| Summary: | We present three new methods called Full, Partial, and Internal Hessian Fitting (FHF, PHF, and IHF) for deriving force constant parameters that are used in molecular mechanics (MM) force fields to describe the bond-stretching, angle-bending, dihedral-torsion, and improper-torsion terms. The MM-calculated Hessian matrices are made as close as possible to the QM-calculated ones. The Hessian fitting processes are done analytically and thus rapidly, yielding force constant parameters as the output. We herein apply our methods to derive force constant parameters for the AMBER-type energy expression. Test calculations on several different molecules show good performance of the parameter sets produced by our methods in terms of how well they can reproduce QM-calculated frequencies. We also notice that the nonbonded interactions sometimes overwhelm the bonded ones, resulting in distorted geometries. This problem is significant when soft bonds are involved in the target molecule as in the case of secondary building units of metal-organic frameworks, where 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 term.
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