Mulliken charges arise from the Mulliken population analysis[1][2] 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[3]) procedures.
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 sum of the gross orbital products is N - the total number of electrons.
, 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.
This choice, although still arbitrary, relates the partitioning in some way to the electronegativity difference between the corresponding atoms.
Another problem is the Mulliken charges are explicitly sensitive to the basis set choice.
In the Mulliken scheme, all the electrons would then be assigned to this atom.
This also means that the charges are ill defined, as there is no exact answer.
As a result, the basis set convergence of the charges does not exist, and different basis set families may yield drastically different results.
These problems can be addressed by modern methods for computing net atomic charges, such as density derived electrostatic and chemical (DDEC) analysis,[6] electrostatic potential analysis,[7] and natural population analysis.