Population Analysis

The density distribution ρ may be viewed as a cloud carrying a charge −Ne, and Eq. (S.1) says that the cloud is composed of the individual clouds of the molecular orbitals, each carrying two electrons. On the other hand, in the LCAO (Linear Combination of Atomic Orbitals) approximation, any molecular orbital is represented by a sum of atomic orbitals. If we insert the LCAO expansion into ρ, then ρ becomes a sum of the contributions, each being a product of two atomic orbitals. There is a temptation to go even further and to divide ρ somehow into contributions of particular atoms, calculate the charge corresponding to such contribution, and locate the (point) charge right on the nucleus.1 We might ask, therefore, what the “electron population” residing on the particular atoms are (hence the name population analysis).