Approximate theoretical model for the five electronic states (¿ = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d9 configuration in nickel halide molecules and for the rotational levels of the two ¿ = 1/2 states in this manifold

Published

January 25, 2011

Author(s)

Jon T. Hougen

Abstract

This paper is divided into two parts. In the first part an effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin-orbit operators is set up to describe the energies of the five spin-orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni+X, with an electronic 3d9 configuration plus closed shells on the Ni+ moiety and a closed shell configuration on the X moiety. From a crystal-field point of view, interactions of the positive d-hole with the cylindrically symmetrical electric charge distribution of the hypothetical NiX closed-shell core can then be parameterized by three terms in a traditional expansion in spherical harmonics: C0 + C2Y20(,) + C4Y40(,). Interaction of the hole with the magnetic field generated by its own orbital motion can be parameterized by a traditional spin-orbit interaction operator ALS. The Hamiltonian matrix is set up in a basis set consisting of the ten Hund’s case (a) basis functions |, that arise when L = 2 and S = ¿. Least-squares fits of the five lowest observed electronic spin-orbit component states in NiF and NiCl are then carried out in terms of the four parameters C0, C2, C4, A which lead to good agreement except for the two || = ¿ states. The large equal and opposite residuals of the || = ¿ states can be reduced to those for the || = 3/2 and || = 5/2 states by fixing A to its value in Ni+ and then introducing an empirical correction factor for one off-diagonal spin-orbit matrix element. In the second part of the paper the usual effective Hamiltonian B(JLS)2 for a rotating diatomic molecule is used to derive expressions for the -type doubling parameter p in the two || = ¿ states. These expressions show (for certain sign conventions) that the sum of the two p values should be 2B, but that their difference can be as large as 10B. These theoretical r

Citation

Journal of Molecular Spectroscopy

Volume

267

Pub Type

Journals

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Keywords

electronic states, d-electrons, crystal-field theory, spin-orbit components, rotational levels, p-type doubling, Ω = 1/2 states

Citation

Hougen, J. (2011), Approximate theoretical model for the five electronic states (¿ = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d9 configuration in nickel halide molecules and for the rotational levels of the two ¿ = 1/2 states in this manifold, Journal of Molecular Spectroscopy, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906144 (Accessed October 10, 2025)