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Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom
Author(s) -
Zhang Zhenghong,
Kozlowski Pawel M.,
Adamowicz Ludwik
Publication year - 1994
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540150107
Subject(s) - helium atom , gaussian , ground state , wave function , variational method , atom (system on chip) , convergence (economics) , mathematics , newton's method , gaussian function , helium , nonlinear system , function (biology) , physics , statistical physics , quantum mechanics , computer science , biology , economics , embedded system , economic growth , evolutionary biology
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.