Numerical search of discontinuities in self-consistent potential energy surfaces

TL;DR

This paper investigates the discontinuities in self-consistent potential energy surfaces, their causes, consequences, and proposes numerical methods to detect, analyze, and transform them into continuous surfaces for more reliable dynamical calculations.

Contribution

It introduces a numerical approach to identify and address discontinuities in potential energy surfaces, improving their reliability for physical applications.

Findings

Discontinuities can hide true energy barriers.

Discontinuities are not due to convergence issues.

Proposed methods can detect and mitigate these discontinuities.

Abstract

Potential energy surfaces calculated with self-consistent mean-field methods are a very powerful tool, since their solutions are, in theory, global minima of the non-constrained subspace. However, this minimization leads to an incertitude concerning the saddle points, that can sometimes be no more saddle points in bigger constrained subspaces (fake saddle points), or can be missing on a trajectory (it missing saddle points). These phenomena are the consequences of discontinuities of the self-consistent potential energy surfaces (SPES). These discontinuities may have important consequences, since they can for example hide the real height of an energy barrier, and avoid any use of a SPES for further dynamical calculations, barrier penetrability estimations, or trajectory predictions. Discontinuities are not related to the quality of the production of a SPES, since even a perfectly converged SPES with an ideally fine mesh can be discontinuous. In this paper we explain what are the discontinuities, their consequences, and their origins. We then propose a numerical method to detect and identify discontinuities on a given SPES, and finally we discuss what are the best ways to transform a discontinuous SPES into a continuous one.