exercises:2017_ethz_mmm:tio2_gap
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— | exercises:2017_ethz_mmm:tio2_gap [2020/08/21 10:15] (current) – created - external edit 127.0.0.1 | ||
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+ | ====== TiO$_2$ Band Gap as a function of %hfx ====== | ||
+ | |||
+ | One problem with standard DFT is that correlation effects can lead to errors in evaluating certain system properties, such as the band gap of semiconductors. More information can be found here: [[doi> | ||
+ | |||
+ | A common approach to correct for electronic self-interaction is the //ad hoc// mixing of a fraction of the exact Hartree-Fock exchange. The goal of this exercise is to identify the needed amount of exact Hartree-Fock exchange (%hfx) to correctly reproduce the anatase TiO$_2$ experimental band gap (3.2 eV). To do so, you will need to run at least 4 single point calculations on bulk TiO$_2$ with varying amount of exact exchange. | ||
+ | |||
+ | Report the result as follows: | ||
+ | ^%hfx^E$_{gap}$^ | ||
+ | | 0 | ... | | ||
+ | | 10 | ... | | ||
+ | | .. | ... | | ||
+ | Then plot E$_{gap}$ | ||
+ | |||
+ | <note tip> | ||
+ | Hybrid calculations can be fairly expensive, because they scale with $\mathcal{O}(N^4)$. Therefore, you should run these jobs on 16 nodes. To further decrease the cost of the calculation, | ||
+ | </ | ||
+ | |||
+ | ===== Questions ===== | ||
+ | - What is the relation between %hfx and $E_\text{gap}$? | ||
+ | - What is the correct amount of exchange needed to reproduce the experimental band gap? | ||
+ | |||
+ | ===== Required files ===== | ||
+ | ==== Parameters for Truncated Coulomb Potential ==== | ||
+ | {{t_c_g.dat.gz| Download here}} | ||
+ | | ||
+ | ==== Restart wave-function ==== | ||
+ | This is useful to speed up the calculation | ||
+ | | ||
+ | |||
+ | < | ||
+ | < | ||
+ | $ gunzip t_c_g.dat.gz tio2_pbe-restart.wfn.gz | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | ==== Input File ==== | ||
+ | <code - anatase_25hfx.inp> | ||
+ | |||
+ | &GLOBAL | ||
+ | PROJECT anatase_25hfx | ||
+ | | ||
+ | &END GLOBAL | ||
+ | |||
+ | & | ||
+ | METHOD Quickstep | ||
+ | &DFT | ||
+ | ! external data-files for basis-set, pseudo-potentials and wave-function to restart from | ||
+ | | ||
+ | | ||
+ | | ||
+ | |||
+ | & | ||
+ | CUTOFF 400 ! for this system the default value is too small | ||
+ | &END MGRID ! and can lead to non-physical results | ||
+ | | ||
+ | & | ||
+ | & | ||
+ | | ||
+ | NHOMO 1 ! but we require 1 HOMO and 1 LUMO in the output | ||
+ | NLUMO 1 ! so that we get the band gap | ||
+ | & | ||
+ | &END | ||
+ | | ||
+ | & | ||
+ | EPS_SCF 1.0E-6 | ||
+ | SCF_GUESS RESTART | ||
+ | MAX_SCF 40 | ||
+ | & | ||
+ | EPS_SCF 1.0E-6 | ||
+ | MAX_SCF 10 | ||
+ | &END | ||
+ | &OT | ||
+ | | ||
+ | | ||
+ | &END OT | ||
+ | &END SCF | ||
+ | | ||
+ | & | ||
+ | & | ||
+ | & | ||
+ | | ||
+ | | ||
+ | & | ||
+ | & | ||
+ | | ||
+ | | ||
+ | & | ||
+ | &END XC_FUNCTIONAL | ||
+ | &HF | ||
+ | FRACTION 0.25 ! this is the hfx section. The amount of hfx must be consistent with above | ||
+ | & | ||
+ | EPS_SCHWARZ 1.0E-6 | ||
+ | SCREEN_ON_INITIAL_P TRUE ! having an external wave-function, | ||
+ | & | ||
+ | &MEMORY | ||
+ | MAX_MEMORY 800 ! uses some memory to store data and not recompute each step | ||
+ | &END | ||
+ | & | ||
+ | POTENTIAL_TYPE TRUNCATED | ||
+ | CUTOFF_RADIUS 3.5 ! at 3.5 A (see above) | ||
+ | T_C_G_DATA ./ | ||
+ | &END | ||
+ | &END | ||
+ | & | ||
+ | &END DFT | ||
+ | &SUBSYS | ||
+ | &CELL | ||
+ | ABC 3.7842 3.7842 9.5146 | ||
+ | | ||
+ | &END CELL | ||
+ | & | ||
+ | MULTIPLE_UNIT_CELL 2 2 1 ! a 2x2x1 system is required to get realistic results. This has to be repeated here. | ||
+ | COORD_FILE_FORMAT CIF ! specifies the type and name of coordinate file | ||
+ | COORD_FILE_NAME tio.cif | ||
+ | &END | ||
+ | &KIND O ! external basis and pseudo-potentials for Ti and O | ||
+ | BASIS_SET cpFIT3 | ||
+ | POTENTIAL GTH-PBE-q6 | ||
+ | &END KIND | ||
+ | &KIND Ti | ||
+ | BASIS_SET FIT | ||
+ | POTENTIAL GTH-PBE-q12 | ||
+ | &END KIND | ||
+ | &END SUBSYS | ||
+ | &END FORCE_EVAL | ||
+ | </ | ||
+ | |||
+ | ==== Basis Set ==== | ||
+ | <code - BASIS_TiO> | ||
+ | |||
+ | # O | ||
+ | O cpFIT3 | ||
+ | 5 | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | |||
+ | #Ti | ||
+ | Ti FIT | ||
+ | 11 | ||
+ | 2 | ||
+ | 4.0993528 | ||
+ | 2 | ||
+ | 1.3253083 | ||
+ | 2 | ||
+ | | ||
+ | 2 | ||
+ | | ||
+ | 2 | ||
+ | 8.9996204 | ||
+ | 2 | ||
+ | 1.6365473 | ||
+ | 2 | ||
+ | | ||
+ | 2 | ||
+ | 3.6633232 | ||
+ | 2 | ||
+ | | ||
+ | 2 | ||
+ | | ||
+ | 2 | ||
+ | | ||
+ | |||
+ | </ | ||
+ | |||
+ | ==== Pseudo-Potential ==== | ||
+ | <code - POTENTIALS_TiO> | ||
+ | # | ||
+ | O GTH-PBE-q6 | ||
+ | 2 4 | ||
+ | | ||
+ | 2 | ||
+ | | ||
+ | | ||
+ | # | ||
+ | Ti GTH-PBE-q12 | ||
+ | 4 6 2 | ||
+ | | ||
+ | 3 | ||
+ | | ||
+ | | ||
+ | | ||
+ | -10.49616087 | ||
+ | | ||
+ | |||
+ | </ | ||
+ | |||
+ | ==== Anatse Crystal Structure ==== | ||
+ | |||
+ | '' | ||
+ | |||
+ | <code - tio.cif> | ||
+ | # | ||
+ | |||
+ | # ANATASE CRYSTAL DATA | ||
+ | |||
+ | # | ||
+ | |||
+ | data_phase_1 | ||
+ | |||
+ | |||
+ | _pd_phase_name | ||
+ | _cell_length_a | ||
+ | _cell_length_b | ||
+ | _cell_length_c | ||
+ | _cell_angle_alpha | ||
+ | _cell_angle_beta | ||
+ | _cell_angle_gamma | ||
+ | _symmetry_space_group_name_H-M | ||
+ | _symmetry_Int_Tables_number | ||
+ | |||
+ | loop_ | ||
+ | _symmetry_equiv_pos_as_xyz | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | loop_ | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | |||
+ | |||
+ | </ | ||
+ | |||
+ | |||
+ | |||
+ | |||
exercises/2017_ethz_mmm/tio2_gap.txt · Last modified: 2020/08/21 10:15 by 127.0.0.1