Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution.

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.

Isolating Pure Donor and Acceptor Signals by Polarization-Controlled Transient Absorption Spectroscopy.

The optical spectra of molecules are often highly congested, inhibiting definite assignment of features and dynamics. In this work, we demonstrate and apply a polarization-based strategy for the decomposition of time-resolved optical spectra to analyze the electronic structure and energy transfer in a molecular donor-acceptor (D-A) dyad. We choose a dyad with orthogonal transition dipole moments for D and A and high fluorescence quantum yield to show that polarization-controlled ultrafast transient absorption spectra can isolate the pure D and A parts of the total signal. This provides a strategy to greatly reduce spectral congestion in complex systems and thus allows for detailed studies of electronic structure and electronic energy transfer.

Correlated spectral fluctuations quantified by line shape analysis of fifth-order two-dimensional electronic spectra.

Correlated spectral fluctuations were suggested to coordinate excitation transport inside natural light harvesting complexes. We demonstrate the capacities of 2D line shapes from fifth-order coherent electronic signals (R5-2D) to report on such fluctuations in molecular aggregates and present a stochastic approach to fluctuations in correlated site and bi-exciton binding energies in the optical dynamics of Frenkel excitons. The model is applied to R5-2D line shapes of a homodimer, and we show that the peak tilt dynamics are a measure for site energy disorder, inter-site correlation, and the strength of bi-exciton binding energy fluctuations.

Anharmonic Molecular Motion Drives Resonance Energy Transfer in peri-Arylene Dyads.

Spectral and dynamical properties of molecular donor-acceptor systems strongly depend on the steric arrangement of the constituents with exciton coupling J as a key control parameter. In the present work we study two peri-arylene based dyads with orthogonal and parallel transition dipoles for donor and acceptor moieties, respectively. We show that the anharmonic multi-well character of the orthogonal dyad's intramolecular potential explains findings from both stationary and time-resolved absorption experiments. While for a parallel dyad, standard quantum chemical estimates of J at 0 K are in good agreement with experimental observations, J becomes vanishingly small for the orthogonal dyad, in contrast to its ultrafast experimental transfer times. This discrepancy is not resolved even by accounting for harmonic fluctuations along normal coordinates. We resolve this problem by supplementing quantum chemical approaches with dynamical sampling of fluctuating geometries. In contrast to the moderate Gaussian fluctuations of J for the parallel dyad, fluctuations for the orthogonal dyad are found to follow non-Gaussian statistics leading to significantly higher effective J in good agreement with experimental observations. In effort to apply a unified framework for treating the dynamics of optical coherence and excitonic populations of both dyads, we employ a vibronic approach treating electronic and selected vibrational degrees on an equal footing. This vibronic model is used to model absorption and fluorescence spectra as well as donor-acceptor transport dynamics and covers the more traditional categories of Förster and Redfield transport as limiting cases.

Magnetic pulses enable multidimensional optical spectroscopy of dark states.

The study and manipulation of low dipole moment quantum states have been challenging due to their inaccessibility by conventional spectroscopic techniques. Controlling the spin in such states requires unfeasible strong magnetic fields to overcome typical decoherence rates. However, the advent of terahertz technology and its application in magnetic pulses opens up a new scenario. In this article, we focus on an electron-hole pair model to demonstrate that it is possible to control the precession of the spins and to modify the transition rates to different spin states. Enhancing transitions from a bright state to a dark state with different spins means that the latter can be revealed by ordinary spectroscopy. We propose a modification of the standard two-dimensional spectroscopic scheme in which a three pulse sequence is encased in a magnetic pulse. Its role is to drive transitions between a bright and a dark spin state, making the latter susceptible to spectroscopic investigation.

Carotenoid-to-bacteriochlorophyll energy transfer through vibronic coupling in LH2 from Phaeosprillum molischianum.

The peripheral light-harvesting antenna complex (LH2) of purple photosynthetic bacteria is an ideal testing ground for models of structure-function relationships due to its well-determined molecular structure and ultrafast energy deactivation. It has been the target for numerous studies in both theory and ultrafast spectroscopy; nevertheless, certain aspects of the convoluted relaxation network of LH2 lack a satisfactory explanation by conventional theories. For example, the initial carotenoid-to-bacteriochlorophyll energy transfer step necessary on visible light excitation was long considered to follow the Förster mechanism, even though transfer times as short as 40 femtoseconds (fs) have been observed. Such transfer times are hard to accommodate by Förster theory, as the moderate coupling strengths found in LH2 suggest much slower transfer within this framework. In this study, we investigate LH2 from Phaeospirillum (Ph.) molischianum in two types of transient absorption experiments-with narrowband pump and white-light probe resulting in 100 fs time resolution, and with degenerate broadband 10 fs pump and probe pulses. With regard to the split Qx band in this system, we show that vibronically mediated transfer explains both the ultrafast carotenoid-to-B850 transfer, and the almost complete lack of transfer to B800. These results are beyond Förster theory, which predicts an almost equal partition between the two channels.

Anharmonic vibrational effects in linear and two-dimensional electronic spectra.

For the description of vibrational effects in electronic spectra, harmonic vibrations are a convenient and widespread model. However, spectra of larger organic molecules in solution usually exhibit signs of vibrational anharmonicity, as revealed by deviation from the mirror image symmetry between linear absorption and emission spectra of the harmonic case. For perylene and terylene, two molecules with rigid Pi-electron systems and strong vibrational-electronic coupling, we employ a simple but effective theoretical model, which introduces cubic anharmonicity in the potentials of electronic surfaces. Vibrational anharmonicity is then readily quantified based on the experimentally measured peak ratio of the first vibronic progression peaks in linear absorption and emission. This method is straightforward but not applicable if emission from the initially excited state is short lived. For such a case, we employ two-dimensional electronic spectroscopy in the visible as a comprehensive time-resolved technique for the experimental determination of the vibrational anharmonicity of pinacyanol iodide, a solvated dye molecule exhibiting ultrafast excited state isomerization. We show that the ratio between certain cross peak amplitudes in two-dimensional electronic spectra is a direct measure of vibrational anharmonicity.

Vibrational relaxation beyond the linear damping limit in two-dimensional optical spectra of molecular aggregates.

We present a computational model for the spectra of molecular aggregates with signatures of vibronic progression. Vibronic dynamics is implemented by coupling the dynamics of Frenkel excitons with underdamped vibrations. Vibrational dynamics includes linear damping resulting in the exponential decay and quadratic damping inducing subexponential or power law relaxation and increasing vibrational decoherence as demonstrated on lineshapes of the absorption spectrum. Simulations of the third-order coherent response account for bath reorganization during excitonic transport, which allows us to study the line-shape evolution of cross peaks of 2D spectra.

Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy.

Center line slope (CLS) analysis in 2D infrared spectroscopy has been extensively used to extract frequency-frequency correlation functions of vibrational transitions. We apply this concept to 2D electronic spectroscopy, where CLS is a measure of electronic gap fluctuations. The two domains, infrared and electronic, possess differences: In the infrared, the frequency fluctuations are classical, often slow and Gaussian. In contrast, electronic spectra are subject to fast spectral diffusion and affected by underdamped vibrational wavepackets in addition to Stokes shift. All these effects result in non-Gaussian peak profiles. Here, we extend CLS-analysis beyond Gaussian line shapes and test the developed methodology on a solvated molecule, zinc phthalocyanine. We find that CLS facilitates the interpretation of 2D electronic spectra by reducing their complexity to one dimension. In this way, CLS provides a highly sensitive measure of model parameters describing electronic-vibrational and electronic-solvent interaction.

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.

Distinguishing Electronic and Vibronic Coherence in 2D Spectra by Their Temperature Dependence.

Long-lived oscillations in 2D spectra of chlorophylls are at the heart of an ongoing debate. Their physical origin is either a multipigment effect, such as excitonic coherence, or localized vibrations. We show how relative phase differences of diagonal- and cross-peak oscillations can distinguish between electronic and vibrational (vibronic) effects. While direct discrimination between the two scenarios is obscured when peaks overlap, their sensitivity to temperature provides a stronger argument. We show that vibrational (vibronic) oscillations change relative phase with temperature, while electronic oscillations are only weakly dependent. This highlights that studies of relative phase difference as a function of temperature provide a clear and easily accessible method to distinguish between vibrational and electronic coherences.

Novel coherent two-dimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules.

We demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The third-order optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k(2) in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (Ornstein-Uhlenbeck, two-state jump, and diffusion in double well) of the dihedral angle that controls the chirality.

Exciton coherence length fluctuations in chromophore aggregates probed by multidimensional optical spectroscopy.

The coherent third order optical response of molecular aggregates with fluctuating frequencies, couplings, and transition dipole moments is studied. We derived stochastic nonlinear exciton equations (SNEEs) by combining the quasiparticle picture of excitons with the path integral over stochastic bath paths described by the stochastic Liouville equations. Coherent two-dimensional (2D) spectra are calculated for a tetramer model system whose transition dipole orientations undergo two-state stochastic jumps on an arbitrary timescale. Correspondence between domains of ordered dipoles, which determine the exciton coherence length and the absorption peaks, is established. Signatures of domain coherence length fluctuations are observed in the cross peak dynamics of the 2D spectra in specific pulse polarization configurations.

Strong field line shapes and photon statistics from a single molecule under anomalous noise.

We revisit the line-shape theory of a single molecule with anomalous stochastic spectral diffusion. Waiting time profiles for bath induced spectral jumps in the ground and excited states become different when a molecule, probed by continuous-wave laser field, reaches the steady state. This effect is studied for the stationary dichotomic continuous-time-random-walk spectral diffusion of a single two-level chromophore with power-law distributions of waiting times. Correlated waiting time distributions, line shapes, two-point fluorescence correlation function, and Mandel Q parameter are calculated for arbitrary magnitude of laser field. We extended previous weak field results and examined the breakdown of the central limit theorem in photon statistics, indicated by asymptotic power-law growth of Mandel Q parameter. Frequency profile of the Mandel Q parameter identifies the peaks of spectrum, which are related to anomalous spectral diffusion dynamics.

Stochastic Liouville equations for coherent multidimensional spectroscopy of excitons.

Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath modulation model of a dimer and a four-state jump bath model of a single chromophore). Slow Gaussian-Markovian spectral diffusion of a symmetric dimer induces new peaks which are damped as the dipole moment is equilibrated. These effects require an explicit treatment of the bath and may not be described by lower-level theories such as the Redfield equations, which eliminate the bath.

Anomalous lineshapes and aging effects in two-dimensional correlation spectroscopy.

Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical pulse. Using the continuous time random walk model for spectral diffusion, we analyze the signatures of anomalous relaxation in two-dimensional four wave mixing signals. Different models which share the same two point joint probability distribution show markedly different lineshapes and may be distinguished. Aging random walks corresponding to waiting time distributions with diverging first moment show dependence of 2D lineshapes on initial observation time, which persist for long times.

Probing anomalous relaxation by coherent multidimensional optical spectroscopy.

We propose to study the origin of algebraic decay of two-point correlation functions observed in glasses, proteins, and quantum dots by their nonlinear response to sequences of ultrafast laser pulses. Power-law spectral singularities and temporal relaxation in two-dimensional correlation spectroscopy signals are predicted for a continuous time random walk model of stochastic spectral jumps in a two-level system with a power-law distribution of waiting times psi(t) approximately t;{-alpha-1}. Spectroscopic signatures of stationary ensembles for 1

Stochastic simulation of chemical exchange in two dimensional infrared spectroscopy.

The stochastic Liouville equations are employed to investigate the combined signatures of chemical exchange (two-state jump) and spectral diffusion (coupling to an overdamped Brownian oscillator) in the coherent response of an anharmonic vibration to three femtosecond infrared pulses. Simulations reproduce the main features recently observed in the OD stretch of phenol in benzene.

Coherence and correlations in multitime quantum measurements of stochastic quantum trajectories.

Quantum effects on multitime distributions and correlation functions of single objects, stemming from both the dynamics and repeated measurements, are calculated for a driven harmonic system using a superoperator generating functional formalism. Marked differences between multipoint observables associated with classical and quantum measurements are identified. The effects of quantum collapse and measurement resolution are discussed.