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

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.

Orientational Coupling of Molecules at Interfaces Revealed by Two-Dimensional Electronic-Vibrational Sum Frequency Generation (2D-EVSFG)

Photoinduced relaxation processes at interfaces are intimately related to many fields such as solar energy conversion, photocatalysis, and photosynthesis. Vibronic coupling plays a key role in the fundamental steps of the interface-related photoinduced relaxation processes. Vibronic coupling at interfaces is expected to be different from that in bulk due to the unique environment. However, vibronic coupling at interfaces has not been well understood due to the lack of experimental tools. We have recently developed a two-dimensional electronic-vibrational sum frequency generation (2D-EVSFG) for vibronic coupling at interfaces. In this work, we present orientational correlations in vibronic couplings of electronic and vibrational transition dipoles as well as the structural evolution of photoinduced excited states of molecules at interfaces with the 2D-EVSFG technique. We used malachite green molecules at the air/water interface as an example, to be compared with those in bulk revealed by 2D-EV. Together with polarized VSFG and ESHG experiments, polarized 2D-EVSFG spectra were used to extract relative orientations of an electronic transition dipole and vibrational transition dipoles at the interface. Combined with molecular dynamics calculations, time-dependent 2D-EVSFG data have demonstrated that structural evolutions of photoinduced excited states at the interface have different behaviors than those in bulk. Our results showed that photoexcitation leads to intramolecular charge transfer but no conical interactions in 25 ps. Restricted environment and orientational orderings of molecules at the interface are responsible for the unique features of vibronic coupling.

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.

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.

Resonance conditions, detection quality, and single-molecule sensitivity in fluorescence-encoded infrared vibrational spectroscopy

Fluorescence-encoded Infrared (FEIR) spectroscopy is a vibrational spectroscopy technique that has recently demonstrated the capability of single-molecule sensitivity in solution without near-field enhancement. This work explores the practical experimental factors that are required for successful FEIR measurements in both the single-molecule and bulk regimes. We investigate the role of resonance conditions by performing measurements on a series of coumarin fluorophores of varying electronic transition frequencies. To analyze variations in signal strength and signal to background between molecules, we introduce an FEIR brightness metric that normalizes out measurement-specific parameters. We find that the effect of the resonance condition on FEIR brightness can be reasonably well described by the electronic absorption spectrum. We discuss strategies for optimizing detection quality and sensitivity in bulk and single-molecule experiments.

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.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Femtosecond X-ray Spectroscopy Directly Quantifies Transient Excited-State Mixed Valency

Quantifying charge delocalization associated with short-lived photoexcited states of molecular complexes in solution remains experimentally challenging, requiring local element specific femtosecond experimental probes of time-evolving electron transfer. In this study, we quantify the evolving valence hole charge distribution in the photoexcited charge transfer state of a prototypical mixed valence bimetallic iron-ruthenium complex, [(CN)₅Fe^IICNRu^III(NH₃)₅]^-, in water by combining femtosecond X-ray spectroscopy measurements with time-dependent density functional theory calculations of the excited-state dynamics. We estimate the valence hole charge that accumulated at the Fe atom to be 0.6 ± 0.2, resulting from excited-state metal-to-metal charge transfer, on an ∼60 fs time scale. Our combined experimental and computational approach provides a spectroscopic ruler for quantifying excited-state valency in solvated complexes.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

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.