Nereis. Interdisciplinary Ibero-American Journal of Methods, Modelling and Simulation.

Buscador

Interpolación de funciones en el marco del formalismo de los espacios de Hilbert con núcleo reproductor y ejemplos de aplicación

Abstract

The interpolation methods in the framework of the reproducing kernel Hilbert space (RKHS) formalism have been successfully applied to obtain the potential energy surface (PES) of small molecular systems over the last decade. The interpolation is usually based on high level ab initio calculations from solving the many-body Schrödinger equation. The right representation of the PES is a central issue when carrying out classical molecular dynamics simulations of molecular systems. Specifically, the interpolation methods in the framework of the RKHS show several advantages over other methods, for instance, they are generic and parameter-free. In this work, a kernel based on the Gauss hypergeometric function is used. One advantage of this type of kernel is that the asymptotic behavior of the PES goes to zero when the separation between any two atoms is taken to infinity. Examples of PES interpolations in the context of molecular systems and other contexts are described.

Keywords: interpolation, kernels, reproducing kernel Hilbert space

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