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

[Tatiana Korona]

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
>