de càrrega en compostos para-MVC-PTM? Gràcies a la gran estabilitat dels PTMs i la facilitat per reduir-los a l’estat negatiu, s’ha pogut estudiar amb detall el comportament de MVC basats en aquests radicals orgànics.63–66 En els estudis més recents s’ha proposat principalment dos mecanismes electrònics diferents per explicar el procés de transferència de càrrega: els anomenats túnel electrònic i salts de càrrega (o tunneling i charge hopping, en anglès). La Fig. 8.18 representa cadascun d’aquests mecanismes. Fig. 8.18 a) En el mecanisme de túnel els electrons no interaccionen amb el pont π-conjugat, saltant directament d’una unitat de PTM a l’altra. b) En el mecanisme de salts de càrrega, la càrrega negativa viatja d’una unitat de PTM a l’altra, passant abans per cadascuna de les unitats del pont i, per tant, es pot arribar a detectar la càrrega localitzada al pont (el que s’anomena polaró). Com es veu a la Fig. 8.18a, el mecanisme túnel explica la transferència de càrrega com salts de la càrrega negativa directament d’un PTM l’altre, sense interaccionar amb el pont π-conjugat. Aquest mecanisme està directament relacionat amb l’efecte túnel explicat dins del camp de la mecànica quàntica. El mecanisme de salts de càrrega (Fig. 8.18b) explica la transferència de càrrega mitjançant salts de càrrega puntuals a través de cadascuna de les unitats moleculars que componen el pont π-conjugat. Així doncs, en aquest segon mecanisme, la càrrega negativa dins del MVC-PTM es pot trobar localitzada en el pont πconjugat en un moment determinat, el que s’anomena polaró.62 El mecanisme túnel s’ha assignat als MVC-PTM on el pont és de curta longitud, i el mecanisme de salts de càrrega als de pont de llarga longitud.62 Durant aquesta tesi doctoral he participat en l’estudi d’una sèrie de compostos MVC-PTM on les unitats PTM estan connectades per mitjà d’un pont de tiofè-vinil (TV), com es representa en la Fig. 8.19. Com es demostra en aquest treball, Publication #7, mitjançant diferents tècniques espectrocòpiques (com les esmentades anteriorment), afegint en aquest cas l’espectroscòpia Raman, per als MVC-PTM amb ponts llargs el mecanisme de transferència de càrrega entre els dos PTMs es basa en l’anteriorment explicat salts de càrrega. Per als compostos curts, però, els nostres càlculs basats en l’esquema DFT apuntaven a 260 Chapter 8 un mecanisme diferent al mecanisme túnel proposat en treballs anteriors.62 Fig. 8.19 MVC-PTM estudiats amb ponts de TV de mida creixent. En el Publication #7 vam realitzar una dinàmica molecular a 300K i vam estudiar la localització o deslocalització de la densitat d’espín associada l’electró desaparellat. Vam trobar que per una meitat de les conformacions tèrmicament activades a 300K l’espín es trobava localitzat en una de les unitats PTM i, per tant, la càrrega negativa localitzada en l’altra unitat. L’altra meitat de les conformacions però, la densitat d’espín estava totalment deslocalitzada entre les dues unitats PTM, la qual cosa també implicava una deslocalització de la càrrega negativa en ambdues unitats PTM i sobre el pont π-conjugat. Aquests resultats, com expliquem en aquesta contribució, apunta a un mecanisme anomenat ressonància parpelleig (o flickering resonance, FR, de l’anglès). Així doncs, el mecanisme FR entén que la carrega negativa té la capacitat de deslocalitzar-se a través del pont π-conjugat entre les dues unitats PTM en l’estat fonamental però que no totes les conformacions ho permeten. Així doncs a temperatura ambient, algunes conformacions localitzaran la càrrega en una unitat PTM i, unes altres, la deslocalitzaran en tota la molècula, així permeten que la càrrega vagi localitzant-se en una unitat PTM o a l’altra. Val la pena esmentar que aquest mecanisme està relacionat amb la conducció balística demostrada en el grafè.67 8.5.4 De MVC-PTM a materials orgànics de Dirac post-grafè Aquest efecte tan important de les connectivitats metai paraprovades per compostos multi-radicals (Fig. 8.16) i en els corresponents MVC (Fig. 8.17) haurien de tenir un efecte anàleg en les xarxes covalents basades en TAM (TAM 2D-COFs). En el treball Publication #5 el TAM 2D-COF estudiats presentaven una estructura on les unitats TAM estan connectades en metauna respecte l’altra (Fig. 8.20a). Com s’explica en aquell treball, aquestes xarxes presenten una estructura electrònica d’aïllant elèctric, on cada electró desaparellat es troba localitzat en la unitat TAM corresponent. Resum en Català 261 Fig. 8.20 a) Estructura química del TAM 2D-COF connectat en metaestudiat en el treball Publication #5 b) del connectat en paraestudiat en el treball Publication #8. Quines propietats electròniques mostraria un TAM 2D-COF on les unitats TAM estiguin connectades en parauna respecte de l’altra? Resulta que, com va publicar Adjizian et al.68,69 aquest tipus de xarxes 2D es comporten com a semimetalls, tal com el grafè, mostrant un con de Dirac en l’estructura de bandes corresponent (veure Fig. 8.21). Aquesta interessant característica electrònica està associada a la conducció balística ja demostrada experimentalment en grafè.70,71 Fig. 8.21 a) Estructura periòdica del TAM 2D-COF connectat en paraproposat per Adjizian et al. b) Estructura de bandes de tal xarxa covalent mostrant la presència d’un encreuament lineal de bandes al nivell de Fermi (anomenat con de Dirac) c) Representació 3D del con de Dirac en aquest tipus de xarxes. En el treball Publication #8 hem fet una connexió entre una sèrie de materials orgànics de Dirac postgrafè (PGODs, de l’anglès) i els bi-radicals basats en TAM connectats en para-. Com s’ha mostrat anteriorment aquests bi-radicals mostren dues formes ressonants, sent aquestes l’anti-ferromagnètica de capa oberta (és a dir, bi-radical) i la quinoide de capa tancada (veure Fig. 8.16). Aquestes formes ressonants però, també haurien d’existir en els PGODs, ja que en aquests materials els centres radicalaris 262 Chapter 8 també estan connectats en paraun respecte de l’altre. Tot i així, per a la sèrie de PGODs mostrats en la Fig. 8.22 aquestes solucions electròniques localitzades no s’han informat. Fig. 8.22 Sèrie de materials PGODs estudiats en el treball Publication #8. Tots aquests materials presenten un con de Dirac en l’estructura de bandes corresponent, la qual cosa indica la seva naturalesa com a semimetalls, com el grafè. Per tant, en el treball Publication #8, hem realitzat un estudi sistemàtic on demostrem en detall l’existència d’aquestes solucions localitzades (la AFM i quinoide) per primera vegada. Aquest estudi s’ha basat en càlculs DFT utilitzant el funcional híbrid PBE0 i comparant els resultats en dos programes que utilitzen un tipus diferent de representacions electròniques. Els resultats obtinguts coincideixen per ambdós enfocaments. Així doncs, els nostres resultats demostren que els materials PGODs presenten una estructura altament tunejable a la nano-escala i que, per tant, tenen un potencial per a futures aplicacions en nano-electrònica molt important. 8.6 Conclusions En la meva opinió la contribució intel·lectual més important d’aquesta tesi és el disseny dels materials 2D TAM 2D-COFs. Aquests materials, no sintetitzats encara al laboratori, presenten tota una sèrie de propietats que els fan molt interessants per a aplicacions futures en nano-electrònica. Com s’ha vist amb els resultats presentats en els treballs Publications #4 – 6, el gir dels anells aril determinen la localització/deslocalització de l’electró desaparellat en els TAMs. Aquesta característica es pot utilitzar per dissenyar TAM 2D-COFs on, per mitjà d’un estirament mono-direccional l’angle de gir dels anells aril es pot manipular externament. Aquesta manipulació estructural dóna lloc, al seu torn, a un control extern de propietats electròniques fonamentals del material tal com la localització d’espín, les interaccions magnètiques i el band gap del material, totes elles variant linealment amb la mitjana del cosinus al quadrat de l’ angle de gir de tots els anells aril del material. Així doncs, els TAM 2D-COFs es podrien utilitzar com a sensors mecànics. D’altra banda, en canviar la connectivitat entre els TAMs dins del material, fa que aquest es comporti com a un semi-metall amb solucions semiconductores properes en energia. Per tant, simplement canviant la manera en la qual els TAMs estan covalentment units permet dissenyar aïllants elèctrics o conductors 2D, la qual cosa torna a ressaltar la gran versatilitat electrònica Resum en Català 263 d’aquests materials. En general, aquest treball de tesi m’ha permès experimentar dos modes del químic computacional: el mode on es col·labora amb grups experimentals estudiant sistemes ja sintetitzats per aprofundir en la seva comprensió i, d’altra banda, el mode on s’utilitza la simulació com a eina per predir materials i sistemes no sintetitzats al laboratori. Poder aprofitar ambdós enfocaments per nodrir-los l’un de l’altre (com es pot veure entre els últims treballs Publications #7 i #8) és per a mi un dels millors aprenentatges que trec d’aquesta tesi doctoral. 8.7 Referències 1 M. Gomberg, J. Am. Chem. Soc., 1900, 22, 757–771. 2 A. E. Tschitschibabin, Berichte der Dtsch. Chem. Gesellschaft, 1907, 40, 1810–1819. 3 G. Kothe and H. Zimmermann, Tetrahedron, 1973, 29, 2305–2313. 4 A. Rajca, K. Lu and S. Rajca, J. Am. Chem. Soc., 1997, 119, 10335–10345. 5 A. Rajca, J. Wongsriratanakul and S. Rajca, Science, 2001, 294, 1503–1505. 6 N. M. Shishlov, Russ. Chem. Rev., 2006, 75, 863–884. 7 M. Gomberg, J. Am. Chem. Soc., 1903, 25, 1274–1277. 8 M. Ballester and J. Riera-Figueras, J. Am. Chem. Soc., 1971, 4254, 2215–2225. 9 J. Veciana and I. Ratera, in Stable Radicals: Fundamentals and Applied Aspects of Odd-Electron Compounds, ed. R. G. Hicks, John Wiley & Sons, Inc., 2010, pp. 33–80. 10 A. Rajca, S. Rajca and J. Wongsriratanakul, J. Am. Chem. Soc., 1999, 121, 6308–6309. 11 S. Rajca, A. Rajca, J. Wongsriratanakul, P. Butler and S. M. Choi, J. Am. Chem. Soc., 2004, 126, 6972–86. 12 D. Maspoch, D. Ruiz-Molina, K. Wurst, N. Domingo, M. Cavallini, F. Biscarini, J. Tejada, C. Rovira and J. Veciana, Nat. Mater., 2003, 2, 190–5. 13 C. Simão, M. Mas-Torrent, N. Crivillers, V. Lloveras, J. M. Artés, P. Gorostiza, J. Veciana and C. Rovira, Nat. Chem., 2011, 3, 359–64. 14 R. Frisenda, R. Gaudenzi, C. Franco, M. Mas-Torrent, C. Rovira, J. Veciana, I. Alcon, S. T. Bromley, E. Burzurí and H. S. J. van der Zant, Nano Lett., 2015, 15, 3109–3114. 15 M. Abel, S. Clair, O. Ourdjini, M. Mossoyan and L. Porte, J. Am. Chem. Soc., 2011, 133, 1203–1205. 16 M. Bieri, M. Treier, J. Cai, K. Aït-Mansour, P. Ruffieux, O. Gröning, P. Gröning, M. Kastler, R. Rieger, X. Feng, K. Müllen and R. Fasel, Chem. Commun. (Camb)., 2009, 6919–21. 17 X.-H. Liu, Y.-P. Mo, J.-Y. Yue, Q.-N. Zheng, H.-J. Yan, D. Wang and L.-J. Wan, Small, 2014, 10, 4934–9. 18 X.-H. Liu, C.-Z. Guan, S.-Y. Ding, W. Wang, H.-J. Yan, D. Wang and L.-J. Wan, J. Am. Chem. Soc., 2013, 135, 10470–4. 264 Chapter 8 19 C. Steiner, J. Gebhardt, M. Ammon, Z. Yang, A. Heidenreich, N. Hammer, A. Görling, M. Kivala and S. Maier, Nat. Commun., 2017, 8, 14765. 20 Q. Fan, J. M. Gottfried and J. Zhu, Acc. Chem. Res., 2015, 48, 2484–2494. 21 W. Liu, X. Luo, Y. Bao, Y. P. Liu, G.-H. Ning, I. Abdelwahab, L. Li, C. T. Nai, Z. G. Hu, D. Zhao, B. Liu, S. Y. Quek and K. P. Loh, Nat. Chem., 2017, 9, 563–570. 22 A. Basagni, F. Sedona, C. A. Pignedoli, M. Cattelan, L. Nicolas, M. Casarin and M. Sambi, J. Am. Chem. Soc., 2015. 23 A. Basagni, G. Vasseur, C. A. Pignedoli, M. Vilas-Varela, D. Peña, L. Nicolas, L. Vitali, J. Lobo-Checa, D. G. de Oteyza, F. Sedona, M. Casarin, J. E. Ortega and M. Sambi, ACS Nano, 2016, 10, 2644–2651. 24 W. Dong, L. Wang, H. Ding, L. Zhao, D. Wang, C. Wang and L.-J. Wan, Langmuir, 2015, 31, 11755–11759. 25 Q. Sun, C. Zhang, L. Cai, L. Xie, Q. Tan and W. Xu, Chem. Commun., 2015, 51, 2836–2839. 26 G. Gu, N. Li, L. Liu, X. Zhang, Q. Wu, D. Nieckarz, P. Szabelski, L. Peng, B. K. Teo, S. Hou, Y. Wang, R. Bhosale, A. Mateo-Alonso, J. V. Barth, K. Wu and Y. F. Wang, RSC Adv., 2016, 6, 66548–66552. 27 J. P. Llinas, A. Fairbrother, G. Borin Barin, W. Shi, K. Lee, S. Wu, B. Yong Choi, R. Braganza, J. Lear, N. Kau, W. Choi, C. Chen, Z. Pedramrazi, T. Dumslaff, A. Narita, X. Feng, K. Müllen, F. Fischer, A. Zettl, P. Ruffieux, E. Yablonovitch, M. Crommie, R. Fasel and J. Bokor, Nat. Commun., 2017, 8, 633. 28 P. Ruffieux, S. Wang, B. Yang, C. Sanchez, J. Liu, T. Dienel, L. Talirz, P. Shinde, C. A. Pignedoli, D. Passerone, T. Dumslaff, X. Feng, K. Muellen and R. Fasel, Nature, 2015, 531, 15. 29 A. Narita, X.-Y. Wang, X. Feng and K. Müllen, Chem. Soc. Rev., 2015, 44, 6616–6643. 30 S. Kawai, S. Saito, S. Osumi, S. Yamaguchi, A. S. Foster, P. Spijker and E. Meyer, Nat. Commun., 2015, 6, 8098. 31 L. H. Thomas, Proc. Camb. Phil. Soc., 1927, 23, 542. 32 E. Fermi, Rend. Accad. Lincei, 1927, 6, 602. 33 P. A. M. Dirac, Proc. Camb. Phil. Soc., 1930, 26, 376. 34 F. Bloch, Z. Phys., 1929, 57, 545. 35 P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864. 36 W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133. 37 A. D. Becke, Phys. Rev. A, 1988, 38, 3098. 38 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 39 A. D. Becke, J. Chem. Phys., 1993, 98, 1372. 40 C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158. 41 R. Improta and V. Barone, Chem. Rev., 2004, 104, 1231–54. 42 F. Rissner, Z. Ma, O. T. Hofmann, C. Slugovc, Z. Shuai and E. Zojer, J. Mater. Chem., 2012, 22, 4269. 43 M. Mas-Torrent, N. Crivillers, V. Mugnaini, I. Ratera, C. Rovira and J. Veciana, J. Mater. Chem., 2009, 19, 1691. 44 M. Mas-Torrent, N. Crivillers, C. Rovira and J. Veciana, Chem. Rev., 2012, 112, 2506–27. 45 J. Guasch, X. Fontrodona, I. Ratera, C. Rovira and J. Veciana, Acta Crystallogr., 2013, C69, 255–7. 46 N. Crivillers, M. Mas-Torrent, J. Vidal-Gancedo, J. Veciana and C. Rovira, J. Am. Chem. Soc., 2008, 130, 5499–5506. Resum en Català 265 47 C. Dugave and L. Demange, Chem. Rev., 2003, 103, 2475–2532. 48 W.-G. Han, T. Lovell, T. Liu and L. Noodleman, ChemPhysChem, 2002, 3, 167–178. 49 D. Gegiou, K. A. Muszjat and E. Fischer, J. Am. Chem. Soc., 1968, 90, 3907–3918. 50 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Had and D. J. Fox, 2009. 51 F. C. Adam and S. I. Weissman, J. Am. Chem. Soc., 1958, 80, 2057–2059. 52 M. Karplus and G. K. Fraenkel, J. Chem. Phys., 1961, 35, 1312–1323. 53 J. A. Pople and D. L. Beveridge, J.Chem.Phys., 1968, 49, 4725–4726. 54 M. J. S. Dewar, J. Am. Chem. Soc., 1952, 74, 3345–3350. 55 G. N. Lewis, D. Lipkin and T. T. Magel, J. Am. Chem. Soc., 1944, 66, 1579–1583. 56 M. Ballester, J. Riera, J. Castañer, C. Badía and J. M. Monsó, J. Am. Chem. Soc., 1971, 93, 2215–2225. 57 N. M. Gallagher, A. Olankitwanit and A. Rajca, J. Org. Chem., 2015, 80, 1291–8. 58 L. K. Montgomery, J. C. Huffman, E. A. Jurczak and M. P. Grendze, J. Am. Chem. Soc., 1986, 108, 6004–6011. 59 P. Ravat and M. Baumgarten, Phys. Chem. Chem. Phys., 2015, 17, 983–991. 60 C. Rovira, D. Ruiz-Molina, O. Elsner, J. Vidal-Gancedo, J. Bonvoisin, J.-P. Launay and J. Veciana, Chemistry (Easton)., 2001, 7, 240–250. 61 V. Lloveras, J. Vidal-Gancedo, D. Ruiz-Molina, T. M. Figueira-Duarte, J.-F. Nierengarten, J. Veciana and C. Rovira, Faraday Discuss., 2006, 131, 291. 62 V. Lloveras, J. Vidal-Gancedo, T. M. Figueira-Duarte, J. F. Nierengarten, J. J. Novoa, F. Mota, N. Ventosa, C. Rovira and J. Veciana, J. Am. Chem. Soc., 2011, 133, 5818–33. 63 J. Sedo, D. Ruiz, J. Vidal-Gancedo, C. Rovira, J. Bonvoisin, J.-P. Launay and J. Veciana, Adv. Mater., 1996, 8, 748– 752. 64 A. Heckmann and C. Lambert, J. Am. Chem. Soc., 2007, 129, 5515–5527. 65 A. Heckmann, S. Dümmler, . Pauli, M. Margraf, . K hler, D. Stich, C. Lambert, I. Fischer and U. Resch-Genger, J. Phys. Chem. C, 2009, 113, 20958–20966. 66 J. Wu, X. Wu, J. O. Kim, S. Medina, F. J. Ramírez, P. M. Burrezo, S. Wu, Z. L. Lim, C. Lambert, J. Casado and D. Kim, Chem. - A Eur. J., 2017. 67 J. Blumberger, Chem. Rev., 2015, 115, 11191–11238. 68 J.-J. Adjizian, P. Briddon, B. Humbert, J.-L. Duvail, P. Wagner, C. Adda and C. Ewels, Nat. Commun., 2014, 5, 5842. 69 J.-J. Adjizian, A. Lherbier, S. M.-M. Dubois, A. R. Botello-Méndez and J.-C. Charlier, Nanoscale, 2016, 8, 1642– 1651. 70 V. E. Calado, S.-E. Zhu, S. Goswami, Q. Xu, K. Watanabe, T. Taniguchi, G. C. A. M. Janssen and L. M. K. Vandersypen, Appl. Phys. Lett., 2014, 104, 23103. 71 J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp and W. A. de Heer, Nature, 2014, 506, 349–354.