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’.