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.     

Ultrafast 2D-IR spectroscopy of transient species.

Multidimensional spectroscopic experiments offer fascinating insights into molecular structure and dynamics in the field of NMR spectroscopy. With the introduction of ultrafast two-dimensional infrared spectroscopy (2D-IR), multidimensional concepts have entered the optical domain, measuring couplings and correlations between molecular vibrations with femtosecond time resolution. In the transient 2D-IR (T2D-IR) experiments described in this minireview we exploit the high time resolution of 2D-IR to study transient species during fast nonequilibrium processes in real time. Information on molecular structure and dynamics is obtained that is not available from one-dimensional spectroscopy. We discuss examples from chemistry, physics and biophysics.     

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.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

Transient two-dimensional infrared spectroscopy: exploring the polarization dependence

We present a general expression for the polarization dependence of transient two-dimensional IR spectroscopy (T2D-IR), a technique designed to measure 2D-IR spectra of transient species. T2D-IR is a UV pump narrowband-IR-pump broadband-IR-probe experiment of fifth order in the laser field which involves up to three different transition dipole moments. The UV pulse adds an additional degree of freedom in polarization as compared to 2D-IR spectroscopy and increases the versatility of signal manipulation and the potential structural information content of the signals. The polarization conditions leading to a maximum of structural information are discussed. Important special cases of polarization conditions are formulated. The application of polarization selectivity is demonstrated for different types of T2D-IR experiments on photo triggered metal-to-ligand charge transfer in the model system [Re(CO)(3)(dmbpy)Cl].     

Structure and vibrational dynamics of model compounds of the [FeFe]-hydrogenase enzyme system via ultrafast two-dimensional infrared spectroscopy

Ultrafast two-dimensional infrared (2D) spectroscopy has been applied to study the structure and vibrational dynamics of (mu-S(CH2)3S)Fe2(CO)6, a model compound of the active site of the [FeFe]-hydrogenase enzyme system. Comparison of 2D-IR spectra of (mu-S(CH2)3S)Fe2(CO)6 with density functional theory calculations has determined that the solution-phase structure of this molecule is similar to that observed in the crystalline phase and in good agreement with gas-phase simulations. In addition, vibrational coupling and rapid (<5 ps) solvent-mediated equilibration of energy between vibrationally excited states of the carbonyl ligands of the di-iron-based active site model are observed prior to slower (approximately 100 ps) relaxation to the ground state. These dynamics are shown to be solvent-dependent and form a basis for the future determination of the vibrational interactions between active site and protein.     

Double-resonance versus pulsed Fourier transform two-dimensional infrared spectroscopy: an experimental and theoretical comparison

In this study we focus on the differences and analogies of two experimental implementations of two-dimensional infrared (2D-IR) spectroscopy: double-resonance or dynamic hole burning 2D-IR spectroscopy and pulsed Fourier transform or heterodyne detected photon echo spectroscopy. A comparison is done theoretically as well as experimentally by contrasting data obtained from both methods. As an example we have studied the strongly coupled asymmetric and symmetric carbonyl stretching vibrations of dicarbonylacetylacetonato rhodium dissolved in hexane. Both methods yield the same peaks in a 2D-IR spectrum. Within certain approximations we derive an analytic expression which shows that the 2D-IR spectra are broadened in one frequency dimension in the double-resonance experiment by convolution with the pump pulse spectral width, while the spectral resolution in the other frequency direction is the same in both cases.     

Analysis and identification of different animal horns by a three-stage infrared spectroscopy

In this study, a new method, a three-stage infrared spectroscopy (Fourier transform infrared spectroscopy (FT-IR) integrated with second derivative infrared spectroscopy and two-dimensional correlation infrared spectroscopy (2D-IR)) was developed to analyze the organic and inorganic compositions of three different horns (Cornu Antelopis, Cornu Bubali and Pulvis Cornus Bubali Concentratus). In IR spectra, all the three horns had their own macroscopic fingerprints especially for those compositions containing amide groups, CH groups and Ca(3)(PO(4))(2). Their second derivative spectra amplified the differences and revealed the potentially characteristic IR absorption bands 1350-400 cm(-1) to be investigated in 2D-IR. Subsequently, many covered characteristic fingerprints were disclosed in 2D-IR spectra in the range of 1350-400 cm(-1) and the three horns were therefore effectively discriminated. Meanwhile, the analysis results of inorganic constituents were verified by atomic spectroscopy. Furthermore, thirty different horn samples including ten of each horn were also successfully classified by soft independent modeling of class analogy (SIMCA). It was demonstrated that the above three-stage infrared spectroscopy could be applicable for quick, non-destructive and effective analysis and identification of very complicated and similar mixture systems (e.g. traditional Chinese medicines).     

Conformational preferences and vibrational frequency distributions of short peptides in relation to multidimensional infrared spectroscopy.

Molecular dynamics simulations of the structural distributions and the associated amide-I vibrational modes are carried out for dialanine peptide in water and carbon tetrachloride. The various manifestations in nonlinear-infrared spectroscopic experiments of the distributions of conformations of solvated dialanine are examined. The two-dimensional infrared (2D-IR) spectrum of dialanine exhibits the coupling between the amide oscillators and the correlations of the frequency fluctuations. An internally hydrogen-bonded conformation exists in CCl(4) but not in H(2)O where two externally hydrogen-bonded forms are preferred. Simulations of solvated dialanine show how the 2D-IR spectra expose the underlying structural distributions and dynamics that are not deducible from linear-infrared spectra. In H(2)O the 2D-IR shows cross-peaks from large coupling in the alpha-helical conformer and an elongated higher frequency diagonal peak, reflecting the broader distribution of structures for the more flexible acetyl end. In CCl(4), the computed cross-peak portion of the 2D-IR shows evidence of two amide-I transitions in the high-frequency region which are not apparent from the diagonal peak profile. The vibrational frequency inhomogeneity of the amide-I band arises from fluctuations of the instantaneous normal modes of these conformers rather than the shifts induced by hydrogen bonding. The simulation shows that there are correlations between fluctuations of the acetyl and amino end frequencies in H(2)O that arise from mechanical coupling and not from hydrogen bonding at the two ends of the molecule. The angular relationships between the two amide units which also show up in 2D-IR were computed, and spectral manifestations of them are discussed. The simulations also permit a calculation of the rate of energy transfer from one side of the molecule to the other. From these calculations, 2D-IR spectroscopy in conjunction with simulations is seen to be a promising tool for determining dynamics of structure changes in dipeptides.     

Study on Angelica and its different extracts by Fourier transform infrared spectroscopy and two-dimensional correlation IR spectroscopy

In order to develop a rapid and effective analysis method for studying integrally the main constituents in the medicinal materials and their extracts, discriminating the extracts from different extraction process, comparing the categories of chemical constituents in the different extracts and monitoring the qualities of medicinal materials, we applied Fourier transform infrared spectroscopy (FT-IR) associated with second derivative infrared spectroscopy and two-dimensional correlation infrared spectroscopy (2D-IR) to study the main constituents in traditional Chinese medicine Angelica and its different extracts (extracted by petroleum ether, ethanol and water in turn). The findings indicated that FT-IR spectrum can provide many holistic variation rules of chemical constituents. Use of the macroscopical fingerprint characters of FT-IR and 2D-IR spectrum can not only identify the main chemical constituents in medicinal materials and their different extracts, but also compare the components differences among the similar samples. This analytical method is highly rapid, effective, visual and accurate for pharmaceutical research.     

Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: a new approach

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.     

Direct identification and decongestion of Fermi resonances by control of pulse time ordering in two-dimensional IR spectroscopy

We show that it is possible to both directly measure and directly calculate Fermi resonance couplings in benzene. The measurement method used was a particular form of two-dimensional infrared spectroscopy (2D-IR) known as doubly vibrationally enhanced four wave mixing. By using different pulse orderings, vibrational cross peaks could be measured either purely at the frequencies of the base vibrational states or split by the coupling energy. This capability is a feature currently unique to this particular form of 2D-IR and can be helpful in the decongestion of complex spectra. Five cross peaks of the ring breathing mode nu13 with a range of combination bands were observed spanning a region of 1500-4550 cm(-1). The coupling energy was measured for two dominant states of the nu13+nu16 Fermi resonance tetrad. Dephasing rates were measured in the time domain for nu13 and the two (nu13+nu16) Fermi resonance states. The electronic and mechanical vibrational anharmonic coefficients were calculated to second and third orders, respectively, giving information on relative intensities of the cross peaks and enabling the Fermi resonance states of the combination band nu13+nu16 at 3050-3100 cm(-1) to be calculated. The excellent agreement between calculated and measured spectral intensities and line shapes suggests that assignment of spectral features from ab initio calculations is both viable and practicable for this form of spectroscopy.     

Identification of arginine residues in peptides by 2D-IR echo spectroscopy

The CN stretching vibrations of the guanidyl group in the arginine dipeptide side chain are examined by two-dimensional infrared spectroscopy. In D(2)O, the spectra display two distinct diagonal peaks. These nearly degenerate modes undergo ultrafast energy transfer. The energy-transfer rate was determined directly from the 2D-IR spectra to be 1/2.1 ps(-1). The cross peaks in 2D-IR arising from the energy transfer provide a definitive identification of arginine in larger proteins. An example of arginine in the transmembrane protein M2, found in influenza viruses, is given.     

Effects of intermolecular vibrational coupling and liquid dynamics on the polarized Raman and two-dimensional infrared spectral profiles of liquid N,N-dimethylformamide analyzed with a time-domain computational method

A time-domain method for calculating polarized Raman and two-dimensional infrared (2D-IR) spectra that includes the effects of both the diagonal frequency modulations (of individual molecules in the system) and the off-diagonal (intermolecular) vibrational coupling is presented and applied to the case of the amide I band of liquid N,N-dimethylformamide. It is shown that the effect of the resonant off-diagonal vibrational coupling and the resulting delocalization of vibrational modes is clearly seen as the noncoincidence effect in the polarized Raman spectrum and some spectral features (especially as asymmetric intensity patterns) in the 2D-IR spectra. The type of 2D-IR spectra (concerning the polarization condition) most appropriate for observing this effect is discussed. On the basis of the agreement between the observed and calculated band profiles of the polarized Raman spectrum, the time dependence of the transient IR absorption anisotropy is also calculated. The method of evaluating the extent of delocalization of vibrational modes that is relevant to the features of these optical signals in the time and frequency domains is discussed. The nature of the molecular motions (concerning the liquid dynamics) that are effective on the diagonal frequency modulations is also examined.     

Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach

The recently proposed multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) approach to evaluating reactive quantum dynamics is applied to two model condensed-phase proton transfer reactions. The models consist of a one-dimensional double-well "system" that is bilinearly coupled to a "bath" of harmonic oscillators parameterized to represent a condensed-phase environment. Numerically exact quantum-mechanical flux correlation functions and thermal rate constants are obtained for a broad range of temperatures and system-bath coupling strengths, thus demonstrating the efficacy of the ML-MCTDH approach. Particular attention is focused on the regime where low temperatures are combined with weak system-bath coupling. Under such conditions it is found that long propagation times are often required and that quantum coherence effects may prevent a rigorous determination of the rate constant.     

Biomolecular hydration dynamics probed with 2D-IR spectroscopy: From dilute solution to a macromolecular crowd

Although it is well known that water is essential for biological function, it has been a challenge to determine how water behaves near biomacromolecular interfaces, and what role water plays in influencing the dynamics of the biochemical machinery. By adopting a vibrational labeling strategy coupled with ultrafast two-dimensional infrared (2D-IR) spectroscopy, it has recently become possible to study hydration dynamics, site specifically at the surface of proteins and model membranes. We review our recent progress in measuring hydration dynamics in contexts ranging from small-molecule solutes to biomacromolecules in dilute, viscous, and crowded environments.     

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.     

Observation of rovibrational transitions of HCl, (HCl)2, and H2O-HCl in liquid helium nanodroplets

We report the infrared spectra of HCl, (HCl)2, and H2O-HCl in liquid helium nanodroplets in the frequency region between 2680 and 2915 cm(-1). For the HCl monomer a line width of 1.0 cm(-1) (H35Cl) corresponding to a lifetime of 5.3 ps was observed. The line broadening indicates fast rotational relaxation similar to that previously observed for HF. For (HCl)2 the free HCl as well as the bound HCl stretching band has been observed. The nu2+ bands of (HCl)2 could be rotationally resolved, and rotational constants were deduced from the spectra. We observed both the allowed and the symmetry forbidden transition. However, the forbidden "broken symmetry" tunneling transition of the mixed dimer shows an intensity that is considerably enhanced compared to the gas phase. Upon the basis of the present measurements we were able to calculate the tunneling splitting in the excited state. The tunneling splitting is found to be reduced by 28% compared to the gas phase. Transitions from the ground state to the Ka=1 level of the free HCl stretch (nu1) are recorded and show considerable line broadening with a line width of 2 cm(-1). The excited state Ka=1 has an additional rotational energy of about 10 cm(-1), thereby allowing fast rotational relaxation by coupling to helium excitations. In addition we observed the HCl stretch of the HCl-H2O dimer, which exhibits an unusually large width (1.7 cm(-1) for H35Cl)) and large red shift (8.5 cm(-1)), compared to the gas-phase values. The large-amplitude motion originating from the libration mode of the HCl-H2O complex is supposed to act as a fast relaxation manifold.     

Coexistence of hydrogen-bonded loop and extended tetrapeptide conformations

The conformations of a protected tetrathiopeptide have been analysed by isotope labelling and two-dimensional infrared spectroscopy (2D-IR). It has been found that Boc-Ala-Gly(=S)-Ala-Aib-OMe in acetonitrile, as well as its oxopeptide analogue, can adopt a hydrogen-bonded loop conformation in coexistence with less restricted structures. The two types of conformations interconvert too quickly to be resolved on the nuclear magnetic resonance (NMR) timescale, but give rise to different cross peaks in two-dimensional infrared spectra. The hydrogen bond between the Boc terminal group and the amide proton of Aib can be broken by photoisomerisation of the thioamide bond.     

红外光谱法对肉苁蓉径向不同部位的分析与评价

采用傅里叶变换红外光谱、二阶导数谱和二维相关红外光谱技术对肉苁蓉由表及里3个部位的药材粉末及其水提物和醇提物进行了分析与评价研究.结果表明,肉苁蓉不同部位的一维光谱非常相似,三者相似系数分别为0.9605,0.944和0.976;二阶导数谱中峰位和峰强的差异明显.1430～1700 cm-1范围内的二维相关谱中皮部自动峰有3个,而中部及髓部均为4个,更直观的反映出三者的差异.不同部位水提物和醇提物的分析结果进一步明确了肉苁蓉皮部芳香类、环烯醚萜类及糖苷类物质与中部和髓部存在明显不同,而髓部的水溶性多糖、半乳糖醇和苯乙醇苷类物质均高于其它部位.可见红外光谱法结合二维相关红外光谱技术为同种药材不同部位的细微差异分析和评价提供了一种快速、全面和客观的方法和手段.