# What are Mulliken atomic charges, and how are they computed?

I was reading about the self-consistent extended Hückel method (SC-EHT), and stumbled upon various formulae for the diagonal elements of the Hamiltonian matrix. I noticed that many formulae depend on either the gross atomic population or Mulliken atomic charges. I know the formula for the Mulliken population analysis, but what is the Mulliken atomic charge and how can I evaluate it?

Thanks!

• This is a helpful resource- cmt.dur.ac.uk/sjc/thesis_prt/node113.html
– user78585
Aug 11 '19 at 17:21
• The charge results from adding up all orbital populations of an atom and subtract it from the nuclear charge. Aug 11 '19 at 23:36

$$q_A = Z_A-\sum_{\mu\in A}\left( \mathbf{P\cdot S} \right)_{\mu\mu} \tag{Szabo 3.196}$$
Here I have used the same notation as in Szabo, with $$\mathbf{P}$$ being the density matrix and $$\mathbf{S}$$ beign the overlap matrix. $$Z$$ is the nuclear charge, and using the greek letter $$\mu$$ as indicies indicates that we are working in atomic orbital basis (not in in molecular orbital basis).
The sum runs over $$\mu\in A$$ meaning, that we only consider atomic orbitals that are centered on the $$A$$th atom. we can therefore note that Mulliken charges are only defined when we used atomic-centered basis functions (which we most often do).