A Green's function for the density

It is shown that the electron density at a point in space is determined by a Green's 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 Poisson's equation for a potential given by the density rho(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.