Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom

Zhenghong Zhang, Pawel M. Kozlowski, Ludwik Adamowicz

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the helium atom. The major problem of this application, as well as in other applications of the explicitly correlated Gaussian functions to compute electronic energies of atoms and molecules, is the optimization of the nonlinear parameters involved in the variational wave function. An effective Newton–Raphson optimization procedure is proposed based on analytic first and second derivatives of the variational functional with respect to the Gaussian exponents. The algorithm of the method and its computational implementation is described. The application of the method to the helium atom shows that the Newton–Raphson procedure leads to a good convergence of the optimization process. © 1994 by John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)54-60
Number of pages7
JournalJournal of Computational Chemistry
Volume15
Issue number1
DOIs
StatePublished - 1994

Fingerprint

Helium
Newton-Raphson
Gaussian Function
Ground state
Ground State
Atoms
Optimization
Second derivative
Wave functions
Process Optimization
Wave Function
Exponent
Molecules
Electronics
Derivatives
Energy

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics

Cite this

Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom. / Zhang, Zhenghong; Kozlowski, Pawel M.; Adamowicz, Ludwik.

In: Journal of Computational Chemistry, Vol. 15, No. 1, 1994, p. 54-60.

Research output: Contribution to journalArticle

@article{4a30e3d666994b048f0a74c891c4c4fd,
title = "Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom",
abstract = "Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the helium atom. The major problem of this application, as well as in other applications of the explicitly correlated Gaussian functions to compute electronic energies of atoms and molecules, is the optimization of the nonlinear parameters involved in the variational wave function. An effective Newton–Raphson optimization procedure is proposed based on analytic first and second derivatives of the variational functional with respect to the Gaussian exponents. The algorithm of the method and its computational implementation is described. The application of the method to the helium atom shows that the Newton–Raphson procedure leads to a good convergence of the optimization process. {\circledC} 1994 by John Wiley & Sons, Inc.",
author = "Zhenghong Zhang and Kozlowski, {Pawel M.} and Ludwik Adamowicz",
year = "1994",
doi = "10.1002/jcc.540150107",
language = "English (US)",
volume = "15",
pages = "54--60",
journal = "Journal of Computational Chemistry",
issn = "0192-8651",
publisher = "John Wiley and Sons Inc.",
number = "1",

}

TY - JOUR

T1 - Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom

AU - Zhang, Zhenghong

AU - Kozlowski, Pawel M.

AU - Adamowicz, Ludwik

PY - 1994

Y1 - 1994

N2 - Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the helium atom. The major problem of this application, as well as in other applications of the explicitly correlated Gaussian functions to compute electronic energies of atoms and molecules, is the optimization of the nonlinear parameters involved in the variational wave function. An effective Newton–Raphson optimization procedure is proposed based on analytic first and second derivatives of the variational functional with respect to the Gaussian exponents. The algorithm of the method and its computational implementation is described. The application of the method to the helium atom shows that the Newton–Raphson procedure leads to a good convergence of the optimization process. © 1994 by John Wiley & Sons, Inc.

AB - Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the helium atom. The major problem of this application, as well as in other applications of the explicitly correlated Gaussian functions to compute electronic energies of atoms and molecules, is the optimization of the nonlinear parameters involved in the variational wave function. An effective Newton–Raphson optimization procedure is proposed based on analytic first and second derivatives of the variational functional with respect to the Gaussian exponents. The algorithm of the method and its computational implementation is described. The application of the method to the helium atom shows that the Newton–Raphson procedure leads to a good convergence of the optimization process. © 1994 by John Wiley & Sons, Inc.

UR - http://www.scopus.com/inward/record.url?scp=84986431491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986431491&partnerID=8YFLogxK

U2 - 10.1002/jcc.540150107

DO - 10.1002/jcc.540150107

M3 - Article

VL - 15

SP - 54

EP - 60

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 1

ER -