The atom in a molecule: A density matrix approach

A method based on first-order density matrices is proposed to define an atom in a molecule, which is in accord with a previously given definition using density functional theory. The promotion energy E_p is expressed in terms of a defined division function α(r). By minimizing E_p with respect to α(r), one can obtain α(r), by which an atom in a molecule is uniquely determined. It is shown that such an ``atom'' satisfies a local virial theorem, depicted intuitively, Some other properties of the atom in a molecule are also discussed. Comparison is made with a definition due to Bader, and an approximate but simple approach to determine an atom in a molecule is proposed.