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物質科学のための計算数理 II
Numerical Analysis for Material Science II
13th: Density Functional Theory (6)Jan. 11 (Fri)

Lecturer: Mitsuaki Kawamura (河村光晶)

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Schedule (This semester W1, W2)

1. Sep. 28 (Fri) Guidance Y
2. Oct. 5 (Fri) Monte Carlo method O
3. Oct. 12 (Fri) Monte Carlo method O
4. Oct. 19 (Fri) Monte Carlo method O
5. Oct. 26 (Fri) Exact diagonalization Y
6. Nov. 2 (Fri) Exact diagonalization Y
7. Nov. 9 (Fri) Molecular dynamics O (1st report problem will be announced.)
8. Nov. 30 (Fri) Density functional theory K
9. Dec. 7 (Fri) Density functional theory K
10. Dec. 14 (Fri) Density functional theory K
11. Dec. 21 (Fri) Density functional theory K
12. Dec. 25 (Tue) Density functional theory K (遠隔講義室)
13. Jan. 11 (Fri) (2nd)Report problem K※ Lecturers: Y … Yamaji, K … Kawamura, O… Ohgoe

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Schedule in this section (DFT)Nov. 30 (Fri) Standard DFT code
• First-principles calculation and Density functional theory (Lecture)• One-body Schrödinger eq. for periodic system and Bloch theorem (L)• Numerical solution of Kohn-Sham (one-body Schrödinger) eq. (L)• Hands-on DFT code (Tutorial)• Version control system : Git (T)Dec. 7 (Fri) Kohn-Sham eq.
• Plane-wave basis and Pseudopotentials (L)• Iterative eigenvalue solution method (L & T)
Dec. 14 (Fri) Self-Consistent loop
• Hartree potential (Poisson eq.), Atomic potential, XC potential• Update (Broyden's method)• Visualization of grid data (T)Dec. 21 (Fri) Total Energy• Total energy• Brillouin-zone integral (Tetrahedron method)• Coulomb potential for periodic point charge (Ewald sum)Dec. 25 (Tue) Advanced subjects for productive calculation (遠隔講義室)• Generalized gradient correction• Non-local pseudopotentials (Norm-conserving, ultrasoft, PAW)
• Magnetics
Jan. 11 (Fri) Practice

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Today’s Schedule

Structure database
Crystallography Open Database
Crystallographic Information Format (CIF) filePractice5/14

How to obtain crystalline structure• Get from someone (e.g. experimental researcher)• Generate by ourselves (e.g. theoretical prediction)• Crystalline structure databases• Inorganic Crystallographic Structure Database (ICSD)• Commercial• AtomWorks by NIMS
• https://crystdb.nims.go.jp/• Needs sign-up (we have to create account)• Crystallographic Open Database (COD)• http://www.crystallography.net/cod/search.html

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Get CIF file from COD

http://www.crystallography.net/cod/search.html“Copy URL”, “Copy Link”, etc.

$ mkdir ~/MgB2$ cd ~/MgB2$ wget paste-url-here$ vesta 1000026.cif“B2 Mg” into “chemical formula”
Alphabetic order7/14

Crystallographic Information Format (CIF)

Various kind of information of a material• Chemical formula• Lattice constants• Space group (Symmetry)• Symmetry operator• Structure• Fractional occupancy (e.g. solid boron, please check it with COD)
• Information of article in which that structure is reported.
• Etc.

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Parse CIF file (1)$ cd ~/pwdft/$ git checkout master$ git pull
$ pip3.7 install spglib pymatgen seekpath pybtex --user
Python modules• Spglib• https://atztogo.github.io/spglib/• Handling crstal symmetries• pymatgen• http://pymatgen.org/• Library for Material Genomics• Parse CIF file
• SeeK-path• https://seekpath.readthedocs.io/en/latest/• Finding appropriate 𝑘-point path for band structure plot

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Generate input files$ cd ~/$ wget https://www.materialscloud.org/discover/data/discover/sssp/downloads/SSSP_efficiency_pseudos.tar.gz$ tar xzvf SSSP_efficiency_pseudos.tar.gz$ wget https://www.materialscloud.org/discover/data/discover/sssp/downloads/sssp_efficiency.json ¥-P SSSP_efficiency_pseudos/$ cd ~/MgB2/$ python3.7 ~/pwdft/tool/cif2qe.py 1000026.cif ~/SSSP_efficiency_pseudos/• Usage$ python3.7 ~/pwdft/tool/cif2qe.py CIF-file Pseudo-dir• Products• scf.in : Input file for SCF calculation (pw.x)• nonscf.in : Input file for band-structure calculation (pw.x)• bands.in : Input file for post-process for band-structure (bands.x)• band.gp : Gnuplot script to plot the band structure• pp.in : Input file for displaying Kohn-Sham orbitals (pp.x)• dense.in : Input file for the dense-k-grid calculation for PDOS (pw.x)• proj.in : Input file for PDOS calculation (projwfc.x)
Magnetism is not considered (Not spin-DFT) in these input.

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Typical procedure$ mpirun -np 2 ~/bin/pw.x -npool 2 -in scf.in | tee scf.out$ mpirun -np 2 ~/bin/pw.x -npool 2 -in nonscf.in$ mpirun -np 2 ~/bin/bands.x -npool 2 -in bands.in$ grep Fermi scf.out
the Fermi energy is7.5595 ev$ gnuplot -e "ef=7.5595;emin=-15;emax=15" band.gp$ open -a Preview.app band.pdf$ mpirun -np 1 ~/bin/pp.x -npool 1 -in pp.in$ vesta tmp.pp_K001_B00*.xsf$ mpirun -np 2 ~/bin/pw.x -npool 2 -in dense.in$ mpirun -np 1 ~/bin/fermi_velocity.x -in dense.in$ fermisurfer vfermi.frmsf$ mpirun -np 2 ~/bin/projwfc.x -npool 2 -in pdos.in > pdos.out$ ~/bin/sumpdos.x pwscf.pdos_*¥(Mg¥)* > Mg
$ ~/bin/sumpdos.x pwscf.pdos_*¥(B¥)* > B$ mv pwscf.pdos_tot Total$ bash ~/pwdft/tool/pdos.sh 7.5595 Total Mg B
$ gnuplot pdos.gp$ open -a Preview.app pdos.pdf
Modify pdos.in for fermi_proj.x$ mpirun -np 1 ~/bin/fermi_proj.x -in pdos.in$ fermisurfer proj.frmsf

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Input file format and usage

Input file format• pw.x : https://www.quantum-espresso.org/Doc/INPUT_PW.html• bands.x : https://www.quantum-espresso.org/Doc/INPUT_BANDS.html• pp.x : https://www.quantum-espresso.org/Doc/INPUT_PP.html• projwfc.x : https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html• fermi_velocity.x : The same as that of pw.x
• fermi_proj.x :http://fermisurfer.osdn.jp/en/_build/html/fermisf_qe_en.html#computeand-display-projection-onto-the-atomic-orbital (English)
http://fermisurfer.osdn.jp/ja/_build/html/fermisf_qe_ja.html#id1 (日本語)Usage• VESTA : https://jp-minerals.org/vesta/archives/VESTA_Manual.pdf• FermiSurfer :http://fermisurfer.osdn.jp/en/_build/html/fermisf_ops_en.html (English)
http://fermisurfer.osdn.jp/ja/_build/html/fermisf_ops_ja.html (日本語)12/14

Report problem 4

Download arbitrary structure from COD, compute the electronic structurewith the script cif2qe.py, and explain that electronic properties in a (veryshort) article format.
Do not need to compute large size system. One ～ few atoms per unit
cell is OK.
Sample$ cd ~/pwdft/sample/report/$ pdflatex report.tex$ bibtex report.aux$ pdflatex report.tex$ pdflatex report.tex$ open -a Preview.app report.pdf••••

Only "Numerical conditions" and "Result" section.
Including figures (for VESTA and FermiSurfer, screenshot is useful).
Explanation of results does not have to be long. (a few sentence)
Numerical condition and citation are important.

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Numerical condition and citation• Used programs with citation• Quantum ESPRESSO, VESTA, FermiSurfer• Exchange-correlation functional (GGA-PBE, LDA, ・・・)
• Plane-wave cutoff for wavefunction• Pseudopotential (Kind and Library)• Kind : Ultrasoft (US), PAW, Norm-conserving (NC)• SG15 (NC), GBRV (US), Pslibrary (rrkjus=US, kjpaw=PAW),
Pseudo Dojo(NC), Wentzcovitch(PAW)• Verification (SSSP)• Brillouin-zone integration method (tetrahedron) and 𝑘-point grids.

For citation, see report.bib which already has citations necessary foreach case.

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Today's summary• Structure database• Crystallography Open Database• Crystallographic Information Format (CIF) file• Practice of calculation and writing paper.