Efficient parameterization of torsional terms for force fields

A novel method is presented for fitting force-field dihedral angles using an ensemble of structures generated from an ab initio Monte Carlo simulation. Importance sampling is used to achieve an efficient algorithm using a low level of theory to minimize the system at each step with the dihedral angles constrained, followed by dihedral fitting using the single point energies at a higher level of theory. The resulting method is an order of magnitude more efficient than the traditional method of doing a constrained scan over each dihedral independently. Also as the sampling is more uniformly distributed, the full surface is approximated to a greater accuracy. The dihedral fitting is done with a nonlinear optimization method to vary the phase as well as the force constant. The utility of the method is demonstrated by fitting dihedrals of methyl L-lactate, diisopropyl fluorophosphate, isopentenyl phosphate, a leucine dipeptide, and two inhibitors of Signal Transducer and Activator of Transcription 5. The results show that the Monte Carlo scheme is more efficient than constrained scans and is particularly effective at approximating the underlying potential energy surface when the dihedral degrees are coupled.