# Mulliken Charge Analysis

From version 2.1.0, ABACUS has the function of Mulliken population analysis. The example can be found in examples/mulliken.
To use this function, set ‘out_mul’ to ‘1’ in the INPUT file. After calculation, there will be an output file named ‘mulliken.txt’ in the output directory. In the file, there are contents like (nspin 1):

CALCULATE THE MULLIkEN ANALYSIS FOR EACH ATOM
Total charge of spin 1:	8
Total charge:	8
Decomposed Mulliken populations
0                 Zeta of Si                        Spin 1
s                        0                       1.2553358
sum over m                                     1.2553358
s                        1                    -0.030782972
sum over m                                  -0.030782972
sum over m+zeta                                1.2245529
px                        0                      0.85945806
py                        0                      0.85945806
pz                        0                      0.85945806
sum over m                                     2.5783742
px                        1                    0.0065801228
py                        1                    0.0065801228
pz                        1                    0.0065801228
sum over m                                   0.019740368
sum over m+zeta                                2.5981145
d3z^2-r^2                        0                       0.0189287
dxy                        0                     0.046491729
dxz                        0                     0.046491729
dx^2-y^2                        0                       0.0189287
dyz                        0                     0.046491729
sum over m                                    0.17733259
sum over m+zeta                               0.17733259
Total Charge on atom:  Si                   4
...


The file gives Mulliken charge in turn according to the order of atoms in the system. For example, the following block is for the first atom in system (nspin 2),

0            Zeta of Si               Spin 1              Spin 2                Sum                Diff
...
Total Charge on atom:  Si                   4
Total Magnetism on atom:  Si      -1.2739809e-14


And the next block is for the second atom in system, and so on.

1            Zeta of Si               Spin 1              Spin 2                Sum                Diff
...


For each atom, the file gives detailed Mulliken population analysis at different levels,

• magnetic quantum number level: such as lines beigin with ‘s,px,py,pz,…’

• azimuthal quantum number level: such as lines begin with ‘sum over m’.

• principal quantum number level: such as lines begin with ‘sum over m+zeta’. Here ‘zeta’ equals ‘zeta’ in the file, which means how many radial atomic orbitals there are for a given orbital angular momentum.

• atomic level: such as lines begin with ‘Total Charge on atom’.

More orbital information can be found in ‘Orbital’ file output with ‘mulliken.txt’ when out_mul 1