| Abstract: | An easy method of approximating the electron density of a molecule by expressing it as a sum of squares of atomic orbitals is described. The coefficients are determined by minimizing the error in the electric field. The optimal population analysis is an integration of this optimized density over the orbitals belonging to one atom. The Mulliken population analysis can be interpreted as the integral of a Mulliken density that is a similar expression with fixed coefficients. The two densities are compared in détail using calculations on the water molecule and, more briefly, HF, LiH, BH, and C2H4. The error in the densities is identified and examined. The optimal population analysis is strongly recommended as a practical improvement to the Mulliken populations. |
