title: Gradient Projection Method for Constraint Optimization and Relaxed Energy Paths on Conical Intersection Spaces and Potential Energy Surfaces.
abstract: A gradient projection algorithm is presented that permits the application of several constraints during geometry optimization on electronic potential energy surfaces (PES) or conical intersection (CI) seams. The algorithm generalizes the idea recently published in this journal (Sicilia et al. J. Chem. Theory Comput. 2008, 4, 257) for the optimization of conical intersection geometries. Singular value decomposition is used to transform all constraints, including those related to maintaining the CI, to a new set of constraints with orthogonal gradients. The constraints need not be satisfied at the initial geometry but will be upon convergence. A procedure is presented that determines relaxed energy paths (REP) connecting two reference structures on a potential energy surface, or the conical intersection space, without the need to assign an internal coordinate as the reaction coordinate. Examples are presented of optimizations of minimum energy structures and REPs in the CI space and REPs on a single electronic PES.
authors.affiliation: Institut für Physikalische and Theoretische Chemie, Universität Regensburg, D 93040 Regensburg, Germany.
authors.forename: Bernhard
authors.initials: B
authors.lastname: Dick