An approximate Hessian for molecular geometry optimization

• Published in: Chemical physics letters 1986, Vol.131 (4), p.359-366
• Main Authors: Head, John D., Zerner, Michael C.
• Format: Article
• Language: English
• Subjects: Atomic and molecular physics; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); Electronic structure of atoms, molecules and their ions: theory; Exact sciences and technology; Physics
• ISSN: 0009-2614; 1873-4448
• DOI: 10.1016/0009-2614(86)87166-4

We develop an expression for an approximate Hessian matrix, or matrix of the second derivatives of the SCF energy with respect to nuclear coordinates that can be used to search the potential-energy surface of a molecule for minima or saddle points. It is formed as a first-order approximation to the coupled perturbed Hartree-Fock theory, and requires much less computer time than does the evaluation of the full Hessian. Its use in quasi-Newton methods that search for molecular geometry requires far fewer steps than other update procedures.