Propagator corrections to adiabatic time-dependent density-functional theory linear response theory

It has long been known that only one-electron excitations are available from adiabatic time-dependent density functional theory (TDDFT). This is particularly clear in Casida's formulation of TDDFT linear response theory [M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995), p. 155]. Nevertheless the explicit inclusion of two- and higher-electron excitations is necessary for an adequate description of some excited states, notably the first excited singlet states of butadiene and quartet excited states of molecules with a doublet ground state. The equation-of-motion superoperator approach is used here to derive a Casida-like propagator equation which can be clearly separated into an adiabatic part and a nonadiabatic part. The adiabatic part is identified as corresponding to Casida's equation for adiabatic TDDFT linear response theory. This equivalence is confirmed by deriving a general formula which includes the result that Gonze and Scheffler derived to show the equivalence of TDDFT and Gorling-Levy adiabatic connection perturbation theory for the exchange-only optimized effective potential [X. Gonze and M. Scheffler, Phys. Rev. Lett. 82, 4416 (1999)]. The nonadiabatic part explicitly corrects adiabatic TDDFT for two- and higher-electron excitations. The "dressed TDDFT" of Maitra, Zhang, Cave, and Burke is obtained as a special case where the ground state is closed shell [N. T. Maitra, F. Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004)]. The extension of dressed TDDFT to the case where the ground state is an open-shell doublet is presented, highlighting the importance of correctly accounting for symmetry in this theory. The extension to other ground state spin symmetries is a straightforward consequence of the present work. (C) 2005 American Institute of Physics.