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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.

A quantum-classical description of the amide I vibrational spectrum of trialanine cation in D2O is given that combines (i) a classical molecular dynamics simulation of the conformational distribution of the system, (ii) comprehensive density functional theory calculations of the conformation-dependent and solvent-induced frequency fluctuations, and (iii) a semiclassical description of the vibrational line shapes which includes nonadiabatic transitions between vibrational eigenstates. Various assumptions that are usually employed in the calculation of condensed-phase vibrational spectra are tested, including the adiabatic, the Franck-Condon, and the second-order cumulant approximations, respectively. All three parts of the theoretical formulation are shown to have a significant impact on the simulated spectrum, suggesting that the interpretation of peptide amide I spectra may require substantial theoretical support.

Recent progress in transient infrared spectroscopy has made it possible to monitor the transient flow of vibrational energy along a peptide helix [V. Botan et al., Proc. Natl. Acad. Sci. U.S.A. 104, 12749 (2007)]. To provide a theoretical description of these experiments, extensive nonequilibrium molecular dynamics simulations of the photoinduced energy transport in a photoswitchable Aib peptide are performed. By calculating the response of the molecule caused by its excitation via optical and infrared pulses as well as temperature jump and stationary heating, it is shown that these methods are equivalent in that they provide approximately the same molecular energy transfer times. The resulting thermal diffusivity of 10 Å2 ps-1 qualitatively agrees with the results of previous normal mode calculations for proteins and with experimental bulk values (e.g., 14 Å2 ps-1 for water). To compare to experiment, a new way of approximating the measured signals is suggested which leads to an improved agreement with the experimental results and explains previous discrepancies. To elucidate the mechanism of energy transfer, modifications to the molecular dynamics force field are introduced, which reveal that the energy transfer occurs mainly through the peptide backbone and depends surprisingly little on the force field parametrization. Employing a harmonic model, quantum-mechanical effects are estimated to moderately (about a factor of 2) speed up the energy transport along the peptide. [ABSTRACT FROM AUTHOR]

Nonlinear time-resolved vibrational spectroscopy is used to compare spectral broadening of the amide I band of the small peptide trialanine with that of N-methylacetamide, a commonly used model system for the peptide bond. In contrast to N-methylacetamide, the amide I band of trialanine is significantly inhomogeneously broadened. Employing classical molecular-dynamics simulations combined with density-functional-theory calculations, the origin of the spectral inhomogeneity is investigated. While both systems exhibit similar hydrogen-bonding dynamics, it is found that the conformational dynamics of trialanine causes a significant additional spectral broadening. In particular, transitions between the poly(Gly)II and the α[SUBR] conformations are identified as the main source of the additional spectral inhomogeneity of trialanine. The experimental and computational results suggest that trialanine adopts essentially two conformations: poly(Gly)II (80%) and α[SUBR] (20%). The potential of the joint experimental and computational approach to explore conformational dynamics of peptides is discussed. [ABSTRACT FROM AUTHOR]

A general nonperturbative approach to calculate femtosecond pump-probe (PP) signals is proposed, which treats both the intramolecular couplings and the field-matter interaction (numerically) exactly. Experimentally as well as in a perturbative calculation it is straightforward to distinguish between different spectroscopic processes through the direction of the wave vector of the emitted radiation. A nonperturbative calculation, on the other hand, yields the overall polarization of the system, which is the sum of all these contributions. We present a general and practical method that allows to extract the individual spectroscopic signals, which are resolved in time, frequency, and direction of the emission, from the overall polarization. We briefly derive the basic expressions for the time- and frequency-resolved PP signals under consideration, and discuss in detail the simplifications that arise when the usual assumptions (i.e., weak laser fields, nonoverlapping pulses, slowly-varying envelope assumption and rotating-wave approximation) are invoked. The computational procedure is illustrated by nonperturbative calculations of the polarizations and PP signals for a one-dimensional shifted harmonic oscillator. To demonstrate the capability of the approach we have evaluated the polarization as well as PP signals for a three-dimensional model system with vibronically coupled potential-energy surfaces, which describes ultrafast nonadiabatic isomerization dynamics triggered by the twisting of a double bond. We consider various wavelengths and pulse durations of the laser fields and study integral and dispersed PP spectra as well as coherent photon-echo signals. It is shown that the time- and frequency-resolved PP signals reflect in real time the disappearance of the reactants and the delayed appearance of the products. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

It is demonstrated that photoinduced large amplitude (LA) dynamics on a picosecond time scale may result in electronic pure dephasing on a time scale of a few tens of femtoseconds. It is shown that LA photodynamics affects continuous-wave (cw) spectra (e.g., absorption and resonance-Raman) and transient spectra (e.g., photon-echo and pump–probe) in a rather different way. Calculations are presented for a two-dimensional model problem, consisting of a fast vibrational mode and a slow LA mode, which is considered as a simple model for isomerization. The spectroscopic signals for this model are compared to the results for a complementary model, where the fast vibrational mode interacts with a bath (e.g., the environment). It is shown that standard cw techniques such as absorption and resonance-Raman spectroscopy fail to clearly distinguish the two (physically rather different) model problems, as the ultrafast optical dephasing results in strong line broadening of these spectra. Time-resolved pump–probe spectroscopy, on the other hand, is not limited by electronic pure dephasing and thus allows for a clear discrimination of the two photophysical processes. Simulations of photon-echo experiments furthermore elucidate that slow intramolecular LA motion results in inhomogeneous broadening of optical spectra. Finally a novel time-resolved technique is proposed that is capable to reveal ‘‘sub-linewidth’’ information on electronic transitions which are strongly broadened by homogeneous and inhomogeneous pure dephasing processes. [ABSTRACT FROM AUTHOR]

A general classical formulation of the spectroscopy of nonadiabatically coupled electronic states is developed within the theoretical framework of the classical electron analog model due to Meyer and Miller. Adopting the Heisenberg representation for the calculation of the electric polarization, several approaches are presented to establish a quantum-classical correspondence. It is shown that a consistent classical formulation is obtained by replacing the quantum-mechanical commutators, which appear in quantum-mechanical perturbation theory, by the corresponding classical Poisson brackets which come from classical perturbation theory. The more usual practice of replacing the Heisenberg dipole operators directly by the corresponding classical dipole functions is shown to be an approximation to classical perturbation theory. For a coupled electronic three-state system explicit expressions are derived for the nonlinear polarization. Furthermore the practical application to femtosecond pump-probe spectroscopy is discussed in some detail. [ABSTRACT FROM AUTHOR]

An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck-Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time- and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabatic cis-trans isomerization of an electronic two-state system, and (ii) the S[sub 2]→S[sub 1] internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe-pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: The mapping formulation of nonadiabatic quantum dynamics is applied to obtain a classical description of the ultrafast dynamics and time-resolved spectroscopy of a photochemical reaction. Adopting a previously studied dissipative two-state two-mode model of nonadiabatic cis–trans photoisomerization, classical mapping simulations are compared to quantum-mechanical reduced density matrix calculations. Overall, the simple classical method is found to reproduce the quantum reference calculations quite well. In particular, it is studied if the classical approach yields the correct long-time cis/trans localization of the wave packet and therefore the correct quantum yield of the photoreaction. As the long-time behavior of the classical mapping formulation suffers from the well-known zero point energy problem of classical mechanics, a new practical method is proposed to determine a zero point energy correction. Employing a second-order Franck–Condon-type approximation, the capability of the classical method to simulate time- and frequency-resolved pump–probe spectra of the nonadiabatic photoreaction is studied. The potential of the classical approach as a practical method to describe condensed-phase photoreactions is discussed. [Copyright &y& Elsevier]

Abstract: A quantum-classical description of the amide I vibrational spectrum of peptides in aqueous solution is given, which is concerned with the effects of nonadiabatic couplings between vibrational eigenstates. It consists of a classical molecular dynamics simulation of the conformational distribution of the system, density functional theory calculations of the conformation-dependent and solvent-induced frequency fluctuations, and a semiclassical description of the vibrational line shapes. The study shows that the adiabatic approximation usually employed in semiclassical line shape theory is generally not valid, because it assumes a time scale separation between the dynamics of the amide I mode (with a period of ≈20fs) and the motion of the solvent and the peptide (which also exhibits sub-100fs dynamics). A practical and general computational scheme is presented, which allows for the calculation of spectroscopic response functions by directly solving the nonadiabatically coupled time-dependent Schrödinger equation. Adopting trialanine and heptaalanine as representative examples, it is shown that nonadiabatic interactions may considerably change the overall shape as well as local details of the amide I spectrum. [Copyright &y& Elsevier]