Magnetic Susceptibility of Diatomic Molecules

Abstract

A variation—perturbation method is presented for the calculation of the magnetic susceptibility tensor χ from a single‐determinant ground‐state wavefunction for a ¹Σ molecule. The diamagnetic contribution χ^d is obtained directly by first‐order perturbation theory and the paramagnetic contribution χ^p is determined by extremizing a functional corresponding to the second‐order energy in an external magnetic field. By an appropriate choice of perturbation function and zero‐order Hamiltonian, the functional is expressed in a relatively simple form requiring only one‐electron matrix elements. The importance of employing Hartree—Fock functions as the zero‐order solution is stressed and an analysis given of the order of the errors in the variation—perturbation treatment. Explicit comparisons of the present method with simplified forms of the variational procedure demonstrate that the neglect of electron exchange or use of an ``average'' perturbation function can introduce significant errors in the results. Calculations are made of the magnetic susceptibility tensor for a series of diatomic molecues. Ransil's minimal basis set functions serve as unperturbed wavefunctions and a four‐term polynomial is used to represent orbital perturbations in the second‐order treatment. The values obtained for χ^d, χ^p, and χ of H₂, Li₂, N₂, F₂, LiH, HF, LiF, and CO are presented. Comparisons with the available magnetic data for these molecules demonstrates that the variation—perturbation method is a useful tool for ab initio susceptibility calculations. For the more difficult paramagnetic term χ^p, criteria for the convergence of the second‐order energy are discussed and applied to the molecules considered. The magnetic anisotropy (Δχ=χ⊥—χ∥) is evaluated theoretically for hydrogen and found to be in reasonable agreement with experiment. The inaccuracies arising in Δ_χ values for more complex species (through differencing in a purely theoretical treatment) are overcome by the inclusion of rotational magnetic moment data to obtain relatively reliable results. To examine the effect of the vibrational state on the susceptibility of a molecule, an exploratory calculation is made for LiH, which demonstrates that small sut significant deviations from the equilibrium‐distance value are to be expected. Finally, some indication is given of the additional experimental and theoretical work that is required in this field.