Understanding TDDFT output - transition moment and oscillator strength

Hello everyone!

I’d like to ask for assistance in interpreting TD-DFT calculation output with regard to transition moments and oscillator strengths.

Here are the relevant parts of TDDFT calculation in solvent (model: cpcm):

---------------------------------------------------
             TDDFT Excitation Energies
 ---------------------------------------------------

 Excited state   1: excitation energy (eV) =        3.9035
 Total energy for state   1:                  -818.77165874 au
    Multiplicity: Singlet
    Trans. Mom.:  1.1816 X   0.2139 Y   0.0070 Z
    Strength   :     0.1379083854
    X: D(   68) --> V(    1) amplitude =  0.9639
 ***************************************************************
 *      Excited-state properties with   relaxed density        *
 ***************************************************************
  Static  dielectric constant (eps_0)   = 36.60
  Optical dielectric constant (eps_inf) = 1.34
 Using non-symmetric K matrix

 ---------------- SUMMARY OF LR-PCM AND SS-PCM -----------------

 Relaxed   singlet excited state    1:
   0th-order excitation energy              =   3.903466 eV
   1st-order ptSS-PCM correction            =  -0.003085 eV
   1st-order ptLR-PCM correction            =  -0.017684 eV
   ptSS-PCM 1st-order corrected exc. energy =   3.900381 eV
   ptLR-PCM 1st-order corrected exc. energy =   3.885781 eV
   Total 1st-order (ptSS+ptLR)  exc. energy =   3.882696 eV
   Dipole Mom. (Debye):   -1.9631 X   -1.2497 Y    0.0027 Z
   Strength |mu - mu_0| (Debye):   1.1396

As I understand it, the Trans. Mom. corresponds to transition dipole moment components, while “Strength” just below corresponds to oscillator strength. Is that correct? If so, why is the magnitude of transition dipole moment not printed directly in the output?

Also, I’d like to ask what Strength |mu - mu_0| in excited state properties box actually means, as it’s not really clear for me.

Best,
Joanna

Magnitude of the transition dipole is easily computed from the components that are given.

|mu - mu_0| is the magnitude of the difference dipole moment (mu = excited-state dipole, mu0 = ground state)