The negative value comes from the known theoretical deficiency of Mulliken population. If you are only interested in atomic contribution, I suggest using Hirshfeld method to evaluate the composition instead, Hirshfeld method is much more robust and the result is always nonnegative.

Best,

Tian

Recently, I have started running some simple tests with Multiwfn 3.8 to analyse hole-electrons formation in small gold clusters. I run default TD-DFT (TDA) calculations on Orca 5.03 and these inicial tests used B3LYP functional in combination with LANL2DZ. I am mainly interested in MO, atoms, and basis function contributions to hole-electrons distribution. However, for some of the contributions given by Multiwfn 3.8,  I get negative percentages. For example:

Using atom contribution from Mulliken method:
Contribution of each non-hydrogen atom to hole and electron:
    1(Au)  Hole:  6.66 %  Electron:  1.59 %  Overlap:  3.26 %  Diff.:  -5.07 %
    2(Au)  Hole:  1.89 %  Electron: -0.46 %  Overlap:  0.00 %  Diff.:  -2.36 %
    3(Au)  Hole:  2.73 %  Electron:  2.12 %  Overlap:  2.41 %  Diff.:  -0.61 %
    4(Au)  Hole: -7.83 %  Electron:  0.51 %  Overlap:  0.00 %  Diff.:   8.34 %
    5(Au)  Hole:  5.14 %  Electron:  7.69 %  Overlap:  6.29 %  Diff.:   2.55 %

Or for basis function contributions:
Sum of hole contributions:      0.921316
Sum of electron contributions:  0.921316

  Basis  Type    Atom    Shell     Hole      Electron     Overlap      Diff.
     3    S        1(Au)    3      2.15 %      0.21 %      0.67 %     -1.94 %
    11    Y        1(Au)    6      1.04 %      0.03 %      0.18 %     -1.01 %
    34    Z        2(Au)   14     -1.29 %     -0.02 %      0.00 %      1.27 %
    55    Y        3(Au)   22      0.11 %      1.12 %      0.35 %      1.01 %
    76    X        4(Au)   30     -0.72 %     -1.77 %      0.00 %     -1.05 %
    77    Y        4(Au)   30     -6.11 %     -0.10 %      0.00 %      6.01 %

I was wondering what could be the origin of this negative percentages and if this could indicate a problem with my TD-DFT calculation. Would this indicate that other contributions that are all positive (atom contribution from Hirshfeld partition method and MO contributions) could be wrong?

Many thanks,
Maicon