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

Double-quantum two-dimensional electronic-vibrational spectroscopy: Theory. Vibronic coherences in nonadiabatic phenomena

Nonadiabatic phenomena are ubiquitous in polyatomic molecular systems and are responsible for many ultrafast dynamics occurring outside of the Born-Oppenheimer approximation. In particular, electronic curve crossings offer ultrafast, sub-100 fs pathways for efficient electronic relaxation between potential energy surfaces, where the electronic and vibrational degrees of freedom become strongly coupled. Due to the unique mixture of temporal and spectral resolution required to detect electronic curve crossings, experimental observation has remained a considerable challenge. Here, double-quantum coherence two-dimensional electronic-vibrational (2Q 2D EV) spectroscopy is introduced for the first time and proposed as an experimental approach to monitor vibronic dynamics near and at electronic curve crossings directly through vibronic coherences using a mixture of broadband visible and infrared pulses. A semi-classical vibronic Hamiltonian is used that characterizes the parametrically defined coupling between high-frequency vibrations and low-frequency vibrational modes involved in tuning electronic potential energy surfaces. This work displays how unique multidimensional pulse sequences can uncover dynamics that are hidden in conventional techniques.

A Cost-Effective Computational Strategy for the Electronic Layout Characterization of a Second Generation Light-Driven Molecular Rotary Motor in Solution

Light-driven molecular rotary motors are nanometric machines able to convert light into unidirectional motions. Several types of molecular motors have been developed to better respond to light stimuli, opening new avenues for developing smart materials ranging from nanomedicine to robotics. They have great importance in the scientific research across various disciplines, but a detailed comprehension of the underlying ultrafast photophysics immediately after photo-excitation, that is, Franck-Condon region characterization, is not fully achieved yet. For this aim, it is first required to rely on an accurate description at ab initio level of the system in this potential energy region before performing any further step, that is, dynamics. Thus, we present an extensive investigation aimed at accurately describing the electronic structure of low-lying electronic states (electronic layout) of a molecular rotor in the Franck-Condon region, belonging to the class of overcrowded alkenes: 9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene. This system was chosen since its photophysics is very interesting for a more general understanding of similar compounds used as molecular rotors, where low-lying electronic states can be found (whose energetic interplay is crucial in the dynamics) and where the presence of different substituents can tune the HOMO-LUMO gap. For this scope, we employed different theory levels within the time-dependent density functional theory framework, presenting also a careful comparison adopting very accurate post Hartree-Fock methods and characterizing also the different conformations involved in the photocycle. Effects on the electronic layout of different functionals, basis sets, environment descriptions, and the role of the dispersion correction were all analyzed in detail. In particular, a careful treatment of the solvent effects was here considered in depth, showing how the implicit solvent description can be accurate for excited states in the Franck-Condon region by testing both linear-response and state-specific formalisms. As main results, we chose two cost-effective (accurate but relatively cheap) theory levels for the ground and excited state descriptions, and we also verified how choosing these different levels of theory can influence the curvature of the potential via a frequency analysis of the normal modes of vibrations active in the Raman spectrum. This theoretical survey is a crucial step towards a feasible characterization of the early stage of excited states in solution during photoisomerization processes wherein multiple electronic states might be populated upon the light radiation, leading to a future molecular-level interpretation of time-resolved spectroscopies.

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.

The development and applications of multidimensional biomolecular spectroscopy illustrated by photosynthetic light harvesting

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies - two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy - and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

Molecular factors determining brightness in fluorescence-encoded infrared vibrational spectroscopy

Fluorescence-encoded infrared (FEIR) spectroscopy is a recently developed technique for solution-phase vibrational spectroscopy with detection sensitivity at the single-molecule level. While its spectroscopic information content and important criteria for its practical experimental optimization have been identified, a general understanding of the electronic and nuclear properties required for highly sensitive detection, i.e., what makes a molecule a "good FEIR chromophore," is lacking. This work explores the molecular factors that determine FEIR vibrational activity and assesses computational approaches for its prediction. We employ density functional theory (DFT) and its time-dependent version (TD-DFT) to compute vibrational and electronic transition dipole moments, their relative orientation, and the Franck-Condon factors involved in FEIR activity. We apply these methods to compute the FEIR activities of normal modes of chromophores from the coumarin family and compare these predictions with experimental FEIR cross sections. We discuss the extent to which we can use computational models to predict the FEIR activity of individual vibrations in a candidate molecule. The results discussed in this work provide the groundwork for computational strategies for choosing FEIR vibrational probes or informing the structure of designer chromophores for single-molecule spectroscopic applications.

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.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

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.

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.

Vibronic coupling in energy transfer dynamics and two-dimensional electronic-vibrational spectra

We introduce a heterodimer model in which multiple mechanisms of vibronic coupling and their impact on energy transfer can be explicitly studied. We consider vibronic coupling that arises through either Franck-Condon activity in which each site in the heterodimer has a local electron-phonon coupling or Herzberg-Teller activity in which the transition dipole moment coupling the sites has an explicit vibrational mode-dependence. We have computed two-dimensional electronic-vibrational (2DEV) spectra for this model while varying the magnitude of these two effects and find that 2DEV spectra contain static and dynamic signatures of both types of vibronic coupling. Franck-Condon activity emerges through a change in the observed excitonic structure, while Herzberg-Teller activity is evident in the appearance of significant side-band transitions that mimic the lower-energy excitonic structure. A comparison of quantum beating patterns obtained from analysis of the simulated 2DEV spectra shows that this technique can report on the mechanism of energy transfer, elucidating a means of experimentally determining the role of specific vibronic coupling mechanisms in such processes.

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.