This tutorial can be downloaded link.
Intro Tutorial 10: Computing Excitation Energies Using Time-Dependent Density Functional Theory (TDDFT)
This tutorial shows how to compute neutral excitation energies of the negatively charged nitrogen-vacancy defect (NV
In this tutorial, the TDDFT calculations are conducted using both the semi-local PBE functional and the dielectric-dependent hybrid (DDH) functional.
Step 1: TDDFT calculation with the PBE functional
A TDDFT calculation with a local or semi-local functional contains three steps:
1.1 Performing a mean-field calculation, using density functional theory (DFT), as the starting point of TDDFT
1.2 Computing the neutral excitation energies of triplet excited states using spin-conserving TDDFT
1.3 Computing the neutral excitation energies of singlet excited states using spin-flip TDDFT
Step 1.1: Mean-field starting point
We first perform the DFT calculation using the Quantum ESPRESSO code.
Download the following files to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/pbe_pw.in
wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/C_ONCV_PBE-1.2.upf
wget -N -q http://www.quantum-simulation.org/potentials/sg15_oncv/upf/N_ONCV_PBE-1.2.upf
We can now inspect the pbe_pw.in file, the input for the pw.x code:
[1]:
%%bash
cat pbe_pw.in
&CONTROL
calculation = 'scf'
prefix = 'pbe'
pseudo_dir = './'
/
&SYSTEM
ibrav = 0
ecutwfc = 50
tot_charge = -1.0
nspin = 2
tot_magnetization = 2.0
nbnd = 150
nat = 63
ntyp = 2
/
&ELECTRONS
diago_full_acc = .true.
/
K_POINTS gamma
CELL_PARAMETERS angstrom
7.136000 0.000000 0.000000
0.000000 7.136000 0.000000
0.000000 0.000000 7.136000
ATOMIC_SPECIES
C 12.01099968 C_ONCV_PBE-1.2.upf
N 14.00699997 N_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS crystal
C 0.1269815510 0.3733371195 0.3775718026
C 0.1253081282 0.3763002936 0.8746894487
C 0.1260060117 0.8738380396 0.3754459361
C 0.1250639790 0.8750661683 0.8749376784
C 0.6248201544 0.3811585813 0.3751813598
C 0.6224309085 0.3733360188 0.8730196975
C 0.6250110086 0.8765296624 0.3749876809
C 0.6245505450 0.8738390861 0.8739957865
C 0.0000259749 0.0000259633 -0.0000256868
C 0.0014358428 -0.0014358100 0.5010495568
C 0.0014328181 0.4989469740 0.0014351388
C 0.0012018772 0.4992148548 0.5007857943
C 0.4989470397 -0.0014328307 0.0014351823
C 0.4992149137 0.0012018289 0.5007857375
C 0.4992116247 0.4992116312 -0.0012034708
C 0.1250667730 0.1250667914 0.1249294365
C 0.1253032977 0.1253032524 0.6237019642
C 0.1260062437 0.6245495725 0.1261632799
C 0.1269771899 0.6224340478 0.6266613449
C 0.6245496185 0.1260062840 0.1261633007
C 0.6224340177 0.1269771772 0.6266613352
C 0.6250092594 0.6250092159 0.1234699036
C 0.6248234427 0.6248234639 0.6188442442
C 0.0009910041 0.2504149699 0.2494871226
C 0.0003716741 0.2501475881 0.7498513998
C 0.0009645933 0.7495989686 0.2503986681
C 0.0009941125 0.7505129665 0.7495871392
C 0.4985394814 0.2524198182 0.2522377911
C 0.5078677486 0.2391591291 0.7608354182
C 0.5003280630 0.7516382226 0.2483618688
C 0.4985401685 0.7477659930 0.7475823593
C 0.3748654285 0.3748654245 0.1250552701
C 0.3749783337 0.8749127142 0.1250879590
C 0.3748650726 0.8749450711 0.6251340225
C 0.8749127198 0.3749782927 0.1250879634
C 0.8749450684 0.3748650501 0.6251340257
C 0.8750493463 0.8750493517 0.1249501816
C 0.8749120516 0.8749120381 0.6250201881
C 0.2504149894 -0.0009909944 0.2494870713
C 0.2501475446 0.0003715462 0.7498514576
C 0.2524198093 0.4985394738 0.2522377661
C 0.2391592245 0.5078678650 0.7608354474
C 0.7495989932 0.0009646155 0.2503986775
C 0.7505130382 -0.0009940706 0.7495871127
C 0.7516382084 0.5003280124 0.2483619045
C 0.7477659502 0.4985401253 0.7475823293
C 0.3733371729 0.1269814887 0.3775717513
C 0.3763002438 0.1253079989 0.8746895222
C 0.3811585422 0.6248202431 0.3751812920
C 0.3733360636 0.6224310126 0.8730197732
C 0.8738379990 0.1260060464 0.3754459661
C 0.8750662653 0.1250640377 0.8749376416
C 0.8765296848 0.6250109436 0.3749877093
C 0.8738390803 0.6245504485 0.8739957771
C 0.2501515174 0.2501515049 -0.0003784384
C 0.2391603565 0.2391602431 0.4921393755
C 0.2504126363 0.7505106105 0.0009953037
C 0.2524180055 0.7477644305 0.5014586422
C 0.7505106094 0.2504126558 0.0009952558
C 0.7477643646 0.2524180264 0.5014586712
C 0.7495988945 0.7495988379 -0.0009639807
C 0.7516394023 0.7516393858 0.4996700487
N 0.5130505433 0.5130506248 0.4869539927
The calculation is spin polarized (i.e., nspin = 2 and tot_magnetization = 2.0), representing the
We run pw.x on 2 cores.
[ ]:
%%bash
mpirun -n 2 pw.x -i pbe_pw.in > pbe_pw.out
Step 1.2: Spin-conserving TDDFT calculation
Now we run the wbse.x executable to compute the excitation energies of triplet states of NV
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/pbe_sc_wbse.in
Let us inspect the pbe_sc_wbse.in file:
[2]:
%%bash
cat pbe_sc_wbse.in
input_west:
qe_prefix: pbe
west_prefix: pbe_sc
outdir: ./
wbse_init_control:
wbse_init_calculation: S
solver: TDDFT
wbse_control:
wbse_calculation: D
n_liouville_eigen: 2
trev_liouville: 0.00000001
trev_liouville_rel: 0.000001
l_preconditioning: True
The solver: TDDFT keyword instructs the code to perform a TDDFT calculation. The wbse_calculation: D keyword instructs the code to compute the neutral excitation energies using the Davidson algorithm. The n_liouville_eigen: 2 keyword specifies that two lowest excitation energies are computed.
We run wbse.x on 2 cores:
[ ]:
%%bash
mpirun -n 2 wbse.x -i pbe_sc_wbse.in > pbe_sc_wbse.out
If the reader does NOT have the computational resources to run the calculation, the WEST output file needed for the next step can be directly downloaded as:
[ ]:
%%bash
mkdir -p pbe_sc.wbse.save
wget -N -q https://west-code.org/doc/training/nv_tddft/pbe_sc_summary.json -O pbe_sc.wbse.save/summary.json
The calculated excitation energys (in Rydberg) can be found in the file pbe_sc.wbse.save/summary.json.
[3]:
%%bash
cat pbe_sc.wbse.save/summary.json
{
"plep": {
"n_plep_eigen": 2,
"eigenval": [
0.14406126316112416,
0.1441942044061179
]
}
}
These two states are the
Step 1.3: Spin-flip TDDFT calculation
Now we run the wbse.x executable to compute the excitation energies of the singlet states of NV
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/pbe_sf_wbse.in
Let us inspect the pbe_sf_wbse.in file:
[4]:
%%bash
cat pbe_sf_wbse.in
input_west:
qe_prefix: pbe
west_prefix: pbe_sf
outdir: ./
wbse_init_control:
wbse_init_calculation: S
solver: TDDFT
wbse_control:
wbse_calculation: D
n_liouville_eigen: 4
trev_liouville: 0.00000001
trev_liouville_rel: 0.000001
l_preconditioning: True
l_spin_flip: True
l_spin_flip_kernel: True
l_spin_flip_alda0: False
The l_spin_flip: True and l_spin_flip_kernel: True keywords instruct the code to perform a spin-flip TDDFT calculation with the spin-flip kernel.
We run wbse.x on 2 cores:
[ ]:
%%bash
mpirun -n 2 wbse.x -i pbe_sf_wbse.in > pbe_sf_wbse.out
If the reader does NOT have the computational resources to run the calculation, the WEST output file needed for the next step can be directly downloaded as:
[ ]:
%%bash
mkdir -p pbe_sf.wbse.save
wget -N -q https://west-code.org/doc/training/nv_tddft/pbe_sf_summary.json -O pbe_sf.wbse.save/summary.json
The calculated excitation energys (in Rydberg) can be found in the file pbe_sf.wbse.save/summary.json.
[5]:
%%bash
cat pbe_sf.wbse.save/summary.json
{
"plep": {
"n_plep_eigen": 4,
"eigenval": [
0.006752572854356471,
0.043495765189432344,
0.043678785251997566,
0.10011245174283542
]
}
}
The four states are the
Step 2: TDDFT calculation with the DDH functional
A TDDFT calculation with a hybrid functional contains five steps:
2.1 Performing a self-consistent DFT calculation as the starting point of TDDFT
2.2 Performing a non-self-consistent DFT including more empty bands to construct the adaptively compressed exchange (ACE) operator, a low-rank approximation to the exact exchange operator
2.3 Computing the Coulomb integrals for pairs of occupied Kohn-Sham orbitals
2.4 Computing the neutral excitation energies of triplet excited states using spin-conserving TDDFT
2.5 Computing the neutral excitation energies of singlet excited states using spin-flip TDDFT
Step 2.1: Mean-field starting point
We first perform the DFT calculation using the Quantum ESPRESSO code.
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_pw.in
We can now inspect the ddh_pw.in file, the input for the pw.x code:
[6]:
%%bash
cat ddh_pw.in
&CONTROL
calculation = 'scf'
prefix = 'ddh'
pseudo_dir = './'
/
&SYSTEM
ibrav = 0
ecutwfc = 50
tot_charge = -1.0
nspin = 2
tot_magnetization = 2.0
nbnd = 150
nat = 63
ntyp = 2
input_dft = 'pbe0'
ecutfock = 100.0
exx_fraction = 0.18
/
&ELECTRONS
diago_full_acc = .true.
/
K_POINTS gamma
CELL_PARAMETERS angstrom
7.136000 0.000000 0.000000
0.000000 7.136000 0.000000
0.000000 0.000000 7.136000
ATOMIC_SPECIES
C 12.01099968 C_ONCV_PBE-1.2.upf
N 14.00699997 N_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS crystal
C 0.1269815510 0.3733371195 0.3775718026
C 0.1253081282 0.3763002936 0.8746894487
C 0.1260060117 0.8738380396 0.3754459361
C 0.1250639790 0.8750661683 0.8749376784
C 0.6248201544 0.3811585813 0.3751813598
C 0.6224309085 0.3733360188 0.8730196975
C 0.6250110086 0.8765296624 0.3749876809
C 0.6245505450 0.8738390861 0.8739957865
C 0.0000259749 0.0000259633 -0.0000256868
C 0.0014358428 -0.0014358100 0.5010495568
C 0.0014328181 0.4989469740 0.0014351388
C 0.0012018772 0.4992148548 0.5007857943
C 0.4989470397 -0.0014328307 0.0014351823
C 0.4992149137 0.0012018289 0.5007857375
C 0.4992116247 0.4992116312 -0.0012034708
C 0.1250667730 0.1250667914 0.1249294365
C 0.1253032977 0.1253032524 0.6237019642
C 0.1260062437 0.6245495725 0.1261632799
C 0.1269771899 0.6224340478 0.6266613449
C 0.6245496185 0.1260062840 0.1261633007
C 0.6224340177 0.1269771772 0.6266613352
C 0.6250092594 0.6250092159 0.1234699036
C 0.6248234427 0.6248234639 0.6188442442
C 0.0009910041 0.2504149699 0.2494871226
C 0.0003716741 0.2501475881 0.7498513998
C 0.0009645933 0.7495989686 0.2503986681
C 0.0009941125 0.7505129665 0.7495871392
C 0.4985394814 0.2524198182 0.2522377911
C 0.5078677486 0.2391591291 0.7608354182
C 0.5003280630 0.7516382226 0.2483618688
C 0.4985401685 0.7477659930 0.7475823593
C 0.3748654285 0.3748654245 0.1250552701
C 0.3749783337 0.8749127142 0.1250879590
C 0.3748650726 0.8749450711 0.6251340225
C 0.8749127198 0.3749782927 0.1250879634
C 0.8749450684 0.3748650501 0.6251340257
C 0.8750493463 0.8750493517 0.1249501816
C 0.8749120516 0.8749120381 0.6250201881
C 0.2504149894 -0.0009909944 0.2494870713
C 0.2501475446 0.0003715462 0.7498514576
C 0.2524198093 0.4985394738 0.2522377661
C 0.2391592245 0.5078678650 0.7608354474
C 0.7495989932 0.0009646155 0.2503986775
C 0.7505130382 -0.0009940706 0.7495871127
C 0.7516382084 0.5003280124 0.2483619045
C 0.7477659502 0.4985401253 0.7475823293
C 0.3733371729 0.1269814887 0.3775717513
C 0.3763002438 0.1253079989 0.8746895222
C 0.3811585422 0.6248202431 0.3751812920
C 0.3733360636 0.6224310126 0.8730197732
C 0.8738379990 0.1260060464 0.3754459661
C 0.8750662653 0.1250640377 0.8749376416
C 0.8765296848 0.6250109436 0.3749877093
C 0.8738390803 0.6245504485 0.8739957771
C 0.2501515174 0.2501515049 -0.0003784384
C 0.2391603565 0.2391602431 0.4921393755
C 0.2504126363 0.7505106105 0.0009953037
C 0.2524180055 0.7477644305 0.5014586422
C 0.7505106094 0.2504126558 0.0009952558
C 0.7477643646 0.2524180264 0.5014586712
C 0.7495988945 0.7495988379 -0.0009639807
C 0.7516394023 0.7516393858 0.4996700487
N 0.5130505433 0.5130506248 0.4869539927
Compared to the file pbe_pw.in, the additional keywords input_dft = 'pbe0' and exx_fraction = 0.18 instruct the DFT calculation to use the PBE0 functional, incorporating an exact exchange fraction of 0.18. This approach is termed the dielectric-dependent hybrid (DDH) functional, as the fraction is derived from the inverse of the macroscopic dielectric constant of diamond.
We run pw.x on 2 cores, and make a copy of the save directory generated by pw.x.
[ ]:
%%bash
mpirun -n 2 pw.x -i ddh_pw.in > ddh_pw.out
cp -r ddh.save ddh_copy.save
Step 2.2: Non-self-consistent-field calculation for the ACE operator
We perform the non-self-consistent-field (nscf) calculation for the ACE operator that is used in the TDDFT calculation in the case of hybrid functionals.
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_nscf.in
We can now inspect the ddh_nscf.in file:
[7]:
%%bash
cat ddh_nscf.in
&CONTROL
calculation = 'nscf'
prefix = 'ddh'
pseudo_dir = './'
/
&SYSTEM
ibrav = 0
ecutwfc = 50
tot_charge = -1.0
nspin = 2
tot_magnetization = 2.0
nbnd = 512
nat = 63
ntyp = 2
input_dft = 'pbe0'
ecutfock = 100.0
exx_fraction = 0.18
/
&ELECTRONS
diago_full_acc = .true.
/
K_POINTS gamma
CELL_PARAMETERS angstrom
7.136000 0.000000 0.000000
0.000000 7.136000 0.000000
0.000000 0.000000 7.136000
ATOMIC_SPECIES
C 12.01099968 C_ONCV_PBE-1.2.upf
N 14.00699997 N_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS crystal
C 0.1269815510 0.3733371195 0.3775718026
C 0.1253081282 0.3763002936 0.8746894487
C 0.1260060117 0.8738380396 0.3754459361
C 0.1250639790 0.8750661683 0.8749376784
C 0.6248201544 0.3811585813 0.3751813598
C 0.6224309085 0.3733360188 0.8730196975
C 0.6250110086 0.8765296624 0.3749876809
C 0.6245505450 0.8738390861 0.8739957865
C 0.0000259749 0.0000259633 -0.0000256868
C 0.0014358428 -0.0014358100 0.5010495568
C 0.0014328181 0.4989469740 0.0014351388
C 0.0012018772 0.4992148548 0.5007857943
C 0.4989470397 -0.0014328307 0.0014351823
C 0.4992149137 0.0012018289 0.5007857375
C 0.4992116247 0.4992116312 -0.0012034708
C 0.1250667730 0.1250667914 0.1249294365
C 0.1253032977 0.1253032524 0.6237019642
C 0.1260062437 0.6245495725 0.1261632799
C 0.1269771899 0.6224340478 0.6266613449
C 0.6245496185 0.1260062840 0.1261633007
C 0.6224340177 0.1269771772 0.6266613352
C 0.6250092594 0.6250092159 0.1234699036
C 0.6248234427 0.6248234639 0.6188442442
C 0.0009910041 0.2504149699 0.2494871226
C 0.0003716741 0.2501475881 0.7498513998
C 0.0009645933 0.7495989686 0.2503986681
C 0.0009941125 0.7505129665 0.7495871392
C 0.4985394814 0.2524198182 0.2522377911
C 0.5078677486 0.2391591291 0.7608354182
C 0.5003280630 0.7516382226 0.2483618688
C 0.4985401685 0.7477659930 0.7475823593
C 0.3748654285 0.3748654245 0.1250552701
C 0.3749783337 0.8749127142 0.1250879590
C 0.3748650726 0.8749450711 0.6251340225
C 0.8749127198 0.3749782927 0.1250879634
C 0.8749450684 0.3748650501 0.6251340257
C 0.8750493463 0.8750493517 0.1249501816
C 0.8749120516 0.8749120381 0.6250201881
C 0.2504149894 -0.0009909944 0.2494870713
C 0.2501475446 0.0003715462 0.7498514576
C 0.2524198093 0.4985394738 0.2522377661
C 0.2391592245 0.5078678650 0.7608354474
C 0.7495989932 0.0009646155 0.2503986775
C 0.7505130382 -0.0009940706 0.7495871127
C 0.7516382084 0.5003280124 0.2483619045
C 0.7477659502 0.4985401253 0.7475823293
C 0.3733371729 0.1269814887 0.3775717513
C 0.3763002438 0.1253079989 0.8746895222
C 0.3811585422 0.6248202431 0.3751812920
C 0.3733360636 0.6224310126 0.8730197732
C 0.8738379990 0.1260060464 0.3754459661
C 0.8750662653 0.1250640377 0.8749376416
C 0.8765296848 0.6250109436 0.3749877093
C 0.8738390803 0.6245504485 0.8739957771
C 0.2501515174 0.2501515049 -0.0003784384
C 0.2391603565 0.2391602431 0.4921393755
C 0.2504126363 0.7505106105 0.0009953037
C 0.2524180055 0.7477644305 0.5014586422
C 0.7505106094 0.2504126558 0.0009952558
C 0.7477643646 0.2524180264 0.5014586712
C 0.7495988945 0.7495988379 -0.0009639807
C 0.7516394023 0.7516393858 0.4996700487
N 0.5130505433 0.5130506248 0.4869539927
The content of ddh_nscf.in is almost identical to that of ddh_pw.in, except that in ddh_nscf.in we request a non-self-consistent-field (nscf) calculation with a larger value of nbnd = 512, which is the number of Kohn-Sham orbitals used to construct the ACE operator.
The calculation is spin polarized (i.e., nspin = 2 and tot_magnetization = 2.0), representing the
We run pw.x again on 2 cores, and copy the file that stores the ACE operator to the directory saved in the previous self-consistent run.
[ ]:
%%bash
mpirun -n 2 pw.x -i ddh_nscf.in > ddh_nscf.out
cp ddh.save/ace* ddh_copy.save/
rm -rf ddh.save ddh.wfc*
mv ddh_copy.save ddh.save
Step 2.3: Coulomb integrals
We compute the Coulomb integrals for pairs of occupied Kohn-Sham orbitals using the wbse_init.x executable.
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_wbse_init.in
Let us inspect the ddh_wbse_init.in file:
[8]:
%%bash
cat ddh_wbse_init.in
input_west:
qe_prefix: ddh
west_prefix: ddh_west
outdir: ./
wbse_init_control:
wbse_init_calculation: S
solver: TDDFT
localization: W
overlap_thr: 0.001
The localization: W keyword instructs the code to use Wannier functions, which are a localized representation of the Kohn-Sham orbitals. If the overlap between two Wannier functions is below overlap_thr: 0.001, the evaluation of the corresponding Coulomb integral is skipped, thus reducing the computational cost.
We run wbse_init.x on 2 cores:
[ ]:
%%bash
mpirun -n 2 wbse_init.x -i ddh_wbse_init.in > ddh_wbse_init.out
Step 2.4: Spin-conserving TDDFT calculation
Now we run the wbse.x executable to compute the excitation energies of triplet states of NV
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_sc_wbse.in
Let us inspect the ddh_sc_wbse.in file:
[9]:
%%bash
cat ddh_sc_wbse.in
input_west:
qe_prefix: ddh
west_prefix: ddh_sc
outdir: ./
wbse_init_control:
wbse_init_calculation: S
solver: TDDFT
localization: W
overlap_thr: 0.001
wbse_control:
wbse_calculation: D
n_liouville_eigen: 2
trev_liouville: 0.00000001
trev_liouville_rel: 0.000001
l_preconditioning: True
n_exx_lowrank: 512
The n_exx_lowrank: 512 keyword means that the ACE operator is constructed with 512 Kohn-Sham orbitals.
We run wbse.x on 2 cores:
[ ]:
%%bash
ln -s ddh_west.wbse_init.save ddh_sc.wbse_init.save
mpirun -n 2 wbse.x -i ddh_sc_wbse.in > ddh_sc_wbse.out
If the reader does NOT have the computational resources to run the calculation, the WEST output file needed for the next step can be directly downloaded as:
[ ]:
%%bash
mkdir -p ddh_sc.wbse.save
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_sc_summary.json -O ddh_sc.wbse.save/summary.json
The calculated excitation energys (in Rydberg) can be found in the file ddh_sc.wbse.save/summary.json.
[10]:
%%bash
cat ddh_sc.wbse.save/summary.json
{
"plep": {
"n_plep_eigen": 2,
"eigenval": [
0.16518277920006938,
0.16529209364139377
]
}
}
These two states are the
Step 2.5: Spin-flip TDDFT calculation
Now we run the wbse.x executable to compute the excitation energies of singlet states of NV
Download the following file to your working directory:
[ ]:
%%bash
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_sf_wbse.in
Let us inspect the ddh_sf_wbse.in file:
[11]:
%%bash
cat ddh_sf_wbse.in
input_west:
qe_prefix: ddh
west_prefix: ddh_sf
outdir: ./
wbse_init_control:
wbse_init_calculation: S
solver: TDDFT
localization: W
overlap_thr: 0.001
wbse_control:
wbse_calculation: D
n_liouville_eigen: 4
trev_liouville: 0.00000001
trev_liouville_rel: 0.000001
l_preconditioning: True
l_spin_flip: True
l_spin_flip_kernel: True
l_spin_flip_alda0: False
n_exx_lowrank: 512
We run wbse.x on 2 cores:
[ ]:
%%bash
ln -s ddh_west.wbse_init.save ddh_sf.wbse_init.save
mpirun -n 2 wbse.x -i ddh_sf_wbse.in > ddh_sf_wbse.out
If the reader does NOT have the computational resources to run the calculation, the WEST output file needed for the next step can be directly downloaded as:
[ ]:
%%bash
mkdir -p ddh_sf.wbse.save
wget -N -q https://west-code.org/doc/training/nv_tddft/ddh_sf_summary.json -O ddh_sf.wbse.save/summary.json
The calculated excitation energys (in Rydberg) can be found in the file ddh_sf.wbse.save/summary.json.
[12]:
%%bash
cat ddh_sf.wbse.save/summary.json
{
"plep": {
"n_plep_eigen": 4,
"eigenval": [
0.010238564822618666,
0.05862318898692176,
0.058865528147033344,
0.1472998272595149
]
}
}
The four states are the
Step 3: Summary of results
We extract the excitation energies from the JSON files.
[13]:
import json
import numpy as np
ry2ev = 13.605662285137
with open("pbe_sc.wbse.save/summary.json", "r") as f:
data = json.load(f)
pbe_sc_vee = np.array(data["plep"]["eigenval"])
pbe_sc_vee *= ry2ev
with open("pbe_sf.wbse.save/summary.json", "r") as f:
data = json.load(f)
pbe_sf_vee = np.array(data["plep"]["eigenval"])
pbe_sf_vee -= pbe_sf_vee[0]
pbe_sf_vee *= ry2ev
with open("ddh_sc.wbse.save/summary.json", "r") as f:
data = json.load(f)
ddh_sc_vee = np.array(data["plep"]["eigenval"])
ddh_sc_vee *= ry2ev
with open("ddh_sf.wbse.save/summary.json", "r") as f:
data = json.load(f)
ddh_sf_vee = np.array(data["plep"]["eigenval"])
ddh_sf_vee -= ddh_sf_vee[0]
ddh_sf_vee *= ry2ev
Now we compare the computed excitation energies with the experimental zero-phonon line (ZPL):
[14]:
import pandas as pd
data = {
"State": ["$^3A_2$", "$^1E$", "$^1A_1$", "$^3E$"],
"TDDFT@PBE (eV)": [0.0, pbe_sf_vee[1], pbe_sf_vee[3], pbe_sc_vee[0]],
"TDDFT@DDH (eV)": [0.0, ddh_sf_vee[1], ddh_sf_vee[3], ddh_sc_vee[0]],
"Expt. ZPL (eV)": [0.0, "0.34 - 0.43", "1.51 - 1.60", 1.945]
}
df = pd.DataFrame(data)
pd.options.display.float_format = "{:.3f}".format
df
[14]:
| State | TDDFT@PBE (eV) | TDDFT@DDH (eV) | Expt. ZPL (eV) | |
|---|---|---|---|---|
| 0 | 0.000 | 0.000 | 0.000 | |
| 1 | 0.500 | 0.658 | 0.34 - 0.43 | |
| 2 | 1.270 | 1.865 | 1.51 - 1.60 | |
| 3 | 1.960 | 2.247 | 1.945 |
The TDDFT@DDH calculations employed two numerical approximations:
the ACE approximation to the exact exchange operator;
the nearsightedness principle to restrict the Coulomb integrals to overlapping Wannier functions.
These approximations introduce minimal errors in the calculated excitation energies, as demonstrated below.
[16]:
data = {
"State": ["$^3A_2$", "$^1E$", "$^1A_1$", "$^3E$"],
"TDDFT@DDH, w/ approximations (eV)": [0.0, ddh_sf_vee[1], ddh_sf_vee[3], ddh_sc_vee[0]],
"TDDFT@DDH, w/o approximations (eV)": [0.0, 0.659, 1.866, 2.250],
}
df = pd.DataFrame(data)
pd.options.display.float_format = "{:.3f}".format
df
[16]:
| State | TDDFT@DDH, w/ approximations (eV) | TDDFT@DDH, w/o approximations (eV) | |
|---|---|---|---|
| 0 | 0.000 | 0.000 | |
| 1 | 0.658 | 0.659 | |
| 2 | 1.865 | 1.866 | |
| 3 | 2.247 | 2.250 |