Study of Different Approximation in the Calculation of g Tensors: H2+

The theory of the g tensor in one-electron systems is briefly reviewed and calculations are done in several ways for the H2+ molecular ion in order to test approximations which must be made for larger systems. Approximate ground state wavefunctions are determined variationally using a power series in elliptic coordinates and as a linear combination of atomic orbitals. The first-order wavefunction with respect to the orbit-field perturbation is calculated variationally and by a Rayleigh–Schrödinger expansion and the second-order g tensor determined. Excited state functions and energies are approximated from the higher roots of the secular equations involved. The results of the various approximate calculations are compared and discussed. It is found that the LCAO method is rather poor and that two center integrals cannot be neglected. It also appears that a single spin–orbit parameter cannot be used for different orbitals on the same atom. The best result, obtained from the variationally determined first-order function, has gxx differing from the free electron value by −0.225 × 10−5.