Analytic second derivatives for semiempirical models based on MNDO

Abstract

An implementation of MNDO-type semiempirical methods is described, which include analytic second derivatives and interface to ONIOM hybrid models. Analytic second derivatives are much more efficient than numerical derivatives and have very low cost even for systems containing hundreds of atoms. ONIOM calculations using a combination of semiempirical and molecular mechanics methods are practical, even for second derivative calculations having hundreds of atoms in the quantum model system and thousands of atoms in the full system.

Keywords:

• AM1
• PM6
• frequencies
• analytic derivatives

Notes

Note

1. for the ab initio case when symmetry is used, then only the symmetry-unique CPHF equations need be solved and B^y is not needed for the other degrees of freedom. In this case, it is more efficient to form B^y, P^y, and G(P^y) for the symmetry-unique degrees of freedom and then use Equation 11 to assemble the second derivatives.