A finite-difference approach to the electron correlation problem

✍ Scribed by W. R. Fimple; M. J. Unwin

• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 625 KB
• Volume: 10
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560100408

✦ Synopsis

Abstract

A variant of the transcorrelated method of Boys and Handy employing finite differences is presented. It is based upon the following two properties of the transcorrelated Hamiltonian operator C^−1^HC: (1) C^−1^HC possesses an energy eigenvalue spectrum which is identical to that associated with H itself; and (2) if \documentclass{article}\pagestyle{empty}\begin{document}$$ C \equiv \begin{array}{*{20}c} \pi & {e^{r_{ij} /2} } \ {i > j} & {} \ \end{array} $$\end{document} then C^−1^HC is free of the singularities of H at the points where the interelectron separation r~ij~ is zero. A bivariational principle for approximating the eigenvalues and the left and right eigenfunctions of C^−1^HC is introduced and the resulting set of coupled integro‐differential equations are solved in finite‐difference form by means of a coupled self‐consistent field, Newton Raphson algorithm. As a preliminary test of the method, a calculation of the ground‐state energy of the helium atom is presented.