Optimization of equilibrium geometries and transition structures

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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.