This paper describes a generalized synchronous transit method for locating transition state structures or first-order saddle points. The algorithm is based on the established scheme of combining the linear or quadratic synchronous transit method with conjugate gradient refinements but generalized to deal with molecular and periodic systems in a seamless manner. We apply the method to a study of the early stage atomic layer deposition (ALD) growth of ZrO2. (C) 2003 Elsevier B.V. All rights reserved.