Unique positive definite extension of Mulliken's charge populations of non-orthogonal atomic basis functions

Abstract

Although Mulliken's charge population concept is widely used in literature, it suffers from the main conceptual disadvantage of not describing a probability distribution of the electron on the constituent atoms; small negative population values can occur as well. This fact prohibits some practical applications, too. Mulliken's AO population can be written as the expectation value of a self-adjoint operator P̂μ, corresponding to each atomic orbital |μ〉. Using the algebra generated by P̂μ, we will give in this paper a positive definite extension of Mulliken's expressions which can be written as the expectation value of a proper self-adjoint operator; it is local in the sense of Mulliken's definition; and it remains in the framework of the usual LCAO techniques (i.e. only the atomic overlap matrix is required for calculations). It is shown that only non-physical populations change significantly, realistic values remain close to Mulliken ones. From computational point of view, the extra work required to calculate this positive definite distribution is practically negligible.