Approximate theoretical model for the five electronic states ( Ω = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d 9 configuration in nickel halide molecules and for rotational levels of the two Ω = 1/2 states in that manifold

Abstract

In the first part of this paper 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 3d 9 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: C 0 + C 2 Y 20( θ, ϕ) + C 4 Y 40( θ, ϕ). Interaction of the hole with the magnetic field generated by its own orbital motion can be parameterized by a traditional spin–orbit interaction operator A L · S . The Hamiltonian matrix is set up in a basis set consisting of the 10 Hund’s case (a) basis functions | L, Λ; S , Σ〉 that arise when L = 2 and S = 1/2. Least-squares fits of the observed five spin–orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the four parameters C 0, C 2, C 4, and A which lead to good agreement, except for the two | Ω| = 1/2 states. The large equal and opposite residuals of the | Ω| = 1/2 states can be reduced to values comparable with those for the | Ω| = 3/2 and | Ω| = 5/2 states by fixing A to its value in Ni + and then introducing an empirical correction factor for one off-diagonal orbital matrix element. In the second part of this paper the usual effective Hamiltonian B( J – L – S ) 2 for a rotating diatomic molecule is used to derive expressions for the Ω-type doubling parameter p in the two | Ω| = 1/2 states. These expressions show (for certain sign conventions) that the sum of the two p values should be −2 B, but that their difference can vary between −10 B and +10 B. These theoretical results are in good agreement with the two observed p values for both NiF and NiCl. The present formalism should in principle be applicable to NiBr and NiI, and to the halides of palladium, since Pd + has a well isolated 4d 9 electronic ground configuration. Extension to metal halides having d n configurations with n < 9, or to platinum halides may present difficulties, since manifolds from the d n and d n −1 s configurations may be heavily mixed, thus requiring “too many” parameters in the electronic part of the problem. Application to linear triatomic molecules may also present problems because of the large number of vibronic perturbations made possible by their four vibrational degrees of freedom.