The Hylleraas‐CI method in molecular calculations. III. Implementation and numerical verification of a three‐electron many‐center theory

Abstract

The general theory of three-electron Hylleraas-Configuration-Interaction method using linear correlation factors of the form r, has been implemented for molecular systems using Cartesian Gaussians as basis sets. A brief review of the theory and the form of the three-electron integrals is presented. Additionally, a table of numerical values of some selected three-electron integrals is given. Results from test calculations on H3 using the full form of the theory are presented for some simple basis sets. A discussion of the computational problems that need to be overcome before this approach is competitive with traditional methods is included.

Explicitly Correlated R12/F12 Methods for Electronic Structure

“…61 Most applications, however, have been limited to extremely accurate computations on few-electron atoms (He, 62 Li, 63 Be 64 ), because the expense of numerical integration in molecules with three and more electrons seemingly outweighs possible benefits. 65 3.2.2. Explicitly Correlated Gaussian Methods.…”

“…The Hylleraas-CI method has been applied successfully to systems with as many as 10 electrons . Most applications, however, have been limited to extremely accurate computations on few-electron atoms (He, Li, Be), because the expense of numerical integration in molecules with three and more electrons seemingly outweighs possible benefits …”

On the use of explicitly correlated functions in variational computations for small molecules

“…In Table V, energies for the equilibrium geometry (R = 1. 46 bohr) obtained with the GJC [74,75] and ECG [72] are compared. In this table, two additional results obtained by Clementi and co-workers [76] with the Hy-CI function and by Alexander et al [30] with the random-tempered ECG function are also listed.…”