Quasi-saddles of Liquids: Computational Study of a bulk Lennard-Jones system

TL;DR

This study investigates how the statistical properties of quasi-saddles in a Lennard-Jones liquid are affected by the convergence criteria of the minimisation process, finding minimal qualitative changes but sensitivity in certain eigenvalues.

Contribution

It provides a detailed analysis of the impact of minimisation convergence criteria on the characterization of inherent saddles in a Lennard-Jones liquid, highlighting the sensitivity of eigenvalues.

Findings

Statistical properties of saddles are stable across a range of error tolerances.

The lowest eigenvalue magnitude decreases as convergence criteria become stricter.

Unambiguous classification of quasi-saddles remains challenging due to sensitivity issues.

Abstract

Quasi-saddles or inherent saddles of the potential energy surface, $U$, of a liquid are defined as configurations which correspond to absolute minima of the pseudo-potential surface, $W =\wf$, as identified by a multi-dimensional minimisation procedure. The sensitivity of statistical properties of inherent saddles to the convergence criteria of the minimisation procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential with continuous zeroth, first and second derivatives at the cut-off distance. The variation in statistical properties of saddles is studied over a range of error tolerances spanning five orders of magnitude. The largest value of the tolerance corresponds to that used for the unshifted LJ liquids in a previous work (J. Chem. Phys. {\bf 115}, 8784 (2001)). Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The lowest magnitude eigenvalue, $| \omega_0^2|$, of the Hessian is, however, found to be very sensitive to the tolerance; as the tolerance is decreased, $| \omega_0^2|$ is found to show an overall decrease. This indicates that if convergence criteria are not strict, absolute or low-lying minima of $W(\br)$ will be diagnosed as having no inflexion directions. The results also show that it is not possible to set up an unambiguous numerical criterion to further classify the quasi-saddles into true saddles which contain no zero curvature, non-translational normal modes and inflexion points which have one or more zero-curvature normal mode directions.