Topological analysis of magnetically induced molecular current distributions

The topology of the first-order current density J(1)(r) induced in a molecule by an applied magnetic field is analyzed and classified in terms of the properties of its critical points, as determined by the 3×3 coefficient matrix of the asymmetric tensor ∇J(1). The eigenvalues of this tensor yield the topological indices for classifying the possible critical points in the J(1)(r) field. The phase portraits describing the current flow associated with these critical points and their role in determining the structure of a molecular current distribution are illustrated. A molecular current distribution is a fully three-dimensional vector field. In addition to closed loops of current, it exhibits one- and two-dimensional sources and sinks which generate surfaces, spirals, and single lines of current. The nonisolated critical points lie on stagnation paths which, along with the isolated critical points, fully characterize the current distribution. The antisymmetric component of ∇J(1) is the curl of J(1) which defines the vorticity of the current distribution. Whether a region of current flow is diamagnetic or paramagnetic depends on the location of its critical point relative to the atomic shell structure exhibited by the vorticity field. The group theoretical classification of the induced current is described.