The efficient optimization of molecular geometries using redundant internal coordinates

Abstract

The optimization of ab initio molecular geometries is discussed. Based on comparisons of 30 minimizations and 15 saddle-point optimizations, the most efficient combination of coordinate system, approximate and exact Hessians, and step control is determined. Use of a proposed set of extra-redundant internal coordinates is shown to reduce the number of geometry steps significantly relative to the use of redundant coordinates. Various update schemes are tested for minimum and saddle-point optimizations, including combination formulas. The complete expressions for the first and second derivatives of the Wilson B matrix are presented, thereby avoiding the need to calculate this by finite-difference methods. The presented scheme appears to be the most efficient, robust and generally applicable scheme to date.

A doubly nudged elastic band method for finding transition states

“…For example, different considerations probably apply if second derivatives can be calculated relatively quickly, as for many empirical potentials [5]. Transformation to an alternative coordinate system may also be beneficial for systems bound by strongly directional forces [6,7,8,9,10,11,12,13,14].…”

Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules

“…As well documented, [43][44][45][46] since internal coordinates are nonlinear, Eq (5) must be solved iteratively to achieve the correct displacements in Cartesian coordinates. Following the recommendations of previous studies, 9,41 the sampling of UM-N was carried out symmetrically for each mode as far as the classical turning points determined by the harmonic frequency…”

Four-Component Relativistic Calculations in Solution with the Polarizable Continuum Model of Solvation: Theory, Implementation, and Application to the Group 16 Dihydrides H2X (X = O, S, Se, Te, Po)

“…The general driver for structure optimizations in DIRAC is the same as in the nonrelativistic code DALTON 109, 110 . The structures optimized in vacuo using the numerical gradient were compared with those obtained using the analytic gradient.…”