The role of single-particle density in chemistry

The definition, properties, and applications of the single-particle (electron) density $\rho \left(\mathrm{r}\right)$ are discussed in this review. Since the discovery of Hohenberg-Kohn theorem, which gave a theoretical justification for considering $\rho \left(\mathrm{r}\right)$, rather than the wave function, for studying both nondegenerate and degenerate ground states of many-electron systems, $\rho \left(\mathrm{r}\right)$ has been acquiring increasing attention. The quantum subspace concept of Bader et al. has further highlighted $\rho \left(\mathrm{r}\right)$ 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 $\rho \left(\mathrm{r}\right)$. Further, $\rho \left(\mathrm{r}\right)$ is a very useful tool for studying various chemical phenomena. The successes and drawbacks of earlier models, such as Thomas-Fermi-Dirac, incorporating $\rho \left(\mathrm{r}\right)$ are examined. The applications of $\rho \left(\mathrm{r}\right)$ 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 $\rho \left(\mathrm{r}\right)$ may be the unifying link between the microscopic world and our perception of it.