Subject: Re: CCL:CC versus CI

From: David Heisterberg <[email-masked]>
Date: Fri, 30 Oct 1998 09:01:46 -0500 (EST)

>Truncated CCSD does *not* generate all excitations. By making use of the
>hausdorff comutator expansion, one can show that the exp-series terminates
>exactly after a certain number of orders.

I think we're talking about two different things.  If |F> is the reference
state, I'm thinking that exp (T1+T2) |F> implicitly generates all possible
excitations.  But exp (-T1-T2) H exp (T1+T2) terminates so only a subset of
excited configuration coefficients are independently determined.  In the
energy expression though, aren't the effects of the higher-excited configurations
included, at least implicitly, with coefficients that are functions of those
that were determined by the CC equations?

Dave Heisterberg

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From: MJR <[email-masked]>
Date: Fri, 30 Oct 1998 17:01:36 -0800

> that were determined by the CC equations?

    It looks like we are getting lost in the terminological thicket.
CCSD generates only single and double excitations, which are fed into
the calculation via the cluster operator whose expansion contains terms
like T1T1T2T1T2; throwing the anticommutation machinery of second
quantisation allows the energy expression to be rewritten containing
only T1 and T2, so that the contributions from the higher excitations
are approximately included.  This works in practice because, for the
kind of systems chemists are interested in, Cijkl is to a good
approximation a linear combination of Cij * Ckl and the other symbols
generated by permuting the labels.

    Szabo and Ostlund would be the reference to look in for this stuff,
in all it's gory detail.

					Mark

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