Some investigations of symmetry and extremal properties of molecular electron momentum densities

Abstract

It is known that the molecular electron momentum density γ(p) is inversion symmetric. In this article, the generalized repercussions of this fact on the symmetries of γ(p) are discussed. A comprehensive study of the symmetry transformation from positional to momentum density due to the introduction of inversion operator i in the symmetry point group of a molecular system (in r space) has been presented. The symmetry enhancement in C3v and Td point groups is brought out via the respective electron momentum density contour maps. Further, the extremal properties of γ(p) have been studied for CH4, H2O, HCN, NH3, C2H2, C2H4, C2H6, and CO molecules. The local maxima are observed at p=0 and elsewhere, whereas the minima and saddle points are invariably found to be at p=0 for the molecules studied here.