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Re: Interpretation of CASSCF/XMCQDPT results

Alex Granovsky

Dear Gena,

just a couple of questions and some suggestions:

Kind regards,
Alex Granovsky

On Wed Jan 11 '12 7:51pm, Gena wrote
>Dear All,

>I would like to ask some questions regarding to CASSCF and XMCQDPT. My goal is to learn to reliably predict absorbance and fluorescence maxima for medium-sized  organic chromophores. So I need an accurate description of ground and first excited states. So far I got good results (within 30 nm of wavelength error) for several chromophores which I chose randomly (fluorescein, rhodamine B, merocyanine etc.) using CASSCF with subsequent XMCQDPT correction. But I found a type of compounds for which I get a really big error that makes such prediction useless in practice. These are compounds of indocyanine green family. For them I get >100 nm error for absorbance and fluorescence maxima. I chose one particular compound and performed a number of calculations to understand the reason.

>I performed state-averaged (for ground and first excited singlets) CASSCF (12,12) and XMCQDPT (12,12) calculations with def2-SVP, def2-SVPD and def2-TZVP basis sets. I wanted to check if the error was related to small basis set. I found that indeed de2-SVPD and def2-TZVP results significantly differ from def2-SVP one, while being in a very good agreement with each other. I also found that def2-SVPD and def2-TZVP basis sets give very similar results for other compounds too, and somewhat differ from def2-SVP results. But for the system studied the error was even bigger with larger basis sets. By the way, the visual shape of resulting MCSCF orbitals was identical for different basis sets in CASSCF and XMCQDPT. I tried to add additional orbitals to active space but they had a very little impact (MCSCF natural orbitals occupation numbers close to 0 or 2 in CASSCF), so I thought I used a sufficient active space.

>I then decided to check if the error was caused by state-averaging approach. So I performed state-specific CASSCF (12,12) and XMCQDPT (12,12) calculation for ground and first excited singlets separately, using def2-SVPD basis set since it's cheaper and gives almost identical to def2-TZVP results. I took the energy for ground state from ground state state-specific XMCQDPT calculation and the energy for first excited singlet from separate excited state state-specific XMCQDPT calculation, and used the difference as a transition energy. And again I got a big error. But I noticed an interesting thing. In CASSCF (12,12) and XMCQDPT (12,12) the energies for ground and first excited states in different calculations look as follows:
>                              CASSCF (12,12)     XMCQDPT (12,12)

>SA (S0 and S1 with equal weights)

>S0                              -1772.2990010033     -1778.316720677664

>S1                              -1772.1704814821     -1778.248305136786

>SS (S0 ground state)

>S0                              -1772.3070884035      -1778.309816455059

>S1                              -1772.0805194505     -1778.176156721206

>SS (S1 1st excited state)

>S0                              -1772.2520699200     -1778.324189586003

>S1                              -1772.1791600589     -1778.244270211607

>As you can see, the energies of S0 and S1 in CASSCF look normal, S0 has the lowest energy in ground state state-specific calculation (SS-S0), S1 has the lowest energy in SS-S1, and state-averaged CASSCF falls between state-specific values. But after XMCQDPT correction it turns out that ground state is better described by orbitals obtained in S1-state specific calculation! State-averaged calculation gives higher energy than SS-S1, but still lower than SS-S0 for ground state singlet S0. In fact, the SS-S1 XMCQDPT result for S0-S1 energy difference is in a very good agreement with experiment: 570 nm vs 546 nm experimental value in water. For example, state-averaged XMCQDPT gives 666 nm. And again, the state-averaged XMCQDPT gives lower energy for S1 than S1-state-specific XMCQDPT, which is strange for me...

>So my questions are:

>1) How should I interpret this situation? Does this mean that CASSCF gives a poor starting approximation of orbitals due to lack of correlation energy correction?
>2) If so, what should I do in these situations? Could the problem being discussed be caused by incorrect (insufficient) active space? Though I really tried to vary starting orbitals, and it seems like these are the best.
>3) Can it be said that in general it is always better to perform state-specific calculations if one is interested only in energy difference between the states (not in transition dipole), of course if the active space kept identical and there are no degenerate states? Or is it better to always perform a set of calculations (state-averaged and state-specific) and look which orbitals describe the states better like in this particular case? For example, if it is decided that in this case SS-S1 gives the best desrciption of S0=>S1 transition, I get a really good prediction, but this is just a particular luck that S1-optimized orbitals described S0 state well.

>I understand that my questions arise from poor understanding of quantum chemistry, but I think this theme could be a good tutorial for beginners like me in future, since I couldn't find the similar discussion in the forum, and on the other hand such situation could be a usual one. I would really appreciate if someone pointed me on the mistakes I made, because I really want to learn :)



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