The Effectiveness of Newton's Method for ImprovingAb InitioForce Fields with Applications to CO2and H2CO

Abstract

Ab initioforce field parameters are refined using modifications to Newton's method in which a figure of merit function is approximated as a Taylor Series truncated at second order. We investigate two versions of Newton's method: the Discrete Newton method where the Hessian is approximated by finite differences and the Gauss–Newton method where the Hessian is approximated as the product of first derivatives. The applicability of both rests on the capability of currentab initiomethods to calculate quartic force fields that accurately reproduce experimental observables such as band centers and inertial constants. As examples, we calculate refined potential energy surfaces for CO2and H2CO. We show that an algorithm depending solely on Newton's methods requires only a small number of iterations. Additionally, Newton-based methods provide a great deal of information about the sensitivity of the force field parameters to the observables being fit. We also demonstrate that the less computationally demanding Gauss–Newton method gives results similar to the less approximate Discrete Newton method.