Using Operators to Expand the Block Matrices Forming the Hessian of a Molecular Potential

Martin Carlsen

Research output: Contribution to journalJournal articleResearchpeer-review

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. © 2014 Wiley Periodicals, Inc.
Original languageEnglish
JournalJournal of Computational Chemistry
Volume35
Issue number15
Pages (from-to)1149-1158
ISSN0192-8651
DOIs
Publication statusPublished - 2014

Keywords

  • second‐order derivatives
  • Hessian
  • internal coordinates
  • operators
  • molecular potentials

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