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Use of the virial theorem in modeling the potential energy surfaces for triatomic collinear reactions
Author(s) -
Nalewajski Roman F.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560180851
Subject(s) - virial theorem , triatomic molecule , scaling , potential energy , maxima and minima , potential energy surface , kinetic energy , virial coefficient , physics , curvature , chemistry , atomic physics , atom (system on chip) , mathematical physics , quantum mechanics , thermodynamics , mathematical analysis , geometry , mathematics , ab initio , molecule , computer science , embedded system , galaxy
The new model potential energy surface for triatomic collinear reactions, W T ( R ), is presented. The surface is generated via the integral virial theorem from the “normalized” electronic kinetic energy surface, T M ( R ), satisfying along each uniform scaling path the condition (A): S 0∞ [ T M ( S R )— T (∞)] ds = V nn ( R ); V nn is the nuclear repulsion energy, s is a scale factor, and ∞ corresponds to the separated atoms limit. The T M ( R ) surface is approximated by the Morse function rotating around the united atom axis. For a given R s = s R , the corresponding W T ( R s ) cut has the form of the modified Morse function: W T ( R s ) = ( a /2 c R s ){exp[‐2 c ( R s — b )]‐4exp[‐ c ( R s — b )]}, parameters of which can be determined from the condition (A) and the coordinates and energy of the corresponding point on the zero‐virial path (ZVP, locus of minima along the uniform scaling directions). Illustrative examples of the T M ( R ) and W T ( R ) surfaces, generated from the BEBO ZVP for the symmetrical (H—H + H → H + H—H) and unsymmetrical (F—H + H → F + H—H) reactions are presented. These preliminary results suggest that the present model offers an efficient way to use the virial theorem in an a priori determining the valleys curvature variations during reaction.