Subject: CAS FREQS, SUMMARY

From: "E. Lewars" <[email-masked]>
Date: Wed, 26 Jun 1996 11:53:25 -0400 (EDT)

1996 June 26

Hello,  Here is a summary of the replies I got to my question on CAS freqs
(Are CAS freqs better than HF?  Better than MP2? What is the correction factor?)

(1)  From Hans-Juergen Aagard Jensen,  [email-masked]
        CASSCF freqs should be better than HF. Comparison with MP2 depends on
        how good the MP2 wavefunction is.
        I don't know of any accepted correction factor. Anyway, you can calc.
        different CASSCF wavefunctions for the same molecule (different
        active spaces).
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(2)  Michael Robb,  [email-masked]
        CASSCF should be used when HF fails to provide a correct zeroth-order
        description. It should *not* be used to describe dynamic correlation.
        Thus, in my view:
        1) Better than HF: almost certainly because you will use this method
        when HF is inapplicable (e.g. an excited state).
        2) Better than MP2: yes, if MP2 is being used incorrectly to recover
        non-dynamic correlation effects.
        3) Better than MP2: no, if the CASSCF wavefunction is "incorrectly" in
        an attmpt to recover part of the dynamic correlation.

        Thus when used correctly CASSCF should provide about the same accuracy
        as HF freqs. However, to my knowledge there are not many tests of this.
        You might look at our recent paper on CASSCF freqs:
        A Direct Derivative MC-SCF Procedure
        N. Yamamoto, T. Vreven, M. A. Robb, M. J. Frisch and H. B. Schlegel,
        Chem. Phys. Lett. _250_, 373-378 (1996).
-------------------------
(3)   Hans-Ulrich Suter,  [email-masked]
        The MCSCF calc must be at least as good as the HF, since the HF
        solution is part of the variational solution. Thus the scaling factor
        will be between the HF factor and 1.0, depending on the quality of the
        MCSCF space, and this depends on the quality of the chemist (and the
        size of the system).
        See J. Phys. Chem. _99_, 1275 (1995); this used a crude active space
        so the scaling was close to the HF one.
        The advantage of MCSCH is that it works where MP2 goes nuts, e.g.
        ozone (see Roos, Theo. Chim. Acta _86_, 467 (1993)).
        For MCSCF and IR, look up papers by Pulay, Schmidt, Dupuis, Werner,
        Shepard and Lischka.
        DFT is faster, sometimes better, and always easier.
------------
(4)  Ole Swang  [email-masked]
        I have no conclusive answer, only some loose thoughts:
        The CASSCF method is designed to deal with near-degenerate systems
        (some like the expression "static correlation"). When used for systems
        that are adequately described by HF, CASSCF may give worse results
        as it will describe dynamical correlation (the stuff you use MP for)
        in a biased way.
        I would guess that for near-degenerate systems, a CASSCF with a
        carefully-chosen active space should give roughly comparable results
        to what HF gives for systems that are not near-degenerate.
        Good luck.
============================

E. Lewars   Chemistry Dept. Trent University Peterborough Ontario
            CANADA K9J 7B8    [email-masked]
====