Signatures of beta-peptide unfolding in two-dimensional vibrational echo spectroscopy: a simulation study

Inconsistent hydrogen bond-mediated vibrational coupling of amide I

Using infrared spectroscopy and density functional theory (DFT) calculations, we scrutinized an amide (dimethylformamide) as a "model" compound to interpret the interactions of amide 1 with different phenol derivatives (para-chlorophenol (PCP) and para-cresol (CP)) as "model guest molecules". We established the involvement of amide I in vibrational coupling with symmetric and asymmetric C[double bond, length as m-dash]C modes of different phenolic derivatives and how their coupling was dependent upon different guest aromatic phenolic compounds. Interestingly, substitution of phenol perturbed the pattern of vibrational coupling with amide I. The symmetric and asymmetric C[double bond, length as m-dash]C modes of PC were coupled significantly with amide 1. For PCP, the symmetric C[double bond, length as m-dash]C mode coupled significantly, but the asymmetric mode coupled negligibly, with amide I. Here, we reveal the nature of vibrational coupling based on the structure of a guest molecule hydrogen-bonded with amide I. Our conclusions could be valuable for depiction of the unusual dynamics of coupled amide-I modes as well as the dependency of vibrational coupling on altered factors.

Vibrational Coupling on Stepwise Hydrogen Bond Formation of Amide I

Despite the key roles of proteins and nucleic acids in biology, understanding their labile structures and hydrogen bond interactions with guest molecules has posed a critical challenge to the scientific community. In this report, I have used dimethylformamide as a model amide to account for amide hydrogen bond interactions of protein. To quantify hydrogen bond conformation and the structural change, I have monitored the amide I infrared (IR) stretching frequencies while varying the pK_a of phenol derivatives. For all phenol derivatives, amide I has formed one hydrogen bond and two hydrogen bond conformation. It has been observed that the formation constant for one hydrogen bond is higher than that of two hydrogen bonds for all phenol derivatives. During the formation of hydrogen bond with amide I, IR absorbance of C═C transition is enhanced for all phenol derivatives. Enhancement of the IR absorbance of the C═C transition indicates hydrogen bond-assisted vibrational coupling between the amide I and phenol ring transition. The relative coupling constant is estimated to be higher for single hydrogen-bonded conformer than the double hydrogen-bonded conformer. This is an intriguing result as the frequency difference between the two coupled transitions predicts otherwise. Using IR absorption spectroscopy, a delicate interplay between hydrogen bonding conformations and intermolecular vibrational coupling between amide I and H-bond donor phenol molecules has been shown. This study can be used as a point of reference for understanding the structural information of proteins, peptides, and nucleosides having hydrogen bond interaction with any drug or ligand molecules. My results as well provide an insight into the vibrational coupling of carbonyl and C═C transition of nucleobases.

Amide-I characteristics of helical β-peptides by linear infrared measurement and computations

In this work, we have examined the amide-I characteristics of three β-peptide oligomers in typical helical conformations (two in 14-helix and one in 12/10-helix), solvated in water, methanol, and chloroform, respectively. Local-mode frequencies and their distributions were computed using a molecular-mechanics force field based frequency map that was constructed on the basis of molecular dynamics simulations. The local-mode frequencies were found to be determined primarily by peptide backbone and side chain, rather by solvent, suggesting their local structural sensitivities. Intermode vibrational couplings computed using a transition dipole scheme were found to be very sensitive to peptide conformation, with their signs and magnitudes varying periodically along the peptide chain. Linear infrared absorption spectra of the three peptides, simulated using a frequency-frequency time-correlation function method, were found to be in fair agreement with experimental results. Normalized potential energy distribution analysis indicated that the amide-I mode can delocalize over a few amide units. However, the IR band structure appears to be more sophisticated in helical β-peptides than in helical α-peptides.

Simulating the T-jump-triggered unfolding dynamics of trpzip2 peptide and its time-resolved IR and two-dimensional IR signals using the Markov state model approach

We proposed a computational protocol of simulating the T-jump peptide unfolding experiments and the related transient IR and two-dimensional IR (2DIR) spectra based on the Markov state model (MSM) and nonlinear exciton propagation (NEP) methods. MSMs partition the conformation space into a set of nonoverlapping metastable states, and we can calculate spectra signal for each of these states using the NEP method. Thus the overall spectroscopic observable for a given system is simply the sum of spectra of different metastable states weighted by their populations. We show that results from MSMs constructed from a large number of simulations have a much better agreement with the equilibrium experimental 2DIR spectra compared to that generated from straightforward MD simulations starting from the folded state. This indicates that a sufficient sampling of important relevant conformational states is critical for calculating the accurate spectroscopic observables. MSMs are also capable of simulating the unfolding relaxation dynamics upon the temperature jump. The agreement of the simulation using MSMs and NEP with the experiment not only provides a justification for our protocol, but also provides the physical insight of the underlying spectroscopic observables. The protocol we developed has the potential to be extended to simulate a wide range of fast triggering plus optical detection experiments for biomolecules.

Amide vibrations and their conformational dependences in β-peptide

The characteristics of the amide-A and amide-I modes in a β-homoalanine dipeptide (β-HADP) have been examined as a function of backbone dihedral angles. The harmonic frequencies were obtained using the density functional theory. The anharmonic frequencies and diagonal anharmonicities were obtained by using the Morse potential. Local-mode frequencies and intermode couplings were obtained using the computed normal-mode frequencies and eigenvectors. It was found that the vibrational frequencies for the two types of amide modes are both conformational-dependent. The inter-amide-A and inter-amide-I couplings in the β-peptides were predicted to be generally weaker than those in the α-peptides. Structural bases of the amide-A and amide-I local modes in the β-peptides are discussed.

Amide I'-II' 2D IR spectroscopy provides enhanced protein secondary structural sensitivity

We demonstrate how multimode 2D IR spectroscopy of the protein amide I' and II' vibrations can be used to distinguish protein secondary structure. Polarization-dependent amide I'-II' 2D IR experiments on poly-l-lysine in the beta-sheet, alpha-helix, and random coil conformations show that a combination of amide I' and II' diagonal and cross peaks can effectively distinguish between secondary structural content, where amide I' infrared spectroscopy alone cannot. The enhanced sensitivity arises from frequency and amplitude correlations between amide II' and amide I' spectra that reflect the symmetry of secondary structures. 2D IR surfaces are used to parametrize an excitonic model for the amide I'-II' manifold suitable to predict protein amide I'-II' spectra. This model reveals that the dominant vibrational interaction contributing to this sensitivity is a combination of negative amide II'-II' through-bond coupling and amide I'-II' coupling within the peptide unit. The empirically determined amide II'-II' couplings do not significantly vary with secondary structure: -8.5 cm(-1) for the beta sheet, -8.7 cm(-1) for the alpha helix, and -5 cm(-1) for the coil.

Infrared signature and folding dynamics of a helical beta-peptide

Synthetic foldamers consisting of beta-amino acids offer excellent model systems for examining the effect of backbone flexibility on the dynamics of protein folding. Herein, we study the folding-unfolding kinetics of a beta-peptide that folds into a 14-helical structure in water. We find that the T-jump induced relaxation kinetics of this peptide occur on the nanosecond time scale and are noticeably slower than those of alanine-based alpha-helical peptides, and additionally, the relaxation rates show a weaker dependence on temperature. These differences appear to indicate that the folding energy landscapes of these peptides are different. In addition, we find that the amide I' band of this beta-peptide exhibits a sharp feature at approximately 1612 cm(-1), which we believe is a distinct infrared reporter of 14-helix.

Probing the folding of mini-protein Beta3s by two-dimensional infrared spectroscopy; simulation study

We propose to use infrared coherent two-dimensional correlation spectroscopy (2DCS) to characterize the folding mechanism of the mini-protein Beta3s. In this study Beta3s was folded by molecular dynamics (MD) simulation and intermediate conformational ensembles were identified. The one and two-dimensional correlation spectrum was calculated for the intermediate and native states of the mini-protein. A direct structure-spectra relationship was determined by analysis of conformational properties and specific residue contributions. We identified the structural origin of diagonal and off-diagonal peaks in the 2DCS spectra for the native and intermediate conformational ensembles in the folding mechanism. This work supports the implementation of computational techniques in conjunction with experimental 2DCS to study the folding mechanism of proteins. In addition to exploring the folding mechanism the work presented here can be applied in combination with experiment to refine and validate current molecular dynamics force fields.

PACS Codes: 87.15.Cc, 87.15.hm, 87.15.hp

Applications of 2D IR spectroscopy to peptides, proteins, and hydrogen-bond dynamics

Following a survey of 2D IR principles, this article describes recent experiments on the hydrogen-bond dynamics of small ions, amide-I modes, nitrile probes, peptides, reverse transcriptase inhibitors, and amyloid fibrils.

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.

Vibrational spectral diffusion and hydrogen bond dynamics in heavy water from first principles

We present a first-principles theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in heavy water without using any empirical model potentials. The calculations are based on ab initio molecular dynamics simulations for trajectory generation and a time series analysis using the wavelet method for frequency calculations. It is found that, in deuterated water, although a one-to-one relation does not exist between the instantaneous frequency of an OD bond and the distance of its associated hydrogen bond, such a relation does hold on average. The dynamics of spectral diffusion is investigated by means of frequency-time correlation and spectral hole dynamics calculations. Both of these functions are found to have a short-time decay with a time scale of approximately 100 fs corresponding to dynamics of intact hydrogen bonds and a slower long-time decay with a time constant of approximately 2 ps corresponding to lifetimes of hydrogen bonds. The connection of the slower time scale to the dynamics of local structural relaxation is also discussed. The dynamics of hydrogen bond making is shown to have a rather fast time scale of approximately 100 fs; hence, it can also contribute to the short-time dynamics of spectral diffusion. A damped oscillation is also found at around 150-200 fs, which is shown to have come from underdamped intermolecular vibrations of a hydrogen-bonded water pair. Such assignments are confirmed by independent calculations of power spectra of intermolecular motion and hydrogen bond kinetics using the population correlation function formalism. The details of the time constants of frequency correlations and spectral shifts are found to depend on the frequencies of chosen OD bonds and are analyzed in terms of the dynamics of hydrogen bonds of varying strengths and also of free non-hydrogen-bonded OD groups.

Two-dimensional infrared spectroscopy as a probe of the solvent electrostatic field for a twelve residue peptide

The linear IR and two-dimensional (2D) IR spectra of the amide-I modes of the 12-residue beta-hairpin peptide tryptophan zipper-2 (SWTWENGKWTWK) and its two 13C isotopomers were simulated, with local mode frequencies evaluated by two solution-phase peptide amide-I frequency maps proposed recently: an electrostatic potential map and an electrostatic field map. Both maps predict a set of nondegenerate local amide-I mode transition energies for the hairpin. Spectral simulations using both maps predict the main spectral features of the linear IR and 2D IR experimental results of the (13)C-labeled and -unlabeled hairpin. The radial distribution functions obtained using trajectories from classical molecular dynamics simulations demonstrate different water distributions at different sites of the hairpin. Our results suggest that the observed difference of the (13)C-shifted band, including its peak position and frequency distributions for different isotopomers, in both linear IR and 2D IR spectra, is likely to be due to the difference in the local environment of the solvated peptide. Ab initio density functional theory calculations show a residue-independent (13)C shift of the amide-I mode, further supporting the result. The variations of these shifts are attributed to the residue level heterogeneity of the electrostatic environment of the peptide. Our results show that 2D IR of peptide with single (13)C isotopic labeling can be used to probe the electrostatic environment of the peptide local structure.

Dipeptide Structure Determination by Vibrational Circular Dichroism Combined with Quantum Chemistry Calculations

The solution structure and the local solvation environments of alanine dipeptide (AD, 1 a) and its isotopomer (AD*, 1 b, 13C on the acetyl end C==O) are studied by using infrared (IR) spectroscopy and vibrational circular dichroism (VCD). From the amide I IR spectra of AD* in various protic solvents, it is found that each of the two carbonyl groups is fully H-bonded to two water molecules. However, the number of alcohol molecules H-bonded to each C==O varies from one to two, and the local solvation environments are asymmetric around the two peptides of AD* in alcohol solutions. The amide I VCD spectra of AD and AD* in D2O are also measured, and a series of density functional theory (DFT, B3LYP/6-311++G**) calculations are performed to obtain the amide I normal-mode rotational strengths of AD and the intrinsic rotational strengths of its two peptide fragments. By combining the VCD-measurement and DFT-calculation results and employing a coupled oscillator theory, we show that the aqueous-solution structure of the dipeptide can be determined. We believe that the present method will be of use in building up a library of dipeptide solution structures in water.

Two-Dimensional Infrared Spectral Signatures of 310- and α-Helical Peptides

Two-dimensional infrared (2D IR) spectra of Calpha-alkylated model octapeptides Z-(Aib)8-OtBu, Z-(Aib)5-L-Leu-(Aib)2-OMe, and Z-[L-(alphaMeVal)]8-OtBu have been measured in the amide I region to acquire 2D spectral signatures characteristic of 3(10)- and alpha-helical conformations. Phase-adjusted 2D absorptive spectra recorded with parallel polarizations are dominated by intense diagonal peaks, whereas 2D rephasing spectra obtained at the double-crossed polarization configuration reveal cross-peak patterns that are essential for structure determination. In CDCl3, all three peptides are of the 3(10)-helix conformation and exhibit a doublet cross-peak pattern. In 1,1,1,3,3,3-hexafluoroisopropanol, Z-[L-(alphaMeVal)]8-OtBu undergoes slow acidolysis and 3(10)-to-alpha-helix transition. In the course of this conformational change, its 2D rephasing spectrum evolves from an elongated doublet, characteristic of a distorted 3(10)-helix, to a multiple-peak pattern, after becoming an alpha-helix. The linear IR and 2D absorptive spectra are much less informative in discerning the structural changes. The experimental spectra are compared to simulations based on a vibrational exciton Hamiltonian model. The through-bond and through-space vibrational couplings are modeled by ab initio coupling maps and transition dipole interactions. The local amide I frequency is evaluated by a new approach that takes into account the effects of hydrogen-bond geometry and sites. The static diagonal and off-diagonal disorders are introduced into the Hamiltonian through statistical models to account for conformational fluctuations and inhomogeneous broadening. The sensitivity of cross-peak patterns to different helical conformations and the chain length dependence of the spectral features for short 3(10)- and alpha-helices are discussed.

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.

Normal mode analysis using the driven molecular dynamics method. II. An application to biological macromolecules

The driven molecular-dynamics (DMD) method, recently proposed by Bowman, Zhang, and Brown [J. Chem. Phys. 119, 646 (2003)], has been implemented into the TINKER molecular modeling program package. The DMD method yields frequencies and normal modes without evaluation of the Hessian matrix. It employs an external harmonic driving term that can be used to scan the spectrum and determine resonant absorptions. The molecular motions, induced by driving at resonant frequencies, correspond to the normal-mode vibrations. In the current work we apply the method to a 20-residue protein, Trp-cage, that has been reported by Neidigh, Fesinmeyer, and Andersen [Nature Struct. Biol. 9, 425 (2002)]. The structural and dynamical properties of this molecule, such as B-factors, root-mean square fluctuations, anisotropies, vibrational entropy, and cross-correlations coefficients, are calculated using the DMD method. The results are in very good agreement with ones calculated using standard normal-mode analysis method. Thus, the DMD method provides a viable alternative to the standard Hessian-based method and has considerable potential for the study of large systems, where the Hessian-based method is not feasible.

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.

DNA Vibrational Coupling Revealed with Two-Dimensional Infrared Spectroscopy: Insight into Why Vibrational Spectroscopy Is Sensitive to DNA Structure

Two-dimensional infrared (2D IR) spectroscopy was used to study the carbonyl vibrational modes of guanine and cytosine bases in A- and B-form DNA. Located between 1600 and 1700 cm(-1), these modes are often used to monitor DNA secondary structure with traditional infrared spectroscopies such as FTIR, but traditional spectroscopies lack the necessary observables to unravel the coupling mechanisms that make these modes sensitive to secondary structure. By using 2D IR spectroscopy and electronic structure calculations on d(G(5)C(5)) and d(GC)(8) model nucleic acids, we find that hydrogen-bonded guanine/cytosine base pairs are primarily electrostatically coupled and that the coupling between these modes can be modeled with a transition dipole density approach. In comparison, electrostatics is insufficient to model stacked bases because of cooperative charge-sharing effects, but the coupling can be accurately calculated using a finite difference method. We find that the coupling is very strong for both hydrogen-bonded and stacked base geometries, creating vibrational modes that extend both across the base pairs and along the lengths of the helices. Our results provide a physical basis for understanding how strong coupling gives rise to the empirically established relationship between infrared spectroscopy and DNA/RNA secondary structure.

Photoinduced conformational dynamics of a photoswitchable peptide: a nonequilibrium molecular dynamics simulation study

Employing nonequilibrium molecular dynamics simulations, a comprehensive computational study of the photoinduced conformational dynamics of a photoswitchable bicyclic azobenzene octapeptide is presented. The calculation of time-dependent probability distributions along various global and local reaction coordinates reveals that the conformational rearrangement of the peptide is rather complex and occurs on at least four timescales: 1) After photoexcitation, the azobenzene unit of the molecule undergoes nonadiabatic photoisomerization within 0.2 ps. 2) On the picosecond timescale, the cooling (13 ps) and the stretching (14 ps) of the photoexcited peptide is observed. 3) Most reaction coordinates exhibit a 50-100 ps component reflecting a fast conformational rearrangement. 4) The 500-1000 ps component observed in the simulation accounts for the slow diffusion-controlled conformational equilibration of the system. The simulation of the photoinduced molecular processes is in remarkable agreement with time-resolved optical and infrared experiments, although the calculated cooling as well as the initial conformational rearrangements of the peptide appear to be somewhat too slow. Based on an ab initio parameterized vibrational Hamiltonian, the time-dependent amide I frequency shift is calculated. Both intramolecular and solvent-induced contributions to the frequency shift were found to change by < or = 2 cm(-1), in reasonable agreement with experiment. The potential of transient infrared spectra to characterize the conformational dynamics of peptides is discussed in some detail.

Non-Gaussian statistics of amide I mode frequency fluctuation of N-methylacetamide in methanol solution: linear and nonlinear vibrational spectra

By carrying out molecular dynamics simulations of an N-methylacetamide (NMA) in methanol solution, the amide I mode frequency fluctuation and hydrogen bonding dynamics were theoretically investigated. Combining an extrapolation formula developed from systematic ab initio calculation studies of NMA-(CH3OH)n clusters with a classical molecular dynamics simulation method, we were able to quantitatively describe the solvatochromic vibrational frequency shift induced by the hydrogen-bonding interaction between NMA and solvent methanol. It was found that the fluctuating amide I mode frequency distribution is notably non-Gaussian and it can be decomposed into two Gaussian peaks that are associated with two distinctively different solvation structures. The ensemble-average-calculated linear response function associated with the IR absorption is found to be oscillating, which is in turn related to the doublet amide I band shape. Numerically calculated infrared absorption spectra are directly compared with experiment and the agreement was found to be excellent. By using the Onsager's regression hypothesis, the rate constants of the interconversion process between the two solvation structures were obtained. Then, the nonlinear response functions associated with two-dimensional infrared pump-probe spectroscopy were simulated. The physics behind the two-dimensional line shape and origin of the cross peaks in the time-resolved pump-probe spectra is explained and the result is compared with 2D spectra experimentally measured recently by Woutersen et al.

Two-dimensional Raman spectra of atomic solids and liquids

We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.

Infrared and Raman Line Shapes of Dilute HOD in Liquid H2O and D2O from 10 to 90 °C

A combined electronic structure/molecular dynamics approach was used to calculate infrared and isotropic Raman spectra for the OH or OD stretches of dilute HOD in D2O or H2O, respectively. The quantities needed to compute the infrared and Raman spectra were obtained from density functional theory calculations performed on clusters, generated from liquid-state configurations, containing an HOD molecule along with 4-9 solvent water molecules. The frequency, transition dipole, and isotropic transition polarizability were each empirically related to the electric field due to the solvent along the OH (or OD) bond, calculated on the H (or D) atom of interest. The frequency and transition dipole moment of the OH (or OD) stretch of the HOD molecule were found to be very sensitive to its instantaneous solvent environment, as opposed to the isotropic transition polarizability, which was found to be relatively insensitive to environment. Infrared and isotropic Raman spectra were computed within a molecular dynamics simulation by using the empirical relationships and semiclassical expressions for the line shapes. The line shapes agree well with experiment over a temperature range from 10 to 90 degrees C.

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.

Amide I Vibrational Dynamics ofN-Methylacetamide in Polar Solvents: The Role of Electrostatic Interactions

The vibrational frequency of the amide I transition of peptides is known to be sensitive to the strength of its hydrogen bonding interactions. In an effort to account for interactions with hydrogen bonding solvents in terms of electrostatics, we study the vibrational dynamics of the amide I coordinate of N-methylacetamide in prototypical polar solvents: D2O, CDCl3, and DMSO-d6. These three solvents have varying hydrogen bonding strengths, and provide three distinct solvent environments for the amide group. The frequency-frequency correlation function, the orientational correlation function, and the vibrational relaxation rate of the amide I vibration in each solvent are retrieved by using three-pulse vibrational photon echoes, two-dimensional infrared spectroscopy, and pump-probe spectroscopy. Direct comparisons are made to molecular dynamics simulations. We find good quantitative agreement between the experimentally retrieved and simulated correlation functions over all time scales when the solute-solvent interactions are determined from the electrostatic potential between the solvent and the atomic sites of the amide group.

Collective Oscillations and the Linear and Two-Dimensional Infrared Spectra of Inhomogeneous β-Sheets

We numerically calculate the collective amide I oscillations and the associated linear and two-dimensional infrared (2DIR) spectra for model antiparallel beta-sheets and study the effect of inhomogeneity. To visualize the collective vibrational exciton states, a new method is introduced, which proves very useful in classifying the optically dominant states with respect to their symmetry properties and phase relations, even in the absence of exact symmetries. We find that energy (diagonal) and interaction (off-diagonal) disorder may have profoundly different effects on the main peaks in the linear spectrum. We also show that in the 2DIR spectra energy disorder leads to diagonal stretching of the diagonal peaks, while the cross-peaks are typically stretched more horizontally. This offers an explanation for the recently observed overall Z-shape in experimental spectra. Finally, we find that the anharmonic splitting between associated positive and negative features in the 2DIR spectra scales inversely proportionally with the exciton delocalization size imposed by the disorder, thus offering a spectroscopic ruler for this size.

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.

Nonadiabatic effects on peptide vibrational dynamics induced by conformational changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH(3)-CO-NH-CH(2)-CO-NH-CH(3)). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (DFT) [B3LYP/6-31+G(d)] level. The ordering of the energetically most stable isomers (C(7) and C(5)) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C(7) and C(5) minimum energy structures occur on a sub-picosecond time scale (700...800 fs). Vibrationally nonadiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly nonadiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a time scale of 200...500 fs with population transfer of more than 50% between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy.

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.