Mapping Vibronic Couplings in a Solar Cell Dye with Polarization-Selective Two-Dimensional Electronic-Vibrational Spectroscopy

Time-resolved vibronic spectra with nuclear-electronic orbital time-dependent configuration interaction

Time-resolved spectroscopy is an important tool for probing photochemically induced nonequilibrium dynamics and energy transfer. Herein, a method is developed for the ab initio simulation of vibronic spectra and dynamical processes. This framework utilizes the recently developed nuclear-electronic orbital time-dependent configuration interaction (NEO-TDCI) approach, which treats all electrons and specified nuclei quantum mechanically on the same footing. A strategy is presented for calculating time-resolved vibrational and electronic absorption spectra from any initial condition. Although this strategy is general for any TDCI implementation, utilizing the NEO framework allows for the explicit inclusion of quantized nuclei, as illustrated through the calculation of vibrationally hot spectra. Time-resolved spectra produced by either vibrational or electronic Rabi oscillations capture ground-state absorption, stimulated emission, and excited-state absorption between vibronic states. This methodology provides the foundation for fully ab initio simulations of multidimensional spectroscopic experiments.

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Observing vibronic coupling in a strongly hydrogen bonded system with coherent multidimensional vibrational-electronic spectroscopy

The coupled structural and electronic parameters of intramolecular hydrogen bonding play an important role in ultrafast chemical reactions, such as proton transfer processes. We perform one- and two-dimensional vibrational-electronic (1D and 2D VE) spectroscopy experiments to understand the couplings between vibrational and electronic coordinates in 10-Hydroxybenzo[h]quinoline, an ultrafast proton transfer system. The experiments reveal that the OH stretch (νOH) is strongly coupled to the electronic excitation, and Fourier analysis of the 1D data shows coherent oscillations from the low frequency backbone vibrational modes coupled to the νOH mode, resulting in an electronically detected vibronic signal. In-plane low-frequency vibrations at 242 and 386 cm-1 change the hydrogen bond distance and modulate the observed electronic signal in the polarization-selective 1D VE experiment through orientation-dependent coupling with the νOH mode. Resolution of the excitation frequency axis with 2D VE experiments reveals that excitation frequency, detection frequency, and experimental delay affect the frequency and strength of the vibronic transitions observed. Our results demonstrate evidence of direct coupling of the high frequency νOH mode with the S1 ← S0 electronic transition in 10-Hydroxybenzo[h]quinoline (HBQ), and orientation-dependent couplings of the low-frequency 242 and 386 cm-1 modes to the νOH mode and the electronic transition. This demonstration of multidimensional VE spectroscopy on HBQ reveals the potential of using 1D and 2D VE spectroscopy to develop a quantitative understanding of the role of vibronic coupling in hydrogen bonding and ultrafast proton transfer for complex systems.

Second-Order Mass-Weighting Scheme for Atom-Centered Density Matrix Propagation Molecular Dynamics

The atom-centered density matrix propagation (ADMP) method is an extended Lagrangian approach to ab initio molecular dynamics, which includes the density matrix in an orthonormalized atom-centered Gaussian basis as additional, fictitious, electronic degrees of freedom, classically propagated along with the nuclear ones. A high adiabaticity between the nuclear and electronic subsystems is mandatory in order to keep the trajectory close to the Born-Oppenheimer (BO) surface. In this regard, the fictitious electronic mass μ, being a symmetric, nondiagonal matrix in its most general form, represents a free parameter, exploitable to optimize the propagation of the electronic density. Although mass-weighting schemes in ADMP exist, a systematic procedure to define an optimal value of the fictitious masses is not available yet. In this work, in order to rationally evaluate the electronic mass, fictitious electronic normal modes are defined through the diagonalization of the Hessian of the electronic density matrix. If the same frequency is imposed on all such modes (compatible with the chosen integration time step), then the corresponding μ matrix can be calculated and then employed for the following propagation. Analysis of several ADMP test simulations reveals that such Hessian-based mass-weighting approach is able to ensure, together with a 0.1/0.2 fs time steps, a high separation between the (real) nuclear and the (fictitious) electronic frequencies, which determines a high adiabaticity. This high, unprecedented, accuracy in the propagation leads, in turn, to low errors in the estimated nuclear vibrational frequencies, making the ADMP method totally comparable to a fully converged BO molecular dynamics simulation but more computationally efficient. This work, therefore, contributes to a further development of the ADMP ab initio molecular dynamics method, aimed at improving its accuracy through a more rational evaluation of the fictitious electronic mass parameter.

Watching the Interplay between Photoinduced Ultrafast Charge Dynamics and Nuclear Vibrations

Here is presented the ultrafast hole-electron dynamics of photoinduced metal to ligand charge-transfer (MLCT) states in a Ru(II) complex, [Ru(dcbpy)2(NCS)2]4- (dcbpy = 4,4'-dicarboxy-2,2'-bipyridine), a photoactive molecule employed in dye sensitized solar cells. Via cutting-edge computational techniques, a tailored computational protocol is here presented and developed to provide a detailed analysis of the electronic manifold coupled with nuclear vibrations to better understand the nonradiative pathways and the resulting overall dye performances in light-harvesting processes (electron injection). Thus, the effects of different vibrational modes were investigated on both the electronic levels and charge transfer dynamics through a theoretical-computational approach. First, the linear response time-dependent density functional (LR-TDDFT) formalism was employed to characterize excitation energies and spacing among electronic levels (the electronic layouts). Then, to understand the ultrafast (femtosecond) charge dynamics on the molecular scale, we relied on the nonperturbative mean-field quantum electronic dynamics via real-time (RT-) TDDFT. Three vibrational modes were selected, representative for collective nuclear movements that can have a significant influence on the electronic structure: two involving NCS- ligands and one involving dcbpy ligands. As main results, we observed that such MLCT states, under vibrational distortions, are strongly affected and a faster interligand electron transfer mechanism is observed along with an increasing MLCT character of the adiabatic electronic states approaching closer in energy due to the vibrations. Such findings can help both in providing a molecular picture of multidimensional vibro-electronic spectroscopic techniques, used to characterize ultrafast coherent and noncoherent dynamics of complex systems, and to improve dye performances with particular attention to the study of energy or charge transport processes and vibronic couplings.

Observation of parallel intersystem crossing and charge transfer-state dynamics in [Fe(bpy)3]2+ from ultrafast 2D electronic spectroscopy

Transition metal-based charge-transfer complexes represent a broad class of inorganic compounds with diverse photochemical applications. Charge-transfer complexes based on earth-abundant elements have been of increasing interest, particularly the canonical [Fe(bpy)3]2+. Photoexcitation into the singlet metal-ligand charge transfer (1MLCT) state is followed by relaxation first to the ligand-field manifold and then to the ground state. While these dynamics have been well-studied, processes within the MLCT manifold that facilitate and/or compete with relaxation have been more elusive. We applied ultrafast two-dimensional electronic spectroscopy (2DES) to disentangle the dynamics immediately following MLCT excitation of this compound. First, dynamics ascribed to relaxation out of the initially formed 1MLCT state was found to correlate with the inertial response time of the solvent. Second, the additional dimension of the 2D spectra revealed a peak consistent with a ∼20 fs 1MLCT → 3MLCT intersystem crossing process. These two observations indicate that the complex simultaneously undergoes intersystem crossing and direct conversion to ligand-field state(s). Resolution of these parallel pathways in this prototypical earth-abundant complex highlights the ability of 2DES to deconvolve the otherwise obscured excited-state dynamics of charge-transfer complexes.

Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (J. Chem. Phys., 2018, 148, 102326), the Split-Liouvillian (SL) (Chem. Phys., 2017, 482, 124-134), and the algorithm in J. Chem. Phys., 2012, 136, 084101 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyze the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem, and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.

Theoretical investigation of solvent and oxidation/deprotonation effects on the electronic structure of a mononuclear Ru-aqua-polypyridine complex in aqueous solution

Mononuclear polypyridine ruthenium (Ru) complexes can catalyze various reactions, including water splitting, and can also serve as photosensitizers in solar cells. Despite recent progress in their synthesis, accurately modeling their physicochemical properties, particularly in solution, remains challenging. Herein, we conduct a theoretical investigation of the structural and electronic properties of a mononuclear Ru-aqua polypyridine complex in aqueous solution, considering five of its possible oxidation/protonation states species: [RuII(H2O)(py)(bpy)2]2+, [RuII(OH)(py)(bpy)2]+, [RuIII(H2O)(py)(bpy)2]3+, [RuIII(OH)(py)(bpy)2]2+ and [RuIV(O)(py)(bpy)2]2+, where py = pyridine and bpy = 2,2'-bipyridine. At first, we investigate the impact of proton-coupled and non-coupled electron transfer reactions on the geometry and electronic structure of the complexes in vacuum and in solution, using an implicit solvent model. Then, using a sequential multiscale approach that combines quantum mechanics and molecular mechanics (S-QM/MM), we examine the explicit solvent effects on the electronic excitations of the complexes, and compare them with the experimental results. The complexes were synthesized, and their absorption spectra measured in aqueous solution. To accurately describe the QM interactions between the metal center and the aqueous ligand in the MM simulations, we developed new force field parameters for the Ru atom. We analyze the solvent structure around the complexes and account for its explicit influence on the polarization and electronic excitations of the complexes. Notably, accounting for the explicit solvent polarization effects of the first solvation shells is essential to correctly describe the energy of the electronic transitions, and the explicit treatment of the hydrogen bonds at the QM level in the excitation calculations improves the accuracy of the description of the metal-to-ligand charge-transfer bands. Transition density matrix analysis is used to characterize all electronic transitions in the visible and ultraviolet ranges according to their charge-transfer (CT) character. This study elucidates the electronic structure of those ruthenium polypyridyl complexes in aqueous solution and underscores the importance of precisely describing solvent effects, which can be achieved employing the S-QM/MM method.

Nature of the Ultrafast Interligands Electron Transfers in Dye-Sensitized Solar Cells

Charge-transfer dynamics and interligand electron transfer (ILET) phenomena play a pivotal role in dye-sensitizers, mostly represented by the Ru-based polypyridyl complexes, for TiO2 and ZnO-based solar cells. Starting from metal-to-ligand charge-transfer (MLCT) excited states, charge dynamics and ILET can influence the overall device efficiency. In this letter, we focus on N34- dye ( [Ru(dcbpy)2(NCS)2]4-, dcbpy = 4,4'-dicarboxy-2,2'-bipyridine) to provide a first direct observation with high time resolution (<20 fs) of the ultrafast electron exchange between bpy-like ligands. ILET is observed in water solution after photoexcitation in the ∼400 nm MLCT band, and assessment of its ultrafast time-scale is here given through a real-time electronic dynamics simulation on the basis of state-of-the-art electronic structure methods. Indirect effects of water at finite temperature are also disentangled by investigating the system in a symmetric gas-phase structure. As main result, remarkably, the ILET mechanism appears to be based upon a purely electronic evolution among the dense, experimentally accessible, MLCT excited states manifold at ∼400 nm, which rules out nuclear-electronic couplings and proves further the importance of the dense electronic manifold in improving the efficiency of dye sensitizers in solar cell devices.

Understanding Charge Dynamics in Dense Electronic Manifolds in Complex Environments

Photoinduced charge transfer (CT) excited states and their relaxation mechanisms can be highly interdependent on the environment effects and the consequent changes in the electronic density. Providing a molecular interpretation of the ultrafast (subpicosecond) interplay between initial photoexcited states in such dense electronic manifolds in condensed phase is crucial for improving and understanding such phenomena. Real-time time-dependent density functional theory is here the method of choice to observe the charge density, explicitly propagated in an ultrafast time domain, along with all time-dependent properties that can be easily extracted from it. A designed protocol of analysis for real-time electronic dynamics to be applied to time evolving electronic density related properties to characterize both in time and in space CT dynamics in complex systems is here introduced and validated, proposing easy to be read cross-correlation maps. As case studies to test such tools, we present the photoinduced charge-transfer electronic dynamics of 5-benzyluracil, a mimic of nucleic acid/protein interactions, and the metal-to-ligand charge-transfer electronic dynamics in water solution of [Ru(dcbpy)2(NCS)2]4-, dcbpy = (4,4'-dicarboxy-2,2'-bipyridine), or "N34-", a dye sensitizer for solar cells. Electrostatic and explicit ab initio treatment of solvent molecules have been compared in the latter case, revealing the importance of the accurate modeling of mutual solute-solvent polarization on CT kinetics. We observed that explicit quantum mechanical treatment of solvent slowed down the charge carriers mobilities with respect to the gas-phase. When all water molecules were modeled instead as simpler embedded point charges, the electronic dynamics appeared enhanced, with a reduced hole-electron distance and higher mean velocities due to the close fixed charges and an artificially increased polarization effect. Such analysis tools and the presented case studies can help to unveil the influence of the electronic manifold, as well as of the finite temperature-induced structural distortions and the environment on the ultrafast charge motions.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Electronic and Vibrational Manifold of Tetracyanoethylene-Chloronaphthalene Charge Transfer Complex in Solution: Insights from TD-DFT and Ab Initio Molecular Dynamics

The interplay between light absorption and the molecular environment has a central role in the observed photophysics of a wide range of photoinduced chemical and biological phenomena. The understanding of the interplay between vibrational and electronic transitions is the focus of this work, since it can provide a rationale to tune the optical properties of charge transfer (CT) materials used for technological applications. A clear description of these processes poses a nontrivial challenge from both the theoretical and experimental points of view, where the main issue is how to accurately describe and probe drastic changes in the electronic structure and the ultrafast molecular relaxation and dynamics. In this work we focused on the intermolecular CT reaction that occurs upon photon absorption in a π-stacked model system in dichloromethane solution, in which the 1-chloronaphthalene (1ClN) acts as the electron donor and tetracyanoethylene (TCNE) is the electron acceptor. Density functional theory calculations have been carried out to characterize both the ground-state properties and more importantly the low-lying CT electronic transition, and excellent agreement with recently available experimental results [Mathies, R. A.; et al. J. Phys. Chem. A 2018, 122 (14), 3594] was obtained. The minima of the ground state and first singlet excited state have been accurately characterized in terms of spatial arrangements and vibrational Raman frequencies, and the CT natures of the first two low-lying electronic transitions in the absorption spectra have been addressed and clarified too. Finally, by modeling the possible coordination sites of the TCNE electron acceptor with respect to monovalent ions (Na+, K+) in an implicit solution of acetonitrile, we find that TCNE can accommodate a counterion in two different arrangements, parallel and orthogonal to the C═C axis, leading to the formation of a contact ion pair. The nature of the counterion and its relative position entail structural modifications of the TCNE radical anion, mainly the central C═C and C≡N bonds, compared to the isolated case. An important red shift of the C═C stretching frequency was observed when the counterion is orthogonal to the double bond, to a greater extent for Na+. On the contrary, in the second case, where the counterion ion lies along the internuclear C═C axis, we find that K+ polarizes the electron density of the double bond more, resulting in a greater red shift than with Na+.

2D electronic-vibrational spectroscopy with classical trajectories

Two-dimensional electronic-vibrational (2DEV) spectra have the capacity to probe electron–nuclear interactions in molecules by measuring correlations between initial electronic excitations and vibrational transitions at a later time. The trajectory-based semiclassical optimized mean trajectory approach is applied to compute 2DEV spectra for a system with excitonically coupled electronic excited states vibronically coupled to a chromophore vibration. The chromophore mode is in turn coupled to a bath, inducing redistribution of vibrational populations. The lineshapes and delay-time dynamics of the resulting spectra compare well with benchmark calculations, both at the level of the observable and with respect to contributions from distinct spectroscopic processes.

Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Direct observation of the solvent organization and nuclear vibrations of [Ru(dcbpy)2(NCS)2]4-, [dcbpy = (4,4'-dicarboxy-2,2'-bipyridine)], via ab initio molecular dynamics

Environmental effects can drastically influence the optical properties and photoreactivity of molecules, particularly in the presence of polar and/or protic solvents. In this work we investigate a negatively charged Ru(II) complex, [Ru(dcbpy)₂(NCS)₂]^4- [dcbpy = (4,4'-dicarboxy-2,2'-bipyridine)], in water solution, since this system belongs to a broader class of transition-metal compounds undergoing upon photo-excitation rapid and complex charge transfer (CT) dynamics, which can be dictated by structural rearrangement and solvent environment. Ab initio molecular dynamics (AIMD) relying on a hybrid quantum/molecular mechanics scheme is used to probe the equilibrium microsolvation around the metal complex in terms of radial distribution functions of the main solvation sites and solvent effects on the overall equilibrium structure. Then, using our AIMD-based generalized normal mode approach, we investigate how the ligand vibrational spectroscopic features are affected by water solvation, also contributing to the interpretation of experimental Infra-Red spectra. Two solvation sites are found for the ligands: the sulfur and the oxygen sites can interact on average with ∼4 and ∼3 water molecules, respectively, where a stronger interaction of the oxygen sites is highlighted. On average an overall dynamic distortion of the C₂ symmetric gas-phase structure was found to be induced by water solvation. Vibrational analysis reproduced experimental values for ligand symmetric and asymmetric stretchings, linking the observed shifts with respect to the gas-phase to a complex solvent distribution around the system. This is the groundwork for future excited-state nuclear and electronic dynamics to monitor non-equilibrium processes of CT excitation in complex environments, such as exciton migration in photovoltaic technologies.

Two-dimensional electronic-vibrational spectroscopy: Exploring the interplay of electrons and nuclei in excited state molecular dynamics

Two-dimensional electronic-vibrational spectroscopy (2DEVS) is an emerging spectroscopic technique which exploits two different frequency ranges for the excitation (visible) and detection (infrared) axes of a 2D spectrum. In contrast to degenerate 2D techniques, such as 2D electronic or 2D infrared spectroscopy, the spectral features of a 2DEV spectrum report cross correlations between fluctuating electronic and vibrational energy gaps rather than autocorrelations as in the degenerate spectroscopies. The center line slope of the spectral features reports on this cross correlation function directly and can reveal specific electronic-vibrational couplings and rapid changes in the electronic structure, for example. The involvement of the two types of transition moments, visible and infrared, makes 2DEVS very sensitive to electronic and vibronic mixing. 2DEV spectra also feature improved spectral resolution, making the method valuable for unraveling the highly congested spectra of molecular complexes. The unique features of 2DEVS are illustrated in this paper with specific examples and their origin described at an intuitive level with references to formal derivations provided. Although early in its development and far from fully explored, 2DEVS has already proven to be a valuable addition to the tool box of ultrafast nonlinear optical spectroscopy and is of promising potential in future efforts to explore the intricate connection between electronic and vibrational nuclear degrees of freedom in energy and charge transport applications.

Two-dimensional vibrational-electronic spectra with semiclassical mechanics

Two-dimensional vibrational-electronic (2DVE) spectra probe the effects on vibronic spectra of initial vibrational excitation in an electronic ground state. The optimized mean trajectory (OMT) approximation is a semiclassical method for computing nonlinear spectra from response functions. Ensembles of classical trajectories are subject to semiclassical quantization conditions, with the radiation-matter interaction inducing discontinuous transitions. This approach has been previously applied to two-dimensional infrared and electronic spectra and is extended here to 2DVE spectra. For a system including excitonic coupling, vibronic coupling, and interaction of a chromophore vibration with a resonant environment, the OMT method is shown to well approximate exact quantum dynamics.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity

Two-dimensional Electronic-Vibrational (2D EV) spectroscopy and two-dimensional Vibrational-Electronic (2D VE) spectroscopy are among the newest additions to the coherent multidimensional spectroscopy toolbox, and they are directly sensitive to vibronic couplings. In this first of two papers, the complete orientational response functions are developed for a model system consisting of two coupled anharmonic oscillators and two electronic states in order to simulate polarization-selective 2D EV and 2D VE spectra with arbitrary combinations of linearly polarized electric fields. Here, we propose analytical methods to isolate desired signals within complicated spectra and to extract the relative orientation between vibrational and vibronic dipole moments of the model system using combinations of polarization-selective 2D EV and 2D VE spectral features. Time-dependent peak amplitudes of coherence peaks are also discussed as means for isolating desired signals within the time-domain. This paper serves as a field guide for using polarization-selective 2D EV and 2D VE spectroscopies to map coupled vibronic coordinates on the molecular frame.

The role of mixed vibronic Qy-Qx states in green light absorption of light-harvesting complex II

The importance of green light for driving natural photosynthesis has long been underappreciated, however, under the presence of strong illumination, green light actually drives photosynthesis more efficiently than red light. This green light is absorbed by mixed vibronic Q_y-Q_x states, arising from chlorophyll (Chl)-Chl interactions, although almost nothing is known about these states. Here, we employ polarization-dependent two-dimensional electronic-vibrational spectroscopy to study the origin and dynamics of the mixed vibronic Q_y-Q_x states of light-harvesting complex II. We show the states in this region dominantly arise from Chl b and demonstrate how it is possible to distinguish between the degree of vibronic Q_y versus Q_x character. We find that the dynamics for states of predominately Chl b Q_y versus Chl b Q_x character are markedly different, as excitation persists for significantly longer in the Q_x states and there is an oscillatory component to the Q_x dynamics, which is discussed. Our findings demonstrate the central role of electronic-nuclear mixing in efficient light-harvesting and the different functionalities of Chl a and Chl b.

The green component of the solar spectrum can efficiently drive natural photosynthesis, but the process has been little investigated due to the complexity of the excited states involved. Here the authors utilize polarization-dependent two-dimensional electronic-vibrational spectroscopy to define the origin and dynamics of these states in light-harvesting complex II.

Monitoring the evolution of intersite and interexciton coherence in electronic excitation transfer via wave-packet interferometry

We detail an experimental strategy for tracking the generation and time-development of electronic coherence within the singly excited manifold of an energy-transfer dimer. The technique requires that the two monomers have nonparallel electronic transition-dipole moments and that these possess fixed orientations in space. It makes use of two-dimensional wave-packet interferometry (WPI or whoopee) measurements in which the A, B, C, and D pulses have respective polarizations e, e, e, and e'. In the case of energy-transfer coupling that is weak or strong compared to electronic-nuclear interactions, it is convenient to follow the evolution of intersite or interexciton coherence, respectively. Under weak coupling, e could be perpendicular to the acceptor chromophore's transition dipole moment and the unit vector e' would be perpendicular to the donor's transition dipole. Under strong coupling, e could be perpendicular to the ground-to-excited transition dipole to the lower exciton level and e' would be perpendicular to the ground-to-excited transition dipole to the upper exciton level. If the required spatial orientation can be realized for an entire ensemble, experiments of the kind proposed could be performed by either conventional four-wave-mixing or fluorescence-detected WPI methods. Alternatively, fluorescence-detected whoopee experiments of this kind could be carried out on a single energy-transfer dimer of fixed orientation. We exhibit detailed theoretical expressions for the desired WPI signal, explain the physical origin of electronic coherence detection, and show calculated observed-coherence signals for model dimers with one, two, or three internal vibrational modes per monomer and both weak and strong energy-transfer coupling.

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

Determining the Orientation and Vibronic Couplings between Electronic and Vibrational Coordinates with Polarization-Selective Two-Dimensional Vibrational-Electronic Spectroscopy

We experimentally demonstrate polarization-selective two-dimensional (2D) vibrational-electronic (VE) spectroscopy on a transition-metal mixed-valence complex where the cyanide stretching vibrations are coupled to the metal-to-metal charge-transfer transition. A simultaneous fitting of the parallel and crossed polarized 2D VE spectra quantifies the relative vibronic coupling strengths and angles between the charge-transfer transition and three coupled cyanide stretching vibrations in a mode-specific manner. In particular, we find that the bridging vibration, which modulates the distance between the transition-metal centers, is oriented nearly parallel to the charge-transfer axis and is 9 times more strongly coupled to the electronic transition than the radial vibration, which is oriented almost perpendicular to the charge-transfer axis. The results from this experiment allow us to map the spectroscopically observed vibronic coordinates onto the molecular frame providing a general method to spatially resolve vibronic energy transfer on a femtosecond time scale.

Vibronic coherence evolution in multidimensional ultrafast photochemical processes

The complex choreography of electronic, vibrational, and vibronic couplings used by photoexcited molecules to transfer energy efficiently is remarkable, but an unambiguous description of the temporally evolving vibronic states governing these processes has proven experimentally elusive. We use multidimensional electronic-vibrational spectroscopy to identify specific time-dependent excited state vibronic couplings involving multiple electronic states, high-frequency vibrations, and low-frequency vibrations which participate in ultrafast intersystem crossing and subsequent relaxation of a photoexcited transition metal complex. We discover an excited state vibronic mechanism driving long-lived charge separation consisting of an initial electronically-localized vibrational wavepacket which triggers delocalization onto two charge transfer states after propagating for ~600 femtoseconds. Electronic delocalization consequently occurs through nonadiabatic internal conversion driven by a 50 cm^-1 coupling resulting in vibronic coherence transfer lasting for ~1 picosecond. This study showcases the power of multidimensional electronic-vibrational spectroscopy to elucidate complex, non-equilibrium energy and charge transfer mechanisms involving multiple molecular coordinates.

Two-Dimensional Electronic-Vibrational Spectroscopy of Coupled Molecular Complexes: A Near-Analytical Approach

This work presents theoretical calculations of the two-dimensional electronic-vibrational (2DEV) spectrum of a vibronically coupled molecular dimer using a near-analytical method. In strongly coupled dimers, where the IR mode is resonant with the electronic energy gap between the excitons, multiple infrared transitions become allowed that are forbidden in weakly coupled systems that have a nonresonant IR mode. This formalism enables the coherences and population contributions to be explored separately and allows efficient calculation of relaxation rates between the vibronic states. At short times, we find strong contributions of vibronic coherences to the 2DEV spectra. They decay fairly rapidly, giving rise to strong population signals. Although the interpretation of 2DEV spectra is considerably more complex than that for weakly coupled systems, the richness of the spectra and the necessity to consider both visible and infrared transition moments suggest that such analysis will be very valuable in characterizing the role of vibronic effects in ultrafast molecular dynamics.