Vibrational Dephasing Research Articles

Frequency Selected Ultrafast Infrared Vibrational Echo Studies of Liquids, Glasses, and Proteins

Ultrafast infrared frequency selected vibrational echo (FSVE) experiments are used to study temperature-dependent dynamic interactions in liquids, glasses, and proteins. Vibrational echo experiments measure vibrational dephasing. In general, the large bandwidths associated with ultrashort IR pulses will excite multiple vibrational transitions of a molecular system. In addition to the 0- 1 transition of a particular mode of interest, the 1-2 transition, other modes, combination bands, and modes of other species can be excited. A one-dimensional vibrational echo experiment involving multiple transitions can be difficult to address theoretically. By selecting the proper detection wavelengths (a frequency slice through a 2D time-frequency vibrational echo), FSVE makes it possible to effectively isolate a two state system (in terms of the dynamical experimental observables) from within a complex multistate system. First, the FSVE method is used to study the dynamics of CO stretching mode of RuTPPCOPy (TPP = 5,10,15,20-tetraphenylporphyrin, Py = pyridine) in two solvents: poly(methyl methacrylate) (PMMA) and 2-methyltetrahydrofuran (2-MTHF). The results demonstrate the fundamental difference in the influence of a glassy and a liquid solvent on vibrational dephasing. In PMMA, a glass at all temperatures studied, the dephasing rate is linear in temperature. In 2-MTHF, the dephasing is linear for temperatures below Tg, but it changes form, becoming very steep slightly above Tg. Calculations using a model frequency-frequency correlation function (FFCF) show that the different temperature dependences in PMMA and 2-MTHF can be modeled in a unified manner, with at least two solvent motions contributing to the dephasing in liquids, that is, inertial and diffusive motions. FSVE is then applied to the study of the dynamics of the protein myoglobin in water by observing the vibrational dephasing of the stretching mode of CO bound to the active site of myoglobin (Mb-CO). The A 1 and A 3 conformational substates of Mb-CO are found to have different dephasing rates with different temperature dependences. A frequency-frequency correlation function derived from molecular dynamics simulations of Mb-CO at 298 K is used to calculate the vibrational echo decay. The calculated decay shows substantial agreement with the experimentally measured decays. The FSVE experiment probes protein dynamics and provides an observable that can be used to test structural assignments for the Mb-CO conformational substates.

Temperature-dependent vibrational dephasing: Comparison of liquid and glassy solvents using frequency-selected vibrational echoes

Frequency-selected vibrational echo experiments were used to investigate the temperature dependences of vibrational dephasing associated with the 0-1 transition of the CO stretching mode of RuTPPCOPy (TPP=5,10,15,20-tetraphenylporphyrin, Py=pyridine) in two solvents: polymethylmethacrylate (PMMA) and 2-methyltetrahydrofuran (2-MTHF). In PMMA, a glass, the echo decay is exponential at all the temperatures studied, and the dephasing rate increases linearly with increasing temperature. In 2-MTHF, there is a change in the functional form of the temperature dependence when the solvent goes through the glass transition temperature (Tg). Below Tg, the dephasing rate increases linearly with temperature, while above Tg, it rises very steeply in a nonlinear manner. In the liquid at higher temperatures, the vibrational echo decays are nonexponential. A model frequency-frequency correlation function (FFCF) is proposed in which the FFCF differs for a glass and a liquid because of the intrinsic differences in the nature of the dynamics. At least two motions, inertial and diffusive, contribute to the vibrational dephasing in the liquids. The different temperature dependences of inertial and diffusive motions are discussed. Comparison of the model calculations of the vibrational echo temperature dependence and the data show reasonable, but not quantitative agreement.

Intermolecular Dynamics of Room-Temperature Ionic Liquids: Femtosecond Optical Kerr Effect Measurements on 1-Alkyl-3-methylimidazolium Bis((trifluoromethyl)sulfonyl)imides

Using optically heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) with 40 fs laser pulses, the transient birefringence in the room-temperature ionic liquids (RTILs), 1-alkyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)imides, [Cnmim]NTf2 with n = 2, 4, 5, 6, 8, 10 (C2, C4, C5, C6, C8, C10), has been studied at room temperature and ambient pressure. Near zero delay, the OHD-RIKES response is dominated by the instantaneous electronic response. The nuclear response appears as a shoulder on the electronic response. Between 0 and 1 ps, the nuclear response is dominated by the intermolecular vibrational (nondiffusive) response. For C4, C5, C6, and C8, the 1/e time of the pseudo-exponential tail of the intermolecular response decreases with viscosity, in accord with the hydrodynamic model for vibrational dephasing. Superimposed on the OHD-RIKES response for C4, C5, and C6 is a coherent oscillation with a frequency of ∼140 cm-1. The intermolecular vibrational spectra for these RTILs obtained from the reduced OHD-RIKES data by using a Fourier transform procedure extend from 0 to 200 cm-1 and are bimodal with a low-frequency component at ∼22 cm-1 and a high-frequency component at ∼84 cm-1. The relative contribution of the high-frequency component to the total band increases in going from C2 to C5 and remains constant for C5, C6, and C8. The behavior of the reduced spectral densities is consistent with increasing order in the liquid. It is proposed that the 140 cm-1 oscillation arises from collective motions of locally ordered domains in the liquid.

Freezing molecular vibrational energy flow with coherent control

In a previous report, we examined the possibility of ‘freezing’ intramolecular vibrational energy redistribution (IVR) in organic molecules by using optimal coherent control. Here we describe the new methodology developed to achieve stabilization of initially excited nonstationary states. Our approach combines an approximate but full-dimensional molecular vibrational Hamiltonian, a frequency-domain wavelet representation of the electric field, a fast symplectic propagator to compute the IVR decay, and simulated annealing optimization of the electric field parameters. We find that the complexity of the vibrational wavepacket increases sufficiently slowly with time, so that with available pulse shapers, vibrational dephasing can be ‘frozen’ for 1–2 orders of magnitude in time beyond the usual IVR decay time. Slowing the IVR clock into the multi-picosecond regime may allow the natural selective reactivity (via Franck–Condon factors) of the initially excited nonstationary vibrational states to emerge.

Nuclear dynamics in electronic ground and excited states probed by spectrally resolved four wave mixing

Time-resolved ground-state bleach and excited-state stimulated emission spectra have been measured for indocyanine green dissolved in methanol by employing spectrally resolved four wave mixing (SRFWM). The separation of the SRFWM signals into the ground-state bleach and excited-state stimulated emission contributions allows observation of intramolecular vibrational wave packet motions and intermolecular solvation dynamics upon impulsive excitation, while the molecule resides either in the ground or in the excited state. Frequencies of the indocyanine green intramolecular vibrational modes in the ground and excited states are practically the same. Vibrational dephasing times in the excited state range from a few hundred fs to ∼2 ps, and they are consistently shorter than those in the ground state. When excitation frequency is centered near the 0-0 transition, center frequencies of the stimulated emission redshift due to solvation of the excited state in nonequilibrium solvent configuration, whereas those of the ground-state bleach blueshift due to equilibrium fluctuation of the solvent molecules around the chromophore in the ground state. At early times, the solvation function obtained from the time-resolved ground-state bleach spectra is slower than the solvation function obtained from the time-resolved excited-state stimulated emission spectra.

Temperature dependence of the pure vibrational dephasing rate in a heteropolymer

The temperature dependence of the pure vibrational dephasing rate in two different model heteropolymers is examined. One model is an anharmonic chain of atoms coupled by random forces, for which the pure dephasing rate of one mode is calculated. The second is a CO ligand coupled to an α-helix of the protein myoglobin. In both models the rate of pure dephasing due to coupling to vibrational modes of the heteropolymer is found to obey an apparent power-law temperature dependence T α , α≈1.3–1.4, over the temperature range of the calculations, from well below 100 to about 200 K.

Instantaneous collision complexes in molten alkali halides: Picosecond dynamics from low-frequency Raman data

The picosecond dynamics of molten alkali halides is discussed, and the low-frequency Raman spectra of molten LiCl, CsCl, and the LiCl–CsCl eutectic are fitted to the model enabling to obtain the times of vibrational dephasing, τV and vibrational frequency modulation τω. In terms of the Wilmshurst criterion [J. Chem. Phys. 39, 1779 (1963)] and using the data of NMR studies and molecular dynamics simulations, a conclusion is drawn that molten alkali halides cannot contain long-lived stable complexes with lifetimes greater than 10−8 s. The low-frequency Raman spectra of molten alkali halides and their mixtures probe the presence of instantaneous spatial configurations of MXn−n+1 type, where M+ is the alkali metal cation and X− is the halide anion existing in melts during the time intervals equal to the time of duration of collision of oppositely charged ions τd, which is less than 0.5 ps. This time is sufficient to a collision complex to execute several (at least one) vibrations. Vibrational dephasing and modulation processes elapse during this same time, thereby indicating the instantaneous nature of configurations in question. To discern between short-lived and long-lived complexes, we propose relations between the minimal damping time of the probe oscillator set equal to the half-period of vibration T/2, τV, τω, and τd, as well as the time between collisions τBC. The duration of an act resulting in the vibrational phase shift (or energy transfer) must be equal to (or longer than) the half-period of vibration of the probe oscillator, τV⩾T/2. The modulation time may vary from this same half-period of vibration or the time between collisions τBC to very long times, τω⩾T/2, τω⩾τBC. For short-lived complexes, the longest of two characteristic times describing the phase decay cannot exceed possible duration of collision, τω⩽τd, τV⩽τd. Cs-containing configurations follow this definition and therefore should be considered instantaneous short-lived collision complexes: their τV≈T/2∼0.1 ps, and τω≈τBC∼0.03 ps. Li-containing configurations appear to be relatively long-lived: their lifetimes could be associated with τω∼0.17 ps, which is several times longer than any other shortest possible characteristic time in the system (τBC∼0.026 ps or T/2∼0.05 ps). In light of these conclusions, an a priori assumption of autocomplex MX4n−4 anions and Mn+ cations as being structural elements of molten halides made in the so-called autocomplex model by Smirnov, Shabanov, and Khaimenov [Elektrohim. 2, 1240 (1966)] is discussed, and the autocomplexes are identified as instantaneous short-lived configurations detectable by the Raman method.

Coherent multidimensional vibrational spectroscopy

Coherent multidimensional vibrational spectroscopy (CMDVS) is an emerging field that offers new oportunities to probe specifically intramolecular and intermolecular interactions in complex samples with the improved resolution and selectivity expected of a multidimensional method. In particular, it provides structural and dynamical information about correlations between modes. It provides this information on the picosecond time scales characteristic of vibrational dephasing. CMDVS is based on the perturbations that are induced in a mode when other coupled modes are excited. It is the vibrational analogue to multidimensional nucler magnetic resonance (NMR). In this review, we present the background that led to the development of CMDVS, a brief summary of the different methods of non-linear laser spectroscopy and how they can achieve CMDVS, the relationships between CMDVS and multidimensional NMR, and the theory necessary to understand the experimental results. The experimental approaches reviewed fall into three main classes: non-degenerate four-wave mixing which is doubly vibrationally enhanced, degenerate four-wave mixing which is triply vibrationally enhanced and six-wave mixing which has three Raman transitions. CMDVS has been implemented in both the time domain and the frequency domain. Finally, the review describes possible extensions of CMDVS and speculates on its future.

Analysis of the Solvent- and Temperature-Dependent Raman Spectral Changes of S1trans-Stilbene and the Mechanism of the trans to cis Isomerization: Dynamic Polarization Model of Vibrational Dephasing and the CC Double-Bond Rotation

Solvent- and temperature-dependent band shape changes of the olefinic CC stretch Raman band of S1 trans-stilbene have been analyzed on the basis of the dynamic polarization model. The analysis has shown that the solvent-induced dynamic polarization gives rise to the dephasing of the CC stretch vibration and, concomitantly, triggers and facilitates the rotation around the CC bond leading to the trans to perpendicular (and eventually to cis) isomerization. Picosecond time-resolved Raman spectra have been measured in the three alkane solvents, hexane, octane, and decane at a number of different temperatures ranging from 268 to 338 K and a total of 40 peak positions and the bandwidths have been determined for the CC stretch band. The correlation plot of the bandwidth against peak position shows a clear linear relationship that is predicted by the dynamic polarization model. Picosecond time-resolved fluorescence measurements have been performed in the same three alkane solvents at five different temperatures f...

Dephasing of the ν1 vibration of isotopic molecules of carbon tetrachloride

AbstractThe isotopic structure of the ν1 line in the isotropic Raman spectrum of liquid carbon tetrachloride was studied. A new fitting procedure was employed enabling one to fit overlapping lines, obtaining dynamic parameters at the same time. The time‐correlation functions of vibrational dephasing were first found for each isotopic species present in the liquid at their natural abundance. The isotopic dependence of the characteristic times of vibrational dephasing and vibrational frequency modulation was analysed. The isotopic dependence of dephasing times is contained primarily in the frequency factor: the dephasing times decrease with decreasing line frequency. This dependence entirely outweighs the opposite relationship between the dephasing times and masses. The frequency modulation times show the same trend, which contradicts the simple collision model. Copyright © 2002 John Wiley & Sons, Ltd.

Femtosecond mid-infrared photon echo study of an intramolecular hydrogen bond

The vibrational dephasing dynamics of O–H stretching excitations in a sterically well-defined intramolecular hydrogen bond (H bond) is studied by femtosecond photon echo spectroscopy in the mid-infrared. The O–H stretching vibration of phthalic acid monomethyl ester in inert solution displays a fast decay of phase coherence on a sub-100 fs time scale. Anharmonic coupling of the stretching motion to an underdamped low-frequency mode of the H bond gives rise to oscillations in the transient grating decay and the 3-pulse photon echo peak shift. Spectral diffusion dynamics on longer time scales is absent in such intramolecular H bonds, as opposed to the weaker intermolecular H bonds in water.

Vibrational dynamics of isolated hydrogen in germanium

Absorption line shapes associated with the stretch mode of bond-center hydrogen (H ( + ) B C at 1794 cm - 1 and the twofold degenerate mode of hydrogen near the tetrahedral site (H ( - ) ) at 745 cm - 1 in germanium are measured with infrared-absorption spectroscopy. The H ( + ) B C line shape measured at 10 K for the case of low hydrogen concentrations gives a lifetime between 15 and 23 ps. Similar in magnitude to the 7.8′0.2 ps observed for the same defect in silicon [M. Budde et al, Phys. Rev. Lett. 85, 1452 (2000)]. this observation indicates that the lifetime of the bond-centered mode is largely insensitive to the phonon frequency distributions of the host material. Pure dephasing dynamics of hydrogen in germanium are studied by measuring the shape of the 1794- and 745-cm - 1 lines as a function of temperature. These measurements are analyzed using a recently formulated exchange model for vibrational dephasing. The temperature dependence of the 1794-cm - 1 line shape is attributed to thermal fluctuations in the occupation number of a pseudolocalized mode at 75′2 cm - 1 .

Vibrational Dynamics in Hydrogen-Bonded (Pyridine + Water) Complexes Studied by Spectrally Resolved Femtosecond CARS

The technique of femtosecond time-resolved coherent anti-Stokes Raman spectroscopy (fs-CARS) was used to study the vibrational dephasing dynamics in hydrogen-bonded (pyridine + water) complexes as a function of pyridine mole fraction

A Theoretical Analysis of the Sum Frequency Generation Spectrum of the Water Surface. II. Time-Dependent Approach

Sum frequency generation (SFG) spectroscopy is a powerful experimental technique to probe surface structures. This paper presents a new theoretical mode of nonempirical analysis of SFG spectra for interfacial structures, which considerably generalizes our previous effort (Chem. Phys. 2000, 258, 371), which involved several empirical elements. The method is based on a time correlation function for the frequency-dependent hyperpolarizability, which can be straightforwardly evaluated via molecular dynamics simulations and which explicitly takes into account, for example, intramolecular vibrations and electronic polarization. The new theory is capable of precisely describing a number of factors significant for the spectrum, such as the dielectric local field correction, vibrational dephasing, inter/intramolecular vibrational coupling, etc., and is fairly nonempirical and rigorous, within the dipole approximation. The results for the water−vapor interface reproduce the experimental spectra fairly well, although with some discrepancies; possible reasons for these are suggested.

Energy gap dependence of vibrational dephasing rates in a bath: a semigroup description

The quantum dynamical semigroup formalism provides an appealing general framework for discussing factors that affect pure vibrational dephasing rates in chemical systems. Within this framework, we formulate a Poisson model of pure vibrational dephasing which is more generally applicable than the commonly employed stochastic Gaussian dephasing model. In the limit of small and frequent phase changes, the Poisson model reduces to the stochastic Gaussian form. We find that for certain vibrational states of the lithium dimer in argon, the stochastic Gaussian model is valid, while for other states large and abrupt phase changes clearly require application of the Poisson model. In the former case, dephasing rates increase with the difference in quantum number between constituent vibrational states, while in the latter case, the dependence on quantum number difference or energy gap can become negligible. Recent experimental advances described by Amitay and Leone are expected to permit experimental tests of our theoretical predictions.

Raman free-induction-decay measurements in low viscosity and supercooled toluene: Vibrational dephasing by shear fluctuations

Total dephasing decay profiles of the ν12 (1002 cm−1) ring-stretching mode of toluene have been measured in the time domain in a range extending from the low viscosity, normal liquid (380 K, 0.26 cP) to the high viscosity, supercooled liquid (140 K, 4600 cP). In the region from 1 to 5 cP (250 to 200 K), the profile makes a transition from exponential to partially Gaussian, consistent with a loss of motional narrowing. In contrast to many interpretations of dephasing in terms of collisional dynamics, these data clearly indicate an important role for diffusive dynamics in vibrational dephasing. Above 10 cP, oscillations appear, and their period decreases with increasing viscosity. An analysis of the low to moderate viscosity region with a Kubo model shows that the frequency modulation time is dependent on the viscosity. The dephasing decay profiles are used to test a recent viscoelastic theory of dephasing [Chem. Phys. 233, 257 (1998)], which attributes the perturbation of the vibrational frequency to shear fluctuations in the liquid. A second dephasing process must be included to obtain reasonable fits in the viscosity range below 10 cP. The second process is consistent with a Gaussian frequency modulation whose modulation time is weakly viscosity dependent or has no viscosity dependence. We speculate that this process is due to rapid rotation about the toluene z axis and that the same process also causes the oscillations seen at higher viscosity. There is a good correspondence between the value of the infinite frequency shear modulus found from fitting the Raman free-induction-decay data and the value recently found by Larsen, Ohta, and Fleming by fitting photon-echo-peak-shift measurements in toluene [J. Chem. Phys. 111, 8970 (1999)]. This correspondence supports the idea that both vibrational dephasing and nonpolar electronic solvation are caused by the same physical mechanism.

Ionic interactions in molten complex chlorides from vibrational dephasing

In this article we present the first quantitative estimates of the spectroscopically active part of the interaction potential in molten complex chlorides based on dephasing studies. We have selected the molten salt systems containing quasispherical complex MCl4−2 anions (M=Mn+2 and Zn+2) and performed the study of their ν1(A1) isotropic Raman line profiles as a function of the temperature and concentration. We have analyzed the form of the time correlation function of vibrational dephasing and determined the type of modulation events, which cause the line broadening processes in these systems; these are found to be purely discrete Markovian. Within the formalism of the purely discrete Markovian modulation, we have made a judgement about spectroscopically active interactions in these systems. Interionic potential in complex chlorides is dominated by the attraction forces, which depend on the interparticle distance r as r−4, and by repulsion of the r−7-type.

Investigation of Two-Dimensional Vibrational Spectrum by a Diagrammatic Approach

Abstract We have theoretically investigated two-dimensional vibrational spectra for a two-mode system in terms of a diagrammatic approach. The two vibrational modes are anharmonically coupled. The perturbed stationary states are obtained by treating the cubic anharmonicity as a perturbation, and expressions for the third order response functions are derived. A physical origin of cross peaks in the spectrum is discussed. It is found that the vibrational dephasing time as well as the anharmonicity is important for the appearance of cross peaks.

Calculation of the two-dimensional vibrational response function

We present a complete analytical expression of the two-dimensional (2D) vibrational response function without invoking the factorization approximations based on the Wick’s theorem that have been used in most previously reported theories. Since the harmonic approximation to the vibrational degrees of freedom is not required in this new formulation, the vibrational-level dependencies of the transition frequencies and the vibrational relaxation rates are fully incorporated in the obtained formula for the 2D vibrational response function. Furthermore, the non-Markovian nature of the vibrational dephasing process in condensed phases is also fully taken into account by carrying out the resummation of the associated diagrams with the linked diagram theory. It is found that there exists an additional contribution to the 2D vibrational response function, which was completely ignored due to the approximations based on the Wick’s theorem.

Evidence for negative cross correlations in vibrational dephasing in liquids: isotropic raman-line shift and width phenomena in isotopic mixtures of N2 and O2

To experimentally confirm the hypothesis of negative cross terms between different dephasing mechanisms, potentially leading to a broadening of the isotropic Raman line upon isotopic dilution, we present a detailed study on the concentration dependencies of all of the line shifts and widths in the four isotopic mixtures of type (15N14N)(x)-(14N2)(1-x), (15N2)(x)-(14N2)(1-x), (15N2)(x)-(15N14N)(1-x), and (16O2)(x)-(18O2)(1-x) near the normal boiling point of nitrogen at T = 77.35 K. A quite disparate behavior of the nitrogen oscillators compared to the oxygen oscillators was observed in respect to a change of their isotopic baths.