Interpolating Moving Least-squares Methods for Fitting Potential Energy Surfaces: Computing High-density Potential Energy Surface Data from Low-density Ab Initio Data Points
A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.
R. Dawes et al., "Interpolating Moving Least-squares Methods for Fitting Potential Energy Surfaces: Computing High-density Potential Energy Surface Data from Low-density Ab Initio Data Points," Journal of Chemical Physics, vol. 126, no. 18, American Institute of Physics (AIP), May 2007.
The definitive version is available at https://doi.org/10.1063/1.2730798
Keywords and Phrases
Gradient methods; Interpolation; Least squares approximations; Neural networks; Parameter estimation; Spectroscopy; Data points; Gradient evaluations; Neural network fitting; Potential energy surfaces
International Standard Serial Number (ISSN)
Article - Journal
© 2007 American Institute of Physics (AIP), All rights reserved.