Geometry optimization

Geometry optimization is an important part of most quantum chemical calculations. This article surveys methods for optimizing equilibrium geometries, locating transition structures, and following reaction paths. The emphasis is on optimizations using quasi-Newton methods that rely on energy gradients, and the discussion includes Hessian updating, line searches, trust radius, and rational function optimization techniques. Single-ended and double-ended methods are discussed for transition state searches. Single-ended techniques include quasi-Newton, reduced gradient following and eigenvector following methods. Double-ended methods include nudged elastic band, string, and growing string methods. The discussions conclude with methods for validating transition states and following steepest descent reaction paths. (C) 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 790-809 DOI: 10.1002/wcms.34