Gaussian expansions of orbitals

Laura K. McKemmish*, Peter M.W. Gill

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)

    Abstract

    Using numerical calculations and analytic theory, we examine the convergence behavior of Gaussian expansions of several model orbitals. By following the approach of Kutzelnigg, we find that the errors in the energies of the optimal n-term even-tempered Gaussian expansions of s-type, p-type, and d-type exponential orbitals are εns ∼ exp(-π(3n)1/2), εnp ∼ exp(-π(5n)1/2), and εnd ∼ exp(-π(7n)1/2), respectively. We show that such "root-exponential" convergence patterns are a consequence of the orbital cusps at r = 0, rather than the over-rapid decay of Gaussians at large r. We find that even-tempered expansions of the cuspless Lorentzian orbital also exhibit root-exponential convergence but that this is a consequence of its fat tail.

    Original languageEnglish
    Pages (from-to)4891-4898
    Number of pages8
    JournalJournal of Chemical Theory and Computation
    Volume8
    Issue number12
    DOIs
    Publication statusPublished - 11 Dec 2012

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