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To whom it concerns,
At this moment, I would like to obtain transition dipole moment between two excited states and electron dipole moment of two states by mwfn. It could be simply achieved by opening .fchk file via mwfn and undergo 18 and 5 options.
However, I found that Gaussian at TDDFT level of theory calculates transition dipole moment based on relaxed density, which is a functional derivative of the energy with respect to an external one-particle potential, requiring the solution of so-called 'Z vector equations'. On the contrary, mwfn obtain transition dipole moment by unrelaxed density which can be calculated by direct integration of approximate wavefunction. Basically, relaxed density is generally considered to be more appropriate in calculating molecular properties.
So may I directly calculate such information of two excited states by mwfn employing relaxed density?
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Note that only "dipole moment of an excited state" rather than "transition dipole moment between two excited states" can be calculated based on relaxed excited state density. Subfunction 5 of main function 18 of Multiwfn is mainly used to calculate the latter. However, this function is also able to print electric dipole moments of all excited states, which are calculated based on unrelaxed excited state density and, as you said, not accurate as those evaluated based on relaxed density (despite this, this function is still useful, since all electric dipole moments can be given at once without evident additional computational cost).
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Perhaps your files for Multiwfn analysis is incorrect. Please make sure that at least IOp(9/40=4) has been used during Gaussian calculation, otherwise Multiwfn is unable to gain enough information for this kind of analysis.
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