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Re^3: MCSCF and XMCQDPT2: selection of CSFs, transition moments

Thomas Pijper

Dear Alex,

>there is a typo in the formula given by Thomas. It should read
>f_mn = 2/3 * (E_n - E_m) * (d_mn^2)

That's indeed what the formula should read, thanks for correcting.

Kind regards,

On Mon Jun 16 '14 10:08pm, Alex Granovsky wrote
>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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