Without any extension
Mulliken population analyses (MPA) are carried out for all densities present in
the respective program, e.g. total (and spin) densities leading to Mulliken
charges (and unpaired electrons) per atom in RHF(UHF)-type calculations in `dscf`
or `ridft`, SCF+MP2 densities in `rimp2` or `mpgrad`, excited state densities in
`egrad`. Suboptions (see Section 15.2.17) also allow for calculation of
Mulliken contributions of selectable atoms to selectable MOs including provision of
data for graphical output (simulated density of states).

With `$pop nbo` a Natural Population Analysis (NPA) [127] is
done. Currently only the resulting charges are calculated.

With `$pop paboon` a population analyses based on occupation numbers
[128] is performed yielding "shared electron numbers (SENs)" and
multicenter contributions. For this method always the total density is used,
i.e. the sum of alpha and beta densities in case of UHF, the SCF+MP2-density
in case of MP2 and the GHF total density for (two-component-)GHF.
Note that the results of such an analysis may depend on the choice of the
number of modified atomic orbitals ("MAOs"). By default, numbers of MAOs which are
reasonable in most cases are taken (see Section 15.2.17). Nevertheless
it is warmly recommended to carefully read the information concerning MAOs given in the
output before looking at the numbers for atomic charges and shared electron numbers.
For different ways of selecting MAOs see Section 15.2.17.