Terminal exercise: DFT via Quantum ESPRESSO
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1 Terminal exercise: DFT via Quantum ESPRESSO Ari Paavo SEITSONEN Département de Chimie École Normale Supérieure, Paris École de Sidi-BelAbbès de Nanomateriaux // Octobre 8-12, 2016 apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 1 / 19
2 Summary 1 Information on Quantum ESPRESSO 2 Exercise: Graphene 3 Exercise: Graphite 4 Exercise: Silicene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 2 / 19
3 Summary 1 Information on Quantum ESPRESSO 2 Exercise: Graphene Cut-off energy Lattice constant Band structure Phonon (vibrational) modes at Γ point Small comments 3 Exercise: Graphite 4 Exercise: Silicene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 3 / 19
4 Graphene Change to the directory graphene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 4 / 19
5 Cut-off energy Change value of input variable ecutwfn from 20 Ry upwards in steps of 5 Ry until the total energy changes less than 10 mev per atom between subsequent calculations Execute pw.x for the input file relax.in (mpirun -np 2 pw.x -in relax.in > relax.out &) You can find the energy (in Ry!! 1 Ry ev) with grep! relax.out tail -n 1; remember to note down the value (or write into a different file) Question: Why does the calculation terminate immediately, without doing further optimisation steps of the ionic structure? Hint: Symmetry apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 5 / 19
6 Lattice constant Change the lattice constant (input variable a) in steps of ±0.01 Å until you have found the lattice constant of lowest energy Use the value in the sub-sequent calculations apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 6 / 19
7 Band structure After the latest calculation with your chosen value of ecutwfn and a, run once again pw.x Then modify into the file bs.in your values Execute pw.x for the input file bs.in Execute bands.x for the input file bands.in (mpirun -np 2 pw.x -in bands.x -in bands.in); you can directly plot the file bands.out.gnu, or you can execute the following steps Execute plotband.x; try how the input variables modify the resulting plot Use gnuplot or xmgrace to plot the output files generated in the latest step (with the filename prefix that you used) apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 7 / 19
8 Phonon (vibrational) modes at Γ point Execute pw.x for the input file relax.in Execute ph.x for the input file ph.in Study the output file Execute dynmat.x for the input file dynmat.in Study the phonon displacement modes with xcrysden --axsf dynmat.axsf; press f to view the displacement pattern drawn as arrows, pressing F you can modify the length scaling of the vectors (Length Factor). Which modes are lateral (along atomic plane), which ones vertical? What are the other modes? Study the symmetries of the modes; which modes are degenerate? apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 8 / 19
9 Small comments The value for the convergence in total energy is arbitrary. Actually one better use the target quantity (for example geometry, frequencies,... ) as the observable to choose reasonable cut-off energy Also the number of k points should be optimised (more points, better accuracy, but slower computations). This was not done here due to limitations in duration of the course One would actually fit the total energy as a function of time instead of only looking at the minimum of the energy (due to eg incomplete convergence of basis set etc) apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 9 / 19
10 Summary 1 Information on Quantum ESPRESSO 2 Exercise: Graphene 3 Exercise: Graphite Structure Band structure Small comments 4 Exercise: Silicene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 10 / 19
11 Graphite Change to the directory graphite apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 11 / 19
12 Structure Investigate the geometry How do you obtain graphene from the structure of graphite? How many different kind of atoms (different coordination/number of neighbours) are there in graphite? What about graphene? apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 12 / 19
13 Band structure With your chosen values of ecutwfn and a for graphene, run pw.x on relax.in Then modify into the file bs.in your values Execute pw.x for the input file bs.in Execute bands.x for the input file bands.in Execute plotband.x; try how the input variables modify the resulting plot Use gnuplot or xmgrace to plot the output files generated in the latest step (with the filename prefix that you used) Compare the band structures of graphene and graphite. Question: Why the additional bands in the latter are flat? Hint: Strength of interaction apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 13 / 19
14 Small comments The example is again quite over-simplified: Actually the cell has two degrees of freedom, as also the length of the cell perpedicular to the planes, c, should be optimised. This is, however, a more complicated issue, as the GGAs are not able to capture the weak interaction between the layers (Question: Why?); thus a more appropriate treatment would be necessary, which we cannot go here in detail apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 14 / 19
15 Summary 1 Information on Quantum ESPRESSO 2 Exercise: Graphene 3 Exercise: Graphite 4 Exercise: Silicene Band structure Phonon (vibrational) modes at Γ point Small comments apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 15 / 19
16 Silicene Change to the directory silicene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 16 / 19
17 Band structure Run pw.x for the file relax.in Execute pw.x for the input file bs.in Execute bands.x for the input file bands.in Execute plotband.x; try how the input variables modify the resulting plot Use gnuplot or xmgrace to plot the output files generated in the latest step (with the filename prefix that you used) Compare the structures and band structures of graphene and silicene apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 17 / 19
18 Phonon (vibrational) modes at Γ point Execute pw.x for the input file relax.in Execute ph.x for the input file ph.in Study the output file Execute ph.x for the input file ph.in Visualise the phonon modes What is striking in the resulting results? What does this mean? Hint: Look at the corresponding phonon displacement mode with xcrysden If you have time, what can one try to do to fix the problem? What is the result? Calculate the electronic band structure; is it qualitatively different from the first calculation? Why? Hint: Symmetry apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 18 / 19
19 Small comments As hint for the last point, try moving one of the two atoms out of plain in positive direction in z, the other one with the same amount in negative direction (this is the kind of distortion of lattice suggested by the normal mode having an imaginary, or negative frequency), and perform again the relaxation. Afterwards, run the rest of the calculation in the optimised geometry. You can also optimise the lateral lattice constant (a) before running the other calculations, if you have time apsi (ENS, UPMC, CNRS) Examples of DFT Sidi-BelAbbès 19 / 19
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