Properties of atoms in molecules: Magnetic susceptibilities

The molecular magnetic susceptibility tensor χ is expressible as a sum of atomic or group contributions. An atomic contribution consists of a basin and a surface component; the former is given by the integral of a magnetization density over the basin of the atom, and the latter, by the integral of the flux in the position weighted current density through the interatomic surfaces that the atom shares with its bonded neighbors. The surface component is obtained as a consequence of the atomic hypervirial theorem defining the average of the velocity operator. Magnetic properties are determined by the observable electron current density, and the atomic behavior of this field has been correlated with corresponding behavior of the electron density. Thus the importance of the magnetization within an atomic basin relative to the flux in current through its interatomic surfaces parallels the extent to which the electron density is localized within the individual atomic basins. For example, 77% of the pronounced anisotropy in benzene arises from the flux in current through the interatomic surfaces of the ring atoms induced by a field applied perpendicular to the ring surface. The methyl and methylene group contributions to χ̄ are found to be transferable in the homologous series of hydrocarbons and to equal Pascal’s group increments within experimental error.