Exploring the Mechanisms Behind Non Aromatic Fluorescence with Density Functional Tight Binding Method

Exploring the Mechanisms Behind Non Aromatic Fluorescence with the Density Functional Tight Binding Method Gonzalo D´ıaz Mir´on,∗,†Carlos R. Lien-Medrano,‡Debarshi Banerjee,†,¶Uriel N. Morzan,§Michael A. Sentef,‡,∥Ralph Gebauer,†and Ali Hassanali∗,† †Condensed Matter and Statistical Physics, The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy ‡Institute for Theoretical Physics and Bremen Center for Computational Materials Science, University of Bremen, 28359 Bremen, Germany ¶Scuola Internazionale Superiore di Studi Avanzati (SISSA), 34136 Trieste, Italy §Instituto de Fisica de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, C1428EGA Buenos Aires, Argentina ∥Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), 22761 Hamburg, Germany E-mail: gdiaz [email protected]; [email protected] 1 arXiv:2401.09990v3 [physics.chem-ph] 9 Apr 2024 Abstract Recent experimental findings reveal non-conventional fluorescence emission in biological systems devoid of conjugated bonds or aromatic compounds, termed NonAromatic Fluorescence (NAF). This phenomenon is exclusive to aggregated or solid states, remaining absent in monomeric solutions. Previous studies focused on small model systems in vacuum show that the carbonyl stretching mode along with strong interaction of short hydrogen bonds (SHBs) remain the primary vibrational mode explaining NAF in these systems. In order to simulate larger model systems taking into account the effects of the surrounding environment, in this work we propose using the density functional tight-binding (DFTB) method in combination with non-adiabatic molecular dynamics (NAMD) and the mixed quantum/molecular mechanics (QM/MM) approach. We investigate the mechanism behind NAF in the crystal structure of Lpyroglutamine-ammonium, comparing it with the related non-fluorescent amino acid L-glutamine. Our results extend our previous findings to more realistic systems, demonstrating the efficiency and robustness of the proposed DFTB method in the context of NAMD in biological systems. Furthemore, due to its inherent low computational cost, this method allows for a better sampling on the non-radiative events at the conical intersection which is crucial for a complete understanding of this phenomenon. Beyond contributing to the ongoing exploration of NAF, this work paves the way for future application of this method in more complex biological systems such as amyloid aggregates, biomaterials and non-aromatic proteins. 2 1 Introduction Over the last decade, a growing body of experimental evidence has revealed the emergence of non-conventional fluorescence signals in biomolecular systems. In contrast to conventional spectroscopic intuition attributing fluorescence in biological systems to aromatic or conjugated groups, recent experiments have shown that non-aromatic systems exhibit inherent absorption and fluorescence in the UV-visible range.1–4 These fluorescent signals appear to be enhanced in aggregated forms, analogous to the aggregation-induced emission observed in organic materials.5,6 Noteworthy examples include amyloid structures,7–9 individual amino acids,10,11 compounds derived from amino acids,10,12 poly-amidoamines13 and small organic molecules.14,15 While the detailed molecular mechanism underlying Non-Aromatic Fluorescence (NAF) remains an open question, several possible explanations have been proposed.1,5 These include electron delocalization along peptide bonds in ordered secondary structures,3the constriction of the carbonyl stretching mode caused by intense local interactions such as strong hydrogen bonds,12,16 proton transfer along short hydrogen bonds17 and inter-residue charge-transfer excitations followed by charge recombination.4These molecular phenomena are believed to introduce low lying fluorescent electronic states in the visible regime arising from the supramolecular assemblies that do not rely on the presence of π-delocalized electrons. Since fluorescence emission involves the de-activation from electronic excited states, it requires a complex interplay involving the dynamics of both nuclear and electronic degrees of freedom which are notoriously difficult to model. Over the last few years, our group has been leading theoretical and computational efforts to investigate the spectroscopic origins of this phenomenon.1,9,12,16,18 We have recently investigated NAF in model amyloid proteins9,18 and L-glutamine/L-glutamine-derived12,16 amino-acids combining both experiments and theory. Employing trajectory surface hopping (TSH)19,20 simulations in combination with time-dependent density functional theory (TDDFT) level,21 we have shown that carbonyl groups (CO) appear to play a critical role in 3 modulating the observation of NAF in a wide variety of systems. Upon an initial photoexcitation to the first excited state S1, which is mainly localized around the CO group, strong inter-molecular interactions involving hydrogen bonds within certain biological aggregates hinder the stretching of the CO bond. This leads to a restriction of the non-radiative relaxation pathways, thus boosting the fluorescence quantum yield. The CO stretching mode is strongly coupled to the proton transfer and deplanarization modes in the amide group, which are also restrained due to environment effects.16 Our previous research has been based on dimer model systems carved out of crystal structures; in these studies we have accounted for the steric effect of the surrounding molecules by incorporating specific constraints in our simulations.9,12,16 The computational demands associated with simulating the photophysics of these systems make TSH calculations extremely challenging. Furthermore, the inherent variability in the electronic relaxation pathways can introduce problems with convergence. Consequently, the inclusion of a substantial number of trajectories becomes essential to derive meaningful and reliable results. We have recently employed hybrid Quantum-Classical Mechanical (QM/MM) approaches to enable a realistic description of environmental effects on the fluorescence.16 However, these approaches are computationally limited by the size of the relevant quantum-mechanical subsystem. These limitations have sparked our interest in exploring alternative methods to effectively tackle these challenges. In this regard, the density functional tight-binding (DFTB) method,22,23 a semi-empirical approach based on density functional theory (DFT), has emerged as a promising avenue. DFTB achieves computational efficiency through a combination of the two-center approximation, pre-tabulated integrals, and the use of a minimal basis set.24–26 This accelerates DFTB calculations by a factor of 2-3 order of magnitude compared to traditional DFT.25 Moreover, the pre-tabulation of integrals at DFT level ensures the precision of DFTB in predicting electronic properties for molecular, nano, and periodic systems, effectively emulating DFT.27–32 This framework has also been extended to include the modeling of excited state dynamics leading to the time-dependent density functional tight-binding 4 method (TD-DFTB). These extensions include both the frequency33,34(TD-DFTB) and the time domain35,36 (real-time TD-DFTB). In addition, TD-DFTB has been coupled to the Ehrenfest approach35,36 and TSH37–39 to perform non-adiabatic dynamics with semiclassical ion motion. The goal of the present work is to comprehensively assess the potential of the TDDFTB method in investigating the photophysics underlying NAF phenomenon employing the DFTB+ code.40 The primary focus of our investigation is on amino-acid crystals which have recently been studied in our group using both ab-initio electronic methods (TD-DFT) and experiments. It was found that L-glutamine, characterized by regular hydrogen bond interactions, is a non-fluorescent system. However, following a chemical transformation into L-pyroglutamine-ammonium (L-pyro-ammonium, pyroglutamic acid complexed with an ammonium ion), the system undergoes a transition to a short hydrogen bond configuration and displays a remarkable fluorescent signal. Panels a and b of Figure 1 show the molecular structure of these systems. By comparing and contrasting the mechanisms obtained with TD-DFTB to our previous work, we demonstrate that the DFTB approach correctly captures the non-radiative decay pathways occurring in L-glutamine as well as the origins of fluorescence in L-pyro-ammonium. With this validation in hand, we use TD-DFTB to understand the role of environmental effects using a QM/MM approach allowing for an accurate characterization of the experimentally observed Stokes shift between the excitation and emission spectra in this system. We also highlight aspects of non-radiative decay mechanisms which are different from our previous studies paving the way for future directions and developments needed to use Tight-Binding approaches to study non-aromatic fluorescence. 2 Theoretical Approaches The objective of this section is to provide a background on the various theories and techniques employed in our methodologies to study non-aromatic fluorescence. In this section, we 5 will summarize some of the most important aspects of DFTB, as well as its Time-Dependent extension to the frequency domain (TD-DFTB), with a special focus on the implementations in the DFTB+ code.40 Additionally, we will describe the key aspects of non-adiabatic dynamics in the context of Trajectory Surface Hopping (TSH), with a specific emphasis on the different analytical expressions used to calculate the non-radiative probability decay. 2.1 Density Functional Tight-Binding (DFTB and TD-DFTB) DFTB equations are derived from DFT by expansion of the total energy in a Taylor series of the electron density fluctuations δρ around a reference density ρ0.40 The chosen reference density is usually a summation of overlapping, spherical and noninteracting atomic charge densities. Up to the third order, the total energy can be approximated as:41 EDFT[ρ0+δρ]≈E0[ρ0] + E1st[ρ0, δρ] + E2nd[ρ0,(δρ)2] + E3rd[ρ0,(δρ)3].(1) The initial term E0can be represented by summing pairwise repulsive potential energies Erep AB. The truncation up to first order in the energy can be expressed as EDFTB1 =E0+E1st =X A>B Erep AB + occ. X i ni⟨ψi|H[ρ0]|ψi⟩,(2) where |ψi⟩is the ith molecular orbital in a linear combination of atomic orbitals (LCAO), ni is the occupation and H[ρ0] is the Hamiltonian operator in a two-center approximation. In the second-order DFTB (DFTB2) method, the E2nd term is incorporated through a monopole approximation,23 where the electron density fluctuations are approximated as a sum of atomic Slater-type spherical charge densities: EDFTB2 =EDFTB1 +1 2X AB γAB∆qA∆qB.(3) Here, ∆qAis the Mulliken charge on atom Aand γAB represents the electron interaction of 6 two Slater-type spherical charge densities on atoms Aand B. The inclusion of the secondorder term requires a self-consistent solution since the Mulliken charges depend on the molecular orbitals. This provides a more accurate description of charge-transfer and charge-charge interactions. DFTB3 allows the chemical hardness of an atom to change with its charge states by including third order terms: EDFTB3 =EDFTB2 +1 3X AB ΓAB∆q2 A∆qB,(4) where ΓAB is the derivative of γAB with respect to the ∆qA. Corrections for both van-der-Waals42,43 and hydrogen-bonding interactions44,45 were also implemented in the method owing to the fact that these types of weak interactions are not accurately captured by DFT based methods including DFTB. Within the DFTB+40 code there are several available approaches to determine excited states. We employed the Casida formalism21 within the framework of DFTB, following the same ansatz as in the original version of TD-DFT.33,34 The electronic excitation energy ωI in TD-DFTB can be obtained by solving the following eigenvalue problem: ΩFI=ω2 IFI.(5) Here, Ω is the response matrix and its elements are Ωijσ,klτ =δikδjlδστ ω2 ij + 2√ωijKijσ,klτ √ωkl,(6) where ωij =ϵj−ϵi,i, k and j, l are occupied and unoccupied KS orbitals respectively, σ and τare spin indices, whereas Kis the so-called coupling matrix. Within the monopole approximation, the coupling matrix elements Kijσ,klτ adopt simple expressions, reducing the computational cost.33 7 Moreover, the incorporation of Long-range Corrections (LC) into the two-electron integrals have also been implemented in the DFTB+ code46 with the aim to provide a reduction in the self-interaction error in DFT (and also present in DFTB) yielding a correct behaviour of the asymptotic potential. This implementation along with a new reparametrization of the Slater-Koster parameters enables a more accurate description of the excited states, mainly for those which involves charge transfer excitations.47,48 It is worth noting that in previous literature, the term TD-LC-DFTB denotes the incorporation of LC into TD equations. However, in our current work, we will use the term TD-DFTB since all calculations within this theory were conducted with LC. 2.2 Trajectory Surface Hopping (TSH) Trajectory Surface Hopping (TSH) is one of the most widely employed techniques to model non-adiabatic dynamics.20 The non-radiative relaxation is a non-equilibrium process and therefore the dynamics strongly depends on the initial conditions. For this reason, the simulation of a large number of thermally distributed independent trajectories, with varying initial conditions becomes essential.49,50 In each TSH trajectory, the electronic states are propagated using quantum mechanics, while the nuclear motion is handled classically employing the forces coming from a single potential energy surface from the quantum method. For more information on the theoretical and practical details, the reader is referred to previous studies.20,51 Bellow, we highlight specific details relevant to our present work. The TSH workflow involves propagating the system on distinct potential energy surfaces. At each timestep, the non-radiative probability is computed and a stochastic algorithm is employed to decide which potential energy surface the system will proceed along. The most common expression for the transition probability is the Fewest Switches Surface Hopping (FSSH) proposed by Tully:19 Pij(t) = −2Zt+δt t dt′Ci(t′)Cj(t′)∗gij(t′) Ci(t′)Ci(t′)∗,(7) 8 where Ciare the electronic coefficients of the potential energy surfaces iand the gij terms are the non adiabatic coupling (NAC) elements, one of the key components in non-adiabatic dynamics. Several alternatives approaches have been developed in order to avoid the explicit determination of the non adiabatic coupling elements,52–54 since sometimes there are no analytical expressions available or because they are computationally expensive to determine for large systems. One of the most popular in this context is the Landau-Zener (LZSH) approximation:55 Pij(t) = exp    −π 2¯hv u u u t ∆E3 ij(t) d2 dt2∆Eij(t)     ,(8) where ∆Eij is the adiabatic energy gap.51,56 Within the context of our TD-DFTB simulations, we employ the LZSH approximation instead of Tully’s method due to its easy implementation into our computational framework. 3 Computational Details In this section, we summarize the computational protocols applied to L-glutamine (L-gln) and L-pyroglutamine ammonium (L-pyro-amm) to simulate the ground-state molecular dynamics in periodic boundary conditions, the determination of the absorption spectra, the excited states surface hopping dynamics and finally the QM/MM simulations with DFTB and TD-DFTB. In the present study, we employed the DFTB+ package40 for the electronic structure calculations. The Genesis57,58 software was used to perform classical and QM/MM simulations. 3.1 Ground State DFTB Molecular Dynamics Ab-initio molecular dynamics simulations of both L-gln and L-pyro-amm were conducted using DFTB in the ground-state with periodic boundary conditions (PBC) using the gamma 9 coming from the carbonyl bonds and the SHB (see Figure S3 in the Supplementary Information). It is also worth noting that this prediction is also fully consistent with the results that were previously obtained at TD-DFT level in our previous work.12 4.3 Excited State TSH Simulations in Gas phase The two molecular systems (L-gln and L-pyro-amm) display substantially different photophysical properties. Specifically in L-pyro-amm, non-radiative decay pathways are effectively shut off16 thereby enhancing the excited state lifetime and subsequently increasing the fluorescence yield. From the TSH simulations on both systems, we extracted the average populations of the S1and S0electronic states over time which are illustrated in Figure 3 for the dimer systems in vacuum. The solid lines come from the TD-DFTB simulations in this work, while the dotted lines are obtained from our previous TD-DFT calculations.16 From the evolution of the electronic states, we can observe that TD-DFTB captures the essential photophysics of both systems. In L-gln dimers, an ultra-fast non-radiative decay is evident, with a characteristic lifetime of ∼90 fs for TD-DFT and ∼50 fs with TD-DFTB. Conversely, L-pyro-amm exhibits a much longer S1lifetime with both theory levels. These findings are again, fully consistent with the experimental findings12 where fluorescence is only observed in the L-pyro-amm molecular crystal. 16 Figure 3: Average populations of the electronic states obtained from TSH trajectories for L-gln (left panel) and L-pyro-amm (right panel) dimer systems in vacuum. Results using TD-DFT are depicted as dashed lines while those obtained with TD-DFTB in solid lines. The evolution of S1and S0are denoted in red and blue lines, respectively. In our previous studies employing TD-DFT, we observed that the transition from S1→S0 occurs via a conical intersection (CoIn) where the essential vibrational modes coupled to the process involves the extension of the carbonyl bond, proton transfer along the SHB, and finally, the deplanarization of the amide group. In this context, it is recognized that singledeterminant methods such as TD-DFT (or TD-DFTB) present an inaccurate description of the S1/S0CoIn. However, in our prior work (see Figure 5 in the SI in the reference16), we validated the CoIn identified with TD-DFT using the CASPT2 method. We found very good agreement between both theory levels. Examining each of the modes mentioned before in the ground and excited state as well as in the CoIn, a very specific structural signature becomes apparent. Figure 4 depicts the histograms for each of these modes obtained from TSH simulations employing both TD-DFT (top) and TD-DFTB (bottom) theory levels for L-gln dimer. The histograms were computed using data from all TSH trajectories. At each time step, we identified the current potential energy surface (S1or S0), or if the system transitioned to the other surface (CoIn). 17 Figure 4: Structural features characterizing ground (blue dashed line) and excited states (red solid line) as well as CoIn (green dashed-dot line) crossing for L-gln system. Molecular structures showing the parameters to describe the carbonyl stretching (panel a), the proton transfer (panel d) and the deplanarization (panel g). Probability Distribution Function (PDF) for the CO distance (panels b and c), PTC (panels e and f) and Deplanarization modes (panels h and i) for L-gln dimers in vacuum obtained from TSH trajectories using TD-DFT (middle panels) and TD-DFTB (lower panels). All PDFs were normalized independently. The comparison between TD-DFTB and TD-DFT reveals excellent agreement both in terms of the overall trends observed but also in the specific details of how the modes change during non-radiative decay. The variation observed in the maximum peak intensities of the PDFs for both S1and S0across all depicted modes in Figure 4 arises from the significant displacement between the minima on both potential energy surfaces. This displacement is a consequence of the substantial distortions experienced by the system upon excitation, a feature effectively captured by the DFTB approach. In particular, we observe that an 18 additional stretching for CO respect to S1distribution is necessary for the system to reach the CoIn (green dashed-dot lines in panel b and c). Similar behavior is also observed for the PTC (panels e and f). The primary difference arises in relation to the deplanarization mode. In TD-DFT (panel h), we observe a higher degree of deplanarization at the CoIn compared to the distribution of this mode in the S0state. In contrast, although the distributions obtained with TD-DFTB reflect the same trends (panel i), the deplanarization mode appears to be much more constrained compared to our previous findings. Despite the differences, it should be underscored that, based in our previous work,16 the deplanarization mode is less critical for the photophysics of both L-pyro-amm and L-gln. We next turn to comparing the behavior of the non-radiative decay modes that are important for L-pyro-amm. Since this system is fluorescent, extracting the decay mechanisms that emerge from the excited state simulations is particularly challenging due to the fact that there are fewer statistics of reactive events. In our previous study16 for example, out of a total of 100 trajectories, 4 displayed non-radiative decay from the excited to the ground-state. 19 Figure 5: Structural features characterizing ground (blue dashed line) and excited states (red solid line) as well as CoIn (green dashed-dot line) crossing for L-pyro-amm system. Molecular structures showing the parameters to describe the carbonyl stretching and the proton transfer are in panel a and d, respectively. Probability Distribution Function (PDF) for the CO distance (panels b and c), PTC (panels e and f) for L-pyro-amm dimers in vacuum obtained from TSH trajectories using TD-DFT (middle panels) and TD-DFTB (lower panels). All PDFs were normalized independently. In Figure 5 we show the most relevant features, namely the carbonyl stretching and the proton transfer modes obtained from the TSH simulations at TD-DFT and TD-DFTB levels. Specifically, we are able to reproduce the significant overlap in the distribution of the two modes between the S1and S0electronic states (red solid and blue dashed lines). These findings indicate that the energy minimum in the potential energy surfaces for each of these modes do not exhibit significant displacement, suggesting that these modes are restricted in L-pyro-amm. This feature is also fully consistent with typical aromatic fluorescent systems,69 where the restriction arises from the high electron delocalization in the planar arrangement 20 of these compounds. In the case of non-aromatic systems, like the ones we are tackling, the strong interactions due to SHBs induce this restriction on different modes. It is important to highlight when comparing the top and bottom panels of Figure 5, that due to the reduced computational complexity, we are able to run significantly more TSH trajectories compared to our previous TDDFT simulations (600 vs 100). DFTB thus permits the observation of many more non-radiative decays yielding statistics which allow the construction of histograms of various modes near the CoIn, for instance the green distribution in the case of TD-DFTB represents 122 decays (panels c and f) and the green vertical lines for TD-DFT represents only 4 decays (panels b and e). The examination of the distribution of these modes at the CoIn reveals that the mechanism observed in L-pyro-amm is similar to that observed in the L-gln system. Specifically, we find with the DFTB approach that the CO stretching mode undergoes two distinct signatures at the CoIn. One exhibits a more subtle stretching in comparison to the distribution of S1, while the other shows a more significant stretching of approximately 1.6˚ A(green dashed-dot line in panel c in Figure 5). Our previous TD-DFT simulations sample a few events between these two peaks. The effect of having more statistics with DFTB is observed more clearly in the PTC distributions (panels e and f) which display more structure compared to those obtained with TD-DFT. For example, we can capture the double-well character of the PTC (blue line in panel f) with TD-DFTB, while with TD-DFT we observe one main peak along with a shoulder (blue dashed line panel e). A distinction emerges when comparing the behavior of proton transfer between the excited and ground states in TD-DFTB. Notably, in the excited state, there is a significant reduction in proton transfer events, evidenced by the presence two peaks located at ±0.5˚ A with different intensity in the PDF (depicted by the red line in panel f). A similar trend is observed in TD-DFT, albeit with less intensity. In this case, a narrow distribution is noted in S1compared to the ground state, with the hydrogen positioned equidistant from the two oxygen atoms involved in the SHB (illustrated by the red line in panel e). Additionally, we observe that the SHB experiences a deformation at 21 the CoIn (green dashed-dot line in panel f in Figure 5), transforming into a transient normal HB. This is evident from the peaks at higher values of approximately ±2.5˚ A, which is also present in TD-DFT (green dashed-dot lines in panel e). Although we cannot rule out the possibility that some of these differences arise from the underlying potential energy surface along various vibrational modes, the limited statistics with TD-DFT are more likely to be the source of the differences we observe. However, we can see that the mechanism predicted by TD-DFTB is in excellent agreement with our previous studies.12,16 4.4 Optical Properties in Realistic Biological Environments The preceding results provide evidence that DFTB is a very viable approach for studying the non-radiative decay mechanisms in organic molecular crystals implicated in non-aromatic fluorescence. As previously mentioned, to simulate a more realistic system beyond vacuum dimers, we adopted the QM/MM framework to account for environmental effects. Consequently, in the following section we utilize TD-DFTB to investigate the optical properties of L-gln and L-pyro-amm within this approach. 4.4.1 L-Pyroglutamine-Ammonium We constructed two model QM regions embedded within an MM crystallographic environment including a dimer and the unit cell as shown in the Figure 6. 22 Figure 6: Dimer and Unit cell systems in the QM/MM simulations. The QM region is depicted in ball and stick while the MM in line representations. The real systems were replicated in the three directions; for the sake of clarity, here we are showing a 2D representation. The experimental data used to compare the optical properties in this system was the excitation and emission spectra, as reported in ref.12 It can be observed that the maximum of the experimental excitation spectrum is around 350 nm (red solid lines in the right panel in Figure 7), which corresponds to the low lying transitions in the absorption spectrum in L-pyro-amm crystal (red solid line in the left panel of Figure 2). Therefore, to allow for a one-to-one comparison, we determined the excitation spectra instead of the absorption, i.e., including only the lower energy transitions in our calculations. We first decided to compute the excitation spectra using only the first transition (S0→S1). Calculated and experimental results are shown in Figure 7. 23 Figure 7: Excitation (solid lines) and Fluorescence (dashed lines) spectra for L-pyro-amm. Left panel shows the average spectra obtained from QM/MM simulations using the dimer (red line) and the unit cell (blue line) in the QM region. Right panel shows the experimental spectra (extracted from reference,12 red line) and the average calculated from the QM/MM simulations for the unit cell in the QM region, where the calculated spectra were shifted to match the maximum in the experimental fluorescence spectra. All the spectra were normalized independently. The left panel in Figure 7 shows the results for both QM systems in L-pyro-amm in the QM/MM simulation. We can observe that both systems show similar excitation maximum (approx. 215 nm) and emission (approx. 290 nm). When we compared these values with the experimental data (red lines in the right panel) we observe notable differences. This finding is a well known fact that TD-DFT and therefore in its approximate variant TD-DFTB, tend to exhibit a notable shift in the absolute magnitude of the transition energies when comparing with experimental measurements.70,71 An additional factor contributing to the discrepancy between our computational outcomes and experimental findings lies in the inherent limitations of the QM/MM approach in representing the environmental effects. As demonstrated in Section 4.2, our methodology achieves outstanding agreement with experimental results when employing a sampling coming from ab-initio ground state simulations with periodic boundary conditions (see Figure 2). Regrettably, this level of concordance is not replicated in our QM/MM simulations. To illustrate the impact of the MM environment, we conducted excited state calculations for the unit cell system using the same conformations employed for 24 calculating the excitation spectra (blue solid line in the left panel of Figure 7), with all MM atoms removed. The results are presented in Figure S4 in the Supplementary Information. We successfully reproduced the calculated absorption spectra depicted in Figure 2 (red solid line in the right panel), thereby demonstrating the significant blue-shift effect induced by the MM environment. However, as we will elucidate in the following, these disparities persist not only in the ground state but also in excited state simulations. Consequently, focusing on energy differences becomes a more pertinent and meaningful avenue for comparison. We have thus determined the Stokes shift, defined as the difference between the maximum of the emission band and the absorption or excitation spectra the results of which are summarized in Table 1. Notably, we find remarkable agreement between the experimental results and the two model systems for the Stokes shift. It is also interesting to observe that the dimer system appears to fully capture the energetics associated with the fluorescence Stokes shift which reinforces the use of the dimer model systems in disentangling the non-radiative decay mechanisms. Table 1: Stokes shift for the different models in the QM/MM simulations System Absorption/Emission Max. [nm] FWHMa[nm] Stokes shift [nm] Dimer 211/298 120 87 Unit Cell 218/295 121 77 Experimentb354/441 92 87 aFWHM denotes the Full Width at Half Maximum for the fluorescence spectra. bExperimental results were extracted from the reference.12 The right panel of Figure 7 presents the excitation and fluorescence spectra for both experimental and calculated using the unit cell of L-pyro-amm in the QM/MM simulations. The calculated spectra were adjusted to align with the peak of the emission spectra. Impressively, our calculations are in rather modest agreement with the experimental data. The deviation of 10 nm in the Stokes shift and also the slight shoulders at 320 nm present in the experimental excitation spectra (red solid line) which are absent in the emission (red dashed line) are an indication that the excitation spectra involves more than only one transition 25 NAFAA-HP10B4ZBB2 and V-CoIns-HP10BY0AET). CRL-M and MAS acknowledge financial support from the German Research Foundation (DFG) through Grant No. FR 2833/821. CRL-M extends special thanks to UNM for the invitation to the ”Workshop on Frontiers in Excited State Electronic Structure Methods: from Spectroscopy to Photochemistry” last year in Trieste, which served as the catalyst for initiating this collaboration between our groups. References (1) Morzan, U. N.; D´ıaz Mir´on, G.; Grisanti, L.; Gonz´alez Lebrero, M. C.; Kaminski Schierle, G. S.; Hassanali, A. Non-Aromatic Fluorescence in Biological Matter: The Exception or the Rule? The Journal of Physical Chemistry B 2022,126, 7203–7211. (2) Ma, Y.; Zhang, H.; Wang, K.; Cao, D.; Wang, K.; Guan, R.; Zhou, C. The bright fluorescence of non-aromatic molecules in aqueous solution originates from pH-induced CTE behavior. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 2021,254, 119604–119611. (3) Shukla, A.; Mukherjee, S.; Sharma, S.; Agrawal, V.; Kishan, K. R.; Guptasarma, P. A novel UV laser-induced visible blue radiation from protein crystals and aggregates: scattering artifacts or fluorescence transitions of peptide electrons delocalized through hydrogen bonding? Archives of biochemistry and biophysics 2004,428, 144–153. (4) Del Mercato, L. L.; Pompa, P. P.; Maruccio, G.; Torre, A. D.; Sabella, S.; Tamburro, A. M.; Cingolani, R.; Rinaldi, R. Charge transport and intrinsic fluorescence in amyloid-like fibrils. Proceedings of the National Academy of Sciences 2007,104, 18019–18024. (5) Tang, S.; Yang, T.; Zhao, Z.; Zhu, T.; Zhang, Q.; Hou, W.; Yuan, W. Z. Nonconven32 tional luminophores: characteristics, advancements and perspectives. Chemical Society Reviews 2021,50, 12616–12655. (6) Zhou, Q.; Cao, B.; Zhu, C.; Xu, S.; Gong, Y.; Yuan, W. Z.; Zhang, Y. Clusteringtriggered emission of nonconjugated polyacrylonitrile. Small 2016,12, 6586–6592. (7) Pinotsi, D.; Buell, A. K.; Dobson, C. M.; Kaminski Schierle, G. S.; Kaminski, C. F. A label-free, quantitative assay of amyloid fibril growth based on intrinsic fluorescence. ChemBioChem 2013,14, 846–850. (8) Pansieri, J.; Josserand, V.; Lee, S.-J.; Rongier, A.; Imbert, D.; Sallanon, M. M.; K¨ovari, E.; Dane, T. G.; Vendrely, C.; Chaix-Pluchery, O., et al. Ultraviolet–visible– near-infrared optical properties of amyloid fibrils shed light on amyloidogenesis. Nature photonics 2019,13, 473–479. (9) Grisanti, L.; Sapunar, M.; Hassanali, A.; Doˇsli´c, N. Toward understanding optical properties of amyloids: a reaction path and nonadiabatic dynamics study. Journal of the American Chemical Society 2020,142, 18042–18049. (10) Arnon, Z. A.; Kreiser, T.; Yakimov, B.; Brown, N.; Aizen, R.; Shaham-Niv, S.; Makam, P.; Qaisrani, M. N.; Poli, E.; Ruggiero, A., et al. On-off transition and ultrafast decay of amino acid luminescence driven by modulation of supramolecular packing. Iscience 2021,24, 102695–102980. (11) Homchaudhuri, L.; Swaminathan, R. Novel absorption and fluorescence characteristics of l-lysine. Chemistry Letters 2001,30, 844–845. (12) Stephens, A. D.; Qaisrani, M. N.; Ruggiero, M. T.; D´ıaz Mir´on, G.; Morzan, U. N.; Gonz´alez Lebrero, M. C.; Jones, S. T.; Poli, E.; Bond, A. D.; Woodhams, P. J., et al. Short hydrogen bonds enhance nonaromatic protein-related fluorescence. Proceedings of the National Academy of Sciences 2021,118, e2020389118. 33 (13) Tsai, Y.-J.; Hu, C.-C.; Chu, C.-C.; Imae, T. Intrinsically fluorescent PAMAM dendrimer as gene carrier and nanoprobe for nucleic acids delivery: bioimaging and transfection study. Biomacromolecules 2011,12, 4283–4290. (14) Guan, R.; Dong, B.; Xu, C.; Zhang, H.; Cao, D.; Lin, W. A strategy to construct fluorescent non-aromatic small-molecules: hydrogen bonds contributing to the unexpected fluorescence. Chemical Communications 2020,56, 4424–4427. (15) Fang, M.; Yang, J.; Xiang, X.; Xie, Y.; Dong, Y.; Peng, Q.; Li, Q.; Li, Z. Unexpected room-temperature phosphorescence from a non-aromatic, low molecular weight, pure organic molecule through the intermolecular hydrogen bond. Materials Chemistry Frontiers 2018,2, 2124–2129. (16) Mir´on, G. D. et al. The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter. Nature Communications 2023,14, 7325–7338. (17) Pinotsi, D.; Grisanti, L.; Mahou, P.; Gebauer, R.; Kaminski, C. F.; Hassanali, A.; Kaminski Schierle, G. S. Proton Transfer and Structure-Specific Fluorescence in Hydrogen Bond-Rich Protein Structures. Journal of the American Chemical Society 2016, 138, 3046–3057, PMID: 26824778. (18) Grisanti, L.; Pinotsi, D.; Gebauer, R.; Schierle, G. S. K.; Hassanali, A. A. A computational study on how structure influences the optical properties in model crystal structures of amyloid fibrils. Physical Chemistry Chemical Physics 2017,19, 4030– 4040. (19) Tully, J. C. Molecular dynamics with electronic transitions. The Journal of Chemical Physics 1990,93, 1061–1071. (20) Barbatti, M. Nonadiabatic dynamics with trajectory surface hopping method. Wiley Interdisciplinary Reviews: Computational Molecular Science 2011,1, 620–633. 34 (21) Casida, M. E. Time-dependent density-functional theory for molecules and molecular solids. Journal of Molecular Structure: THEOCHEM 2009,914, 3–18. (22) Cui, Q.; Elstner, M. Density functional tight binding: Values of semi-empirical methods in an ab initio era. Physical Chemistry Chemical Physics 2014,16, 14368–14377. (23) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Physical Review B 1998,58, 7260–7268. (24) Koskinen, P.; M¨akinen, V. Density-functional tight-binding for beginners. Computational Materials Science 2009,47, 237–253. (25) Elstner, M.; Seifert, G. Density functional tight binding. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2014,372, 20120483 2012048. (26) Gaus, M.; Cui, Q.; Elstner, M. Density functional tight binding: application to organic and biological molecules. Wiley Interdisciplinary Reviews: Computational Molecular Science 2014,4, 49–61. (27) Gaus, M.; Goez, A.; Elstner, M. Parametrization and benchmark of DFTB3 for organic molecules. Journal of Chemical Theory and Computation 2013,9, 338–354. (28) Gruden, M.; Andjelkovic, L.; Jissy, A. K.; Stepanovi´c, S.; Zlatar, M.; Cui, Q.; Elstner, M. Benchmarking density functional tight binding models for barrier heights and reaction energetics of organic molecules. Journal of Computational Chemistry 2017, 38, 2171–2185. (29) Poidevin, C.; Duplaix-Rata, G.; Costuas, K.; Fihey, A. Evaluation of tight-binding DFT performance for the description of organic photochromes properties. The Journal of chemical physics 2023,158, 074303. 35 (30) Fihey, A.; Hettich, C.; Touzeau, J.; Maurel, F.; Perrier, A.; K¨ohler, C.; Aradi, B.; Frauenheim, T. SCC-DFTB parameters for simulating hybrid gold-thiolates compounds. Journal of Computational Chemistry 2015,36, 2075–2087. (31) Maghrebi, K.; Chantrenne, I.; Messaoudi, S.; Frauenheim, T.; Fihey, A.; LienMedrano, C. R. Rapid Access to Groundand Excited-State Properties of Gold Nanoclusters Coated with Organic Ligands: Evaluation of the DFTB Method Performance. Journal of Physical Chemistry C 2023,144, 19675–19686. (32) Dolgonos, G.; Aradi, B.; Moreira, N. H.; Frauenheim, T. An improved self-consistentcharge density-functional tight-binding (SCC-DFTB) set of parameters for simulation of bulk and molecular systems involving titanium. Journal of Chemical Theory and Computation 2010,6, 266–278. (33) Niehaus, T. A. Approximate time-dependent density functional theory. Journal of Molecular Structure: THEOCHEM 2009,914, 38–49. (34) Niehaus, T. A.; Suhai, S.; Della Sala, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, T. Tight-binding approach to time-dependent density-functional response theory. Physical Review B 2001,63, 085108. (35) Bonaf´e, F. P.; Aradi, B.; Hourahine, B.; Medrano, C. R.; Hern´andez, F. J.; Frauenheim, T.; S´anchez, C. G. A real-time time-dependent density functional tight-binding implementation for semiclassical excited state electron–nuclear dynamics and pump– probe spectroscopy simulations. Journal of Chemical Theory and Computation 2020, 16, 4454–4469. (36) Uratani, H.; Nakai, H. Scalable Ehrenfest Molecular Dynamics Exploiting the Locality of Density-Functional Tight-Binding Hamiltonian. Journal of chemical theory and computation 2021,17, 7384–7396. 36 (37) Stojanovic, L.; Aziz, S. G.; Hilal, R. H.; Plasser, F.; Niehaus, T. A.; Barbatti, M. Nonadiabatic dynamics of cycloparaphenylenes with TD-DFTB surface hopping. Journal of Chemical Theory and Computation 2017,13, 5846–5860. (38) Mitric, R.; Werner, U.; Wohlgemuth, M.; Seifert, G.; Bonacic-Koutecky, V. Nonadiabatic dynamics within time-dependent density functional tight binding method. The Journal of Physical Chemistry A 2009,113, 12700–12705. (39) Posenitskiy, E.; Rapacioli, M.; Lepetit, B.; Lemoine, D.; Spiegelman, F. Non-adiabatic molecular dynamics investigation of the size dependence of the electronic relaxation in polyacenes. Physical Chemistry Chemical Physics 2019,21, 12139–12149. (40) Hourahine, B.; Aradi, B.; Blum, V.; Bonaf´e, F.; Buccheri, A.; Camacho, C.; Cevallos, C.; Deshaye, M.; Dumitric˘a, T.; Dominguez, A., et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. The Journal of chemical physics 2020,152, 124101. (41) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB). Journal of Chemical Theory and Computation 2011,7, 931–948. (42) Brandenburg, J. G.; Grimme, S. Accurate modeling of organic molecular crystals by dispersion-corrected density functional tight binding (DFTB). The journal of physical chemistry letters 2014,5, 1785–1789. (43) Miriyala, V. M.; ˇ Rez´aˇc, J. Description of non-covalent interactions in SCC-DFTB methods. Journal of Computational Chemistry 2017,38, 688–697. (44) Rezac, J. Empirical self-consistent correction for the description of hydrogen bonds in DFTB3. Journal of Chemical Theory and Computation 2017,13, 4804–4817. 37 (45) Rezac, J.; Fanfrlik, J.; Salahub, D.; Hobza, P. Semiempirical quantum chemical PM6 method augmented by dispersion and H-bonding correction terms reliably describes various types of noncovalent complexes. Journal of Chemical Theory and Computation 2009,5, 1749–1760. (46) Niehaus, T. A.; Della Sala, F. Range separated functionals in the density functional based tight-binding method: Formalism. physica status solidi (b) 2012,249, 237–244. (47) Lutsker, V.; Aradi, B.; Niehaus, T. A. Implementation and benchmark of a long-range corrected functional in the density functional based tight-binding method. The Journal of chemical physics 2015,143, 184107. (48) Vuong, V. Q.; Akkarapattiakal Kuriappan, J.; Kubillus, M.; Kranz, J. J.; Mast, T.; Niehaus, T. A.; Irle, S.; Elstner, M. Parametrization and Benchmark of Long-Range Corrected DFTB2 for Organic Molecules. Journal of Chemical Theory and Computation 2018,14, 115–125. (49) Subotnik, J. E.; Jain, A.; Landry, B.; Petit, A.; Ouyang, W.; Bellonzi, N. Understanding the surface hopping view of electronic transitions and decoherence. Annual review of physical chemistry 2016,67, 387–417. (50) Subotnik, J. E.; Shenvi, N. Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation? The Journal of chemical physics 2011,134. (51) Crespo-Otero, R.; Barbatti, M. Recent advances and perspectives on nonadiabatic mixed quantum–classical dynamics. Chemical reviews 2018,118, 7026–7068. (52) Nikitin, E. Theory of non-adiabatic transitions. recent developement of the LandauZener (Linear) model. Chemische elementarprozesse 1968, 43–77. 38 (53) Hayashi, S.; Tajkhorshid, E.; Schulten, K. Photochemical reaction dynamics of the primary event of vision studied by means of a hybrid molecular simulation. Biophysical journal 2009,96, 403–416. (54) Zhu, C.; Nakamura, H. The two-state linear curve crossing problems revisited. III. Analytical approximations for Stokes constant and scattering matrix: Nonadiabatic tunneling case. The Journal of chemical physics 1993,98, 6208–6222. (55) Zener, C. Non-adiabatic crossing of energy levels. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 1932, 137, 696–702. (56) Xie, W.; Sapunar, M.; Doˇsli´c, N.; Sala, M.; Domcke, W. Assessing the performance of trajectory surface hopping methods: Ultrafast internal conversion in pyrazine. The Journal of chemical physics 2019,150. (57) Kobayashi, C.; Jung, J.; Matsunaga, Y.; Mori, T.; Ando, T.; Tamura, K.; Kamiya, M.; Sugita, Y. GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms. Journal of Computational Chemistry 2017,38, 2193–2206. (58) Jung, J.; Mori, T.; Kobayashi, C.; Matsunaga, Y.; Yoda, T.; Feig, M.; Sugita, Y. GENESIS: a hybrid-parallel and multi-scale molecular dynamics simulator with enhanced sampling algorithms for biomolecular and cellular simulations. Wiley Interdisciplinary Reviews: Computational Molecular Science 2015,5, 310–323. (59) Cochran, W.; Penfold, B. R. The crystal structure of L-glutamine. Acta Crystallographica 1952,5, 644–653. (60) Gaus, M.; Goez, A.; Elstner, M. Parametrization and benchmark of DFTB3 for organic molecules. Journal of Chemical Theory and Computation 2013,9, 338–354. 39 (61) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field. Journal of computational chemistry 2004,25, 1157–1174. (62) Xie, W.; Holub, D.; Kubar, T.; Elstner, M. Performance of Mixed Quantum-Classical Approaches on Modeling the Crossover from Hopping to Bandlike Charge Transport in Organic Semiconductors. Journal of Chemical Theory and Computation 2020,16, 2071–2084. (63) Xie, W.; Domcke, W. Accuracy of trajectory surface-hopping methods: Test for a twodimensional model of the photodissociation of phenol. The Journal of Chemical Physics 2017,147. (64) Suchan, J.; Janoˇs, J.; Slavicek, P. Pragmatic approach to photodynamics: Mixed Landau–Zener surface hopping with intersystem crossing. Journal of Chemical Theory and Computation 2020,16, 5809–5820. (65) Crespo, A.; Scherlis, D. A.; Mart´ı, M. A.; Ordej´on, P.; Roitberg, A. E.; Estrin, D. A. A DFT-based QM-MM approach designed for the treatment of large molecular systems: Application to chorismate mutase. The Journal of Physical Chemistry B 2003,107, 13728–13736. (66) Senn, H. M.; Thiel, W. QM/MM methods for biomolecular systems. Angewandte Chemie International Edition 2009,48, 1198–1229. (67) Morzan, U. N.; Alonso de Armino, D. J.; Foglia, N. O.; Ramirez, F.; Gonzalez Lebrero, M. C.; Scherlis, D. A.; Estrin, D. A. Spectroscopy in complex environments from QM–MM simulations. Chemical reviews 2018,118, 4071–4113. (68) Boulanger, E.; Harvey, J. N. QM/MM methods for free energies and photochemistry. Current Opinion in Structural Biology 2018,49, 72–76. 40 (69) Strickler, S.; Berg, R. A. Relationship between absorption intensity and fluorescence lifetime of molecules. The Journal of chemical physics 1962,37, 814–822. (70) Caricato, M.; Trucks, G. W.; Frisch, M. J.; Wiberg, K. B. Electronic transition energies: A study of the performance of a large range of single reference density functional and wave function methods on valence and Rydberg states compared to experiment. Journal of Chemical Theory and Computation 2010,6, 370–383. (71) Leang, S. S.; Zahariev, F.; Gordon, M. S. Benchmarking the performance of timedependent density functional methods. The Journal of chemical physics 2012,136. (72) Li, Q.; Mennucci, B.; Robb, M. A.; Blancafort, L.; Curutchet, C. Polarizable QM/MM multiconfiguration self-consistent field approach with state-specific corrections: Environment effects on cytosine absorption spectrum. Journal of Chemical Theory and Computation 2015,11, 1674–1682. (73) Kulik, H. J.; Zhang, J.; Klinman, J. P.; Mart´ınez, T. J. How large should the QM region be in QM/MM calculations? The case of catechol O-methyltransferase. The Journal of Physical Chemistry B 2016,120, 11381–11394. (74) Isborn, C. M.; Gotz, A. W.; Clark, M. A.; Walker, R. C.; Mart´ınez, T. J. Electronic absorption spectra from MM and ab initio QM/MM molecular dynamics: Environmental effects on the absorption spectrum of photoactive yellow protein. Journal of chemical theory and computation 2012,8, 5092–5106. 41