A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO 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 initioSCF–MO calculations.

Optimization of equilibrium geometries and transition structures

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach. © 1996 by John Wiley & Sons, Inc.

Using redundant internal coordinates to optimize equilibrium geometries and transition states

A linear synchronous transit or quadratic synchronous transit approach is used to get closer to the quadratic region of the transition state and then quasi-newton or eigenvector following methods are used to complete the optimization. With an empirical estimate of the hessian, these methods converge efficiently for a variety of transition states from a range of starting structures.

Combining Synchronous Transit and Quasi-Newton Methods to Find Transition States

An algorithm for locating transition states designed for use in the ab initio program package GAUSSIAN 82 is presented. It is capable of locating transition states even if started in the wrong region of the energy surface, and, by incorporating the ideas on hessian mode following due to Cerjan and Miller, can locate transition states for alternative rearrangement/dissociation reactions from the same initial starting point. It can also be used to locate minima.

An algorithm for the location of transition states

https://isiarticles.com/bundles/Article/pre/pdf/22294.pdf

Stephen Bell

Papers

Far IR Spectrum, Barrier to Internal Rotation, r0 Structure, and ab initio Calculations for Acetyl Cyanide.