Efficient gradient and Hessian calculations for numerical optimization algorithms applied to atomistic molecular simulations

Computer simulations of chemical systems can be used to reliably predict physical properties. Accurate molecular models, which are indispensable, are mathematically described by force fields, which have to be parameterized. Recently, an automated gradient-based parametrization procedure was published by the authors based on the minimization of a loss function between simulated and experimental physical properties. The applicability of the utilized algorithms is not trivial at all because of two reasons: First, simulation data is affected by statistical noise and second, the molecular simulations required for the loss function evaluations (involving finite differences approximations of gradients and Hessians) are extremely time-consuming. In this work, a more efficient approach to compute gradients and Hessians is presented. The method developed here is based on directional instead of partial derivatives. It is shown that up to 75% of the simulations can be avoided using this method.