project time dependent wavefunction onto ground state wavefunction in TDDFT

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Background

It is helpful to project the dynamic wavefunction onto the ground state wavefunction, so the coefficient could represent the occupation number of the ground state band.

Describe the solution you'd like

add options like TDAP(http://tdap.iphy.ac.cn/TDAP.pdf) for analysis the result of TDDFT:

TD.WriteDMOfSelectiveOrbitals (logical): Whether to output the partial DM of centain
band and orbital projection.
Default value: false
TD.PartialDMBand (data block): Specify the band to output and orbital projection. See
also TD.PartialDMSumOrbitals.
Multiple lines with each of them include one band index. The corresponding charge density
will be projected to the selected orbital blocks, and output to file: chgBand Index.txt
For instance:
%block PartialDMBand
1
2
%endblock PartialDMBand
will analysis the band 1-2 and projected them to the orbital blocks. Default value: No
default values
TD.PartialDMSumOrbitals (data block): Specify orbital blocks for projection. See also
TD.PartialDMBand.
Multiple lines with each of them include the start index and the end index of the orbital.
The corresponding charge density will be projected to the selected orbital blocks, and
output to file: chgBand Index.txt
For instance:
%block PartialDMSumOrbitals
1 10
11 22
%endblock PartialDMSumOrbitals
will analysis the selected band (using TD.PartialDMBand) and projected them to the
two orbital blocks: 1 to 10 and 11 to 22. Default value: No default values

According to the option used in TDAP, it seems all the post-processing could be done by using the reduced density matrix and doesn't need too many hardware resources.

Additional Context

No response