Symmetry and Spin-Orbit Couplings using TD-DFT: Si5H12 vs Si4GeH12

Hello,

We are currently trying to understand the link between the SOC obtained through TD-DFT calculations and the symmetry of our molecules. Right now, we are comparing Si5H12 and Si4GeH12, both with Td symmetry.

What is of particular interest to us are the symmetries of the triplet excited states T1, T2 and T3. For both Si5H12 and Si4GeH12, as far as our understanding goes, those states should have the orbital symmetry T2, which means their SOC value with the ground state should be greater than zero, since the ground state has the orbital symmetry A1. But when we look at the value given by Q-CHEM, it doesn’t look to match what we have for Si4GeH12.

Si5H12

Total SOC between the singlet ground state and excited triplet states:
T1      10.900458    cm-1
T2      10.900458    cm-1
T3      10.900458    cm-1

Si4GeH12

Total SOC between the singlet ground state and excited triplet states:
T1      0.000002    cm-1
T2      0.000002    cm-1
T3      0.000000    cm-1

Here are the input files for each calculation:

Si5H12

$molecule
0 1
Si        1.360840033313     -1.360840033313      1.360840033313
Si        1.360840033313      1.360840033313     -1.360840033313
Si       -1.360840033313      1.360840033313      1.360840033313
Si        0.000000000000      0.000000000000      0.000000000000
Si       -1.360840033313     -1.360840033313     -1.360840033313
H         2.226738754740     -0.522677561432      2.226738754740
H         2.226738754740     -2.226738754740      0.522677561432
H         0.522677561432     -2.226738754740      2.226738754740
H         2.226738754740      2.226738754740     -0.522677561432
H         0.522677561432      2.226738754740     -2.226738754740
H         2.226738754740      0.522677561432     -2.226738754740
H        -0.522677561432      2.226738754740      2.226738754740
H        -2.226738754740      0.522677561432      2.226738754740
H        -2.226738754740      2.226738754740      0.522677561432
H        -2.226738754740     -0.522677561432     -2.226738754740
H        -2.226738754740     -2.226738754740     -0.522677561432
H        -0.522677561432     -2.226738754740     -2.226738754740
$end
 
$rem
MEM_TOTAL            2000
JOBTYPE              sp
EXCHANGE             b3lyp
BASIS                def2-tzvp
CIS_N_ROOTS          4
SCF_ALGORITHM        diis_gdm
SYM_TOL              4
CIS_SINGLETS         true
CIS_TRIPLETS         true
CALC_SOC             true
STS_MOM              true
IQMOL_FCHK           true
$end

Si4GeH12

$molecule
0 1
Si        1.387052972184     -1.387052972184      1.387052972184
Si        1.387052972184      1.387052972184     -1.387052972184
Si       -1.387052972184      1.387052972184      1.387052972184
Si       -1.387052972184     -1.387052972184     -1.387052972184
Ge        0.000000000000      0.000000000000      0.000000000000
H         2.251918652130      2.251918652130     -0.548031589165
H         0.548031589165      2.251918652130     -2.251918652130
H         2.251918652130      0.548031589165     -2.251918652130
H        -0.548031589165      2.251918652130      2.251918652130
H        -2.251918652130      0.548031589165      2.251918652130
H        -2.251918652130      2.251918652130      0.548031589165
H         2.251918652130     -0.548031589165      2.251918652130
H         2.251918652130     -2.251918652130      0.548031589165
H         0.548031589165     -2.251918652130      2.251918652130
H        -2.251918652130     -0.548031589165     -2.251918652130
H        -2.251918652130     -2.251918652130     -0.548031589165
 H        -0.548031589165     -2.251918652130     -2.251918652130
$end

$rem
MEM_TOTAL            2000
JOBTYPE              sp
EXCHANGE             b3lyp
BASIS                def2-tzvp
CIS_N_ROOTS          4
SCF_ALGORITHM        diis_gdm
SYM_TOL              4
CIS_SINGLETS         true
CIS_TRIPLETS         true
CALC_SOC             true
STS_MOM              true
IQMOL_FCHK           true
$end

Just in case, here are the output files (it is too long to just paste it here so I had to rely on a third-party website)

Si5H12 : https://file.io/gjCdjCysdwxd
Si4GeH12: https://file.io/hooUIB7sM7WB

Are we missing something?

On another, related note, since we are also working with bigger molecules where doing symmetry analysis by hand will prove to be a bit tiresome, is there a way to obtain the electronic configuration of the excited states?

Thank you for your help!

Iacobellis Nicolas, PhD. Student

Not sure about SOCs, but the only way to get “electronic configuration of the excited state” (which is a made-up concept that doesn’t survive particularly well in quantitative electronic structure calculations) is to look at the list of printed TDDFT coefficients, which are the largest elements of the corresponding CIS-type eigenvector, i.e., coefficients of singly-excited Slater determinants.

1 Like

Q-Chem reports the following ground-triplet excited spin-orbit coupling constants.

For Si5H12:

Total SOC between the singlet ground state and excited triplet states:
T1      10.869959    cm-1
T2      10.869959    cm-1
T3      10.869959    cm-1
T4      0.000000    cm-1
T5      0.000000    cm-1
T6      0.000000    cm-1
T7      0.000000    cm-1
T8      0.000000    cm-1
T9      0.000000    cm-1
T10      0.000000    cm-1
T11      0.000000    cm-1
T12      0.000000    cm-1
T13      0.000000    cm-1
T14      0.000002    cm-1
T15      0.000002    cm-1

For Si4GeH12:

Total SOC between the singlet ground state and excited triplet states:
T1      0.000001    cm-1
T2      0.000001    cm-1
T3      0.000000    cm-1
T4      187.028151    cm-1
T5      187.028152    cm-1
T6      187.028152    cm-1
T7      0.000000    cm-1
T8      0.000001    cm-1
T9      0.000003    cm-1
T10      0.000002    cm-1
T11      0.000000    cm-1
T12      0.000000    cm-1

For both systems states T1-T3 and T4-T6 come as triply degenerate manifolds due to point group symmetry. The manifolds are close in energy:

  • 5.7232 eV and 5.7729 eV for Si5H12, and
  • 5.7300 eV and 5.8698 eV for Si4GeH12.

One possibility is that the order of these manifolds switches going from one system to the other, which is reflected by SOCs.

1 Like

Our excitation energies are the same, but I have the following results for the SOCs:

For Si5H12:

Total SOC between the singlet ground state and excited triplet states:
T1      10.900458    cm-1
T2      10.900458    cm-1
T3      10.900458    cm-1
T4      0.000000    cm-1
T5      0.000000    cm-1
T6      0.000000    cm-1

For Si4GeH12:

Total SOC between the singlet ground state and excited triplet states:
T1      0.000002    cm-1
T2      0.000002    cm-1
T3      0.000000    cm-1
T4      187.028147    cm-1
T5      187.028149    cm-1
T6      187.028150    cm-1
T7      0.000000    cm-1
T8      0.000001    cm-1
T9      0.000005    cm-1
T10      0.000004    cm-1
T11      0.000000    cm-1
T12      0.000000    cm-1

The values are close enough, but why was my number of roots for Si5H12 altered from 4 to 6 while yours went up to 15?

These differences between our results appear because I ran the jobs with disabled symmetry, tight thresholds, and requested more roots. Sometimes loose cutoffs alter the numerical results quite significantly, but not in this case. Your original inputs are fine. If you’d like to reproduce my posted results, modify your $rem input as follows:

CIS_N_ROOTS          12
THRESH 14
SYMMETRY FALSE

Nicolas, NTO analysis of the transitions is a legitimate way to get electronic configuration of the excited state (or, rather, of the transition). You can watch webinar by Felix Plasser and read more about it following this post:
Orbital concepts in quantum chemistry

Anna.