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Re: Problem with MRMP2/XMCQDPT2

Alex Granovsky

Dear Matthieu,

in the first series of your computations, the perturbation theory
was constructed using state-specific CASSCF-optimized orbitals
and using density matrices/orbital energies specific to the
particular state of interest.

This results in different H0 being used for different states in
perturbation theory computations. This sounds good if all states
of interest are described similarly and uniformly well at CASSCF
level. If they are not, this becomes the real source of
problems. For instance, it may be difficult to directly compare
energies obtained with different zero-order Hamiltonians.

Specifically. in pyrazine there are two distinct types (npi* and pipi*)
of excited states which are, most likely, non-uniformly described at
state-specific CASSCF level. To examine this, let's look at your
initial results:

3.53 B3u(npi*) 4.13 Au(npi*) 4.55 B2u(pipi*) 5.17 B2g(npi*).

The energy of B2u(pipi*) state seems to be described best, while npi*
transitions seems to be shifted a bit. I think this is because the
ground state is "similar" to B2u (pipi*) state in the sense the lone
pairs do not mix with pi-system. On the other hand, all three
(simirar) npi* states are shifted by the approximately constant

The uniform quality of description already at a MCSCF level is
very important in multireference perturbation theory computations.
This is why I'd recommend you to always use state-averaged MCSCF
orbitals and state-averaged density matrices in MRMP2 and XMCQDPT2
computations when the differences in energies of different states
are of importance. This is exactly what has been done in your last
input file and hence it is not surprising at all you got better results with it.

As to the paper you mentioned. I have carefully read it and found
that, despite the very detailed description of a computation
protocol, I do not have enough information and courage to
reproduce these computations. Specifically, some results marked
as CASPT2 are actually from MS-CASPT2 computations, while other
are not.

Finally, I'd suggest to try switching to aug-cc-PVTZ basis set
and check the effect of the basis set extension. It can be very

Hope this helps.

Kind regards,
Alex Granovsky

On Thu Dec 12 '13 8:07pm, Matthieu Sala wrote
>Dear Firefly users,

>I would like to report some problems I have with MRMP2/XMCQDPT2 calculations on the four lowest excited states of pyrazine.

>Pyrazine has D2h symmetry at its ground state equilibrium geometry and the four lowest singlet excited states are B3u(npi*) Au(npi*) B2u(pipi*) and B2g(npi*).

>There has been a number of calculations of these states using various methods. Several CASPT2 studies have given good results compared to experiments and are all more or less consistent with each other in terms of accuracy. For instance, Woywod et al. Theor Chem. Acc. 125, 521 (2010) obtained 3.93, 4.58, 4.79 and 5.54 eV for the vertical excitation energies using a triple zeta basis set.

>I performed MRMP2 calculations using the aug-cc-pVDZ basis set and using the D2h symmetry. I obtained 3.53, 4.13, 4.55 and 5.17 eV.
>These values are well below the CASPT2 results. Note that already the CASPT2 results tend to underestimate the experimental results.

>I then performed a XMCQDPT2 calculation ignoring symmetry and using a state averaged CASSCF wavefunction. The five states were included into averaging. And only those five state are included in the XMCQDPT2 model space. Since they are of different symmetry the CASSCF states are not mixed by the XMCQDPT2 procedure but it was just to obtain the five energies in one calculation. I obtained results in good agreement with CASPT2 results : 3.93, 4.45, 4.79 and 5.38.

>This is surprising since the second approach makes no sense and the first approach would be expected to be more accurate. Inspection of the orbitals in each case show that they keep the same character in all the calculations.

>The corresponding files are attached.

>Can anyone tell me what I am doing or thinking wrong here ?
>Any help or comment would be greatly appreciated.

>Best regards
>Matthieu Sala

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