Correlated line broadening in multidimensional vibrational spectroscopy

Elucidating phonon dephasing mechanisms in layered perovskites with coherent Raman spectroscopies

Organic-inorganic hybrid perovskite quantum wells exhibit electronic structures with properties intermediate between those of inorganic semiconductors and molecular crystals. In these systems, periodic layers of organic spacer molecules occupy the interstitial spaces between perovskite sheets, thereby confining electronic excitations to two dimensions. Here, we investigate spectroscopic line broadening mechanisms for phonons coupled to excitons in lead-iodide layered perovskites with phenyl ethyl ammonium (PEA) and azobenzene ethyl ammonium (AzoEA) spacer cations. Using a modified Elliot line shape analysis for the absorbance and photoluminescence spectra, polaron binding energies of 11.2 and 17.5 meV are calculated for (PEA)2PbI4 and (AzoEA)2PbI4, respectively. To determine whether the polaron stabilization processes influence the dephasing mechanisms of coupled phonons, five-pulse coherent Raman spectroscopies are applied to the two systems under electronically resonant conditions. The prominence of inhomogeneous line broadening mechanisms detected in (AzoEA)2PbI4 suggests that thermal fluctuations involving the deformable organic phase broaden the distributions of phonon frequencies within the quantum wells. In addition, our data indicate that polaron stabilization primarily involves photoinduced reorganization of the organic phases for both systems, whereas the impulsively excited phonons represent less than 10% of the total polaron binding energy. The signal generation mechanisms associated with our fifth-order coherent Raman experiments are explored with a perturbative model in which cumulant expansions are used to account for time-coincident vibrational dephasing and polaron stabilization processes.

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Semi-empirical Quantum Optics for Mid-Infrared Molecular Nanophotonics

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geome- tries have emerged as new platforms for implementing cavity QED at room temperature. The use of infrared (IR) nano-antennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer and femtosecond resolution. To accelerate the development of molecule-based quantum nano-photonic devices in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures, and also provide phys- ical insights for the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the exper- imental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses, and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first- principles techniques based on Maxwell's equations, but its lower computational cost suggests its use a rapid design tool for the development of strongly-coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.

Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath

The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.

Simulating the peptide folding kinetic related spectra based on the Markov State Model

Optical spectroscopic tools are used to monitor protein folding/unfolding dynamics after a fast triggering such as the laser induced temperature jump. These techniques provide new opportunities for comparison between theory and simulations and atom-level understanding protein folding mechanism. However, the direct comparison still face two main challenges: a gap between folding relevant timescales (microseconds or above) and length of molecular dynamics simulations (typically tens to hundreds of nanoseconds), and difficulty in directly calculating spectroscopic observables from simulation configurations. Markov State Model (MSM) approach is one of the most powerful means which can increase simulations timescale up to microsecond or even millisecond. We address progress on modeling infrared and fluorescence spectroscopic signals of temperature jump induced unfolding dynamics for a few small proteins. The harmoniousness between experiment and theoretical can both improve our understanding of protein folding mechanisms and provide direct validation of those theoretical models.

N-H stretching modes of adenosine monomer in solution studied by ultrafast nonlinear infrared spectroscopy and ab initio calculations

The N-H stretching vibrations of adenine, one of the building blocks of DNA, are studied by combining infrared absorption and nonlinear two-dimensional infrared spectroscopy with ab initio calculations. We determine diagonal and off-diagonal anharmonicities of N-H stretching vibrations in chemically modified adenosine monomer dissolved in chloroform. For the single-quantum excitation manifold, the normal mode picture with symmetric and asymmetric NH(2) stretching vibrations is fully appropriate. For the two-quantum excitation manifold, however, the interplay between intermode coupling and frequency shifts due to a large diagonal anharmonicity leads to a situation where strong mixing does not occur. We compare our findings with previously reported values obtained on overtone spectroscopy of coupled hydrogen stretching oscillators.

Exact quantum master equation for a molecular aggregate coupled to a harmonic bath

We consider a molecular aggregate consisting of N identical monomers. Each monomer comprises two electronic levels and a single harmonic mode. The monomers interact with each other via dipole-dipole forces. The monomer vibrational modes are bilinearly coupled to a bath of harmonic oscillators. This is a prototypical model for the description of coherent exciton transport, from quantum dots to photosynthetic antennae. We derive an exact quantum master equation for such systems. Computationally, the master equation may be useful for the testing of various approximations employed in theories of quantum transport. Physically, it offers a plausible explanation of the origins of long-lived coherent optical responses of molecular aggregates in dissipative environments.

Analysis of 2D CS spectra for systems with non-gaussian dynamics

We investigate how accurate different methods of the spectral line shape analysis work in two-dimensional correlation spectroscopy (2D CS) for systems with non-gaussian dynamics. A direct link is established between the frequency dependent correlation functions and a number of line shape metrics. Two model systems are constructed mimicking a typical molecular system with conventional gaussian and non-gaussian spectral dynamics. The frequency dependent correlation function and several line shape parameters extracted from the 2D CS spectra at different waiting times reveal dissimilar dynamics in different frequency domains in the non-gaussian case and similar dynamics in all domains in the gaussian case. The extracted frequency dependent correlation times agree well with the local dynamics in the underlying model for all analysis methods. We also find an extension of the existing line shape analysis methods that allows the extraction of the third-order correlation function.

Quest for spatially correlated fluctuations in the FMO light-harvesting complex

The light absorption in light-harvesting complexes is performed by molecules such as chlorophyll, carotenoid, or bilin. Recent experimental findings in some of these complexes suggest the existence of long-lived coherences between the individual pigments at low temperatures. In this context, the question arises if the bath-induced fluctuations at different chromophores are spatially correlated or not. Here we investigate this question for the Fenna-Matthews-Olson (FMO) complex of Chlorobaculum tepidum by a combination of atomistic theories, i.e., classical molecular dynamics simulations and semiempirical quantum chemistry calculations. In these investigations at ambient temperatures, only weak correlations between the movements of the chromophores can be detected at the atomic level and none at the more coarse-grained level of site energies. The often-employed uncorrelated bath approximations indeed seem to be valid. Nevertheless, correlations between fluctuations in the electronic couplings between the pigments can be found. Depending on the level of theory employed, also correlations between the fluctuations of site energies and the fluctuations in electronic couplings are discernible.

Toward the origin of exciton electronic structure in phycobiliproteins

Femtosecond laser spectroscopies are used to examine the electronic structures of two proteins found in the phycobilisome antenna of cyanobacteria, allophycocyanin (APC) and C-phycocyanin (CPC). The wave function composition involving the pairs of phycocyanobilin pigments (i.e., dimers) found in both proteins is the primary focus of this investigation. Despite their similar geometries, earlier experimental studies conducted in our laboratory and elsewhere observe clear signatures of exciton electronic structure in APC but not CPC. This issue is further investigated here using new experiments. Transient grating (TG) experiments employing broadband quasicontinuum probe pulses find a redshift in the signal spectrum of APC, which is almost twice that of CPC. Dynamics in the TG signal spectra suggest that the sub-100 fs dynamics in APC and CPC are respectively dominated by internal conversion and nuclear relaxation. A specialized technique, intraband electronic coherence spectroscopy (IECS), photoexcites electronic and nuclear coherences with nearly full suppression of signals corresponding to electronic populations. The main conclusion drawn by IECS is that dephasing of intraband electronic coherences in APC occurs in less than 25 fs. This result rules out correlated pigment fluctuations as the mechanism enabling exciton formation in APC and leads us to propose that the large Franck-Condon factors of APC promote wave function delocalization in the vibronic basis. For illustration, we compute the Hamiltonian matrix elements involving the electronic origin of the alpha84 pigment and the first excited vibronic level of the beta84 pigment associated with a hydrogen out-of-plane wagging mode at 800 cm(-1). For this pair of vibronic states, the -51 cm(-1) coupling is larger than the 40 cm(-1) energy gap, thereby making wave function delocalization a feasible prospect. By contrast, CPC possesses no pair of vibronic levels for which the intermolecular coupling is larger than the energy gap between vibronic states. This study of APC and CPC may be important for understanding the photophysics of other phycobiliproteins, which generally possess large vibronic couplings.

Modeling, calculating, and analyzing multidimensional vibrational spectroscopies

Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In multidimensional vibrational spectroscopy, the nonlinear response functions of a molecular dipole or polarizability are measured using ultrashort pulses to monitor inter- and intramolecular vibrational motions. Because a complex profile of such signals depends on the many dynamic and structural aspects of a molecular system, researchers would like to have a theoretical understanding of these phenomena. In this Account, we explore and describe the roles of different physical phenomena that arise from the peculiarities of the system-bath coupling in multidimensional spectra. We also present simple analytical expressions for a weakly coupled multimode Brownian system, which we use to analyze the results obtained by the experiments and simulations. To calculate the nonlinear optical response, researchers commonly use a particular form of a system Hamiltonian fit to the experimental results. The optical responses of molecular vibrational motions have been studied in either an oscillator model or a vibration energy state model. In principle, both models should give the same results as long as the energy states are chosen to be the eigenstates of the oscillator model. The energy state model can provide a simple description of nonlinear optical processes because the diagrammatic Liouville space theory that developed in the electronically resonant spectroscopies can easily handle three or four energy states involved in high-frequency vibrations. However, the energy state model breaks down if we include the thermal excitation and relaxation processes in the dynamics to put the system in a thermal equilibrium state. The roles of these excitation and relaxation processes are different and complicated compared with those in the resonant spectroscopy. Observing the effects of such thermal processes is more intuitive with the oscillator model because the bath modes, which cause the fluctuation and dissipation processes, are also described in the coordinate space. This coordinate space system-bath approach complements a realistic full molecular dynamics simulation approach. By comparing the calculated 2D spectra from the coordinate space model and the energy state model, we can examine the role of thermal processes and anharmonic mode-mode couplings in the energy state model. For this purpose, we employed the Brownian oscillator model with the nonlinear system-bath interaction. Using the hierarchy formalism, we could precisely calculate multidimensional spectra for a single and multimode anharmonic system for inter- and intramolecular vibrational modes.

Coherent multidimensional vibrational spectroscopy of biomolecules: concepts, simulations, and challenges

The response of complex molecules to sequences of femtosecond infrared pulses provides a unique window into their structure, dynamics, and fluctuating environments. Herein we survey the basic principles of modern two-dimensional infrared (2DIR) spectroscopy, which analogous to those of multidimensional NMR spectroscopy. The perturbative approach for computing the nonlinear optical response of coupled localized chromophores is introduced and applied to the amide backbone transitions of proteins, liquid water, membrane lipids, and amyloid fibrils. The signals are analyzed using classical molecular dynamics simulations combined with an effective fluctuating Hamiltonian for coupled localized anharmonic vibrations whose dependence on the local electrostatic environment is parameterized by an ab initio map. Several simulation methods, (cumulant expansion of Gaussian fluctuation, quasiparticle scattering, the stochastic Liouville equations, direct numerical propagation) are surveyed. Chirality-induced techniques which dramatically enhance the resolution are demonstrated. Signatures of conformational and hydrogen-bonding fluctuations, protein folding, and chemical-exchange processes are discussed.

Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.

Conformations of N-acetyl-L-prolinamide by two-dimensional infrared spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy has been applied to study the conformations of a model dipeptide, N-acetyl-L-prolinamide (AcProNH2) in deuterated chloroform (CDCl3). Spectral features in the amide-I and -II regions are obtained by rephasing (R), nonrephasing (NR), and reverse photon echo (RPE) pulse sequences with two polarization conditions. The 2D spectra obtained by the RPE and NR sequences with (0, 0, 0, 0) polarization reveal new spectral features associated with the multiple conformers of AcProNH2 that are difficult to discern using R sequence and linear-IR spectroscopy. The high resolving power of the RPE sequence comes from destructive interference between the positive and negative peaks of nearby vibrators, similar to the NR sequence. The RPE response functions that are useful for 2D spectral simulations are evaluated, including the effects of vibrational frequency correlations. The 2D spectra obtained with (45, -45, 90, 0) polarization exhibit clear cross-peak patterns in the off-diagonal region for the R and RPE sequences but in the diagonal region for the NR sequence. These patterns, free from strong diagonal contributions, are crucial for structure determination. DFT calculations, normal-mode analysis, Hessian matrix reconstruction, and vibrational exciton Hamiltonian diagonalization yield molecular parameters needed for quantitative simulations of 2D spectra: angles between transition dipoles, coupling constants, and off-diagonal anharmonicities of the amide-I and -II modes are obtained for solvated trans-C7 and cis structures and for gas-phase trans conformers in the region of phi = -120 degrees to 0 degrees and psi = -100 degrees to 180 degrees in the Ramachandran space. Systematic simulations based on a 4:1 population ratio of the solvated trans-C7 and cis structures reproduce well the 2D spectral features obtained at both polarization conditions. However, better agreement between the experimental and simulated cross-peak patterns can be reached if the dihedral angles of the major trans conformer are close to (phi, psi) = (-80 degrees , 100 degrees ). Our results suggest that the major conformer of AcProNH2 in CDCl3 deviates from the gas-phase global minimum, the trans-C7 form, to an extended intermediate between the C7 and polyproline-II structure. These results are discussed in relationship with earlier findings obtained by NMR, transient IR studies, and MD simulations.

Simulation protocols for coherent femtosecond vibrational spectra of peptides

Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D(2)O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.

Heterodyned fifth-order 2D-IR spectroscopy of the azide ion in an ionic glass

A heterodyned fifth-order infrared pulse sequence has been used to measure a two-dimensional infrared (2D-IR) spectrum of azide in the ionic glass 3KNO3:2Ca(NO3)2. By rephasing a two-quantum coherence, a process not possible with third-order spectroscopy, the 2D-IR spectra are line narrowed, allowing the frequencies, anharmonicities, and their correlations to be measured for the first four (nu=0-3) antisymmetric stretch vibrational levels. In this glass, the vibrational levels are extremely inhomogeneously broadened. Furthermore, the glass shifts the energy of the nu=3 state more than the others, causing an inhomogeneous distribution in the anharmonic constants that are partially correlated to the inhomogeneous distribution of the fundamental frequency. These effects are discussed in light of the strong interactions that exist between the charged solute and solvent. Since this is the first example of a heterodyned fifth-order infrared pulse sequence, possible cascaded contributions to the signal are investigated. No evidence of cascaded signals is found. Compared to third-order spectroscopies, fifth-order pulse sequences provide advanced control over vibrational coherence and population times that promise to extend the capabilities of ultrafast infrared spectroscopy.

Correlated hydrogen bonding fluctuations and vibrational cross peaks in N-methyl acetamide: Simulation based on a complete electrostatic density functional theory map

The coherent nonlinear response of the entire amide line shapes of N-methyl acetamide to three infrared pulses is simulated using an electrostatic density functional theory map. Positive and negative cross peaks contain signatures of correlations between the fundamentals and the combination state. The amide I-A and I-III cross-peak line shapes indicate positive correlation and anticorrelation of frequency fluctuations, respectively. These can be ascribed to correlated hydrogen bonding at C[double bond]O and N-H sites. The amide I frequency is negatively correlated with the hydrogen bond on carbonyl C[double bond]O, whereas the amide A and III are negatively and positively correlated, respectively, with the hydrogen bond on amide N-H.

Stochastic simulation of chemical exchange in two dimensional infrared spectroscopy

The stochastic Liouville equations are employed to investigate the combined signatures of chemical exchange (two-state jump) and spectral diffusion (coupling to an overdamped Brownian oscillator) in the coherent response of an anharmonic vibration to three femtosecond infrared pulses. Simulations reproduce the main features recently observed in the OD stretch of phenol in benzene.

Site-specific vibrational dynamics of the CD3zeta membrane peptide using heterodyned two-dimensional infrared photon echo spectroscopy

Heterodyned two-dimensional infrared (2D IR) spectroscopy has been used to study the amide I vibrational dynamics of a 27-residue peptide in lipid vesicles that encompasses the transmembrane domain of the T-cell receptor CD3zeta. Using 1-(13)C[Double Bond](18)O isotope labeling, the amide I mode of the 49-Leucine residue was spectroscopically isolated and the homogeneous and inhomogeneous linewidths of this mode were measured by fitting the 2D IR spectrum collected with a photon echo pulse sequence. The pure dephasing and inhomogeneous linewidths are 2 and 32 cm(-1), respectively. The population relaxation time of the amide I band was measured with a transient grating, and it contributes 9 cm(-1) to the linewidth. Comparison of the 49-Leucine amide I mode and the amide I band of the entire CD3zeta peptide reveals that the vibrational dynamics are not uniform along the length of the peptide. Possible origins for the large amount of inhomogeneity present at the 49-Leucine site are discussed.

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.

Multidimensional vibrational spectroscopy for tunneling processes in a dissipative environment

Simulating tunneling processes as well as their observation are challenging problems for many areas. In this study, we consider a double-well potential system coupled to a heat bath with a linear-linear (LL) and square-linear (SL) system-bath interactions. The LL interaction leads to longitudinal (T1) and transversal (T2) homogeneous relaxations, whereas the SL interaction leads to the inhomogeneous dephasing (T2*) relaxation in the white noise limit with a rotating wave approximation. We discuss the dynamics of the double-well system under infrared (IR) laser excitations from a Gaussian-Markovian quantum Fokker-Planck equation approach, which was developed by generalizing Kubo's stochastic Liouville equation. Analytical expression of the Green function is obtained for a case of two-state-jump modulation by performing the Fourier-Laplace transformation. We then calculate a two-dimensional infrared signal, which is defined by the four-body correlation function of optical dipole, for various noise correlation time, system-bath coupling parameters, and temperatures. It is shown that the bath-induced vibrational excitation and relaxation dynamics between the tunneling splitting levels can be detected as the isolated off-diagonal peaks in the third-order two-dimensional infrared (2D-IR) spectroscopy for a specific phase matching condition. Furthermore, this spectroscopy also allows us to directly evaluate the rate constants for tunneling reactions, which relates to the coherence between the splitting levels; it can be regarded as a novel technique for measuring chemical reaction rates. We depict the change of reaction rates as a function of system-bath coupling strength and a temperature through the 2D-IR signal.

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.

Vibrational echo correlation spectroscopy probes of hydrogen bond dynamics in water and methanol

Multidimensional vibrational echo correlation spectroscopy with full phase resolution is used to measure hydrogen bond dynamics in water and methanol. The OD hydroxyl stretches of methanol-OD oligomers in CCl(4) and HOD in H(2)O are studied using the shortest mid-IR pulses (<50 fs, <4 cycles of light) produced to date. The pulses have sufficient spectral bandwidth to span the very broad (>400 cm(-1)) spectrum of the 0-1 and 1-2 transitions. Hydrogen bond population dynamics are extricated with exceptional detail in MeOD oligomers because the different hydrogen bonded species are spectrally distinct. The experimental results along with detailed calculations indicate the strongest hydrogen bonds are selectively broken through a non-equilibrium relaxation pathway following vibrational relaxation of the hydroxyl stretch. The correlation spectra are also a sensitive probe of the fluctuations in water and provide a stringent test of water models that are widely used in simulations of aqueous systems. The analysis of the 2D band shapes demonstrates that different hydrogen bonded species are subject to distinct (wavelength dependent) ultrafast (~100 fs) local fluctuations and essentially identical slow (0.4 and ~2 ps) structural rearrangements. Observation of wavelength dependent dynamics demonstrates that standard theoretical approaches assuming Gaussian fluctuations cannot adequately describe water dynamics.

Two-dimensional optical spectroscopy: Two-color photon echoes of electronically coupled phthalocyanine dimers

Two-color photon echo peak shift spectroscopy was used to study electronic coupling in a phthalocyanine homodimer. Two optical parametric amplifiers were used to produce pulses to excite the split lower states of LuPc2-. The existence of a two-color peak shift indicates the existence of correlation between these two dipole-allowed states. The nature of this correlation is discussed based on theoretical predictions of the interactions between exciton and charge resonance states.

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.