Irene Burghardt

Ultrafast charge separation in organic photovoltaics enhanced by charge delocalization and vibronically hot exciton dissociation.

In organic photovoltaics, the mechanism by which free electrons and holes are generated, overcoming the Coulomb attraction, is a currently much debated topic. To elucidate this mechanism at a molecular level, we carried out a combined electronic structure and quantum dynamical analysis that captures the elementary events from the exciton dissociation to the free carrier generation at polymer/fullerene donor/acceptor heterojunctions. Our calculations show that experimentally observed efficient charge separations can be explained by a combination of two effects: First, the delocalization of charges which substantially reduces the Coulomb barrier, and second, the vibronically hot nature of the charge-transfer state which promotes charge dissociation beyond the barrier. These effects facilitate an ultrafast charge separation even at low-band-offset heterojunctions.

Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method

A consistent treatment of environmental effects is proposed in the framework of the multiconfiguration time-dependent Hartree (MCTDH) method. The method is extended in view of treating complex molecular systems which require an exact quantum dynamics for a certain number of “primary” modes while an approximate dynamics is adequate for a class of “secondary” modes. The latter may correspond to the weakly coupled modes in a polyatomic molecule, or the first solvent shell in a solute-solvent complex. For these modes, a description in terms of parameterized functions is introduced. The MCTDH working equations are generalized to allow for the nonorthogonality of these functions, which may take, e.g., a multidimensional Gaussian form. The formalism is developed on the level of both the wave function description and the density matrix description. Dissipative effects are accounted for in terms of a stochastic Hamiltonian approach versus master equation approach in the respective descriptions.

Direct observation of ultrafast collective motions in CO myoglobin upon ligand dissociation

Observing ultrafast myoglobin dynamics The oxygen-storage protein myoglobin was the first to have its three-dimensional structure determined and remains a workhorse for understanding how protein structure relates to function. Barends et al. used x-ray free-electron lasers with femtosecond short pulses to directly observe motions that occur within half a picosecond of CO dissociation (see the Perspective by Neutze). Combining the experiments with simulations shows that ultrafast motions of the heme couple to subpicosecond protein motions, which in turn couple to large-scale motions. Science, this issue p. 445, see also p. 381 Time-resolved crystallography at an x-ray laser reveals ultrafast structural changes in myoglobin upon ligand dissociation. [Also see Perspective by Neutze] The hemoprotein myoglobin is a model system for the study of protein dynamics. We used time-resolved serial femtosecond crystallography at an x-ray free-electron laser to resolve the ultrafast structural changes in the carbonmonoxy myoglobin complex upon photolysis of the Fe-CO bond. Structural changes appear throughout the protein within 500 femtoseconds, with the C, F, and H helices moving away from the heme cofactor and the E and A helices moving toward it. These collective movements are predicted by hybrid quantum mechanics/molecular mechanics simulations. Together with the observed oscillations of residues contacting the heme, our calculations support the prediction that an immediate collective response of the protein occurs upon ligand dissociation, as a result of heme vibrational modes coupling to global modes of the protein.

Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics

The MCTDH method has been used successfully to treat the non-adiabatic dynamics of a number of systems. These are hard problems due to the number of modes that need to be included in a calculation, and the strong coupling between the nuclear and electronic motion at conical intersections connecting electronic states in these systems. In this review, an overview of the basic theory of the method is given highlighting how it is able to treat larger systems than other quantum dynamics methods. The vibronic coupling model Hamiltonian is also described, which provides a good starting point for the description of these systems. Examples of calculations made and systems treated are given. Finally, a development of the basic MCTDH method in which some of the usual time-dependent basis functions are replaced by Gaussian wavepackets is outlined. This method promises not only to treat larger systems, but to provide a consistent quantum–semiclassical framework.

Full quantum mechanical molecular dynamics using Gaussian wavepackets

Abstract We present the first application of a promising new method for quantum dynamics calculations. Based on the efficient multiconfiguration time-dependent Hartree wavepacket propagation algorithm, it can treat part, or all, of the wavepacket using Gaussian functions. The Gaussian parameters evolve using variational, coupled equations of motion. In this way the Gaussian basis functions evolve so as to optimally describe the wavepacket. Here, a four-dimensional Henon–Heiles potential surface is used to demonstrate that only a few Gaussian functions are required, and convergence on the full quantum mechanical result is rapid.

Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine

The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method is applied to calculate the S(2)(pipi( *)) absorption spectrum of the pyrazine molecule, whose diffuse structure results from the ultrafast nonadiabatic dynamics at the S(2)-S(1) conical intersection. The 24-mode second-order vibronic-coupling model of Raab et al. [J. Chem. Phys. 110, 936 (1999)] is employed, along with 4-mode and 10-mode reduced-dimensional variants of this model. G-MCTDH can be used either as an all-Gaussian approach or else as a hybrid method using a partitioning into primary modes, treated by conventional MCTDH basis functions, and secondary modes described by Gaussian particles. Comparison with standard MCTDH calculations shows that the method converges to the exact result. The variational, nonclassical evolution of the moving Gaussian basis is a key element in obtaining convergence. For high-dimensional systems, convergence is significantly accelerated if the method is employed as a hybrid scheme.

Multiconfigurational system-bath dynamics using Gaussian wave packets: Energy relaxation and decoherence induced by a finite-dimensional bath

The quantum dynamics of an anharmonic oscillator coupled to a bath of up to 60 harmonic oscillators is investigated by a new multiconfigurational hybrid method for wave packet propagation. The method, originally proposed in [Burghardt, Meyer, and Cederbaum, J. Chem. Phys. 111, 2927 (1999)], represents a variant of the multiconfiguration time-dependent Hartree method including a moving basis of Gaussian functions. Energy relaxation and quantum decoherence induced by the zero-temperature oscillator bath are shown to be accurately described by the new method. Decoherence rates for a bath with a discretized ohmic spectral density are found to be consistent with golden-rule predictions for T=0.

Phonon-Driven Ultrafast Exciton Dissociation at Donor-Acceptor Polymer Heterojunctions

A quantum-dynamical analysis of exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parametrized for three electronic states and 28 vibrational modes. Two representative interfacial configurations are considered, both of which exhibit an ultrafast exciton decay. The efficiency of the process depends critically on the presence of intermediate bridge states, and on the dynamical interplay of high- vs low-frequency phonon modes. The ultrafast, highly nonequilibrium dynamics is consistent with time-resolved spectroscopic observations.

Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics

An approach to non-Markovian system-environment dynamics is described which is based on the construction of a hierarchy of coupled effective environmental modes that is terminated by coupling the final member of the hierarchy to a Markovian bath. For an arbitrary environment, which is linearly coupled to the subsystem, the discretized spectral density is replaced by a series of approximate spectral densities involving an increasing number of effective modes. This series of approximants, which are constructed analytically in this paper, guarantees the accurate representation of the overall system-plus-bath dynamics up to increasing times. The hierarchical structure is manifested in the approximate spectral densities in the form of the imaginary part of a continued fraction similar to Mori theory. The results are described for cases where the hierarchy is truncated at the first-, second-, and third-order level. It is demonstrated that the results generated from a reduced density matrix equation of motion and large dimensional system-plus-bath wavepacket calculations are in excellent agreement. For the reduced density matrix calculations, the system and hierarchy of effective modes are treated explicitly and the effects of the bath on the final member of the hierarchy are described by the Caldeira-Leggett equation and its generalization to zero temperature.

Exciton dissociation at donor-acceptor polymer heterojunctions: Quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a semiconducting polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C==C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree method.