TDDFT Excitation Energies

Questions
#1

Greetings everyone, I have been delving into the results of time-dependent density functional theory (TDDFT) and noticed something. When I enabled the random phase approximation (RPA) for a doublet system, initially the TDDFT/TDA excitation energies were accompanied by <S^22> value. However, subsequently, the TDDFT excitation energies appeared without a <S^2> value. I am now pondering how to assign the multiplicity for these TDDFT excitation energies.

Input file:

$rem
jobtype = SP
method = wB97M-V
basis = def2-SVP
cis_n_roots = 25
RPA = true
thresh = 10
scf_convergence = 6
max_scf_cycles = 500
sym_ignore = true
gui = 2
$end

Output file:

     TDDFT/TDA Excitation Energies

Excited state 1: excitation energy (eV) = 1.2249
Total energy for state 1: -3934.71082846 au
<S**2> : 0.7533
Trans. Mom.: -0.0834 X 0.0016 Y -0.0270 Z
Strength : 0.0002305629
D( 163) → S( 1) amplitude = 0.1816 beta
D( 166) → S( 1) amplitude = -0.2613 beta
D( 179) → S( 1) amplitude = 0.2070 beta
D( 180) → S( 1) amplitude = 0.1846 beta
D( 182) → S( 1) amplitude = -0.1569 beta
D( 185) → S( 1) amplitude = -0.3069 beta
D( 205) → S( 1) amplitude = -0.6965 beta

         TDDFT Excitation Energies

Excited state 1: excitation energy (eV) = 1.1779
Total energy for state 1: -3934.71255431 au
Trans. Mom.: -0.0787 X 0.0011 Y -0.0260 Z
Strength : 0.0001983889
X: D( 163) → S( 1) amplitude = 0.1822 beta
X: D( 166) → S( 1) amplitude = -0.2617 beta
X: D( 179) → S( 1) amplitude = 0.2082 beta
X: D( 180) → S( 1) amplitude = 0.1857 beta
X: D( 182) → S( 1) amplitude = -0.1583 beta
X: D( 185) → S( 1) amplitude = -0.3080 beta
X: D( 205) → S( 1) amplitude = -0.6959 beta

Thank you for your attention.

#2

The <S^2> formulas for full TDDFT was apparently never coded in Q-Chem. You can assign the multiplicities by matching the states to the TDA ones, there is typically very little difference in the excitation energies and looking at oscillator strengths can also help.

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