In the ORCA output for a TD-DFT calculation, there are two types of spectra printed. One is called "transition electric dipole moment" and "transition velocty dipole moment".
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ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
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State Energy Wavelength fosc T2 TX TY TZ
(cm-1) (nm) (au**2) (au) (au) (au)
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1 27648.0 361.7 0.719341268 8.56537 -2.87788 0.45802 -0.27090
2 30253.3 330.5 0.184731134 2.01022 -1.38229 0.30293 -0.08792
3 33113.8 302.0 0.000596722 0.00593 -0.06749 -0.02846 0.02383
4 33958.2 294.5 0.016666067 0.16157 -0.23836 -0.26972 0.17890
5 35481.0 281.8 0.001963234 0.01822 0.07587 -0.09746 0.05442
6 36251.0 275.9 0.082087211 0.74547 0.30134 0.67418 -0.44737
7 36892.9 271.1 0.007036359 0.06279 -0.18262 -0.04896 0.16444
8 40296.4 248.2 0.163705579 1.33744 -1.15180 0.10363 0.00712
9 40712.6 245.6 0.085961535 0.69511 -0.81462 -0.01219 0.17707
10 41670.1 240.0 0.002721111 0.02150 0.08394 -0.09869 -0.06864
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ABSORPTION SPECTRUM VIA TRANSITION VELOCITY DIPOLE MOMENTS
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State Energy Wavelength fosc P2 PX PY PZ
(cm-1) (nm) (au**2) (au) (au) (au)
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1 27648.0 361.7 0.179172895 0.03386 0.18109 -0.00384 -0.03240
2 30253.3 330.5 0.036126643 0.00747 0.08535 0.01325 -0.00302
3 33113.8 302.0 0.007496146 0.00170 0.03852 0.00888 -0.01156
4 33958.2 294.5 0.001365959 0.00032 0.01150 -0.01299 -0.00401
5 35481.0 281.8 0.002616796 0.00063 -0.00588 0.01407 0.02005
6 36251.0 275.9 0.011772984 0.00292 -0.04163 0.03367 -0.00706
7 36892.9 271.1 0.000265060 0.00007 -0.00315 0.00212 0.00724
8 40296.4 248.2 0.075499769 0.02079 0.14370 -0.00400 -0.01129
9 40712.6 245.6 0.028944201 0.00805 0.08950 0.00244 -0.00615
10 41670.1 240.0 0.000916239 0.00026 -0.00984 0.01137 0.00590
The oscillator strenghts are different in each, but the wavelengths are the same.
I am working on predicting UV/visible spectra. I do not need the exact intensities (extinction coefficients), however, I need to be able to get the relative order of the intensities of the peaks right, so that I can match the TD-DFT result to the experimental result with a script. Notice that the order of the intensities between root 3 and 7 are not the same between the two spectra.
Which of the oscillator strengths are better correlated with the experimental extinction coefficient (in the experimental absorption spectrum)? (And more generally, why are the two different?)