TD-DFT with SOC: Kramers pairs
Quartet state with SOC
$COMPASS Title CS molecule Basis cc-pvdz Geometry C 0. 0. 0. S 0. 0. 1.1151 END geometry $END $XUANYUAN scalar heff 0 soint hsoc 0 $END $SCF UKS DFT SVWN5 charge 1 spin 2 $END $TRAINT utddft orbi hforb $END $tddft imethod 2 isf 1 itda 1 idiag 1 istore 1 nexit 2 2 2 2 $END $TDDFT isoc 2 nfiles 1 ifgs 0 imatsoc -1 $END
The quartets are split into Kramers pairs by SOC interaction with higher quartet states.
*** List of SOC-SI results ***
No. ExEnergies Dominant Excitations Esf dE Eex(eV) (cm^-1)
--------> Quartet: Sigma^+
1 8.3501 eV 99.9% Spin: |S+,1> 1-th A1 8.3516 -0.0015 0.0000 0.00
2 8.3501 eV 99.9% Spin: |S+,4> 1-th A1 8.3516 -0.0015 0.0000 0.00
3 8.3512 eV 100.0% Spin: |S+,3> 1-th A1 8.3516 -0.0004 0.0011 8.50
4 8.3512 eV 100.0% Spin: |S+,2> 1-th A1 8.3516 -0.0004 0.0011 8.50
--------> Quartet: Delta
5 8.8949 eV 50.0% Spin: |S+,4> 2-th A1 8.9015 -0.0066 0.5448 4393.72
6 8.8949 eV 50.0% Spin: |S+,1> 2-th A1 8.9015 -0.0066 0.5448 4393.72
7 8.8988 eV 49.9% Spin: |S+,3> 2-th A1 8.9015 -0.0027 0.5486 4425.14
8 8.8988 eV 49.9% Spin: |S+,2> 2-th A1 8.9015 -0.0027 0.5486 4425.14
9 8.9030 eV 49.9% Spin: |S+,2> 1-th A2 8.9015 0.0015 0.5529 4459.10
10 8.9030 eV 49.9% Spin: |S+,3> 1-th A2 8.9015 0.0015 0.5529 4459.10
11 8.9075 eV 49.9% Spin: |S+,1> 1-th A2 8.9015 0.0061 0.5574 4495.86
12 8.9075 eV 49.9% Spin: |S+,4> 1-th A2 8.9015 0.0061 0.5574 4495.86
--------> Quartet: Pi
13 9.3335 eV 48.2% Spin: |S+,1> 1-th B1 9.3505 -0.0170 0.9834 7931.49
14 9.3335 eV 48.2% Spin: |S+,4> 1-th B1 9.3505 -0.0170 0.9834 7931.49
15 9.3446 eV 48.7% Spin: |S+,2> 1-th B1 9.3505 -0.0059 0.9945 8021.16
16 9.3446 eV 48.7% Spin: |S+,3> 1-th B1 9.3505 -0.0059 0.9945 8021.16
17 9.3555 eV 40.3% Spin: |S+,2> 1-th B2 9.3505 0.0050 1.0054 8108.95
18 9.3555 eV 40.3% Spin: |S+,3> 1-th B2 9.3505 0.0050 1.0054 8108.95
19 9.3671 eV 49.7% Spin: |S+,1> 1-th B2 9.3505 0.0166 1.0170 8202.80
20 9.3671 eV 49.7% Spin: |S+,4> 1-th B2 9.3505 0.0166 1.0170 8202.80
--------> Quartet: Sigma-
21 9.4651 eV 98.1% Spin: |S+,3> 2-th A2 9.4627 0.0025 1.1150 8993.28
22 9.4651 eV 98.1% Spin: |S+,2> 2-th A2 9.4627 0.0025 1.1150 8993.28
23 9.4653 eV 98.8% Spin: |S+,4> 2-th A2 9.4627 0.0026 1.1151 8994.24
24 9.4653 eV 98.8% Spin: |S+,1> 2-th A2 9.4627 0.0026 1.1151 8994.24
--------> Quartet: Pi
25 15.9875 eV 50.0% Spin: |S+,4> 2-th B2 16.0102 -0.0227 7.6374 61599.53
26 15.9875 eV 50.0% Spin: |S+,1> 2-th B2 16.0102 -0.0227 7.6374 61599.53
27 16.0026 eV 44.1% Spin: |S+,2> 2-th B2 16.0102 -0.0076 7.6525 61721.52
28 16.0026 eV 44.1% Spin: |S+,3> 2-th B2 16.0102 -0.0076 7.6525 61721.52
29 16.0177 eV 50.0% Spin: |S+,3> 2-th B1 16.0102 0.0076 7.6676 61843.52
30 16.0177 eV 50.0% Spin: |S+,2> 2-th B1 16.0102 0.0076 7.6676 61843.52
31 16.0329 eV 50.0% Spin: |S+,4> 2-th B1 16.0102 0.0227 7.6827 61965.52
32 16.0329 eV 50.0% Spin: |S+,1> 2-th B1 16.0102 0.0227 7.6827 61965.52Similarly, in the case O2 ground state, the ZFS can be computed as follows (K*Psi = Psi):
No. ExEnergies Dominant Excitations Esf dE Eex(eV) (cm^-1)
--->
1 -0.0001 eV 100.0% Spin: |Gs,2> 0-th B1g 0.0000 -0.0001 0.0000 0.00
--->
2 -0.0001 eV 100.0% Spin: |Gs,1> 0-th B1g 0.0000 -0.0001 0.0000 0.11
3 -0.0001 eV 100.0% Spin: |Gs,3> 0-th B1g 0.0000 -0.0001 0.0000 0.11
--->The spin-spin interaction will be implemented in future!