Quantum-Mechanical Calculations for the Electric Field Gradients and other Electronic Properties of Lithium Hydride: The Use of Mixed Orbital Sets

Abstract

We propose for quantum-mechanical calculations on diatomic molecules the use of mixed orbital sets composed of both Slater-type orbitals and elliptic orbitals. The Slater-type orbitals provide a good representation of the essentially spherical charge distributions near atoms in molecules and the elliptic orbitals provide good electronic distributions for the delocalized valence electrons. We have carried out calculations with up to 28 terms of the mixed orbital set on the lithium hydride molecule and obtained the most accurate wave function yet published. Our values for the several molecular parameters are as follows: (the experimental values are given in parenthesis) $\ensuremath{-}E=8.0561 \mathrm{a}.\mathrm{u}.(8.0703); {R}_{e}=3.046 \mathrm{a}.\mathrm{u}.(3.013);$ ${\ensuremath{\omega}}_{e}=1438 {\mathrm{cm}}^{\ensuremath{-}1}(1406); {\ensuremath{\omega}}_{e}{x}_{e}=86 {\mathrm{cm}}^{\ensuremath{-}1}(23);$ ${\ensuremath{\mu}}_{0}=5.93(5.88); {\ensuremath{\mu}}_{1}=6.00(5.99); {\ensuremath{\mu}}_{2}=6.05(6.10); [\frac{{\ensuremath{\mu}}_{e}}{({R}_{e}{\frac{\ensuremath{\partial}\ensuremath{\mu}}{\ensuremath{\partial}R}|}_{{R}_{e}})}]=1.74(1.8\ifmmode\pm\else\textpm\fi{}0.3).$As is usually the case, our results are superior to self-consistent field calculations. We have calculated the electric field gradients at both nuclei. The quadrupole coupling for D in LiD was obtained using ${q}_{\mathrm{H}}$ and yielding $\frac{e{q}_{\mathrm{D}}{Q}_{\mathrm{D}}}{h}=34.2$ kc/sec (33\ifmmode\pm\else\textpm\fi{}1 kc/sec). When ${q}_{\mathrm{Li}}$ is combined with the experimental quadrupole coupling constant we estimate ${Q}_{\mathrm{Li}}=\ensuremath{-}4.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ ${\mathrm{cm}}^{2}$. This is considerably larger than the shell-model estimate and supports the proposal that for odd-proton nuclei nucleons external to a shell deform it.