Linear Response Calculations for Polymers

Abstract

In general, finite field DFT and TDDFT calculations yield accurate values for the response properties of molecular systems when standard approximations for the exchange-correlation functionals are used [Gross 1996]. In combination with their high efficiency, this makes these theoretical approaches ideal candidates for the calculation of physical properties of large molecular systems of technological interest. For an important class of materials, however, this potential is not yet realized. It has been observed that density functional calculations on the static response properties of long π-conjugated molecular chains give large overestimations for the polarizability [Champagne 1998] when local and gradient-corrected exchange-correlation functionals are used. The errors become even worse for their nonlinear response properties [Champagne 1998]. Similarly, the static polarization of p-conjugated push-pull systems is incorrectly described [Champagne 2000], even if it is obtained in the absence of an external field. Closely related to these findings, also large errors have been reported in the calculated excitation energies [Grimme 2003]. The reason for these deviations is by now well understood: both local and gradientcorrected density approximations are unable to correctly describe the induced contribution to the exact exchange-correlation potential (see Chap. 9). It contains a component that increases linearly along the chain counteracting the external field [van Gisbergen 1999b, Gritsenko 2000]. The density, on the other hand, remains more-or-less periodic in the bulk of the chains, and changes only at the chain ends. The same phenomenon that is responsible for the macroscopic exchange-correlation field in insulating solids [Gonze 1995b, Gonze 1997b, Martin 1997a] seems to be at work here. In the infinite systems this additional screening field can be viewed as a polarization dependent exchange-correlation effect. In the finite molecular systems, however, the complete density is known, and no polarization dependence of the exchange-correlation functional needs to be invoked. It becomes clear that the failure of the standard density functionals is related to their local density dependence: the exchange-correlation potential is relatively insensitive to the polarization charge induced by the external electric field at the chain ends. The external field is insufficiently screened, and a too strong response is obtained in these approximations.