Capturing non-local through-bond effects in molecular mechanics force fields: II. Using fractional bond orders to fit torsion parameters

Accurate small molecule force fields are crucial for predicting thermodynamic and kinetic properties of drug-like molecules in biomolecular systems. Torsion parameters, in particular, are essential for determining conformational distribution of molecules. However, they are usually fit to computationally expensive quantum chemical torsion scans and generalize poorly to different chemical environments. Torsion parameters should ideally capture local through-space non-bonded interactions such as 1-4 steric and electrostatics and non-local through-bond effects such as conjugation and hyperconjugation. Non-local through-bond effects are sensitive to remote substituents and are a contributing factor to torsion parameters poor transferability. Here we show that fractional bond orders such as the Wiberg Bond Order (WBO) are sensitive to remote substituents and correctly captures extent of conjugation and hyperconjugation. We show that the relationship between WBO and torsion barrier heights are linear and can therefore serve as a surrogate to QC torsion barriers, and to interpolate torsion force constants. Using this approach we can reduce the number of computationally expensive QC torsion scans needed while maintaining accurate torsion parameters. We demonstrate this approach to a set of substituted benzene rings.