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High-Precision Hy-CI and E-Hy-CI studies of Atomic and Molecular Properties



James S. Sims, Maria Ruiz, Bholanath Padhy


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, without going into detail about mathematical formulations. The importance of representing the electronic cusp well in the wave function, which a configuration interaction (CI) wave function doesn't do, is stressed first along with the shortcomings of the other implicitly correlated wave functions in this regard. This is followed by a short review of the types of explicitly correlated wave functions, culminating with an exploration of a generalization of the Hylleraas-configuration Interaction method (Hy-CI) first proposed in a previous study, the exponentially correlated Hylleraas-Configuration Interaction method (E-Hy-CI) in which the single rij of an Hy-CI wave function is generalized to a form of the generic type rij times an exponential rij. Included in the presentation are (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 H2 and H3 molecules using both Slater-type and Gaussian-type orbitals, and (3) calculations of various atomic and molecular properties beyond the energy.
Advances in Quantum Chemistry
Publisher Info
Elsevier, New York, NY


Exponentially correlated Hylleraas-Configuration Interaction, E-Hy-CI, Hy-CI, Configuration Interaction, Slater-type orbitals (STOs), Atoms


Sims, J. , Ruiz, M. and Padhy, B. (2021), High-Precision Hy-CI and E-Hy-CI studies of Atomic and Molecular Properties, Advances in Quantum Chemistry, Elsevier, New York, NY, [online],, (Accessed December 1, 2021)
Created September 29, 2021