Approximate valence-shell electron unrestricted Hartree-Fock calculations with orthogonalized atomic orbitals: proton hyperfine splittings in benzyl and related radicals

Abstract

A modified INDO procedure has been used to calculate the proton hyperfine splittings in benzyl and the isoelectronic anilino, phenoxy and 2-azabenzyl as well as 2- and 3-thenyl radicals. The present procedure differentiates between s-, p- and d-orbitals on an atom in estimating various integrals involving them, satisfies the rotational invariance requirements and employs an orthogonalized basis set of atomic orbitals for obtaining core-Hamiltonian matrix elements. The calculations based on using the exponents which depend only on the type of orbital and the nature of atom fail to provide correct relative order of ortho and para proton splittings in benzyl as well as anilino, phenoxy and 2-azabenzyl radicals. On the other hand, use of the exponents which are modified according to the charge densities in various orbitals leads to a high absolute value for para proton splitting compared to that for ortho proton splitting which in case of all these radicals is in agreement with experiment. A spin density calculation on benzyl, anilino and phenoxy radicals considering the variation of one-center one-electron and one-center two-electron integrals for different protons with their charges is found to yield further improvement in the relative order of ortho and para proton splittings in all these radicals. In 2- and 3-thenyl radicals the role of 3d-orbitals on sulfur has also been examined. To our knowledge, no unrestricted INDO calculations including 3d-orbitals on sulfur have been reported in the literature so far.