Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems
Journal of Chemical Physics
Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: ͑a͒ Totally wrong behavior of the excited state surface along a bond-breaking coordinate, ͑b͒ lack of doubly excited configurations, affecting again excited state surfaces, and ͑c͒ much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory ͑TDDMFT͒. For two-electron systems the exact exchange-correlation
... correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned ͑which are all strikingly exhibited by prototype two-electron systems such as dissociating H 2 and HeH + ͒. At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: ͑a͒ In the fully nonadiabatic ͑-dependent, exact͒ formulation of linear response TDDMFT, it can be shown that linear response ͑LR͒-TDDMFT is able to provide exact excitation energies, in particular, the first order ͑linear response͒ formulation does not prohibit the correct representation of doubly excited states; ͑b͒ within previously formulated simple adiabatic approximations the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; ͑c͒ an adiabatic approximation is formulated in which also the double excitations are fully accounted for.