Mulliken population analysis

Mulliken charges arise from the Mulliken population analysis and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR) procedures. The method was developed by Robert S. Mulliken, after whom the method is named. If the coefficients of the basis functions in the molecular orbital are Cμi for the μ'th basis function in the i'th molecular orbital, the density matrix terms are: Mulliken charges arise from the Mulliken population analysis and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR) procedures. The method was developed by Robert S. Mulliken, after whom the method is named. If the coefficients of the basis functions in the molecular orbital are Cμi for the μ'th basis function in the i'th molecular orbital, the density matrix terms are: for a closed shell system where each molecular orbital is doubly occupied. The population matrix P {displaystyle mathbf {P} } then has terms S {displaystyle mathbf {S} } is the overlap matrix of the basis functions. The sum of all terms of P ν μ {displaystyle mathbf {P_{ u mu }} } summed over μ {displaystyle mathbf {mu } } is the gross orbital product for orbital ν {displaystyle mathbf { u } } - G O P ν {displaystyle mathbf {GOP_{ u }} } . The sum of the gross orbital products is N - the total number of electrons. The Mulliken population assigns an electronic charge to a given atom A, known as the gross atom population: G A P A {displaystyle mathbf {GAP_{A}} } as the sum of G O P ν {displaystyle mathbf {GOP_{ u }} } over all orbitals ν {displaystyle mathbf { u } } belonging to atom A. The charge, Q A {displaystyle mathbf {Q_{A}} } , is then defined as the difference between the number of electrons on the isolated free atom, which is the atomic number Z A {displaystyle mathbf {Z_{A}} } , and the gross atom population: One problem with this approach is the equal division of the off-diagonal terms between the two basis functions. This leads to charge separations in molecules that are exaggerated. In a modified Mulliken population analysis, this problem can be reduced by dividing the overlap populations P μ ν {displaystyle mathbf {P_{mu u }} } between the corresponding orbital populations P μ μ {displaystyle mathbf {P_{mu mu }} } and P ν ν {displaystyle mathbf {P_{ u u }} } in the ratio between the latter. This choice, although still arbitrary, relates the partitioning in some way to the electronegativity difference between the corresponding atoms.