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

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.

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.

Bidirectional Energy Flow in the Photosystem II Supercomplex

The water-splitting capability of Photosystem II (PSII) of plants and green algae requires the system to balance efficient light harvesting along with effective photoprotection against excitation in excess of the photosynthetic capacity, particularly under the naturally fluctuating sunlight intensity. The comparatively flat energy landscape of the multicomponent structure, inferred from the spectra of the individual pigment-protein complexes and the rather narrow and featureless absorption spectrum, is well known. However, how the combination of the required functions emerges from the interactions among the multiple components of the PSII supercomplex (PSII-SC) cannot be inferred from the individual pigment-protein complexes. In this work, we investigate the energy transfer dynamics of the C2S2-type PSII-SC with a combined spectroscopic and modeling approach. Specifically, two-dimensional electronic-vibrational (2DEV) spectroscopy provides enhanced spectral resolution and the ability to map energy evolution in real space, while the quantum dynamical simulation allows complete kinetic modeling of the 210 chromophores. We demonstrate that additional pathways emerge within the supercomplex. In particular, we show that excitation energy can leave the vicinity of the charge separation components, the reaction center (RC), faster than it can transfer to it. This enables activatable quenching centers in the periphery of the PSII-SC to be effective in removing excessive energy in cases of overexcitation. Overall, we provide a quantitative description of how the seemingly contradictory functions of PSII-SC arise from the combination of its individual components. This provides a fundamental understanding that will allow further improvement of artificial solar energy devices and bioengineering processes for increasing crop yield.

Multidimensional Widefield Infrared-Encoded Spontaneous Emission Microscopy: Distinguishing Chromophores by Ultrashort Infrared Pulses

Photoluminescence (PL) imaging has broad applications in visualizing biological activities, detecting chemical species, and characterizing materials. However, the chemical information encoded in the PL images is often limited by the overlapping emission spectra of chromophores. Here, we report a PL microscopy based on the nonlinear interactions between mid-infrared and visible excitations on matters, which we termed MultiDimensional Widefield Infrared-encoded Spontaneous Emission (MD-WISE) microscopy. MD-WISE microscopy can distinguish chromophores that possess nearly identical emission spectra via conditions in a multidimensional space formed by three independent variables: the temporal delay between the infrared and the visible pulses (t), the wavelength of visible pulses (λvis), and the frequencies of the infrared pulses (ωIR). This method is enabled by two mechanisms: (1) modulating the optical absorption cross sections of molecular dyes by exciting specific vibrational functional groups and (2) reducing the PL quantum yield of semiconductor nanocrystals, which was achieved through strong field ionization of excitons. Importantly, MD-WISE microscopy operates under widefield imaging conditions with a field of view of tens of microns, other than the confocal configuration adopted by most nonlinear optical microscopies, which require focusing the optical beams tightly. By demonstrating the capacity of registering multidimensional information into PL images, MD-WISE microscopy has the potential of expanding the number of species and processes that can be simultaneously tracked in high-speed widefield imaging applications.

Intraband Exciton Transitions in Photosynthetic Complexes Revealed by Novel Five-Wave-Mixing Spectroscopy

We calculate the χ(4) optical response of an oriented photosystem II reaction center of purple bacteria described by the Frenkel exciton model using nonlinear exciton equations (NEE). This approach treats each chromophore as an anharmonic oscillator and provides an intuitive quasiparticle picture of nonlinear spectroscopic signals of interacting excitons. It provides a computationally powerful description of nonlinear spectroscopic signals that avoids complete diagonalization of the total Hamiltonian. Expressions for the second- and the fourth-order nonlinear signals are derived. The NEE have been successfully employed in the past to describe even-order-wave-mixing. Here, we extend them to aggregates with broken inversion symmetries. Even-order susceptibilities require the introduction of permanent dipoles, which allow to directly probe low-frequency intraband transitions of excitons.

Rapid-Scan Resonant Two-Dimensional Impulsive Stimulated Raman Spectroscopy of Excited States

Photochemical reactions occur in the electronically excited state, which is effectively represented by a multidimensional potential energy surface (PES) with a vast degree of freedom of nuclear coordinates. The elucidation of the intricate shape of the PES constitutes an important topic in the field of photochemistry and has long been studied both experimentally and theoretically. Recently, fully time-domain resonant two-dimensional Raman spectroscopy has emerged as a potentially powerful tool to provide unique information about the coupling between vibrational manifolds in the excited state. However, the wide application of this technique has been significantly hampered by the technical difficulties associated with experimental implementation and remains challenging. Herein, we demonstrate time-domain resonant two-dimensional impulsive stimulated Raman spectroscopy (2D-ISRS) of excited states using sub-10 fs pulses based on the rapid scan of the time delay, which facilitates the efficient collection of time-domain vibrational signals with high sensitivity. As a proof-of-principle experiment, we performed 2D-ISRS of 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-pentacene) in solution. Through 2D Fourier transformation of the high-quality time-time oscillatory signal, we obtained a 2D frequency-frequency correlation map of excited-state TIPS-pentacene in the broad frequency window of 0-2000 cm^-1. The data clearly resolve a number of cross peaks that signify the correlations among excited-state vibrational manifolds. The high capability of the rapid-scan-based 2D-ISRS spectrometer presented in this study enables the systematic investigation of various photochemical reaction systems, thereby further promoting the understanding and applications of this new multidimensional spectroscopy.

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.

Infrared Signatures of Phycobilins within the Phycocyanin 645 Complex

Aquatic photosynthetic organisms evolved to use a variety of light frequencies to perform photosynthesis. Phycobiliprotein phycocyanin 645 (PC645) is a light-harvesting complex in cryptophyte algae able to transfer the absorbed green solar light to other antennas with over 99% efficiency. The infrared signatures of the phycobilin pigments embedded in PC645 are difficult to access and could provide useful information to understand the mechanism behind the high efficiency of energy transfer in PC645. We use visible-pump IR-probe and two-dimensional electronic vibrational spectroscopy to study the dynamical evolution and assign the fingerprint mid-infrared signatures to each pigment in PC645. Here, we report the pigment-specific vibrational markers that enable us to track the spatial flow of excitation energy between the phycobilin pigment pairs. We speculate that two high-frequency modes (1588 and 1596 cm^-1) are involved in the vibronic coupling leading to fast (<ps) and direct energy transfer from the highest to lowest exciton, bypassing the intermediate excitons.

Connecting the dots for fundamental understanding of structure-photophysics-property relationships of COFs, MOFs, and perovskites using a Multiparticle Holstein Formalism

Photoactive organic and hybrid organic-inorganic materials such as conjugated polymers, covalent organic frameworks (COFs), metal-organic frameworks (MOFs), and layered perovskites, display intriguing photophysical signatures upon interaction with light. Elucidating structure-photophysics-property relationships across a broad range of functional materials is nontrivial and requires our fundamental understanding of the intricate interplay among excitons (electron-hole pair), polarons (charges), bipolarons, phonons (vibrations), inter-layer stacking interactions, and different forms of structural and conformational defects. In parallel with electronic structure modeling and data-driven science that are actively pursued to successfully accelerate materials discovery, an accurate, computationally inexpensive, and physically-motivated theoretical model, which consistently makes quantitative connections with conceptually complicated experimental observations, is equally important. Within this context, the first part of this perspective highlights a unified theoretical framework in which the electronic coupling as well as the local coupling between the electronic and nuclear degrees of freedom can be efficiently described for a broad range of quasiparticles with similarly structured Holstein-style vibronic Hamiltonians. The second part of this perspective discusses excitonic and polaronic photophysical signatures in polymers, COFs, MOFs, and perovskites, and attempts to bridge the gap between different research fields using a common theoretical construct - the Multiparticle Holstein Formalism. We envision that the synergistic integration of state-of-the-art computational approaches with the Multiparticle Holstein Formalism will help identify and establish new, transformative design strategies that will guide the synthesis and characterization of next-generation energy materials optimized for a broad range of optoelectronic, spintronic, and photonic applications.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Concerted Electron-Nuclear Motion in Proton-Coupled Electron Transfer-Driven Grotthuss-Type Proton Translocation

Photoinduced proton-coupled electron transfer and long-range two-proton transport via a Grotthuss-type mechanism are investigated in a biomimetic construct. The ultrafast, nonequilibrium dynamics are assessed via two-dimensional electronic vibrational spectroscopy, in concert with electrochemical and computational techniques. A low-frequency mode is identified experimentally and found to promote double proton and electron transfer, supported by recent theoretical simulations of a similar but abbreviated (non-photoactive) system. Excitation frequency peak evolution and center line slope dynamics show direct evidence of strongly coupled nuclear and electronic degrees of freedom, from which we can conclude that the double proton and electron transfer processes are concerted (up to an uncertainty of 24 fs). The nonequilibrium pathway from the photoexcited Franck-Condon region to the E2PT state is characterized by an ∼110 fs time scale. This study and the tools presented herein constitute a new window into hot charge transfer processes involving an electron and multiple protons.

The initial charge separation step in oxygenic photosynthesis

Photosystem II is crucial for life on Earth as it provides oxygen as a result of photoinduced electron transfer and water splitting reactions. The excited state dynamics of the photosystem II-reaction center (PSII-RC) has been a matter of vivid debate because the absorption spectra of the embedded chromophores significantly overlap and hence it is extremely difficult to distinguish transients. Here, we report the two-dimensional electronic-vibrational spectroscopic study of the PSII-RC. The simultaneous resolution along both the visible excitation and infrared detection axis is crucial in allowing for the character of the excitonic states and interplay between them to be clearly distinguished. In particular, this work demonstrates that the mixed exciton-charge transfer state, previously proposed to be responsible for the far-red light operation of photosynthesis, is characterized by the ChlD1+Phe radical pair and can be directly prepared upon photoexcitation. Further, we find that the initial electron acceptor in the PSII-RC is Phe, rather than PD1, regardless of excitation wavelength.

Accelerating symmetry-breaking charge separation in a perylenediimide trimer through a vibronically coherent dimer intermediate

Understanding the photophysics and photochemistry of molecular π-stacked chromophores is important for utilizing them as functional photonic materials. However, these investigations have been mostly limited to covalent molecular dimers, which can only approximate the electronic and vibronic interactions present in the higher oligomers typical of functional organic materials. Here we show that a comparison of the excited-state dynamics of a covalent slip-stacked perylenediimide dimer (2) and trimer (3) provides fundamental insights into electronic state mixing and symmetry-breaking charge separation (SB-CS) beyond the dimer limit. We find that coherent vibronic coupling to high-frequency modes facilitates ultrafast state mixing between the Frenkel exciton (FE) and charge-transfer (CT) states. Subsequently, solvent fluctuations and interchromophore low-frequency vibrations promote CT character in the coherent FE/CT mixed state. The coherent FE/CT mixed state persists in 2, but, in 3, low-frequency vibronic coupling collapses the coherence, resulting in ultrafast SB-CS between the distal perylenediimide units.

Spin-Orbit Natural Transition Orbitals and Spin-Forbidden Transitions

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. The present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin-orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be nonzero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole-particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T₂-S₁ state mixing in pyrazine, spin-forbidden versus spin-allowed 4f-5d transitions in the Tb³⁺ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy)₃].