Interpolating moving least-squares methods for fitting potential energy surfaces:Computing high-density potential energy surface data from low-density ab initio data points

摘要

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 EVILS 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.