A Greenʹs function for the density

It is shown that the electron density at a point in space is determined by a Greenʹs function, that is, the density at a point r is determined by contributions from a source function G(r, r′) at r′. This is done in two ways: through the use of the equation of motion for the generator (|r−r′|)−1 for a proper open system, an atom, and by solving Poissonʹs equation for a potential given by the density ρ(r). The source function enables one to equate the value of the density at any point within a molecule to a sum of atomic contributions and to thus view properties of the density from a new perspective. For example, the observation of a characteristic bond path density, as in a terminal H–C group in a hydrocarbon chain, requires that the contribution to the density from atomic sources outside the group remain constant, regardless of the length of the chain.