Optimization of equilibrium geometries and transition structures

TLDR

The paper outlines a modified conjugate gradient algorithm for geometry optimization using ab initio molecular orbital methods. The algorithm evaluates analytical gradients at each energy calculation, updates the second derivative matrix with these gradients, performs a quartic polynomial one‑dimensional minimization followed by an n‑dimensional search, and controls negative eigenvalues to locate transition structures. Timing data show the algorithm efficiently optimizes equilibrium geometries and transition structures in ab initio SCF–MO calculations.

Abstract

Abstract A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initio MO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one‐dimensional minimization using a quartic polynomial is carried out, followed by an n ‐dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initio SCF – MO calculations.