Chapter Ten - Atomic Electronic Structure Computations With Hylleraas-CI Wave Functions

Add time:08/23/2019    Source:sciencedirect.com

The Hylleraas-CI (Hy-CI) method is conventionally defined as based on superposition-of-configurations (also called configuration interaction) wave functions in which each term (configuration) is built from an orbital product to which is appended at most one linear factor rij, where rij is the distance between particles i and j. The functions comprising an orbital product are usually chosen to be Slater-type orbitals that include spherical-harmonic angular dependence. We consider here both the conventional definition and its generalization (called extended Hy-CI or E-Hy-CI) in which the correlation factor rij is replaced by a more general function f(rij). The present communication reviews the mathematical methods presently available for the fully analytical treatment of the integrals arising when these types of explicitly correlated wave functions are used within the framework of both the usual and extended Hylleraas-CI to study atomic and more general single-center systems. The analysis includes novel elements that may improve the efficiency of computations; the chapter also calls attention to new formulas for treating kinetic-energy integrals in Hy-CI methods.

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