# [molpro-user] Computation of the dipole moment with CCSD(T)

Peter Knowles KnowlesPJ at Cardiff.ac.uk
Fri Sep 8 22:30:02 BST 2006

I guess you need to read the literature to understand that ccsd and
ccsd(t) do not satisfy the Hellmann-Feynman theorem in the usual sense,
and that for methods in this class the energy derivative is more
accurate than an expectation-value formulation.

Section 42.1 of the Molpro manual states that analytic energy
derivatives are available for qcisd and qcisd(t). Unfortunately CCSD and
CCSD(T) are not yet coded, so if you want the dipole with these methods
you have to use finite differences.  testjobs/co_qcidip.test gives an
example.

Peter

Lorenzo Lodi wrote:
> I am computing the dipole moment of water with various methods and I'd
> now like to use the CCSD(T) method.
>
> At the CCSD level I can compute the dipole with
> ---
> RHF
> CCSD ; CORE, 0,0,0,0
> EXPEC, DM
> ---
> and I understand that the value given as "orbitally relaxed CCSD dipole
> moment" is the same value as the expectation value of \mu on the CCSD
> wavefunction. (Incidentally, the GEXPEC directive does not work for me,
> is this behaviour normal?)
>
> Now, for the CCSD(T) dipole.
> Looking at some old posts it was suggested to calculate it using the DIP
> keyword with a small field and then taking the derivative of the energy
> at zero field. Now, my objection is as follows: the Hellmann-Feynmann
> theorem, on which this finite-field approach is based, holds for
> 1) the exact wavefunction
> and
> 2) a wavefunction which is variationally optimised in all its parameters
> The coupled cluster method is, of course, non-variational so I don't
> expect the finite-field approach to work well in this case.
> In fact, I verified this comparing the CCSD dipole obtained by
> finite-field and as given by molpro (equilibrium geometry, cc-pV6Z
> basis) and I got a difference of ~0.003 a.u., which is too large for the
> level of accuracy I am looking for.
>
> My conclusion would be that there is no accurate way to compute the
> dipole with the CCSD(T) method (in fact, as there is no CCSD(T)
> wavefunction, this may not be anything new...).
>
> Could anyone confirm these comments and/or give any suggestion about how
> to proceed in this direction?
>
> Thank you.
>
> Lorenzo Lodi
>

--
Prof. Peter J. Knowles
School of Chemistry, Cardiff University, Main Building, Park Place,
Cardiff CF10 3AT, UK
Telephone: +44 29208 79182 Fax: +44 2920874030
Email KnowlesPJ at Cardiff.ac.uk  WWW
http://www.cardiff.ac.uk/chemy/staff/knowles.html