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. (C) 1998 Elsevier Science B.V. All rights reserved.