Visualization and Minima Finding of Multidimensional Hypersurface

Abstract

Analysis of multidimensional function properties is required for industrial applications. The solution of its problems is a challenge in economics, sociology, chemistry, biology, biochemistry, and other sciences. For example, the study of the potential energy surface (PES) of a free molecule is of fundamental importance in structural chemistry because it is necessary to determine the stable conformations of a molecule and the ways of interconversion between them. However, if the PES is a function of more than three rotational coordinates, the costs of its quantum-chemical calculation rapidly increases and the problem of its graphical visualization can be hardly solved for a large number of variables. This work describes how a specially developed multidimensional interpolation procedure can contribute to solve these problems. To visualize a five dimensional (5D) hypersurface, the authors applied a special coordinate system.