Regional virial in diatomic molecules: two criteria for defining zero-flux dividing surfaces

The dividing surfaces defining the regions where a variationally determined virial theorem holds can be taken as the surfaces through which the flux of the gradient of a scalar function that is different from the electronic density vanishes. Alternatively, real space can be partitioned through zero-flux surfaces of the gradient of the electronic density, a process which also renders fragments where the virial theorem holds. In the present study we examined the question of whether these two criteria are the same for very simple model wavefunctions for both homonuclear and heteronuclear diatomic molecules within the Born-Oppenheimer approximation. It was found that in the homonuclear case, which is essentially governed by the symmetry of the problem, the two criteria agree closely, the difference being in the curvature of the gradient contour lines. However, in the heteronuclear model, significant differences were found in both the curvature of the gradient contour lines and the shape of the dividing surface. The chemical and physical implications of these differences were analysed.