Starter Kit for Modeling MoS2 with Quantum Expresso

1 Starter Kit for Modeling MoS2 with Quantum Expresso A.Martí(1), K. Weijon(2), C.Tablero(1), S.A. Svatek(1), and E. Antolín(1) (1) Instituto de Energía Solar – Universidad Politécnica de Madrid, Spain (2) North China Electric Power University, China Quantum Expresso [1], [2] is an open-source suite of codes for electronic-structure calculations and materials modeling at the nanoscale, based on density functional theory, plane waves, and pseudopotentials. It can be downloaded from www.quantum-espresso.org together with the instructions for installing it. We assume that the reader has already Quantum Expresso installed on their computer. Quantum Expresso can be installed both in Windows as in Linux. The examples we provide have been tested on Quantum Expresso 7.3.1 installed under Ubuntu 22.04.5 LTS and tested in a Lenovo ThinkPad 21KVS0DM00 Laptop. The purpose of the files we upload to Zenodo is to provide the interested reader with a starting point for modeling the electronic structure of MoS2, both considered as bulk, bilayer and monolayer Quantum Expresso. In spite of the relative simplicity of the parameters assumed in these input files, they reasonably reproduce a tendency experimentally observed in these materials, to know, the indirect nature of the gap for both the bulk and bilayer materials, and the direct nature of the gap of the monolayer material. [3], [4] (Fig. 1). They also reproduce the tendency of the gaps to increase as the number of layers is reduced although the values of the gaps obtained in comparison to the experimental ones are underestimated by 200-300 meV as the thickness decreases (Table I). Table I. Gaps obtained with the input files provided in this work when executed with Quantum Expresso compared with experimental values. Structure Gap These files Reported [3] 3D-MoS2 Indirect (Γ → 𝐾𝐾) 1.22 eV ~1.3 eV Bilayer-MoS2 Indirect (Γ → 𝐾𝐾) 1.30 eV ~1.6 eV Monolayer-MoS2 Direct (𝐾𝐾 → 𝐾𝐾) 1.67 eV ~1.9 eV The input files provided contain several instructions, but we make no aim in this document to explain what each instruction does since the reader can easily find this information in the Quantum Expresso manual or, nowadays, they can simply ask AI tools such as ChatGPT (https://openai.com/esES/chatgpt/overview/) to obtain a very good summary of what these instructions do adapted to their needs. The files are compressed into the following set of zip files: • “Bulk_MoS2.zip” for the files for modelling the bulk MoS2 • “Bilater_MoS2.zip” for the files for modelling a bilayer of MoS2 • “Mono_MoS2.zip” for the files for modelling a monolayer of MoS2 If you are new to Quantum Expresso, the structure of the folders within the zip files should be preserved, at least, until you become more familiar with what you are doing. The files we provide correspond to the “input” files necessary to run the simulations for the first time plus some additional files corresponding to the plots of the band diagrams obtained from the calculations form these files. We have not included Quantum Expresso output files to save space and because they can be regenerated by running the input files we provide. 2 The input files necessary to run the simulation for the first time are: • The pseudopotentials for Mo and S respectively, downloaded from http://www.quantumsimulation.org/potentials/sg15_oncv/upf/ . They are included within the folder “pseudo”. • Mo_ONCV_PBE-1.2.upf • S_ONCV_PBE-1.2.upf • The file “scf.in”. It is the first file to be run as: > mpirun -np 15 pw.x < scf.in > scf.out if mpi multicore system is installed, or as > pw.x < scf.in > scf.out if they are not (our examples use 15 cores). • The file “bands.in”. It is the second file to be run as: > mpirun -np 15 pw.x < bands.in > bands.out • The file “bands_post.in”. It is the third file to be run as: > mpirun -np 15 bands.x < bands_post.in > bands_post.out • For plotting the actual band diagrams, we shall assume “gnuplot” (www.gnuplot.info/) is also installed in your system. We provide the template “bands.gnuplot”, to be executed as, > gnuplot bands.gnuplot to generate the plot of the band diagram. The output from gnuplot provides a png file with the plot of the band diagram. Plots in Fig. 1 have been obtained with the files we provide here as “starter kits”. The execution times of the files is also reasonable, in the order of 15 minutes in the hardware mentioned above. The following are some additional notes we find useful: • Modeling of the monolayer or bilayer material requires increasing the distance in the c direction of the unit cell. This distance is the number ·”30” (angstroms) appearing in the CELL PARAMETERS block: CELL_PARAMETERS angstrom 3.19 0.00 0.00 -1.595 2.763359 0.00 0.00 0.00 30 Because we do not want the distance between atoms in the lattice to scale as the unit cell is increased, the atomic positions in the ATOMIC_POSITIONS block must be given in angstrom (that is, do not substitute “angstrom” by “crystal” option) as, for example, in the following example. Or if you do, make sure you know the implications. 3 ATOMIC_POSITIONS angstrom Mo 1.595000 0.921120 3.345000 S 0.000000 1.842239 1.781281 S 0.000000 1.842239 4.911919 • Further improvement in the modeling (at the cost of considerably higher execution times) can be carried out by performing relaxation and/or increasing the number of k points. We provide also template files for carrying out relaxation (relax.in file) as well as by performing no self consistent field calculations (nscf.in file). In this case, the order in which files should be executed are: > mpirun -np 15 pw.x < relax.in > relax.out > mpirun -np 15 pw.x < scf.in > scf.out > mpirun -np 15 pw.x < nscf.in > nscf.out > mpirun -np 15 pw.x < bands.in > bands.out > mpirun -np 15 bands.x < bands_post.in > bands_post.out > gnuplot bands.gnuplot In the files provided, the band diagram obtained without relaxing nor executing nscf is labeled “mos2_band_structure_no_relax_no_nscf.png”, the corresponding data for the plot are in the file “mos2_band_structure_no_relax_no_nscf.gnu” and the gnuplot file to generate the plot is labeled “bands_no_relax_no_nscf.gnuplot”. The files labelled “mos2_band_structure.png”, “mos2_band_structure.gnu” and “bands.gnuplot” are the equivalent ones but after relaxing and running nfsc. In this way, the reader can compare the results of both calculations. With our relax.in and nfsc.in files, the values of the gaps shown in Table I have not changed with respect to the case in which only scf.in is used. • If you play with the parameters in the input files, the file “bands.gnuplot” might need to be tweaked in order to plot accordingly a proper energy band diagram. For example, the position of the Fermi level typically changes with each calculation and its value needs to be introduced in the “bands.gnuplot” file template. The position of the Fermi level is obtained in the file scf.out (hint: search for “Fermi” within this file once it is generated) or in the file nscf.out if you refine the calculations with nscf. • The crystal structure of MoS2 has been obtained from https://nextgen.materialsproject.org/materials/mp-2815?chemsys=Mo-S. We have then used ChatGPT to assist us in obtaining the atomic positions for the input files. This page reports a gap of 1.46 eV for the 3D bulk structure instead of 1.3 eV reported in Table I. • The number of k points we set in bands.in file for obtaining the band diagram in our “in files” is the same in all cases (block K_POINTS crystal_b). This number is more than necessary in some cases, in particular, for the monolayer and bilayer calculations. However, we have found more comfortable to preserve the same number of points for all cases because it facilitates comparison of the results between cases. • Some times the following error is generated “The following floating-point exceptions are signalling: IEEE_DENORMAL”. This error is considered non-critical and has been ignored. 4 (a) (b) (c) Fig. 1: Band diagram for MoS2 calculated with Quantum Expresso based on DFT theory (www.quantum-espresso.org/). (a) Bulk material: an indirect gap of value 1.22 eV is obtained; (b) MoS2 bilayer: An indirect gap of 1.30 eV is still observed; c) The formation of a 1.67 eV direct gap at the K point is observed. 5 [1] P. Giannozzi et al., “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials,” J. Phys. Condens. Matter, vol. 21, no. 39, p. 395502, 2009, doi: 10.1088/0953-8984/21/39/395502. [2] P. Giannozzi et al., “Advanced capabilities for materials modelling with Quantum ESPRESSO,” J. Phys. Condens. Matter, vol. 29, no. 46, p. 465901, 2017, doi: 10.1088/1361-648X/aa8f79. [3] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin ${\mathrm{MoS}}_{2}$: A New Direct-Gap Semiconductor,” Phys. Rev. Lett., vol. 105, no. 13, p. 136805, Sept. 2010, doi: 10.1103/PhysRevLett.105.136805. [4] A. Splendiani et al., “Emerging Photoluminescence in Monolayer MoS2,” Nano Lett., vol. 10, no. 4, pp. 1271–1275, Apr. 2010, doi: 10.1021/nl903868w. This work has been funded by the DEFY-CO2 Project (TED2021-129694B-C22), funded by the Spanish Ministry of Science, Innovation and Universities and the European Union through NextGeneration EU funds.