Computational Chemistry 4.28 - Population Analysis

Short lecture on population analysis to obtain atomic partial charges in Hartree-Fock theory.
Population analysis in Hartree-Fock theory allows us to use the resulting coefficient matrix (C) from the self-consistent field (SCF) procedure to assign partial charges to each nuclear center in the molecule. Using the density matrix, the expectation value of any molecular property can be obtained if the form of the one-electron operator for the property is known. An example is given using the dipole moment operator. Mulliken charges for each nuclear center are obtained by subtracting a trace of the product of the density (P) and overlap (S) matrices from the charge of the nucleus. We can also perform an orbital transformation to any desired degree to compute these partial charges. One such choice is to transform the density matrix using the square root of the overlap matrix, resulting in the expression for Lowdin partial atomic charges.
Notes Slide: i.imgur.com/hQ...
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Quick note: one line above the "Mulliken charges" holds because S is symmetric, so S_{\mu u}=S_{ u \mu}.

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