Transition moments from DPLOT cube file transition density

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I am new in the quantum chemistry community and I was playing with transition densities of molecules. I found a problem when I was trying to extract information about transition dipole moments from the transition density and compare it with the value in the NWChem output:

I run excited state calculations on the level of TDDFT-TDA and also RPA and export the transition density for the lowest lying excited states using the DPLOT option into the .cube file.

From NWChem output I can get the oscillator strength which seems to be related to the "Transition moment" as:

oscillator strength=2/3*me/hbar^2*(Excitation energy)*[(moment x)^2+(moment y)^2+(moment z)^2]

which is expected. The transition moments seem to be given in units of electron*bohr (so in Hartree a.u.).

When I try to get the transition moments by integration of the "Transition density" using the .cube files (assuming that the unit of the density is 1/bohr^3) I get a value of the dipole moment which is differing from the value given in the NWChem output by exactly sqrt(2) (it is smaller when integrated from the cube file).

The factor of sqrt(2) makes me wonder whether the cube file transition density assumes the Rydberg a.u. where the electron charge is defined as e^2/2=1, but this is a pure speculation.

I would be really grateful if somebody could help me clarify this discrepancy. I was trying to search for the unit conventions used for the export of the cube files, but I did not succeed.

Thanks a lot in advance!

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