Vibrational Energy Relaxation Rate Research Articles

Assessment of multi-temperature relaxation models for carbon dioxide vibrational kinetics

Several advanced models for multi-temperature vibrational energy relaxation rates are implemented to study adiabatic bath relaxation in carbon dioxide, among them a hybrid model based on state-to-state relaxation rates, the model based on the rigorous Chapman–Enskog theory, and modifications of the Landau–Teller (LT) models. Different sets of rate coefficients for vibrational energy transitions (Schwartz, Slawsky and Herzfeld (SSH) theory, forced harmonic oscillator (FHO) model) are used as well as various techniques for the relaxation time evaluation. Based on isothermal bath simulations it is found that the FHO model provides good agreement with experimentally measured relaxation times. Assessment of relaxation models shows that the three-temperature model based on the Chapman–Enskog theory yields excellent agreement with the detailed hybrid approach while being more computationally efficient; two-temperature models and modifications of the LT formulas cannot provide reliable description of intermode exchanges in polyatomic gases. The choice of the model for transition probabilities is crucial for identifying key relaxation mechanisms. When the FHO model is applied, strongly coupled relaxation in all CO2 modes is found whereas the model of SSH yields overpredicted relaxation rate in the symmetric-bending mode and almost uncoupled slow relaxation in the asymmetric mode. Possible ways for further model validation under glow discharge conditions are discussed.

Intramolecular Vibrational Energy Relaxation of CO2 in Cross-Linked Poly(ethylene glycol) Diacrylate-Based Ion Gels.

Ultrafast two-dimensional infrared spectroscopy (2D-IR) and Fourier transform infrared spectroscopy (FTIR) were used to measure carbon dioxide (CO2) in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N]), cross-linked low-molecular-weight poly(ethylene glycol) diacrylate (PEGDA), and an ion gel composed of a 50 vol % blend of the two. The center frequency of the antisymmetric stretch, ν3, of CO2 shifts monotonically to lower wavenumbers with increasing polymer content, with the largest line width in the ion gel (6 cm-1). Increasing polymer content slows both spectral diffusion and vibrational energy relaxation (VER) rates. An unexpected excited-state absorbance peak appears in the 2D-IR of cross-linked PEGDA due to VER from the antisymmetric stretch into the bending mode, ν2. Thirty-two response functions are necessary to describe the observed features in the 2D-IR spectra. Nonlinear least-squares fitting extracts both spectral diffusion and VER rates. In the ion gel, CO2 exhibits spectral diffusion dynamics that lie between that of the pure compounds. The kinetics of VER reflect both fast excitation and de-excitation of the bending mode, similar to the ionic liquid (IL), and slow overall vibrational population relaxation, similar to the cross-linked polymer. The IL-like and polymer-like dynamics suggest that the CO2 resides at the interface of the two components in the ion gel.

Multi-temperature vibrational energy relaxation rates in CO2

Rates of vibrational energy relaxation in carbon dioxide are studied in the framework of the three-temperature kinetic-theory approach. Vibrational–translational transitions in the bending mode and inter-mode exchange of vibrational quanta are considered. In the zero-order approximation of the generalized Chapman–Enskog method, the energy relaxation rates in the coupled symmetric–bending and asymmetric modes are expressed in terms of thermodynamic forces similar to chemical reaction affinities, and a compact representation for the vibrational energy production rates is proposed. Linearized theory is developed, and analytical ratios of linearized relaxation rates to those defined by the original Landau–Teller (LT) theory are obtained. The relaxation rates are calculated using the Schwartz–Slawsky–Herzfeld (SSH) and forced harmonic oscillator models for the vibrational energy transition probabilities in the temperature range 200 K–10 000 K. For inter-mode exchanges, using the SSH theory yields significantly underpredicted relaxation rates. The ranges of applicability for the LT formula and linearized theory are estimated; the original LT formula for inter-mode vibrational energy exchanges is not capable of accounting for the excitation of both vibrational modes; linearized models yield better results. Possible steps for improving the numerically efficient LT model are proposed.

Time-Dependent Perspective for the Intramolecular Couplings of the N-H Stretches of Protonated Tryptophan.

Quasi-classical direct dynamics simulations, performed with the B3LYP-D3/cc-pVDZ electronic structure theory, are reported for vibrational relaxation of the three NH stretches of the −NH3+ group of protonated tryptophan (TrpH+), excited to the n = 1 local mode states. The intramolecular vibrational energy relaxation (IVR) rates determined for these states, from the simulations, are in good agreement with the experiment. In accordance with the experiment, IVR for the free NH stretch is slowest, with faster IVR for the remaining two NH stretches which have intermolecular couplings with an O atom and a benzenoid ring. For the free NH and the NH coupled to the benzenoid ring, there are beats (i.e., recurrences) in their relaxations versus time. For the free NH stretch, 50% of the population remained in n = 1 when the trajectories were terminated at 0.4 ps. IVR for the free NH stretch is substantially slower than for the CH stretch in benzene. The agreement found in this study between quasi-classical direct dynamics simulations and experiments indicates the possible applicability of this simulation method to larger biological molecules. Because IVR can drive or inhibit reactions, calculations of IVR time scales are of interest, for example, in unimolecular reactions, mode-specific chemistry, and many photochemical processes.

Photo-excitation dynamics of N, N-dimethyl-p-nitroaniline in ionic liquids: Effect of cation alkyl-chain length

Transient absorption spectroscopy has been applied to study the photo-excitation dynamics of N, N-dimethyl-p-nitroaniline in twelve imidazolium/phosphonium cation-based ionic liquids (ILs) with alkyl chains of different lengths. The transient absorption spectra showed an initial bleach signal around the absorption center (400 nm) and a stimulated emission band around 500 nm. The bleach signal was recovered mostly within a few picoseconds, and a hot band absorption appeared around 450 nm. The time profiles of the band integrals for the bleach and absorption spectral regions were simulated by a sum of four exponential decays. The internal conversion rate corresponding to the back electron transfer (b-ET) rate from the charge-separated excited state, was determined by the time profile of the band integral of the bleach region. The vibrational energy relaxation (VER) rate in the ground state was determined from the time profile of the hot band absorption decay band integral. The b-ET rate decreased with increasing number of alkyl carbons in the cation (#C). The solvent dependence was discussed in terms of the free energy change at the Marcus inverted region, which was indicated by the blue-shift of the ground state absorption band. The change of the free energy is ascribed to the change of the charge concentration of ILs. The VER rate decreased slightly with increasing #C. The reason was discussed in terms of the interaction of DMpNA with the polar region of ILs. The intersystem crossing yield also increased with increasing #C, reflecting an increase in the non-polar region of the ILs.

Comparison of vibrational dynamics between non-ionic and ionic vibrational probes in water: Experimental study with two-dimensional infrared and infrared pump-probe spectroscopies

Dynamics of the hydration structure around small vibrational probes have been extensively studied over the past few decades. However, we need to gain insight into how vibrational dynamics is affected by the molecular nature of the probe molecules in water. In this study, 2-nitro-5-thiocyanate benzoic acid (NTBA), which has an SCN group attached to an aromatic ring, and thiocyanate ion (SCN−) were used to investigate the vibrational dynamics of two vibrational probes, including vibrational frequency fluctuations and rotational relaxation. By performing two-dimensional infrared spectroscopic measurements, the vibrational frequency fluctuations of the SCN anti-stretching modes of these solutes were compared. The frequency-frequency time correlation function (FFTCF) of these solutes can be modeled by a delta function plus an exponential function and a constant. The FFTCF of NTBA was characterized by a time constant of 1.1 ps, which is similar to that of SCN−. Moreover, no component was longer than this constant. Consequently, the loss of the correlation in frequency fluctuations of the SCN anti-stretching mode of NTBA may be controlled by a mechanism similar to that of the ionic probe, which involves the hydrogen bonding dynamics of water. Polarization-controlled IR pump-probe measurements were performed for these vibrational probes in water to study the vibrational energy relaxation (VER) and reorientational relaxation processes. The VER rate of NTBA is much smaller than that of SCN−, which indicates that the intramolecular relaxation process is significant for VER of NTBA. Based on the rotational relaxation time of NTBA being shorter than that of SCN−, the internal rotational motion of the SCN group around the Cphenyl–S bond axis, where Cphenyl denotes a carbon atom of the aromatic ring to which the SCN group is attached, may play an important role in the anisotropic decay of NTBA in H2O.

Dissociative Photoionization of He···Li2: A Theoretical Study.

Dissociative photoionization of the He···Li2 van der Waals complex to the ground electronic state of the He···Li2+ ion is investigated theoretically. The photoionization cross section is computed using existing interaction potentials. Resonances are found on top of a structured continuum. They are assigned to vibrational predissociation of the ion by comparison with Fermi Golden Rule calculations. Because of the differences in potential energy surfaces between the neutral and ionic complexes, only the resonances corresponding to quasibound states with the highest excitation in the van der Waals modes are visible. The other quasi bound states obtained in the Fermi Golden Rule calculations can give information on vibrational energy relaxation rates in other collisional processes involving the lithium dimer ion and a helium atom.

Vibrational dynamics of azide-derivatized amino acids studied by nonlinear infrared spectroscopy.

Recently, biomolecules which are labeled by azide or thiocyanate groups in solutions and proteins have been studied to examine microscopic environment around a solute by nonlinear infrared (IR) spectroscopy. In this study, we have performed two-dimensional infrared (2D-IR) spectroscopy to investigate the vibrational frequency fluctuations of two different azide-derivatized amino acids, Ala (N3-Ala) and Pro (N3-Pro), and N3(-) in water. From the 2D-IR experiments, it was found that the frequency-frequency time correlation function (FFTCF) of solute can be modeled by a delta function plus an exponential function and constant. FFTCF for each probe molecule has a decay component of about 1 ps, and this result suggests that the stretching mode of the covalently bonded azide group is sensitive to the fluctuations of hydrogen bond network system, as found in previous studies of N3(-) in water. In contrast to FFTCF of N3(-), FFTCF of the azide-derivatized amino acids contains static component. This static component may reflect dynamics of water affected by the solutes or the structural fluctuations of the solute itself. We also performed the IR pump-probe measurements for the probe molecules in water in order to investigate vibrational energy relaxation (VER) and reorientational relaxation. It was revealed that the charge fluctuations in the azide group are significant for the VER of this mode in water, reflecting that the VER rate of N3(-) is faster than those of the azide-derivatized amino acids. While the behaviors of the anisotropy decay of N3-Ala and N3(-) are similar to each other, the anisotropy decay of N3-Pro contains much slower decaying component. By considering the structural difference around the vibrational probe between N3-Ala and N3-Pro, it is suggested that the structural freedom of the probe molecules can affect the reorientational processes.

Ultrafast Relaxation and Reaction of Diiodide Anion after Photodissociation of Triiodide in Room-Temperature Ionic Liquids

Vibrational dephasing, vibrational relaxation, and rotational relaxation of diiodide (I(2)(-)) after photodissociation of triiodide (I(3)(-)) in room-temperature ionic liquids (RTILs) were investigated by ultrafast transient absorption spectroscopy. The vibrational energy relaxation (VER) rate of I(2)(-) produced by the photodissociation reaction of I(3)(-) was determined from the spectral profile of the transient absorption. The rates in RTILs were slightly slower than those in conventional liquids. On the other hand, the coherent vibration of I(2)(-) was not observed in RTILs, and the vibrational dephasing of the photoproduced I(2)(-) was accelerated. This was explained by the interaction between I(2)(-) and I consisting of a caged contact pair in RTILs. The orientational relaxation time of I(2)(-) determined by the transient absorption anisotropy was much longer in RTILs than in conventional liquids due to their high viscosities although the relaxation time was shorter than the prediction from the Stokes-Einstein-Debye (SED) theory. The deviation from the SED prediction was interpreted by the frequency dependence of the shear stress acting on the molecule. The dynamics of I(2)(-) in 1-butyl-3-methylimidazolium iodide ([BMIm]I) were quite different from those in other conventional RTILs: the coherent vibration of I(2)(-) was observed for the time profile of the transient absorption and the initial value of the anisotropy was reduced to 0.31 from 0.36 in conventional RTILs. These results suggest that an ultrafast reaction between the photofragment I and the solvent I(-) may occur during the photodissociation process of I(3)(-). The anomaly in the ground state coherent vibration and steady state Raman spectrum of I(3)(-) also suggest the possibility that I(3)(-) and I(-) can be located in vicinity and interact strongly with each other in [BMIm]I.

Dielectric response and vibrational energy relaxation in photoactive yellow protein: A molecular dynamics simulation study

Molecular dynamics simulations of the dielectric response and vibrational energy relaxation (VER) from the chromophore to the protein and solvent environment following photoexcitation of photoactive yellow protein are presented. The computed protein response to photoexcitation appears prominently between times of 0.1 and 0.3 ps. Contributions from individual residues to this response are analyzed. The frequency-dependent VER rate also reveals dynamic coupling between the chromophore and residues that hydrogen bond to it. Resonances in the VER rate appear at frequencies comparable to the oscillations observed in recent fluorescence decay studies.

Vibrational Energy Relaxation in Liquid HCl and DCl via the Linearized Semiclassical Method: Electrostriction versus Quantum Delocalization

The rate constant for vibrational energy relaxation of the H-Cl stretch in liquid HCl (T = 188K, ρ = 19.671 nm(-3)) is calculated within the framework of the Landau-Teller formula. The force-force correlation function is calculated via the recently introduced force-derivative-free linearized semiclassical method [Vázquez et al. J. Phys. Chem. A2010, 114, 5682]. The calculated vibrational energy relaxation rate constant is found to be in excellent agreement with experiment, and the electrostatic force is found to contribute significantly to the high frequency component of the force-force correlation function. In contrast, the corresponding classical vibrational energy relaxation rate constant is found to be 2 orders of magnitude slower than the experimental value, and the classical force-force correlation function is found to be dominated by the Lennard-Jones forces. These observations suggest that quantum delocalization, enhanced by the light mass of hydrogen, amplifies the contribution of repulsive Coulombic forces to the force-force correlation function, thereby making electrostriction an unlikely mechanism for vibrational energy relaxation in the case of hydrogen stretches. This interpretation is reinforced by the results of a similar calculation in the case of the D-Cl stretch in liquid DCl under the same conditions. In this case, the quantum enhancement of the vibrational energy relaxation rate constant is observed to be greatly diminished in comparison to HCl, thereby giving rise to a reversal of the isotope effect in comparison to that predicted by the corresponding classical treatment (i.e., whereas the classical vibrational energy relaxation rate of DCl is faster than that of HCl, the opposite trend is predicted by the linearized semiclassical treatment). It is also shown that the vibrational energy relaxation of DCl is completely dominated by the Lennard-Jones forces within either classical and semiclassical treatments, thereby suggesting that electrostriction is the underlying mechanism in this case.

Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath

The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed.

Short Time Scale Dynamics and a Second Correlation between Liquid and Gas Phase Chemical Rates: Diffusion Processes in Noble Gas Fluids

A theoretical formula for single-atom diffusion rates that predicts an isothermal correlation relation between the liquid (l) and gas (g) phase diffusion coefficients, D(T, ρl) and D(T, ρg) is developed. This formula is based on a molecular level expression for the atom’s diffusion coefficient, D(T, ρ), and on numerical results for 1715 thermodynamic states of 25 rare gas fluids. These numerical results show that at fixed temperature, T, the decay time, τDIF, which governs the shortest time decay of an appropriate force autocorrelation function, F(t) F0, is density (ρ)-independent. This independence holds since τDIF arises from the ρ-independent shortest time inertial motions of the solvent. The ρ independence implies the following l−g diffusion coefficient correlation equation: D−1(T, ρl) = (ρl/ρg) D−1(T, ρg) [ρl−1F0,l2/ρg−1F0,g2]. This relation is identical in form to the familiar (isolated binary-collision-like) empirical correlation formula for vibrational energy relaxation rate constants. This is because both correlation relations arise from inertial dynamics. Inertial dynamics always determines short-time fluid motions, so it is likely that similar correlation relations occur for all liquid phase chemical processes. These correlation relations will be most valuable for phenomena dominated by short time scale dynamics.

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.

Vibrational Spectroscopy and Dynamics of the Hydrazoic and Isothiocyanic Acids in Water and Methanol

Small anions in polar solvents are benchmark systems for fast vibrational energy relaxation (VER) due to the Coulombic effects that promote solute-solvent interactions. In order to investigate the effects of solute charge and solvent isotope effects on vibrational spectra and dynamics, infrared pump-probe studies have been used to determine VER (T(1)) times for the pseudohalide acids, XNCS and XN(3) (X = H, D), in protic solvents, H(2)O, D(2)O, CH(3)OH, and CD(3)OD. These results are compared with the well-studied azide and thiocyanate anions. Solvent isotope effects of the vibrational frequency shifts of azide and for VER rates of both azide and thiocyanate are similar to those for the hydro- and deutero-protonated species in water. VER times are longer for HN(3)/H(2)O, HN(3)/CH(3)OH, and DN(3)/CD(3)OD (T(1) = 2.3, 5.6, and 3.7 ps, respectively) than for the corresponding anions in solution (0.8, 3.0, and 2.1 ps), which is consistent with the idea that ions relax more quickly than neutrals. But the times measured for DN(3)/D(2)O, HNCS/H(2)O, and DNCS/D(2)O (T(1) = 1.2, 1.5, and 4.4 ps, respectively) are shorter than for the corresponding ions (2.3, 2.7, and 22.0 ps). Fast VER for DN(3) in D(2)O is attributed to strong coupling to nearby solvent bands and/or to Fermi resonances that promote intramolecular vibrational relaxation. For the HNCS and DNCS, the faster rates can be understood by recognizing that the charge displacements are similar to those for the anion.

Vibrational Energy Relaxation Rates via the Linearized Semiclassical Method without Force Derivatives

A new computational scheme for calculating vibrational energy relaxation rate constants is presented that is based on applying the linearized semiclassical approximation to the symmetrized force-force correlation function. Unlike the previous scheme of Geva and Shi [Shi, Q.; Geva, E. J. Phys. Chem A 2003, 107, 9059], which was based on applying the linearized semiclassical approximation to the standard force-force correlation function, the new scheme does not involve a power expansion of the initial force in terms of the Wigner transform integration variable Delta and as a result is more accurate and does not require force derivatives as input. The main disadvantages of the new scheme are its slower convergence rate in comparison to the Shi-Geva scheme and its ambiguity with respect to the choice of configuration around which the local harmonic approximation is performed. The computational feasibility and accuracy of the new approach is demonstrated on a number of benchmark models, including the highly challenging case of nonpolar diatomic liquids. It is observed that performing the local harmonic approximation around the configuration used for computing the initial force yields the best agreement with experiment.

Short Time Scale Dynamics and the Correlation between Liquid and Gas Phase Vibrational Energy Relaxation Rates

Although gas (g) and liquid (l) phase densities rho and rho(l) can differ by 3 orders of magnitude, from experiment the corresponding vibrational energy relaxation (VER) rate constants are at the same temperature T, strongly correlated. Namely, these rate constants obey the empirical correlation equation k(Tau,rho(l)) = (rho(l)/rho(g))k(Tau,rho(g))G where typically G approximately 0.5-2.0. The rate correlation equation is usually explained by the isolated binary collision (IBC) hypothesis, which yields a theoretical result for G. However, the physical assumptions underlying the IBC hypothesis have often been criticized. Thus we propose a new purely mathematical hypothesis, which yields the correlation equation including a molecular formula for G. This hypothesis is that the relaxing molecule's normalized vibrational force autocorrelation function is rho-independent to order t(2). The hypothesis is checked numerically for three model dihalogen solute/rare gas solvent VER systems. It is found to be obeyed for 280 thermodynamic states, usually within 0.02% to 0.30%. An inertial dynamics mechanism is proposed as a tentative physical explanation for our mathematical hypothesis.

Vibrational energy relaxation of perylene in supercritical alcohols

The time resolved fluorescence spectra of perylene in sub- and supercritical methanol have been measured by using a streak camera in the lower-pressure region than 10 MPa and an optical Kerr gate spectroscopic method in the higher-pressure region than 10 MPa. The lineshape of the fluorescence spectrum has been found to be dependent on the time. By comparing the excess energy dependence of the fluorescence lineshape in vapour perylene without energy dissipation process, the spectral change was assigned to the vibrational energy relaxation process in the S1 state. The vibrational energy relaxation time at each solvent density in supercritical region was determined by the time-profile at the 0-0 band peak position in the fluorescence spectrum. The vibrational energy relaxation rate scaled by the square root of the temperature has been compared with the hydrogen-bonding degree between solvent molecules estimated by the NMR measurement (Hoffmann M M and Conradi M S 1998 J. Phys. Chem. B 102 263).

Effect of Hydrogen-Bond Strength on the Vibrational Relaxation of Interfacial Water

Time-resolved sum frequency generation (tr-SFG) reveals that the vibrational energy relaxation rate of O-H stretching of dilute HDO in D(2)O at the silica interface is markedly different from that of bulk water. As compared to the bulk liquid, the vibrational lifetime (T(1)) of HDO is shorter at the charged surface than in the bulk, but longer at the neutral surface. The vibrational decoupling of the O-H of the HDO species leads to the observation of a frequency-dependent T(1) of the O-H stretch, which is shorter at the red than the blue side of the hydrogen-bonded OH spectral region. This correlates with the red-shift of the SFG spectra with increasing surface charge and is consistent with a theoretical model that relates the vibrational lifetime to the strength of the hydrogen-bond network.

Intermolecular Interaction between W(CO)6 and Alkane Molecules Probed by Ultrafast Vibrational Energy Relaxation: Anomalously Strong Interaction between W(CO)6 and Decane

The rate of vibrational energy relaxation (VER) is a valuable probe of microscopic intermolecular interaction. In the present article, the VER rate of the T(1u) CO stretch of W(CO)(6) is measured in binary solutions composed of an alkane (hexane, decane, tetradecane) and cyclohexane or CCl(4), with seven mixing volume ratios. The volume ratio dependence indicates that, among the three alkane-cyclohexane solutions, only decane shows an exceptionally strong contribution to the VER process. It is strongly suggested that decane forms a specific solute-solvent complex with W(CO)(6). The "V-shaped" dependence of the VER rate on the number of carbons in alkane solvents (Banno, M.; Sato, S.; Iwata, K.; Hamaguchi, H. Chem. Phys. Lett. 2005, 412, 464.) is explained by the solute-solvent complex model. There are no experimental results that suggest the formation of the specific solute-solvent complex in alkane-CCl(4) solutions.