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:


CALCULATE THE MULLIkEN ANALYSIS FOR EACH ATOM
8 (Total charge all spin 1)
8 (Total charge of the system)
Decomposed Mulliken populations
0                       Si                       Up spin                     Down spin                           Sum                          Diff
multiple
s                       0                      0.51810998                    0.51810998                       1.03622                           0
sum over m                                  0.51810998                    0.51810998                            1.03622                        0
s                       1                     0.053661483                   0.053661483                    0.10732297                           0
sum over m                                 0.053661483                   0.053661483                         0.10732297                        0
sum over m+mul                           0.57177146                    0.57177146                        1.1435429                            0
px                      0                      0.43730519                    0.43730519                    0.87461038                           0
py                      0                      0.43730519                    0.43730519                    0.87461038                           0
pz                      0                      0.43730519                    0.43730519                    0.87461038                           0
sum over m                                   1.3119156                     1.3119156                          2.6238311                        0
px                      1                    0.0065031719                  0.0065031719                   0.013006344                           0
py                      1                    0.0065031719                  0.0065031719                   0.013006344                           0
pz                      1                    0.0065031719                  0.0065031719                   0.013006344                           0
sum over m                                 0.019509516                   0.019509516                        0.039019031                        0
sum over m+mul                            1.3314251                     1.3314251                        2.6628502                            0
d3z^2-r^2               0                     0.011750855                   0.011750855                   0.023501711                           0
dxy                     0                     0.024433913                   0.024433913                   0.048867826                           0
dxz                     0                     0.024433913                   0.024433913                   0.048867826                           0
dx^2-y^2                0                     0.011750855                   0.011750855                   0.023501711                           0
dyz                     0                     0.024433913                   0.024433913                   0.048867826                           0
sum over m                                 0.096803451                   0.096803451                          0.1936069                        0
sum over m+mul                          0.096803451                   0.096803451                        0.1936069                            0
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,

0 Si Up spin Down spin Sum Diff
...
Total Charge on atom Si 4.0241712


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

1 Si Up spin Down spin 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+mul’. Here ‘mul’ equals ‘multiple’ 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’.