Projection operator method for geometry optimization with constraints

Da‐Hong ‐H Lu, Meishan Zhao, Donald G. Truhlar

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


A new approach is presented for performing geometry optimization for stationary points on potential energy hypersurfaces with equality constraints on the internal coordinates of a polyatomic system. The working equations are the same as for unconstrained Newton–Raphson optimization in Cartesian coordinates except that projection operators are applied to the gradient and Hessian to enforce the constraints. Two reactive systems with different kinds of constraints are treated as examples: OH + H2 → OH 3≠ → H2O + H with one constrained OH bond distance and CH3 + H2 → CH 5≠ → CH4 + H with one constrained HCH bond angle in the CH3 group or with one constrained bond distance and one simultaneously constrained bond angle. In each case we optimized all reactants and products as well as the saddle point, all subject to the constraints.

Original languageEnglish (US)
Pages (from-to)376-384
Number of pages9
JournalJournal of Computational Chemistry
Issue number3
StatePublished - Apr 1991


Dive into the research topics of 'Projection operator method for geometry optimization with constraints'. Together they form a unique fingerprint.

Cite this