Interpolating moving least squares methods for fitting potential energy surfaces : detailed analysis of one dimensional applications.
We present the basic formal and numerical aspects of higher degree interpolated moving least-squares (IMLS) methods. For simplicity, applications of these methods are restricted to two one-dimensional (1D) test cases: a Morse oscillator and a 1D slice of the HN{sub 2}{yields}H+N{sub 2} potential energy surface. For these two test cases, we systematically examine the effect of parameters in the weight function (intrinsic to IMLS methods), the degree of the IMLS fit, and the number and placement of potential energy points. From this systematic study, we discover compact and accurate representations of potentials and their derivatives for first-degree and higher-degree (up to nine degree) IMLS fits. We show how the number of ab initio points needed to achieve a given accuracy declines with the degree of the IMLS. We outline automatic procedures for ab initio point selection that can optimize this decline.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- SC
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 961425
- Report Number(s):
- ANL/CHM/JA-47653
- Journal Information:
- J. Chem. Phys., Journal Name: J. Chem. Phys. Journal Issue: 19 ; Nov. 15, 2003 Vol. 119; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- ENGLISH
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