Subject: How good are non variational methods ?

From: Patrick Bultinck <[email-masked]>
Date: Fri, 22 Nov 2002 14:11:52 +0100

Dear all,

I am curious in your ideas about what good non variational methods are in
quantum chemistry ? In variational techniques (e.g. Hartree-Fock, CI) on
minimizes the variational integral and through the variation theorem you
know you will almost stay just above or equal to the true solution (at
least for the energy). With e.g. perturbation theory, you may end up
anywhere, that is: above, below or on the dot of the true solution.

What is your opinion on techniques such as Coupled Cluster (iterative but
in most formulations not variational, although I naively think this must be
possible), or MP2, MP4, ... ? We often see "highly accurate" results of say
CCSD(T) (using perturbation theory on top of the iterative scheme), but how
to put this in perspective knowing that there is no variational theorem
applicable ?

Has this ever been discussed throughly in some reference ? What are the
experiences of the CCL members ?

Thanks for your ideas/time,

Patrick Bultinck
Quantum Chemistry Group
Ghent University
Belgium

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From: uccatvm <[email-masked]>
Date: Fri, 22 Nov 2002 14:36:01 +0000 (GMT)

Hi Patrick,

> experiences of the CCL members ?

Although it may be useful to know the sign of the error in the computed energy
(as in the case of variational methods), what is more important is that the error
is small. One possible problem of (less than full) CI methods, for example, is 
their lack of size-extensivity, which is a problem when calculating interaction 
energies.  CCSD(T) and MPn are size-extensive methods.

There of course have been many studies comparing the accuracy of the different
methods. A good starting reference is:
"A road map for the calculation of molecular binding energies," TH Dunning, Jr.
J Chem Phys A 104, 9063 (2000), and the many "Benchmark calculations" papers
published by Dunning and co-workers.

There have been many recent publications discussing the (non-)convergence
of the MPn perturbation series, see for example (the list is far from complete);
- Olsen J, Christiansen O, Koch H, et al.  J Chem Phys 105, 5082-5090 (1996) 
- T.H. Dunning, Jr. and KA Peterson, J Chem Phys 108, 4761-4771 (1998)
- Halkier, H. Larsen, J. Olsen, P. Jorgensen J. Chem. Phys. 110, 7127 (1999)
- M.L. Leiniger, W.D. Allen, H.F. Schaefer III, C.D. Sherrill, J. Chem. Phys. 
  112, 9213 (2000)

Hope his helps,

Tanja
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   Tanja van Mourik                                                
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   Chemistry Department 
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