Charge Transfer, Double and Bond-Breaking Excitations with Time-Dependent Density Matrix Functional Theory

Abstract

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bondbreaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H 2 and HeH . We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-toantibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for. DOI: 10.1103/PhysRevLett.101.033004 PACS numbers: 31.15.Aÿ, 31.15.Eÿ, 33.20.ÿt Dissociation of molecular systems poses a serious challenge within the DFT framework. This is already true for the ground state energy curve cf., e.g., Ref.[1]. For excited states, the problems are even worse; there are various kinds of excitations which are not correctly represented in TDDFT calculations. Figure 1(a) displays the failure of TDDFT (in its adiabatic BP86 variant) for the potential energy surface (PES) of the first excited state of H 2 , 1 1 u , corresponding to the g ! u orbital excitation. As highlighted in Ref.[2], this PES goes to zero instead of going asymptotically to ca. 10 eV. B3LYP does not improve the situation at all. In Fig. 1(b), we document the TDDFT problem with double excitations for the g excitation energies of dissociating H 2 . It is evident that there is an exact state (the third at R e 1:4 Bohr) which is missing in the TDDFT calculations. This is the doubly excited g 2 ! u 2 state. The double-excitation nature is indicated with dots on the PES curve, and it is clear that, in the accurate calculations, the doubly excited state becomes lower with increasing R and has avoided crossings with the second and first state, becoming the lowest excited 1 g state (2 1 g ) from ca. 2.5 Bohr onwards. This state is completely missing in the TDDFT calculations. After some initial optimism that such doubly excited states would be accurately calculated in TDDFT, it has become clear this is not the case [3][4][5]. Figure 1(c) gives an example of the charge transfer problem. The excitation energies of HeH are shown along the dissociation coordinate for the lowest three 1 excited states. At long distance, these excitations have strong charge transfer character, from He 1s to H 1s in 2 and from He 1s to H 2s; 2p z in 3 and 4 . The TDDFT excitation energies exhibit at long distance the well-known severe underestimation of charge transfer excitations [6]. The hybrid functional B3LYP improves somewhat on the pure GGA BP86. We note that the excited state energy does not have a 1=R asymptotic behavior for this type of charge transfer excited state, the fragments being He and neutral H. The...

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