No.

I have now recalculated with IOp(9/40=4), but it does not help:

GAUSSIAN:
Mulliken charges:
               1
     1  C   -0.529187
     2  H    0.237978
     3  O    0.053232
     4  H    0.237978

MULTIWFN (using 18 13 ... Multiwfn3.8 NO_0001.mwfn ...):
Population of atoms:
Atom     1(C )    Population:  6.52500478    Net charge: -0.52500478
Atom     2(H )    Population:  0.75219581    Net charge:  0.24780419
Atom     3(O )    Population:  7.97060360    Net charge:  0.02939640
Atom     4(H )    Population:  0.75219581    Net charge:  0.24780419

I have also noticed that Multiwfn can produce the charges (almost) identical to Gaussian's ones
if I do the following:

Multiwfn3.8 td.fchk
200
16
CI Rho(1)

reboot

Multiwfn3.8 new.mwfn
7
5
1

Population of atoms:
Atom     1(C )    Population:  6.52918728    Net charge: -0.52918728
Atom     2(H )    Population:  0.76202245    Net charge:  0.23797755
Atom     3(O )    Population:  7.94676785    Net charge:  0.05323215
Atom     4(H )    Population:  0.76202245    Net charge:  0.23797755

So maybe the problem is with the density matrix itself... ?

Dear Tian Lu,

Thank you for this example.

I think there is a discrepancy between Multiwfn (Version 3.8(dev), release date: 2021-Aug-17) and Gaussian Mulliken charges in case of UNRELAXED density.

Have you added IOp(9/40=4)?
If not, only very limited configuration coefficients will be passed to Multiwfn, and the result will be inaccurate.

Thank you for this example.

I think there is a discrepancy between Multiwfn (Version 3.8(dev), release date: 2021-Aug-17) and Gaussian Mulliken charges in case of UNRELAXED density.

I use the same example, but with "density(RhoCI)":

%nproc=6
%mem=100gb
%chk=td
#p b3lyp/6-31g(d) TD density(RhoCI)

test

0 1
C                  0.00000000    0.00000000    0.52887991
H                  0.00000000    0.93775230    1.12379107
O                  0.00000000    0.00000000   -0.67757652
H                  0.00000000   -0.93775230    1.12379107

Gaussian Mulliken charges are

Mulliken charges:
               1
     1  C   -0.529187
     2  H    0.237978
     3  O    0.053232
     4  H    0.237978

In the case of Multiwfn, I follow 4.18.13 of the manual:

Multiwfn3.8 td.fchk
18
13
td.log
1

reboot

Multiwfn3.8 NO_0001.mwfn
7
5
1

Population of atoms:
Atom     1(C )    Population:  6.52542524    Net charge: -0.52542524
Atom     2(H )    Population:  0.75233290    Net charge:  0.24766710
Atom     3(O )    Population:  7.96990898    Net charge:  0.03009102
Atom     4(H )    Population:  0.75233290    Net charge:  0.24766710

So the charges are not identical.

Why is this so?

Thank you in advance.

Probably some other Multiwfn users also have this question, I paste my reply below:

Please note that Multiwfn only loads orbitals from .fch file. If you want to input wavefunction of excited state into Multiwfn, you have to store natural orbitals of an excited state into Multiwfn.

Below I illustrate how to properly obtain Mulliken charge of an excited state.

This is a Gaussian input file
%chk=C:\gtest\H2CO.chk
#p b3lyp/6-31g(d) TD density

test

0 1
C                  0.00000000    0.00000000    0.52887991
H                  0.00000000    0.93775230    1.12379107
O                  0.00000000    0.00000000   -0.67757652
H                  0.00000000   -0.93775230    1.12379107

The outputted Mulliken charges correspond to the S1 state:
Mulliken charges:
               1
     1  C   -0.206651
     2  H    0.197002
     3  O   -0.187352
     4  H    0.197002

Transform the H2CO.chk to H2CO.fchk, then boot up Multiwfn, input below commands
H2CO.fchk
200
16  // Generate natural orbitals (NOs) based on the density matrix in .fch file
CI  // TDDFT density matrix in the .fch has "CI" label
y
0
Now the orbitals in the memory correspond to NOs of S1 state, you can perform any analysis as usual, for example calculating Mulliken charges:
7
5
1
The result is completely identical to those outputted by Gaussian
Population of atoms:
Atom     1(C )    Population:    6.20665    Net charge:   -0.20665
Atom     2(H )    Population:    0.80300    Net charge:    0.19700
Atom     3(O )    Population:    8.18735    Net charge:   -0.18735
Atom     4(H )    Population:    0.80300    Net charge:    0.19700

In addition, you could find a .molden file have been generated in current folder, it contains NOs of S1 state. In the future, you can directly perform analyses for S1 state by directly using this file as input file.

In fact, above mentioned points have been mentioned at the beginning of Chapter 4 of the manual, please search "Generating .fch file" in the manual.