High-precision Hy-CI and E-Hy-CI studies of atomic and molecular properties

This review presents a survey of the most important achievements in atomic and molecular calculations obtained with the Hylleraas-configuration interaction method (Hy-CI) and its extension, the exponentially correlated Hylleraas-configuration interaction method (E-Hy-CI), explaining what led to it and discussing the main mathematical and computational issues. We stress the importance of representing the electronic cusp well in the wave function, which a configuration interaction (CI) wave function does not do, along with the shortcomings of other implicitly correlated wave functions with respect to this cusp. There follows a short review of the types of explicitly correlated wave functions, culminating with an exploration of a generalization of the Hy-CI first proposed in a previous study, the exponentially correlated Hylleraas-configuration interaction method (E-Hy-CI) in which the single r ij of an Hy-CI wave function is generalized to a form of the generic type rijνije−ωijrij. We include (1) atomic calculations on states of the He through B atoms using the Hy-CI method, including atomic spectra and isoelectronic ions and the first atomic calculations on the ground state of the He atom employing the E-Hy-CI method, (2) molecular calculations by the Hy-CI method of the H 2 molecule using both Slater-type and Gaussian-type orbitals, and (3) calculations of various atomic and molecular properties beyond the energy.