Charge-Transfer Excitations: A Challenge for Time-Dependent Density Functional Theory That Has Been Met

It is well-known that time-dependent density functional theory (TDDFT) yields substantial errors for the excitation energies of charge-transfer (CT) excited states, when approximate standard exchange-correlation (xc) functionals are used, for example, SVWN, BLYP, or B3LYP. Also, the correct 1/R asymptotic behavior of CT states with respect to a distance coordinate R between the separated charges of the CT state is not reproduced by TDDFT employing these xc-functionals. Here, we demonstrate by analysis of the TDDFT equations that the first failure is due to the self-interaction error in the orbital energies from the ground-state DFT calculation, while the latter is a similar self-interaction error in TDDFT arising through the electron transfer in the CT state. Possible correction schemes, such as inclusion of exact Hartree-Fock or exact Kohn-Sham exchange, as well as aspects of the exact xc-functional are discussed in this context. Furthermore, a practical approach is proposed which combines the benefits of TDDFT and configuration interaction singles (CIS) and which does not suffer from electron-transfer self-interaction. The latter approach is applied to a (1,4)-phenylene-linked zincbacteriochlorin-bacteriochlorin complex and to a bacteriochlorophyll-spheroidene complex, in which CT states may play important roles in energy and electron-transfer processes. The errors of TDDFT alone for the CT states are demonstrated, and reasonable estimates for the true excitation energies of these states are given.

Our objective in this Account is 3-fold. First, we provide an overview of the optical and electronic processes that take place in a solid-state organic solar cell, which we define as a cell in which the semiconducting materials between the electrodes are organic, be them polymers, oligomers, or small molecules; this discussion is also meant to set the conceptual framework in which many of the contributions to this Special Issue on Photovoltaics can be viewed. We successively turn our attention to (i) optical absorption and exciton formation, (ii) exciton migration to the donor-acceptor interface, (iii) exciton dissociation into charge carriers, resulting in the appearance of holes in the donor and electrons in the acceptor, (iv) charge-carrier mobility, and (v) charge collection at the electrodes. For each of these processes, we also describe the theoretical challenges that need to be overcome to gain a comprehensive understanding at the molecular level. Finally, we highlight recent theoretical advances, in particular regarding the determination of the energetics and dynamics at organic-organic interfaces, and underline that the right balance needs to be found for the optimization of material parameters that often result in opposite effects on the photovoltaic performance.

Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional [T. Yanai et al. Chem. Phys. Lett. 393, 51 (2004)], together with a standard generalized gradient approximation (GGA) and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity Lambda, and the extent to which excitation energy errors correlate with Lambda is quantified. For a set of 59 excitations of local, Rydberg, and intramolecular charge-transfer character in 18 theoretically challenging main-group molecules, CAM-B3LYP provides by far the best overall performance; no correlation is observed between excitation energy errors and Lambda, reflecting the good quality, balanced description of all three categories of excitation. By contrast, a clear correlation is observed for the GGA and, to a lesser extent, the hybrid functional, allowing a simple diagnostic test to be proposed for judging the reliability of a general excitation from these functionals--when Lambda falls below a prescribed threshold, excitations are likely to be in very significant error. The study highlights the ambiguous nature of the term "charge transfer," providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.