[molpro-user] Computation of the dipole moment with CCSD(T)
Tatiana Korona
tania at tiger.chem.uw.edu.pl
Thu Sep 14 15:01:24 BST 2006
Hi,
As I wrote in my e-mail from 9.9.06 the CCSD properties in MOLPRO are ED
in your notation. ED can be made over CCSD amplitudes only (then we have
the so-called nonrelaxed property, nicknamed as "expectation value" in the
output), or over CCSD amplitudes and orbital coefficients, then we get the
so-called relaxed properties, which can be treated as true ED (since we
made derivatives over all nonvariational parameters). So, if you write
ccsd
expec,relax
you get the following:
Dipole moment expectation values: 0.00000000 0.00000000 (ED over
CCSD amplitudes only)
0.09020035
Orbital relaxation contribution: 0.00000000 0.00000000
-0.03276110
!CCSD dipole moments: 0.00000000 0.00000000
0.05743925 (ED over CCSD amplitudes and orbital coefficients)
As I wrote, the relaxation contribution for CCSD can be now calculated in
molpro for all-electron case only.
If you write
ccsd
expec
you get the following:
Dipole moment SCF : 0.00000000 0.00000000
-0.09812123
Dipole moment - correlation part: 0.00000000 0.00000000
0.18832158
!CCSD_nonrel dipole moment : 0.00000000 0.00000000
0.09020035 (ED over CCSD amplitudes only)
I hope it is clear now.
If you are not satisfied with relaxation only for all-electron case, then
the QCISD properties are available from Rauhut, see the manual.
Best wishes,
Tatiana
Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/index.html
Quantum Chemistry Laboratory
University of Warsaw
Pasteura 1, PL-02-093 Warsaw, POLAND
`The man who makes no mistakes does not usually make anything.'
Edward John Phelps (1822-1900)
On Thu, 14 Sep 2006, Lorenzo Lodi wrote:
> Hello,
> I inquired some days ago about the difference between dipole moments
> calculated as expectation values (XP) or as energy derivatives (ED). As I
> think this may be of interest for other people, I'd like to briefly summarize
> my conclusions, at the same time ask a couple of questions.
> There is a some literature on the subject, starting from the paper (kindly
> pointed out to me by P. Knowles)
>
> -- G.H.F. Diercksen, B.O. Roos, A.J. Sadlej, Legitimate Calculation of
> First-Order Molecular Properties in the Case of Limited CI Functions. Dipole
> Moments., Chem. Phys. 59, 29 (1981)
>
> A couple of more recent papers discussing this issue in more details are:
>
> -- J. Lipinski, On the consequences of the violation of the Hellmann-Feynman
> theorem in calculations of electric properties of molecules, Chem. Phys.
> Lett. 363, 313 (2002)
> -- M. Ernzerhof, C.M. Marian, S.D. Peyerimhoff, On the calculation of
> first-order properties: expectation value versus energy derivative approach,
> Int. J. Quant. Chem. 43, 659 (1992)
>
> For exact wavefunctions the dipole moment can defined either as the
> expectation value of \mu or as the energy derivative E'(\lambda) for the
> perturbed hamiltonian H=H0 + \lambda \mu
> The two way of calculation lead exactly to the same numerical value.
> In the practical case of approximate wavefunctions, the two methods don't
> necessarily give the same result. They do for some classes of approximate
> wavefunctions (Hartree-Fock, CASSCF, Full-CI) but not for many others
> (truncated CI, perturbation theory, coupled cluster).
> In the cases where they differ there are some some reasons to favour the ED
> method (this is all the more true for second-order properties like electron
> polarizability, where the XP method may lead to wrong symmetries between the
> components) but, at the same time, there is no garantee that either the XP or
> the ED value is closer to the exact value.
> Ideally the most sensible strategy I guess would be to converge the
> wavefunction to a level where the difference between XP and ED doesn't
> matter, but this may not be achievable in practice.
>
> I quote some results to give an idea of the level of disagreement. I did some
> sample computations on water (r1=r2=0.95782 ang, theta=104.485) with a large
> aug-cc-pCV6Z basis set and looked at the differences XP-FF for the RHF, CCSD,
> CASSCF, MRCI, ACPF, AQCC and RSPT2 methods (CAS::OCC,5,2,2,0; CLOSED,
> 1,0,0,0; CORE,0,0,0,0 ; \lambda=+/- 0.00075).
> I assumed that the value given by Molpro is calculated via XP (can anyone
> confirm this? It's quite important for me to know exactly how Molpro computes
> dipoles with the various methods)
> Here are the differences \mu(XP) - \mu(FF) (in a.u.):
> RHF 0.00002
> CCSD 0.00001
> MCSCF 0.00000
> MRCI 0.00521
> ACPF 0.00249
> AQCC 0.00320
> RSPT2 0.00204
>
> So all the multi-reference methods show a variance at the level of ~3e-3 a.u.
> with this CAS.
> Any comment on the whole matter would be warmly welcomed!
>
> Lorenzo Lodi
>
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