title: Using operators to expand the block matrices forming the Hessian of a molecular potential.
abstract: We derive compact expressions of the second-order derivatives of bond length, bond angle, and proper and improper torsion angle potentials, in terms of operators represented in two orthonormal bases. Hereby, simple rules to generate the Hessian of an internal coordinate or a molecular potential can be formulated. The algorithms we provide can be implemented efficiently in high-level programming languages using vectorization. Finally, the method leads to compact expressions for a second-order expansion of an internal coordinate or a molecular potential.
authors.affiliation: Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303B, DK-2800, Kongens Lyngby, Denmark.
authors.forename: Martin
authors.initials: M
authors.lastname: Carlsen
keywords: Hessian; internal coordinates; molecular potentials; operators; second-order derivatives