Charge and excitation-energy transfer in time-dependent density functional theory
- Learning about and understanding the mechanisms and pathways of charge and excitation-energy transfer of natural molecular complexes is a promising approach for the tailored design of new artificial energy-converting materials. Therefore, next to extensive experimental investigations, a theoretical method that is able to reliably describe and predict these phenomena from first principles is of practical relevance. In principle, density functional theory (DFT) and time-dependent density functional theory (TDDFT) appear as natural choices to study the relevant sizable molecules on a first-principles scale at bearable computational cost. However, the application of standard local and semilocal density functional approximations suffers from well-known deficiencies, in particular, as far as the simulation of charge-transfer phenomena is concerned. The present thesis approaches charge and excitation-energy transfer with the objective of improving the predictive power and extending the range of applicability of (TD)DFT.
The deficiencies of standard density functional approximations have been related to self-interaction. Hence, one major aspect of this work is the extension of the self-interaction correction in Kohn-Sham DFT that is based on the generalized optimized effective potential to TDDFT using a real-time propagation approach. The multiplicative Kohn-Sham potential allows for a transparent analysis of the exchange-correlation potential during time evolution. It reveals frequency-dependent field-counteracting behavior and step structures that appear in dynamic charge-transfer situations. The latter are important for the proper description of charge transfer. Self-interaction correction allows to access many cases that are difficult for standard TDDFT ranging from chain-like systems over excitonic excitations in semiconductor nanoclusters to short- and long-range charge-transfer excitations. At the same time, it does not spoil the reasonable accuracy that already (semi)local functionals exhibit for local excitations. Moreover, the TDDFT perspective on self-interaction correction sheds new light also on the ground-state formalism. Complex degrees of freedom in the energy-minimizing transformation of the generalized optimized effective potential approach yield smoother orbital densities that appear more reasonable when inserted into approximate functionals in the self-interaction correction formalism. This work provides new insight into the use of different functional approximations. Last but not least, the influence of spin-symmetry breaking and step structures of the potential on the preference to transfer integer units of the elementary electric charge between largely separated donor and acceptor moieties is illustrated when static external electric fields are applied. This work has been reported in three publications and one submitted manuscript.
In the field of excitation-energy transfer, recent discoveries of quantum coherence effects shed new light on the mechanisms behind energy-transfer rates. The latter are affected by a number of different properties of the isolated molecules, but involve also effects due to the environment of the system. This thesis addresses excitation-energy transfer phenomena from two perspectives. First, I use real-time propagation TDDFT to investigate the intermolecular coupling strength and the coupling mechanism between single fragments of supermolecular setups. These investigations base on standard closed quantum system TDDFT and exploit the coherent oscillation of excitation energy between separated molecules after the initial excitation process. Second, I use open quantum system ideas in the framework of TDDFT to study the influence of the system’s environment on the energy-transfer time scales and pathways in a circular arrangement of molecules using an effective energy-dissipation mechanism. The first part of these results is published. The second part is presented in this thesis and includes work in progress.
Describing Charge Transfer in Extended Donor-Acceptor Systems with Density Functional Theory
- It is a long-standing problem of (time-dependent) density functional theory ((TD)DFT) that traditional functionals severely underestimate charge transfer (CT) excitations. In particular, the theoretical description of donor-acceptor (DA) systems is plagued by this shortcoming. DA systems are frequently used as light absorbing components in organic photovoltaic devices. The lowest electronic excitation in these molecules is usually influenced by CT.
In order to support the systematic development of new DA systems that are needed to improve the efficiency of organic solar cells it is a prerequisite for theory to reliably predict the electronic properties of this system class.
We demonstrate that the tuned range-separated hybrid (RSH) approach predicts these excitations in accordance with experiment. The approach can be regarded as an implicitly defined density functional within the generalized Kohn-Sham (GKS) scheme of DFT. Its main ingredient is the range-separation parameter that determines the splitting between long- and short-range exchange. It is obtained from first principles by enforcing the ionization potential theorem of GKS theory.
We consider DA systems of various sizes that are composed of thiophene as donor and benzothiadiazole or naphthalene diimide as acceptor. We show how the optical and electronic properties can be tailored by changing the conjugation length and the arrangement of the donor and acceptor components. We also address the downsides that accompany the use of tuned RSH functionals. Due to the way the approach is implicitly defined anew for each system it is not size consistent. By calculating ground state properties of atoms and diatomic molecules we report size consistency errors and demonstrate consequences of the size consistency violation, e.g., the incorrect prediction of binding energies.
In order to reliably predict CT excitations within the Kohn Sham scheme of DFT the exchange correlation potential approximation has to incorporate particle number discontinuities. A candidate potential with the necessary features is the Becke-Johnson potential that is based on semi-local ingredients and is therefore computationally attractive for the treatment of very large systems. We show, however, that the potential cannot be applied in TDDFT because it is not a functional derivative and violates the zero-force theorem. We discuss a procedure on the basis of density path integrals that transforms the BJ potential into a functional derivative of a corresponding energy expression.