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

✍ Scribed by Zhenghong Zhang; Pawel M. Kozlowski; Ludwik Adamowicz

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 477 KB
• Volume: 15
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540150107

✦ Synopsis

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.