Electronic Density - RT-TDDFT vs TDDFT

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When I compare the electron density difference (excited state minus ground state) of a RT-TDDFT and a normal linear response TDDFT calculation they are quite different. For instance, given that the absorption spectra from both calculations are the same, if I do the RT-TDDFT calculation, shouldn't the electron density at the maximum of the dipole oscillation be the same as the static TDDFT calculation?


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Extracting the excited state density from a RT-TDDFT calculation for a single electron excitation is problematic for a few reasons (e.g. https://aip.scitation.org/doi/10.1063/1.4900514). If you want to compare RT-TDDFT and LR-TDDFT results, your best bet is to calculate the transition density directly, which can be done via a Fourier transform of the density fluctuations in a RT-TDDFT calculation (see https://aip.scitation.org/doi/10.1063/1.4742763 Eq. 20).

It can be a bit cumbersome to do and can potentially require a lot of disk space for all of the density matrices that need to be generated, but it will produce the same results as LR-TDDFT, dependent on the quality of the Fourier transform. We used the same analysis in our paper on excited state absorption from RT-TDDFT, where it worked beautifully (e.g. https://pubs.acs.org/doi/10.1021/acs.jctc.5b00473 Fig. 8, the agreement between LR and RT is not exact in this case for the reasons discussed in the paper).

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