On the construction of hybrid potential energy functions for the treatment of local anharmonicity in molecular vibrations†

Abstract

This paper reports a process by which a local, accurate, and intrinsically anharmonic potential function may be joined with a larger harmonic oscillator representation of the remainder of a molecule to build a hybrid potential energy function. Such functions find use in chemical dynamics in which there is local anharmonic bond breaking and forming, but the remainder of the molecular system behaves essentially as a set of harmonic oscillators. In constructing such a potential, for malonaldehyde as an example, it is assumed that the harmonic-limit potential can be found for the system using a given data set of the Cartesian forces and force constants derived with the use of a computational quantum chemistry program. The Pulay transformation is used to establish a set of internal coordinate forces and force constants consistent with the local model potential function. The success (i.e. faithfulness) of the construction of the hybrid potential strongly depends on the choice of internal coordinates. The Pulay transformation together with the vibrational projection analysis of Grafton and Wheeler allows one to see the strengths or weaknesses of particular choices of internal coordinates. †Approved for Public Release. Distribution Unlimited. Dedicated to Péter Pulay on the occasion of the celebration of his scientific achievements: Budapest, 24 May–3 June 2007.