Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics.

Current simulations of ultraviolet-visible absorption lineshapes and dynamics of condensed phase systems largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems, this approximation no longer suffices. We elucidate nonstandard harmonic and anharmonic effects on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. First, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilized. Using this model, it is shown that curvature difference gives rise to an additional substructure in the vibronic progression of absorption spectra. This effect is explained and subsequently quantified via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential and parameters that correspond to the diatomic molecule H2 for differing displacements and environment interaction. Finally, using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch are presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

Quantifying non-Markovianity in underdamped versus overdamped environments and its effect on spectral lineshape.

Non-Markovian effects in open quantum systems are central to understanding spectral lineshape. Here, we quantify the non-Markovianity associated with both overdamped and underdamped vibrations in terms of information flow between the bath and the system and compare this with the broadening and ellipticity of two-dimensional spectra. Using the Breuer Laine Piilo (BLP) measure, we link the well-known stochastic models for spectral lineshape with modern quantum information theory. Specifically, we study the effect of non-Markovianity in a system in contact with underdamped vibrations and examine the differences observed on increasing the damping to the overdamped limit. The open quantum system dynamics are evolved using the hierarchical equations of motion, efficiently terminated with a Markovian cutoff, where separate hierarchies are derived for the underdamped and overdamped environments. It is shown that the BLP measure is quantitatively correlated with the ellipticity of two-dimensional spectra and memory effects are more pronounced in underdamped environments, due to the long-lived feedback of information between the system and its bath, compared to overdamped environments. Environmental signatures in spectral lineshapes emerge as a result of information flow from the bath back into the system.

Efficient long-distance energy transport in molecular systems through adiabatic passage.

The efficiencies of light-harvesting complexes in biological systems can be much higher than the current efficiencies of artificial solar cells. In this paper, we therefore propose and analyze an energy transport mechanism which employs adiabatic passages between the states of an artificially designed antenna molecular system to significantly enhance the conversion of incoming light into internal energy. It is shown that the proposed transport mechanism is relatively robust against spontaneous emission and dephasing, while also being able to take advantage of collective effects. Our aim is to provide new insight into the energy transport in molecular complexes and to improve the design of solar cells.

Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra.

A light-driven molecular motor system is investigated using a multi-state Brownian ratchet model described by a single effective coordinate with multiple electronic states in a dissipative environment. The rotational motion of the motor system is investigated on the basis of wavepacket dynamics. A current determined from the interplay between a fast photochemical isomerization (photoisomerization) process triggered by pulses and a slow thermal isomerization (thermalization) process arising from an overdamped environment is numerically evaluated. For this purpose, we employ the multi-state low-temperature quantum Smoluchowski equations that allow us to simulate the fast quantum electronic dynamics in the overdamped environment, where conventional approaches, such as the Zusman equation approach, fail to apply due to the positivity problem. We analyze the motor efficiency by numerically integrating the equations of motion for a rotator system driven by repeatedly impulsive excitations. When the time scales of the pulse repetition, photoisomerization, and thermalization processes are separated, the average rotational speed of the motor is determined by the time scale of thermalization. In this regime, the average rotational current can be described by a simple equation derived from a rate equation for the thermalization process. When laser pulses are applied repeatedly and the time scales of the photoisomerization and pulse repetition are close, the details of the photoisomerization process become important to analyze the entire rotational process. We examine the possibility of observing the photoisomerization and the thermalization processes associated with stationary rotating dynamics of the motor system by spectroscopic means, e.g., pump-probe, transient absorption, and two-dimensional electronic spectroscopy techniques.

Ultrafast dissolution and creation of bonds in IrTe2 induced by photodoping.

The observation and control of interweaving spin, charge, orbital, and structural degrees of freedom in materials on ultrafast time scales reveal exotic quantum phenomena and enable new active forms of nanotechnology. Bonding is the prime example of the relation between electronic and nuclear degrees of freedom. We report direct evidence illustrating that photoexcitation can be used for ultrafast control of the breaking and recovery of bonds in solids on unprecedented time scales, near the limit for nuclear motions. We describe experimental and theoretical studies of IrTe2 using femtosecond electron diffraction and density functional theory to investigate bonding instability. Ir-Ir dimerization shows an unexpected fast dissociation and recovery due to the filling of the antibonding dxy orbital. Bond length changes of 20% in IrTe2 are achieved by effectively addressing the bonds directly through this relaxation process. These results could pave the way to ultrafast switching between metastable structures by photoinduced manipulation of the relative degree of bonding in this manner.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model.

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Simulation of photo-excited adenine in water with a hierarchy of equations of motion approach.

We present a theoretical method to simulate the electronic dynamics and two-dimensional ultraviolet spectra of the nucleobase adenine in water. The method is an extension of the hierarchy of equations of motion approach to treat a model with one or more conical intersections. The application to adenine shows that a two-level model with a direct conical intersection between the optically bright state and the ground state, generating a hot ground state, is not consistent with experimental observations. This supports a three-level model for the decay of electronically excited adenine in water as was previously proposed in the work of V. I. Prokhorenko et al. [J. Phys. Chem. Lett. 7, 4445 (2016)].

New Insights into the Photophysics of DNA Nucleobases.

We report the results of an extended time-resolved study of DNA nucleobases in aqueous solutions conducted in the deep UV using broad-band femtosecond transient absorption and electronic two-dimensional spectroscopies. We found that the photodeactivation in all DNA nucleobases occurs in two steps: fast relaxation (500-700 fs) from the excited state ππ* to a "dark" state and its depopulation to the ground state within 1-2 ps. Our experimental observations and performed theoretical modeling allow us to conclude that this dark state can be associated with the nπ* electronic state, which is connected to the excited and ground states via conical intersections.

How two-dimensional brick layer J-aggregates differ from linear ones: Excitonic properties and line broadening mechanisms.

We study the excitonic coupling and homogeneous spectral line width of brick layer J-aggregate films. We begin by analysing the structural information revealed by the two-exciton states probed in two-dimensional spectra. Our first main result is that the relation between the excitonic couplings and the spectral shift in a two-dimensional structure is different (larger shift for the same nearest neighbour coupling) from that in a one-dimensional structure, which leads to an estimation of dipolar coupling in two-dimensional lattices. We next investigate the mechanisms of homogeneous broadening--population relaxation and pure dephasing--and evaluate their relative importance in linear and two-dimensional aggregates. Our second main result is that pure dephasing dominates the line width in two-dimensional systems up to a crossover temperature, which explains the linear temperature dependence of the homogeneous line width. This is directly related to the decreased density of states at the band edge when compared with linear aggregates, thus reducing the contribution of population relaxation to dephasing. Pump-probe experiments are suggested to directly measure the lifetime of the bright state and can therefore support the proposed model.

Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations.

We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.

Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes.

We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.

Coherent Exciton Dynamics in the Presence of Underdamped Vibrations.

Recent ultrafast optical experiments show that excitons in large biological light-harvesting complexes are coupled to molecular vibration modes. These high-frequency vibrations will not only affect the optical response, but also drive the exciton transport. Here, using a model dimer system, the frequency of the underdamped vibration is shown to have a strong effect on the exciton dynamics such that quantum coherent oscillations in the system can be present even in the case of strong noise. Two mechanisms are identified to be responsible for the enhanced transport efficiency: critical damping due to the tunable effective strength of the coupling to the bath, and resonance coupling where the vibrational frequency coincides with the energy gap in the system. The interplay of these two mechanisms determines parameters responsible for the most efficient transport, and these optimal control parameters are comparable to those in realistic light-harvesting complexes. Interestingly, oscillations in the excitonic coherence at resonance are suppressed in comparison to the case of an off-resonant vibration.

Linear and third- and fifth-order nonlinear spectroscopies of a charge transfer system coupled to an underdamped vibration.

We study hole, electron, and exciton transports in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole, and exciton transfers can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional (2D) spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states during two different time periods.

Non-Markovianity: initial correlations and nonlinear optical measurements.

By extending the response function approach developed in nonlinear optics, we analytically derive an expression for the non-Markovianity in the time evolution of a system in contact with a quantum mechanical bath, and find a close connection with the directly observable nonlinear optical response. The result indicates that memory in the bath-induced fluctuations rather than in the dissipation causes non-Markovianity. Initial correlations between states of the system and the bath are shown to be essential for a correct understanding of the non-Markovianity. These correlations are included in our treatment through a preparation function.

Modeling the vibrational dynamics and nonlinear infrared spectra of coupled amide I and II modes in peptides.

The amide vibrational modes play an important role in energy transport and relaxation in polypeptides and proteins and provide us with spectral markers for structure and structural dynamics of these macromolecules. Here, we present a detailed model to describe the dynamic properties of the amide I and amide II modes and the resulting linear and nonlinear spectra. These two modes have large oscillator strengths, and their mutual coupling plays an important role in their relaxation. Using first-principles calculations of NMA-d(7) and a dipeptide in a fluctuating bath described by molecular dynamics simulations, we model the frequencies of the local vibrations as well as the coupling between them. Both the coherent couplings and the fluctuations induced by contact with their environment are taken into account. We apply the resulting model of interacting fluctuating oscillators to study the collective vibrations and the partially coherent transport of vibrational energy through a model α-helix. We find that the instantaneous vibrations are delocalized over a few (up to four) amide units, while the coherences in the helix survive for 0.5-1 ps, leading to coherent transport on a similar time scale.

Non-Markovian entanglement dynamics in the presence of system-bath coherence.

A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.