Subject: CCL:cation calcs

From: [email-masked] (Thomas Bally)
Date: Mon, 3 Jul 1995 17:55:39 +0100

John Pollard wrote:

>I was wondering what people thought about the most viable molecular orbital
>approach to dealing with finding optimized geometries for +1 cations of
>organic molecules.  I have been just using UHF theory.  Are there better
>theories for dealing with these species?

  We have been doing calculations on organic radical cations (and I think
  this must be what you are referring to by "+1 cations") for several years
  and have struggled endlessly with the UHF vs. ROHF problem one the one
  hand and with methods to account for dynamic correlation (CISD, MP2 etc.)
  on the other hand.

  In a nutshell, my present recommendations are the following:

  1) If the <S**2> value of your UHF wavefunction does not deviate too
     much from the correct value of 0.75 for a radical cation (i.e. is
     not higher than, say, 0.8), your UHF geometry is probably alright
     as far as the SCF level goes and you can use UMP2 without any problem
     to include dynamic correlation. However, watch out if you compare
     different isomers (or, generally, different points on a given poten-
     tial energy surface, such as minima and saddle points) because <S**2>
     may vary considerably and thus introduce biases or lead to complete
     nonsense in UMP2.

  2) If your UHF wavefunction is badly contaminated (<S**2> greater than
     0.85), then your UHF *geometry* may still be quite alright, but you
     must be sceptical with regard to (relative) energies. In any event
     UMP2 becomes very questionable. Generally, you may be on safer ground
     if you use ROHF in this case, although this has its own problems, such
     as exclusion of spin polarization effects (which we sometimes find
     to be important even in geometry optimizations) and occasional artifi-
     cial symmetry breaking. Unfortunately, there is no *efficient* ROMP2
     gradient code around so that ROMP2 geometry optimizations are a bit of
     a pain at this point and Hessians are nearly impossible to get.

 2a) An added remark for UMP2/ROMP2: Whenever you use such perturbation
     type treatments, you must be keenly aware that they can only work
     successfully if your zero-order (SCF) wavefunction represents a
     reasonable approximation to the correlated one. We have encountered
     several cases of radical cations where this was *not* the case and
     MP2-type treatments produced complete nonsense because, for example,
     a single determinant (=configuration) did not serve as a reasonable
     description of the state under question. How to become aware and
     handle such problems would require an additional set of recommenda-
     tions.

  3) If you want to stay on the SCF level, CASSCF may be a good alterna-
     tive, because, while it excludes spin contamination (<S**2> is always
     0.75), it still accounts for spin polarization (how much depends on
     the size of your active space) and has the added benefit of showing
     you whether a single-determinant description is adequate (see 2a!).
     Gradients and even second derivatives are now available in several
     programs (Gaussian, Gamess) and the cost is not more than MP2 unless
     your active space is very big. However, when comparing different points
     on a surface you must be very careful in the choice of your active
     space or you run into discontinuities  and artefacts. If you have access
     to Molcas, you can even do MP2(single point) calculations on your CASSCF
     wavefunction.

  4) If the size of your molecule allows this and you have a good vector
     computer at your disposition, you may want to take advantage of the
     fact that QCISD gradients are available in Gaussian. We have done
     geometry optimizations on several C4 and C5 species by QCISD and it
     worked fine. Hessians are, however, usually unaffordable. At the
     QCISD (or CCSD) level of calculations, it no longer really matters
     whether you start out with an ROHF or a UHF wavefunction (the pertur-
     bation treatment corrects for the errors inherent in both) and thus
     you somehow "transcend" the ROHF/UHF problem and you have a very effi-
     cient method for accounting for dynamic correlation.

  5) In our recent (and, admittedly, at this point limited) experience,
     Densitiy Functional methods, in particular the Becke3-LYP variety
     as implemented in Gaussian, gives geometries in very close agreement
     with those found at the QCISD level. Relative energies are another
     matter, but as far as geometries go, DFT may be the panacea we are
     all looking for. UHF-DFT wavefunctions are usually not very badly
     contaminated, but they do take spin polarization into account (which
     is sometimes important in shaping potential energy surfaces). On the
     other hand they are relatively inexpensive unless you use very fine
     grids (such as it is unfortunately default in G94) and appear to account
     quite successfully for dynamic correlation. So far we have not detected
     any case of a bad failure of Becke3-LYP, but do not take this as a
     guarantee!

  I think this is all I can say in this kind of space. I wish you good luck!

    thomas

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From: [email-masked] (Richard Wong)
Date: Tue, 4 Jul 1995 21:38:58 +0900

>theories for dealing with these species?
There is a recent article (J. Phys. Chem. 1995, Vol 99, p8582-8588) which
reported the performance of a variety theoretical procedures, UHF, UMP2, 
PMP2, RMP2, UB-LYP, UQCISD and UQCISD(T), for studying open-shell systems. 
Although the paper is focused on radical addition reactions, the results 
should be applicable to general spin contaminiation problem of open-shell 
systems (radicals and radical cations).

                                                            Cheers! Richard

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