The role of single-particle density in chemistry

The definition, properties, and applications of the single-particle (electron) density ρ (r) are discussed in this review. Since the discovery of Hohenberg-Kohn theorem, which gave a theoretical justification for considering ρ (r), rather than the wave function, for studying both nondegenerate and degenerate ground states of many-electron systems, ρ (r) has been acquiring increasing attention. The quantum subspace concept of Bader et al. has further highlighted ρ (r) since a rigorous decomposition of the three-dimensional (3D) space of a molecule into quantum subspaces or virial fragments is possible, the boundaries of such subspaces being defined solely in terms of ρ (r). Further, ρ (r) is a very useful tool for studying various chemical phenomena. The successes and drawbacks of earlier models, such as Thomas-Fermi-Dirac, incorporating ρ (r) are examined. The applications of ρ (r) to a host of properties-such as chemical binding, molecular geometry, chemical reactivity, transferability, and correlation energy-are reviewed. There has been a recent trend in attempting to bypass the Schrödinger equation and directly consider single-particle densities and reduced density matrices, since most information of physical and chemical interest are encoded in these quantities. This approach, although beset with problems such as N-representability, and although unsuccessful at present, is likely to yield fresh concepts as well as shed new light on earlier ideas. Since charge density in 3D space is a fundamental quantum-mechanical observable, directly obtainable from experiment, and since its use in conjunction with density-functional theory and quantum fluid dynamics would provide broadly similar approaches in nuclear physics, atomic-molecular physics, and solid-state physics, it is not unduly optimistic to say that ρ (r) may be the unifying link between the microscopic world and our perception of it