Subject: CCL:CC versus CI

From: Steven Creve <[email-masked]>
Date: Thu, 29 Oct 1998 12:52:36 +0100 (NFT)

Hi all again!

Another theoretical point which bothers me:

Suppose we perform a CI calculation with all determinants that are
normally generated by CCSD (exp(T1+T2)). Would the obtained result be
worse or better than the CCSD value?

Any comments are welcome?

Steven

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Steven Creve                       [email-masked]
Labo Quantumchemie
Celestijnenlaan 200F
3001-HEVERLEE                      tel: (32) (16) 32 73 93
BELGIUM                            fax: (32) (16) 32 79 92

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From: MJR <[email-masked]>
Date: Thu, 29 Oct 1998 14:31:42 -0800

> Any comments are welcome?

    You ask interesting questions, Steven, and this one I think I can
answer.

    Both CISD and CCSD represent the correlated wavefunction |corr> as a
sum over configuration state functions.  The difference between them is
that CI exploits the variational prinicple to minimise the energy, thus 

  CI:     <E> = <corr|H|corr>

ensuring a strict upper bound to the total energy, while CC solves the
Schroedinger equation within a subspace.  As a consequence, the computed 

  CC:     H|corr> = E|corr>

energy may be greater than or less than the true energy.  Use of the
cluster operator to parameterise |corr> results in the implicit
estimation of contributions from higher excitations ( quadruples, etc )
so the energy in practice tends to be quite accurate.  

    A principle benefit of CC over CI is that it is size consistent: 
the energy of dimer supermolecule is twice the energy of the constituent
monomer, a conventient property when computing binding energies and
whenever large numbers of electrons are being correlated.

    As always, "which method is better" depends upon the problem you are
studying and the important features of the solution required.  Sometimes
the variational principle is critical, sometimes size consistency.

					Mark

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