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Alex Granovsky
gran@classic.chem.msu.su

Sorry for delay with my reply.

As to relaxed vs. expectation value dipole moments,
the first are defined as the derivatives of a total energy
with respect to the strength of an external electric field.
The second are defined as the expectation value of the dipole
operator computed using calculated wavefunction.

These tho are the same only for fully variational methods
like e.g. RHF or single-state MCSCF. Otherwise, they differ.  
Moreover, there as some methods for which expectation value-type
properties cannot be defined at all. Most people believes that
response-type properties are preferred even if both types are
available (e.g., for CI).

To compute numerical polarizabilities using finite differences,
you need to use response-type dipole moments.

I'll split my answer to your post into several parts.

I'll attach the sample input you are asking for to my next post.

As to transition moments, this may require some more time to
be answered. I will answer this when I will have some ideas
or news on this. Meanwhile, I'd welcome any additional input
from your side.

Kind regards,
Alex


On Thu Mar 28 '13 1:07pm, Matthieu Sala wrote
---------------------------------------------
>On Thu Mar 28 '13 2:50am, Alex Granovsky wrote
>----------------------------------------------

>Dear Alex,

>Thank you for answering this fast.

>From what you say, I understand that relaxed dipole moments are more accurate than expectation-value ones. Is that correct ?

>However, as I said I am interested in excited state polarizability for which I don't expect to get very accurate results from CASSCF.
>Indeed we have compared CASSCF (with molpro), zero-order QDPT, MRCI (with molpro) and XMCQDPT2 (by double energy differentiation) and found that dynamic correlation is important.

>Therefore expectation-value dipole would be sufficient four our purpose and an input example would be of great help.

>I attach an input file for pyrazine which we are studying. It has zero dipole moments but we are interested in a field induced dipole so it is a RUNTYP=FFIELD input. I know that I don't use the fastest options for CASSCF and XMCQDPT2 but I like the fullnr and guga combination because it converges well and in this case it remains quite fast.

>I would like to add a comment on zero-order QDPT transition moments.

>In a previous post I was concern with the ZO-QDPT TDMs for aniline, I found that when the XMCQDPT2 model space contains only the states included in the SA-CASSCF part then I obtained good ZO-QDPT TDMs (the same as the CASSCF ones). However when the model space size was increased to include important contributions from higher states then the TDM for the 2nd pipi* excited state was very bad. You sent me a corrected input that did not change the problem (although it was useful for me as an example for good XMCQDPT2 calculations.)

>I find the same behaviour in pyrazine. When increasing the size of the model space the TDM for the third excited state (first pipi*) again become very bad.

>I just wanted to bring this to your attention.

>Thank you for your help and comments.
>Best regards.

>Matthieu
>
>
>>Dear Matthieu,

>>Do you need relaxed or expectation-value dipole moments?

>>Relaxed dipole moments could be computed using the same
>>approach as the one used by SA-CASSCF gradient code, namely,
>>by differentiation of state-averaged dipole moment
>>with respect to a state weight. This is because the differentiation
>>of averaged one and two particle density matrices with respect to
>>a state weight produces response-type state-specific density
>>matrices. This is the most general and powerful statement related
>>to such a differentiation which allows computation of state-specific
>>gradients and any one and two-electron properties using such
>>differentiation.

>>If you can wait a month or so, the code for relaxed dipole moments
>>will be available as a part of Firefly.

>>Computation of expectation-value state-specific dipole moments is
>>even simpler. The dipole moments of this type can be computed
>>by the present code. If this is the type of dipole moments you need,
>>please let me know and I'll post sample input file.

>>Kind regards,
>>Alex Granovsky
>>
>>
>>On Wed Mar 27 '13 7:05pm, Matthieu Sala wrote
>>---------------------------------------------
>>>Dear Firefly users,

>>>I would like to know if there is a way to compute excited state dipole moments from a state averaged CASSCF calculation in Firefly.

>>>The reason is that I would like to compute excited state polarizabilities by finite differentiation of the dipole rather than double differentiation of the energy with respect to an applied field.

>>>I know that I can obtain zero order QDPT dipole moments from a XMCQDPT2 calculation and that these might be better than CASSCF although not of full XMCQDPT2 quality. However I would like to compute pure CASSCF dipole moments, at least for the purpose of comparison.

>>>Best regards.
>>>Matthieu Sala