An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be=1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'.

This paper presents high-accuracy correlation energies, intracule densities and Coulomb hole(s) for the lithium cation, helium, hydride ion and the system with the critical nuclear charge, ZC, for binding two electrons. The fully correlated (FC) wave function and the Hartree–Fock (HF) wave function are both determined using a Laguerre-based wave function. It is found that for the lithium cation and the helium atom a secondary Coulomb hole is present, in agreement with a previous literature finding, confirming a counterintuitive conclusion that electron correlation can act to bring distant electrons closer together. However, no evidence for a tertiary Coulomb hole is found. For the hydride anion and the system just prior to electron detachment only a single Coulomb hole is present and electron correlation decreases the probability of finding the electrons closer together at all radial distances. The emergence of a secondary Coulomb hole is investigated and found to occur between Z = 1.15 and Z = 1.20. The FC and HF energies and intracule densities (in atomic units) used to calculate the correlation energy and Coulomb hole, respectively, are accurate to at least the nano-scale for helium and the cation and at least the micro-scale for the anions.

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Article (Published Version) http://sro.sussex.ac.uk Baskerville, Adam L, King, Andrew W and Cox, Hazel (2016) Quantum effects of nuclear motion in three-particle diatomic ions. Physical Review A, 94. 042512. ISSN 1050-2947 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/65251/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.PHYSICAL REVIEW A 94, 042512 (2016) Quantum effects of nuclear motion in three-particle diatomic ions A high-accuracy, nonrelativistic wave function is used to study nuclear motion in the ground state of three-particle {a + 1 a + 2 a − 3 } electronic and muonic molecular systems without assuming the Born-Oppenheimer approximation. Intracule densities and center-of-mass particle densities show that as the mass ratio m a i /m a 3 , i = 1,2, becomes smaller, the localization of the like-charged particles (nuclei) a 1 and a 2 decreases. A coordinate system is presented to calculate center-of-mass particle densities for systems where a 1 = a 2 . It is shown that the nuclear motion is strongly correlated and depends on the relative masses of the nuclei a 1 and a 2 rather than just their absolute mass. The heavier particle is always more localized and the lighter the partner mass, the greater the localization. It is shown, for systems with m a 1

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