Permutationally invariant potential energy surfaces in high dimensionality

We review recent progress in developing potential energy and dipole moment surfaces for polyatomic systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of thousands of scattered ab initio energies using a special, compact fitting basis of permutationally invari...

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Bibliographic Details
Published inInternational reviews in physical chemistry Vol. 28; no. 4; pp. 577 - 606
Main Authors Braams, Bastiaan J., Bowman, Joel M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.10.2009
Subjects
CHO
invariant fitting
potential energy surfaces
water dimer
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Summary:We review recent progress in developing potential energy and dipole moment surfaces for polyatomic systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of thousands of scattered ab initio energies using a special, compact fitting basis of permutationally invariant polynomials in Morse-type variables of all the internuclear distances. The computational mathematics underlying this approach is reviewed first, followed by a review of the practical approaches used to obtain the data for the fits. A straightforward symmetrization approach is also given, mainly for pedagogical purposes. The methods are illustrated for potential energy surfaces for , (H 2 O) 2 and CH 3 CHO. The relationship of this approach to other approaches is also briefly reviewed.
ISSN:0144-235X
1366-591X
DOI:10.1080/01442350903234923