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Re^2: MCSCF and XMCQDPT2: selection of CSFs, transition moments

Alex Granovsky

Dear Michal,
Dear Thomas,

there is a typo in the formula given by Thomas. It should read

f_mn = 2/3 * (E_n - E_m) * (d_mn^2)

where d_mn is the norm of the transition dipole. I.e. the norm of
transition dipole should be squared in the correct expression.

As to transition velocity, for the exact solution of the molecular
Schrodinger equation (SE), oscillator strength can be also expressed as:

f_mn = 2/3 * (v_mn^2)/(E_n - E_m)

where v_mn^2 is the squared norm of the transition velocity.

This gives the alternative way of computing f_mn. For finite (incomplete)
basis sets and approximate methods of solving SE the two expressions
above are no longer equal. The first of them is considered to me the
most accurate as transition velocity is more sensitive to the quality
of wavefunction.

Hope this helps.

Kind regards,
Alex Granovsky

On Thu Jun 12 '14 10:49pm, Thomas Pijper wrote
>Dear Michal,

>1) Currently, selection of CSFs or determinants at the MCSCF stage is not possible.

>2) For the probability of an excitation, one should typically use the transition dipole moment. It can be converted to an oscillator strength by the formula:

>f_mn = 2/3 * (E_n - E_m) * d_mn   (assuming all values are in atomic units)

>Hereby, you can use PT2 energies from the (X)MCQDPT2 calculation for E_m and E_n. Note that the printed dipole moment (d_mn) is determined at the zeroth-order level, not the PT2 level.

>Oscillator strengths are IMO more useful when considering the probability of excitations as an oscillator strength correlates directly to the area of an absorption band in a UV/vis absorption spectrum.
>Kind regards,
>On Wed Jun 11 '14 4:52pm, Michal P Krompiec wrote
>>Hello, I have 2 questions:
>>1) $XMCQDPT ISELCT=4 $END "allows selection of important CSFs". Does it work only at the PT2 stage, or also in MC-SCF? Is it possible to discard "unimportant" CSFs at MC-SCF stage?
>>2) Regarding the output of XMCQDPT runs. Which value is more related to probability of radiative transition - transition dipole norm or dipole velocity norm? What is the practical difference between these and oscillator strengths?

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