Partial hessian fitting for determining force constant parameters in molecular mechanics.

We present a new protocol for deriving force constant parameters that are used in molecular mechanics (MM) force fields to describe the bond-stretching, angle-bending, and dihedral terms. A 3 × 3 partial matrix is chosen from the MM Hessian matrix in Cartesian coordinates according to a simple rule and made as close as possible to the corresponding partial Hessian matrix computed using quantum mechanics (QM). This partial Hessian fitting (PHF) is done analytically and thus rapidly in a least-squares sense, yielding force constant parameters as the output. We herein apply this approach to derive force constant parameters for the AMBER-type energy expression. Test calculations on several different molecules show good performance of the PHF parameter sets in terms of how well they can reproduce QM-calculated frequencies. When soft bonds are involved in the target molecule as in the case of secondary building units of metal-organic frameworks, the MM-optimized geometry sometimes deviates significantly from the QM-optimized one. We show that this problem is rectified effectively by use of a simple procedure called Katachi that modifies the equilibrium bond distances and angles in bond-stretching and angle-bending terms.