Moving least-squares enhanced Shepard interpolation for the fast marching and string methods

被引：14

作者：

Burger, Steven K. ^{[1
]}

Liu, Yuli ^{[1
]}

Sarkar, Utpal ^{[1
]}

Ayers, Paul W. ^{[1
]}

机构：

[1] McMaster Univ, Dept Chem, Hamilton, ON L8S 4M1, Canada

来源：

JOURNAL OF CHEMICAL PHYSICS | 2009年 / 130卷 / 02期

关键词：

biochemistry; enzymes; interpolation; least squares approximations; molecular biophysics; potential energy surfaces; POTENTIAL-ENERGY SURFACES; NUDGED ELASTIC BAND; HAMILTON-JACOBI EQUATION; LOCAL INTERPOLATION; CHEMICAL-REACTIONS; TRANSITION-STATES; NO DERIVATIVES; SADDLE-POINTS; PATHS; PATHWAYS;

D O I：

10.1063/1.2996579

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

The number of the potential energy calculations required by the quadratic string method (QSM), and the fast marching method (FMM) is significantly reduced by using Shepard interpolation, with a moving least squares to fit the higher-order derivatives of the potential. The derivatives of the potential are fitted up to fifth order. With an error estimate for the interpolated values, this moving least squares enhanced Shepard interpolation scheme drastically reduces the number of potential energy calculations in FMM, often by up 80%. Fitting up through the highest order tested here (fifth order) gave the best results for all grid spacings. For QSM, using enhanced Shepard interpolation gave slightly better results than using the usual second order approximate, damped Broyden-Fletcher-Goldfarb-Shanno updated Hessian to approximate the surface. To test these methods we examined two analytic potentials, the rotational dihedral potential of alanine dipeptide and the S(N)2 reaction of methyl chloride with fluoride.

引用

页数：8

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