Molecular-Orbital Theory of Diamagnetism. I. An Approximate LCAO Scheme

Abstract

An independent-electron molecular-orbital theory is developed for the diamagnetic behavior of electrons in the presence of an applied magnetic field. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the dependence of the (complex) coefficients on the magnetic field being studied by perturbation theory. By making a systematic set of approximations involving the neglect of some interatomic terms, a general expression is derived for the diamagnetic susceptibility tensor as a sum of atomic contributions. Each atomic contribution is made up of two parts, the first being a diamagnetic (Langevin-type) term and the second being a paramagnetic contribution involving the details of the electronic excited states. At a lower level of approximation, this second term can be expressed in terms of atomic charge densities and bond orders together with a mean electronic excitation energy. It is pointed out that the theory provides a convenient basis for detailed interpretation of the Pascal constants used for empirical calculations of diamagnetic susceptibilities of large molecules. In addition, a similar treatment of the theory of nuclear magnetic screening leads to an expression for the shielding constant involving a set of localized contributions closely related to corresponding contributions for the susceptibility.