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

Abstract

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,more » 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« less

Authors:
; ; ; ; ; ; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
915032
Report Number(s):
ANL/CHM/JA-59873
Journal ID: ISSN 0021-9606; JCPSA6; TRN: US200817%%70
DOE Contract Number:  
DE-AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
J. Chem. Phys.
Additional Journal Information:
Journal Volume: 126; Journal Issue: May 11, 2007; Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
ENGLISH
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97; INTERPOLATION; NEURAL NETWORKS; POTENTIAL ENERGY; SURFACES; LEAST SQUARE FIT; HYDROCYANIC ACID; HYDROGEN PEROXIDE

Citation Formats

Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, and Oklahoma State Univ. Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.. United States: N. p., 2007. Web. doi:10.1063/1.2730798.
Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, & Oklahoma State Univ. Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.. United States. doi:10.1063/1.2730798.
Dawes, R., Thompson, D. L., Guo, Y., Wagner, A. F., Minkoff, M., Chemistry, Univ. of Missouri-Columbia, and Oklahoma State Univ. Fri . "Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.". United States. doi:10.1063/1.2730798.
@article{osti_915032,
title = {Interpolating moving least-squares methods for fitting potential energy surfaces : computing high-density potential energy surface data from low-density ab initio data points.},
author = {Dawes, R. and Thompson, D. L. and Guo, Y. and Wagner, A. F. and Minkoff, M. and Chemistry and Univ. of Missouri-Columbia and Oklahoma State Univ.},
abstractNote = {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},
doi = {10.1063/1.2730798},
journal = {J. Chem. Phys.},
issn = {0021-9606},
number = May 11, 2007,
volume = 126,
place = {United States},
year = {2007},
month = {5}
}