Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate.

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Signatures of intramolecular vibrational and vibronic Q[Formula: see text]-Q[Formula: see text] coupling effects in absorption and CD spectra of chlorophyll dimers.

An electron-vibrational coupling model that includes the vibronic (non-adiabatic) coupling between the Q[Formula: see text] and Q[Formula: see text] transitions of chlorophyll (Chl), created by Reimers and coworkers (Scientific Rep. 3, 2761, 2013) is extended here to chlorophyll dimers with interchlorophyll excitonic coupling. The model is applied to a Chl a dimer of the water-soluble chlorophyll binding protein (WSCP). As for isolated chlorophyll, the vibronic coupling is found to have a strong influence on the high-frequency vibrational sideband in the absorption spectrum, giving rise to a band splitting. In contrast, in the CD spectrum the interplay of vibronic coupling and static disorder leads to a strong suppression of the vibrational sideband in excellent agreement with the experimental data. The conservative nature of the CD spectrum in the low-energy region is found to be caused by a delicate balance of the intermonomer excitonic coupling between the purely electronic Q[Formula: see text] transition and the Q[Formula: see text] transition involving intramolecular vibrational excitations on one hand and the coupling to higher-energy electronic transitions on the other hand.

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space.

In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the "Hierarchical Equations of Motion" (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.

Exciton transfer using rates extracted from the "hierarchical equations of motion".

Frenkel exciton population dynamics of an excitonic dimer is studied by comparing the results from a quantum master equation involving rates from second-order perturbative treatment with respect to the excitonic coupling with the non-perturbative results from "Hierarchical Equations of Motion" (HEOM). By formulating generic Liouville-space expressions for the rates, we can choose to evaluate them either via HEOM propagations or by applying the cumulant expansion. The coupling of electronic transitions to bath modes is modeled either as overdamped oscillators for the description of thermal bath components or as underdamped oscillators to account for intramolecular vibrations. Cases of initial nonequilibrium and equilibrium vibrations are discussed. In the case of HEOM, initial equilibration enters via a polaron transformation. Pointing out the differences between the nonequilibrium and equilibrium approach in the context of the projection operator formalism, we identify a further description, where the transfer dynamics is driven only by fluctuations without involvement of dissipation. Despite this approximation, this approach can also yield meaningful results in certain parameter regimes. While for the chosen model, HEOM has no technical advantage for evaluation of the rate expressions compared to cumulant expansion, there are situations where only evaluation with HEOM is applicable. For instance, a separation of reference and interaction Hamiltonian via a polaron transformation to account for the interplay between Coulomb coupling and vibrational oscillations of the bath at the level of a second-order treatment can be adjusted for a treatment with HEOM.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories.

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

Vibronic coupling explains the ultrafast carotenoid-to-bacteriochlorophyll energy transfer in natural and artificial light harvesters.

The initial energy transfer steps in photosynthesis occur on ultrafast timescales. We analyze the carotenoid to bacteriochlorophyll energy transfer in LH2 Marichromatium purpuratum as well as in an artificial light-harvesting dyad system by using transient grating and two-dimensional electronic spectroscopy with 10 fs time resolution. We find that Förster-type models reproduce the experimentally observed 60 fs transfer times, but overestimate coupling constants, which lead to a disagreement with both linear absorption and electronic 2D-spectra. We show that a vibronic model, which treats carotenoid vibrations on both electronic ground and excited states as part of the system's Hamiltonian, reproduces all measured quantities. Importantly, the vibronic model presented here can explain the fast energy transfer rates with only moderate coupling constants, which are in agreement with structure based calculations. Counterintuitively, the vibrational levels on the carotenoid electronic ground state play the central role in the excited state population transfer to bacteriochlorophyll; resonance between the donor-acceptor energy gap and the vibrational ground state energies is the physical basis of the ultrafast energy transfer rates in these systems.

Coherent two-dimensional photocurrent spectroscopy in a PbS quantum dot photocell.

Recently there has been growing interest in the role of coherence in electronic dynamics. Coherent multidimensional spectroscopy has been used to reveal coherent phenomena in numerous material systems. Here we utilize a recent implementation of coherent multidimensional spectroscopy--two-dimensional photocurrent spectroscopy--in which we detect the photocurrent from a PbS quantum dot photocell resulting from its interactions with a sequence of four ultrafast laser pulses. We observe sub-picosecond evolution of two-dimensional spectra consistent with multiple exciton generation. Moreover, a comparison with two-dimensional fluorescence spectra of the quantum dots demonstrates the potential of two-dimensional photocurrent spectroscopy to elucidate detailed origins of photocurrent generating electronic state coherence pathways. Since the measurement is based on detecting the photocell current in situ, the method is well suited to study the fundamental ultrafast processes that affect the function of the device. This opens new avenues to investigate and implement coherent optimization strategies directly within devices.

Combined treatment of relaxation and fluctuation dynamics in the calculation of two-dimensional electronic spectra.

While the theoretical description of population transfer subsequent to electronic excitation in combination with a line shape function description of vibrational dynamics in the context of 2D-spectroscopy is well-developed under the assumption of different timescales of population transfer and fluctuation dynamics, the treatment of the interplay between both kinds of processes lacks a comprehensive description. To bridge this gap, we use the cumulant expansion approach to derive response functions, which account for fluctuation dynamics and population transfer simultaneously. We compare 2D-spectra of a model system under different assumptions about correlations between fluctuations and point out under which conditions a simplified treatment is justified. Our study shows that population transfer and dissipative fluctuation dynamics cannot be described independent of each other in general. Advantages and limitations of the proposed calculation method and its compatibility with the modified Redfield description are discussed.

3D spectroscopy of vibrational coherences in quantum dots: theory.

In semiconductor nanocrystals, called quantum dots (QD), electronic transition energies, phonon frequencies, and electron-phonon coupling strengths are all reported to depend on the size of the crystals. The size dependencies of the transition energies and the mode frequencies are well characterized and understood. At the same time, the electron-phonon coupling dependence on size is controversial-even the sign of the change is not settled. In this article, third-order response functions of a model QD resembling CdSe are calculated. The longitudinal optical (LO) mode is included as a relatively narrow Lorentzian contribution to the spectral density. A novel version of electronic 2D spectroscopy is investigated where a third Fourier transform is taken over a so-called population time, leading to 3D spectral representation. The amplitude and phase of the 2D cuts of the 3D spectral body around the LO mode frequency are analyzed. The analytical power and sensitivity of the cuts in determining the possible Huang-Rhys factor (electron-phonon coupling strength) and the LO mode frequency dependence on the QD size are investigated. Peak structures in the cuts with a tilt relative to the diagonal are identified as sensitive signatures for the size dependencies. The study elucidates the 3D representation of the electronic 2D spectroscopy as a powerful tool for obtaining insight into otherwise hardly accessible characteristics of the system.

Intermolecular torsional motion of a π-aggregated dimer probed by two-dimensional electronic spectroscopy.

The energetic splitting of the two exciton states of a molecular dimer depends strongly on the relative orientation of the monomers with respect to each other. The curvature of the corresponding adiabatic potential energy surfaces can lead to torsional motion of the monomers. It has been suggested recently that this torsional motion could provide a possible relaxation mechanism for the upper state which proceeds via a crossing of the two singly excited state potentials. Another, competing, relaxation mechanism is provided by coupling to the environment, leading to direct exciton relaxation. Here we examine theoretically the combined dynamics of torsional motion and excitonic relaxation for a π-aggregated dimer. Using two-dimensional (2D) spectroscopy, it is shown how torsional motion through a crossing of the adiabatic excitonic potential surfaces could be distinguished from direct relaxation. For the calculations a mixed quantum/classical approach is used, where the torsional motion is treated by an Ehrenfest type of equation, while the excitonic dynamics including dephasing and direct relaxation is described by a quantum master equation.

Probing the geometry dependence of molecular dimers with two-dimensional-vibronic spectroscopy.

Two-dimensional (2D) vibronic correlation spectra of molecular dimers are calculated, taking a single vibration in each monomer into account. Within the employed wave function approach, the coupling to a surrounding is included only phenomenologically. It is shown that this offers a straightforward understanding of the spectra. The influence of the relative orientation of the monomer transition dipole moments and the electronic coupling strength is investigated. Employing a model for perylene bisimide, we predict the 2D-vibronic spectra for the monomer and dimer configurations.

Exciton trapping in pi-conjugated materials: a quantum-chemistry-based protocol applied to perylene bisimide dye aggregates.

Access to excited-state structures and dynamics of pi-chromophor aggregates is needed to understand their fluorescence behavior and the properties of related materials. A quantum-chemistry-based protocol that provides quantitative and qualitative insight into fluorescence spectra has been applied to perylene bisimide dimers and provides excellent agreement with measured fluorescence spectra. Both dispersion and dipol-dipole interactions determine the preferred relative arrangements of the chromophores in ground and excited states of the dimer. An exciton trapping mechanism is identified, which may limit the energy transfer properties of perylene bisimide and other dye materials.

Circular dichroism spectroscopy of small molecular aggregates: dynamical features and size effects.

Circular dichroism (CD) spectra of small molecular aggregates, taking monomer vibrational motion into account, are calculated by employing wave packet propagation techniques. The spectra are related to the population and exciton transfer in the aggregates. It is investigated as to how far this dynamics can be directly extracted from the CD spectra. The method is applied to aggregates of perylene bisimides where temperature dependent spectra have recently been recorded in our laboratory [V. Dehm et al., Org. Lett. 9, 1085 (2007)].

Circular dichroism and absorption spectroscopy of merocyanine dimer aggregates: molecular properties and exciton transfer dynamics from time-dependent quantum calculations.

A wave packet approach to the calculation and interpretation of circular dichroism (CD) spectra is applied to the spectroscopy of aggregates of a merocyanine dye. A combined analysis of absorption and CD spectra allows for the extraction of geometric information and excited state electronic coupling. It is shown that in the case of dimer aggregates of a chiral merocyanine dye, it is possible to infer the dynamics of an exciton transfer directly from the CD spectrum. This relation is established via the Fourier relation to a time-dependent correlation function reflecting the quantum dynamics in the dye aggregate.

Absorption spectroscopy of molecular trimers.

Absorption properties of molecular trimers are studied within a model including a single monomer internal vibrational degree of freedom. Upon photoabsorption, three excited electronic states which are coupled excitonically are accessed. Band shapes resulting from different electronic coupling strengths and geometries are analyzed. It is shown that geometric information can be extracted from the band intensities. Taking data recorded for perylene bisimide aggregates as an example, the spectra for monomer, dimer, and trimer systems are compared.

On the calculation of circular dichroism spectra using quantum wave-packet dynamics with an application to molecular dimers.

Circular dichroism (CD) spectra are calculated from the Fourier transform of a time-correlation function. The latter can efficiently be evaluated by wave-packet propagation methods. This approach is similar to the time-dependent evaluation of absorption or Raman spectra. As an application, correlation functions and CD spectra for a molecular dimer are determined and compared to the case of absorption.

Photoluminescence and conductivity of self-assembled pi-pi stacks of perylene bisimide dyes.

The self-assembly of a new, highly fluorescent perylene bisimide dye 2 into pi stacks, both in solution and condensed phase, has been studied in detail by NMR spectroscopy, vapor pressure osmometry (VPO), UV/Vis and fluorescence spectroscopy, differential scanning calorimetry (DSC), optical polarizing microscopy (OPM) and X-ray diffraction. The NMR and VPO measurements revealed the formation of extended pi-pi stacks of the dye molecules in solution. The aggregate size determined from VPO and DOSY NMR measurements agree well with that obtained from the concentration and temperature-dependent UV/Vis spectral data by employing the isodesmic model (equal K model). In the condensed state, dye 2 possesses a hexagonal columnar liquid crystalline (LC) phase as confirmed by X-ray diffraction analysis. The columnar stacking of this dye has been further explored by atomic force microscopy (AFM). Well-resolved columnar nanostructures of the compound are observed on graphite surface. A color-tunable luminescence from green to red has been observed upon aggregation which is accompanied by an increase of the fluorescence lifetime and depolarization. The observed absorption properties can be explained in terms of molecular exciton theory. The charge transport properties of dye 2 have been investigated by pulse radiolysis-time resolved microwave conductivity measurements and a 1D charge carrier mobility up to 0.42 cm(2) V(-1) s(-1) is obtained. Considering the promising self-assembly, semiconducting, and luminescence properties of this dye, it might serve as a useful functional material for nano(opto)electronics.