The techniques described in the previous section were used to perform calculations of Mulliken and Löwdin atomic charges in four simple molecules. These were compared with Mulliken charges calculated from DFT calculations using LCAO basis sets with GAUSSIAN94 [9].
The basis set used for projection of the PW states in each case was that of the atomic pseudo-orbitals corresponding to the shell occupied by the valence electrons. The LCAO calculations were performed using the STO-3G and 6-311G** basis sets provided with GAUSSIAN94.
Table 1: Gross atomic charges calculated by Mulliken and Löwdin analysis
of PW calculations, and Mulliken analysis of LCAO calculations
performed with GAUSSIAN94.
The results of these calculations are presented in table 1.
It should be noted that the absolute values of these
charges are thought to have little physical meaning as they display an
extreme sensitivity to the atomic basis set with which they are
calculated [10]. It is also generally recognised that the
molecular dipole is not simply related to the sum of the products
as can be seen from the analysis of the 
molecule, for which the dipole naïvely calculated from the
Mulliken charges is 2.83 D, in poor agreement with the experimental
value of 1.87 D. However, the dipole calculated for this molecule from
the full charge density obtained in the plane wave calculation, 1.86
D, is much closer to the experimental value. In contrast to the
absolute values, redistribution of Mulliken charges in response to
system changes may have more significance.
Table 2: Mulliken and Löwdin atomic overlap populations.
Figure 1: The structure of methanol showing the overlap populations
between bonded atoms as calculated by Mulliken analysis of PW
calculation.
The overlap populations between the atoms in CO, 
and
SiO are given in table 2. A large positive value for this
population indicates that the atoms in question are bonded, a large
negative value indicates the atoms are in an antibonded state. The
Mulliken and Löwdin overlap populations for bonded atoms in 
are shown in figure 1. It is notable that
Löwdin analysis of O--H overlap population gives a significantly
smaller results than expected, although this is still significantly
greater than the overlap of unbonded atoms.