1 Your Multiwfn version is too old. Multiwfn updates quite frequently. The current latest version of Multiwfn is not only significantly faster but also more accurate for Mulliken analysis (in fact, all analyses related to overlap matrix) based on CP2K wavefunction.

For latest version, boot up Multiwfn, load .molden file and input following command, then Multiwfn will perform Mulliken analysis and export result to t.txt in current folder:

7
5
-1
t.txt
1

From t.txt, you can find
Population of atoms:
     Atom      Alpha pop.   Beta pop.    Spin pop.     Atomic charge
     1(Fe)      9.63795      5.40172      4.23624         0.96033
     2(Fe)      9.63968      5.39163      4.24804         0.96869
...

The result is completely identical to that printed by CP2K, the following data can be found from your CP2K output file
# Orbital  AO symbol  Orbital population (alpha,beta)  Net charge  Spin moment
...
       1     Fe       1         9.637955     5.401720     0.960324     4.236235
...
       2     Fe       1         9.639677     5.391632     0.968691     4.248045

2 The purposes of functions 7-5 and 8-1 in Multiwfn are very different. Via 7-5 you can obtain population information, because unoccupied MOs do not have any contribution to population, obviously no information about unoccupied MOs could be given. In contrast, 8-1 can compute composition for any MO that you are interested in.

3 I don't find difference in result from Mulliken_NTO_with_fch.txt and Mulliken_NTO_with_mwfn.txt, and according to creating_NTO_orbital.txt, I don't know how S1.mwfn was generated.

Best regards,

Tian

Please compress your file and send it to me via E-mail.
But in the next 7 days I will be extremely busy, my response may be delayed.

Best,

Tian

2- Yes I have added [Cell] and [Nval] into molden file.
I am using the Multiwfn_3.8_dev version which is the latest version.

3- Can I send the results and input files by email?

Thank you,
Lili

1 You need to set ADDED_MOS to request CP2K to solve unoccupied orbitals. Also, diagonalization rather than OT should be used.

2 Please make sure that you have added [Cell] and [Nval] fields in .molden file, see Section 2.9.2.1 of Multiwfn manual for detail. Please also make sure that you are using latest version of Multiwfn.

3 I don't how did you perform the analysis, I need your detailed steps.

Best,

Tian

1- I used cp2k to create the molden file, and with that, I could calculate the Mullikenn analysis for MOs. However, the occupied orbitals are only printed and unoccupied orbitals are not printed. I want to check how electrons go to the unoccupied orbital after photoexcitation. So I need the information of HOMO-10 to LUMO+10 (as I calculated via TDDFT). I think if I change the occupation of unoccupied orbital to 1 in the molden file, it forces multiwfn to print these orbitals too. I checked this, and I could print the unoccupied orbitals. And it showed the results as I expected. I want to check if it is the correct approach.

2- I also did the Mulliken analysis with cp2k, and I checked the population of atoms (Alpha pop. Beta pop, spin pop). The difference between the results from cp2k and multiwfn is up to 0.5. Why is it the case? 

3- I want to do the Mulliken analysis of NTO, I  generated natural transition orbitals (NTOs) with multiwfn and printed NTO orbitals to a molden, fch, and mwfn files. When I used these files as an input file for Mulliken analysis, it gave the same results as when I did analysis of MOs. While I expected another results. 

Can you please help me to do Mulliken analysis for occupied and unoccupied orbitals for MOs and NTOs.

I really appreciate your help,
Best regards,
Lili