# How to compute SOC between reference and SF states with SF-TDDFT?

I wish to calculate the SOC between the ground and excited states of molecular Oxygen using SF-TDDFT. The ground state triplet would then be my reference for generating spin-flipped states and I can include this in the calculation of transition properties with WFA_REF_STATE = 0. However, SOCs are being calculated only among the excited roots. Is there a way to include the reference state in the procedure that computes SOCs? (\$molecule and \$rem sections below)

``````\$molecule
0 3
O                    3.780  -1.656   1.676
O                    4.460  -2.133   0.806
\$end

\$rem
method wb97m-v
basis 6-311G(d,p)
spin_flip 1
cis_n_roots 5
state_analysis 1
calc_soc 2
wfa_ref_state 0
\$end

``````

Goran, please check out Pavel’s awesome answer to a similar query as yours here: Spin-Orbit coupling with SF-TDDFT.

Kaushik, I have some doubts about this. For the case addressed by Pavel, the calculation was able to find the reference state among the spin-flipped states but I don’t think it works in mt case. My output reads:

``````
---------------------------------------------------
SF-DFT Excitation Energies
(The first "excited" state might be the ground state)
---------------------------------------------------

Excited state   1: excitation energy (eV) =       1.7782
Total energy for state   1:                  -150.25536230 au
<S**2>     :  2.0097
S(    1) --> S(    1) amplitude =  0.7065 alpha
S(    2) --> S(    2) amplitude =  0.7065 alpha

Excited state   2: excitation energy (eV) =       1.9766
Total energy for state   2:                  -150.24806990 au
<S**2>     :  0.0086
S(    1) --> S(    1) amplitude =  0.7066 alpha
S(    2) --> S(    2) amplitude = -0.7066 alpha

Excited state   3: excitation energy (eV) =       1.9766
Total energy for state   3:                  -150.24806990 au
<S**2>     :  0.0086
S(    1) --> S(    2) amplitude =  0.7066 alpha
S(    2) --> S(    1) amplitude =  0.7066 alpha

Excited state   4: excitation energy (eV) =       2.1791
Total energy for state   4:                  -150.24063001 au
<S**2>     :  0.0086
S(    1) --> S(    2) amplitude = -0.7067 alpha
S(    2) --> S(    1) amplitude =  0.7067 alpha

Excited state   5: excitation energy (eV) =       8.9422
Total energy for state   5:                  -149.99209155 au
<S**2>     :  1.0081
D(    7) --> S(    2) amplitude =  0.9993

``````

All roots are far above my reference. What do you think?

This is how a typical SF-TDDFT calculation looks like. The triplet state that you seek is “Excited state 1”.