Understanding the unusual g-values and the spin density distribution of hydrogen atoms trapped in silasesquioxanes

Abstract

In a recent EPR study, Gross et al. (B. Gross, H. Dilger, R. Scheuermann, M. Päch and E. Roduner, J. Phys. Chem. A, 2001, 105, 10012) found that hydrogen atoms trapped in silasesquioxanes unexpectedly exhibit g-values significantly larger than the free-electron value, with an appreciable dependence on the external substituents of the cage. Here it is shown by density functional calculations and detailed analyses of the g-values that (a) the positive g-shifts are predominantly due to spin–orbit coupling from the cage oxygen atoms; (b) in second-order perturbation theory the g-shifts arise mainly from couplings of t_1g oxygen-based cage orbitals to the a_1g singly occupied molecular orbital, and (c) the reduction of the g-shifts by external substituents is mainly caused by lower spin density on the cage oxygen atoms, due in part to reduced delocalization of the singly occupied MO onto the cage. Calculations with the hydrogen atom displaced from the center of the cage provide explanations for the negligible temperature dependence of the g-values compared to an experimentally notable dependence of the hyperfine couplings. Large direct halogen spin–orbit contributions and negative g-shifts are predicted for systems with heavy halogen atoms as external substituents. Comparison of different exchange-correlation functionals, and of spin-restricted and -unrestricted calculations reveals unexpected trends for spin density distribution and g-values: Spin polarization increases the computed g-shifts, whereas the admixture of Hartree–Fock exchange in hybrid functionals decreases them.