Vibrational Energy Relaxation Time Research Articles

Stochastic model of collisional energy transfer based on the diffusion equation

Collisional energy transfer from highly excited polyatomic molecules in a heat reservoir is considered as a diffusion process in energy space. It is taken into account that the density of the vibrational states of polyatomic molecules is very high and presented by a continuous energy function. Both the average energy transfer moments per collision and these moments averaged over an ensemble of molecules have been calculated to obtain an exact analytical solution to the diffusion equation. At long times, the solution to the diffusion equation converges to the equilibrium Boltzmann distribution. The conditional probability density decays at long times with a vibrational energy relaxation time. The ensemble averages tend to equilibrium with the same characteristic time.

Diffusion equation analysis of collisional energy transfer between highly excited molecules and a bath gas

Collisional energy transfer from highly excited molecules in a buffer gas is considered as a diffusion process in the energy space. A diffusion approximation is examined, and its accuracy is assessed by comparison with an exact analytical solution to the corresponding master equation. Under certain general conditions, the problem of finding a fundamental solution to the diffusion equation reduces to solving a system of the first-order equations for the time-dependent coefficients of expansion in orthogonal polynomials. An exact explicit solution to the diffusion equation is found where the first two moments of energy transfer are the polynomials of degrees one and two, respectively. At long times, the solution of the diffusion equation converges to the solution of the master equation. The necessary condition is that this time interval must exceed the vibrational energy relaxation time. The sufficient condition is the large average number of collisions for relaxation to equilibrium.

The Rate of Fast Particles Leaving a Planar Channeled Regime in a Quasiclassical Approach

The rate of particles leaving a planar channeling regime is studied in the framework of nonequilibrium statistical theory. In the quasiclassical case, an analytical expression for the corresponding kinetic coefficient $$R_{N}^{{({\text{dec)}}}}$$ is obtained for high-energy particles interacting with valence electrons. At high temperatures, the expression for particle transition is found to agree reasonably well with the probability of thermal (nonradiating) transition of particles from channeling. The rate coefficient $$R_{N}^{{({\text{dec)}}}}$$ including terms of the lowest order with respect to the particle–electron interaction is inversely proportional to vibrational energy relaxation time τν, while the anharmonicity of particle vibration in a planar channel has an effect on the relaxation process only because of its interference with the electron scattering.

Vibrational relaxation of small anions in a polymer film

Steady-state and ultrafast vibrational spectroscopy can help to elucidate the interactions between small anions and their environment because the anions’ infrared absorption frequencies and vibrational energy relaxation (VER) times depend strongly on those interactions. Their strong infrared absorptions also make many of these anions promising candidates for strong coupling to optical fields. Here, we report the vibrational energy relaxation of dicyanamide (DCA) in H2O and D2O and find that the so-called solvent isotope effect on VER is not as pronounced as for other anions. In addition, we report the infrared spectroscopy and VER lifetimes of DCA, N3−, and NCS− embedded in a polyelectrolyte polymer. We find that the polymer matrix accelerates VER in a similar fashion to H2O, but the detailed mechanism of this acceleration remains unclear.

Laser IR fragmentation of molecular clusters: the role of channels for energy input and relaxation, the influence of surroundings, and the dynamics of fragmentation

The results of research into the infrared (IR) laser fragmentation of molecular clusters by resonant vibrational excitation of their constituent molecules are presented with special attention given to the role of cluster environment, the energy input and relaxation channels, and dynamical aspects. For this purpose, the results of experiments with free homogeneous and mixed molecular clusters and of experiments with clusters inside or on the surface of large inert gas clusters are analyzed, the laser excitation pulses varying in wavelength and duration. Data on the character and rate of cluster fragmentation, and on the intramolecular and intracluster vibrational energy relaxation times in clusters are discussed. Results of an investigation into the structure and dynamics of molecular clusters and atomic-molecular complexes obtained by IR photodissociation spectroscopy and the spectroscopy of photofragments are analyzed. Methods for generating heterogeneous molecular clusters, for size-selecting clusters. and for studying the IR dissociation and IR fragmentation of clusters are also briefly considered.

Vibrational relaxation and energy migration of N-methylacetamide in water: the role of nonbonded interactions.

Nonequilibrium molecular dynamics (MD) simulations together with physics-based force fields are used to follow energy flow between vibrationally excited N-methylacetamide (NMA) and water. The simulations are carried out with a previously validated force field for NMA, based on a multipolar representation of the electrostatics, and with a new fluctuating point charge model. For the water solvent, a flexible and a rigid model was employed to distinguish between the role of inter- and intramolecular degrees of freedom. On a 10 ps time scale about 90% of the available energy goes into the solvent. The remaining energy resides within internal NMA-degrees of freedom from where energy flow takes place on longer time scales. The total amount of energy transferred to the solvent on the 10 ps time scale does not depend on whether the water molecules are rigid or flexible during the simulations. Vibrational energy relaxation time scales include two regimes: one on the several 100 fs time scale and a longer one, ranging from 6 to 10 ps. This longer time scale agrees with previous simulations but overestimates the experimentally determined relaxation time by a factor of 2, which can be explained by the classical treatment of the vibrations. Including a previously determined quantum correction factor brings the long time scale into quite favorable agreement with experiment. Coupling to the bending vibration of the water molecules in H-bonding contact with the excited C═O chromophore is substantial. The equilibrium and nonequilibrium distribution of the bending angles of the water molecules in contact with the local oscillator are non-Gaussian, and one approaches the other on the subpicosecond time scale. Analysis of the water velocity distribution suggests that the C═O vibrational energy relaxes into the solvent water shells in an impulsive fashion on a picosecond time scale.

Ratio between phase and energy intramolecular vibrational relaxation times of polyatomic anions in solutions of electrolytes

A comparative analysis of intramolecular vibrational relaxation times of polyatomic anions in solutions of electrolytes and vibrational energy relaxation times was performed. Vibrational relaxation times were calculated by analyzing the form of isotropic Raman scattering bands. The conclusion was drawn that the main process responsible for the formation of the isotropic contour of Raman symmetrical stretching vibration bands of anions in solutions of electrolytes was vibrational dephasing. Because of the formation of ion-molecular H-bonds, vibrational dephasing and energy relaxation times decreased substantially differently.

Vibrational dynamics of tricyanomethanide

Steady-state and time resolved IR spectroscopy have been used to characterize vibrational spectra and relaxation dynamics of the antisymmetric CN stretching band of tricyanomethanide (TCM) in solutions of water, heavy water, methanol, dimethyl sulfoxide, formamide, and the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4]. The vibrational energy relaxation times for tricyanomethanide in these solvents are longer than those previously reported for dicyanamide, another CN containing anion, in the same solvents. Results of ab initio calculations of the vibrational frequencies for tricyanomethanide depend on the method used and compare favorably with experimentally measured values for IR-active and Raman-active bands. Proton and electron affinities were also calculated.

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 dynamics of metal cyanides

Time-resolved IR spectroscopy has been used to characterize vibrational and rotational relaxation dynamics of the C–N stretching bands for aqueous molecular cyanides, Au ( CN ) 2 - , Ni ( CN ) 4 2 - , Pt ( CN ) 4 2 - , Co ( CN ) 6 3 - , Mn ( CN ) 6 3 - , and Ru ( CN ) 6 4 - . The spectra and dynamics of Ru ( CN ) 6 4 - resemble those previously reported for ferrocyanide with a relatively short (<10 ps) vibrational energy relaxation (VER) time. VER times are longer (>30 ps) for Au ( CN ) 2 - , Ni ( CN ) 4 2 - , Pt ( CN ) 4 2 - and Co ( CN ) 6 3 - . Mn ( CN ) 6 3 - is an intermediate case with a VER time of 15 ps in water. These VER dynamics extend and reinforce the trends for metal cyanide CN vibrational band frequencies and intensities.

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).

Vibrational Dynamics of Hydrogen-Bonded Complexes in Solutions Studied with Ultrafast Infrared Pump−Probe Spectroscopy

In aqueous solution, the basis of all living processes, hydrogen bonding exerts a powerful effect on chemical reactivity. The vibrational energy relaxation (VER) process in hydrogen-bonded complexes in solution is sensitive to the microscopic environment around the oscillator and to the geometrical configuration of the hydrogen-bonded complexes. In this Account, we describe the use of time-resolved infrared (IR) pump-probe spectroscopy to study the vibrational dynamics of (i) the carbonyl CO stretching modes in protic solvents and (ii) the OH stretching modes of phenol and carboxylic acid. In these cases, the carbonyl group acts as a hydrogen-bond acceptor, whereas the hydroxyl group acts as a hydrogen-bond donor. These vibrational modes have different properties depending on their respective chemical bonds, suggesting that hydrogen bonding may have different mechanisms and effects on the VER of the CO and OH modes than previously understood. The IR pump-probe signals of the CO stretching mode of 9-fluorenone and methyl acetate in alcohol, as well as that of acetic acid in water, include several components with different time constants. Quantum chemical calculations indicate that the dynamical components are the result of various hydrogen-bonded complexes that form between solute and solvent molecules. The acceleration of the VER is due to the increasing vibrational density of states caused by the formation of hydrogen bonds. The vibrational dynamics of the OH stretching mode in hydrogen-bonded complexes were studied in several systems. For phenol-base complexes, the decay time constant of the pump-probe signal decreases as the band peak of the IR absorption spectrum shifts to lower wavenumbers (the result of changing the proton acceptor). For phenol oligomers, the decay time constant of the pump-probe signal decreases as the probe wavenumber decreases. These observations show that the VER time strongly correlates with the strength of hydrogen bonding. This acceleration may be due to increased coupling between the OH stretching mode and the accepting mode of the VER, because the low-frequency shift caused by hydrogen bond formation is very large. Unlike phenol oligomers, however, the pump-probe signals of phenol-base complexes did not exhibit probe frequency dependence. For these complexes, rapid interconversion between different conformations causes rapid fluctuations in the vibrational frequency of the OH stretching modes, and these fluctuations level the VER times of different conformations. For the benzoic acid dimer, a quantum beat at a frequency of around 100 cm(-1) is superimposed on the pump-probe signal. This result indicates the presence of strong anharmonic coupling between the intramolecular OH stretching and the intermolecular stretching modes. From a two-dimensional plot of the OH stretching wavenumber and the low-frequency wavenumber, the wavenumber of the low-frequency mode is found to increase monotonically as the probe wavenumber is shifted toward lower wavenumbers. Our results represent a quantitative determination of the acceleration of VER by the formation of hydrogen bonds. Our studies merit further evaluation and raise fundamental questions about the current theory of vibrational dynamics in the condensed phase.

Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. III. The ν4 and ν7 modes of nonplanar nickel porphyrin models

The time scales and pathways of vibrational energy relaxation (VER) of the nu(4) and nu(7) modes of three nickel porphyrin models, nickel porphine (NiP), nickel protoporphyrin IX (Ni-heme), and nickel octaethylporphyrin (NiOEP), were studied using a non-Markovian time-dependent perturbation theory at the B3LYP/6-31G(d) level. When NiP is calculated with D(4h) symmetry, it has the planar structure and the same VER properties as ferrous iron porphine (FeP). The porphine cores of both Ni-heme and NiOEP were distorted from a planar geometry, assuming a nonplanar structure, similar to that of the heme structure in cytochrome c. The VER time scales of Ni-heme are found to be similar to those predicted for a planar iron heme, but the derived pathways have distinctly different features. In particular, the strong coupling between the nu(7) mode and the overtone of the approximately 350 cm(-1) gamma(7) mode, observed for planar porphyrins, is absent in both nonplanar nickel porphyrins. Direct energy exchange between the nu(4) and nu(7) modes is not observed in NiOEP, but is found to play an essential role in the VER of the nu(4) mode in Ni-heme. The Ni-heme isopropionate groups are involved in the dominant VER pathways of both the nu(4) and nu(7) modes of Ni-heme. However, in contrast with VER pathways derived in planar iron heme, the isopropionate groups are not observed to play an essential role relative to other side chains in spatially directing the vibrational energy flow.

Comparison of Two Simple Models for High Frequency Friction: Exponential versus Gaussian Wings

Liquid phase vibrational energy relaxation (VER) times T1 typically depend critically on the relaxing mode's high frequency friction or wing function. The wing function may, in principle, be found from the mode's normalized force autocorrelation function (faf) C(t), since it is proportional to lim formula see text C(t)dt. However, the full form of C(t) is never available. Thus, the wing function is typically estimated from a model faf CM(t) which duplicates the known part of C(t) and which (hopefully) approximates its unknown part with enough realism to yield meaningful formula see text behavior. Unfortunately, apparently realistic CM(t)'s can predict unphysical wing functions, and T1's in error by tens of orders of magnitude. Thus, a condition is needed to discriminate between CM(t)'s which yield meaningful and unphysical forms for the high frequency friction. This condition is shown to be that model faf's CM(t) yield physical wing functions if and only if these functions derive from the short time "heads" of the faf's. This test is applied to the model faf's Cga(t) triple bond exp[-1/2(t/tau)2] and Cse(t) triple bond sech(t/tau). These faf's cannot both be physical, since they yield incompatible Gaussian and exponential wing functions. The test accepts Cga(t) as physical. It, however, rejects Cse(t), since its "tail" lim formula see text Cse(t) = 2 exp(-t/tau) (because of its long range) dominates the wing function.

Robust control by two chirped pulse trains in the presence of decoherence

We discuss a novel method to create maximum coherence in a two-level system that is selectively excited among many having similar frequencies by making use of two specifically chirped pulses in the Raman configuration. The feasibility of the method is analyzed in the presence of decoherence caused by vibrational energy relaxation and collisional dephasing. It has been demonstrated that a high value of coherence may be sustained by the implementation of two chirped pulse trains prepared in accordance with the proposed method and having the same period as the vibrational energy relaxation time.

Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. II. The ν4 and ν7 modes of iron-protoporphyrin IX and iron porphine

The mode-specific vibrational energy relaxation (VER) of the iron-protoporphyrin IX (the heme) was studied using a non-Markovian time-dependent perturbation theory at the UB3LYP/6-31G(d) level. The derived VER time constants of the excited nu(4) and nu(7) modes, 1.2+/-0.1 and 2.1+/-0.1 ps, respectively, agree well with previous experimental results for MbCO (1.1+/-0.6 ps for the nu(4) mode and 1.9+/-0.6 ps for the nu(7) mode). The energy transfer pathways from the excited nu(4) and nu(7) modes were identified. The different symmetries of the nu(4) and nu(7) modes are reflected in distinct relaxation pathways. No direct energy transfer between the nu(4) and nu(7) modes was observed. The overtone of the approximately 350 cm(-1) iron out-of-plane gamma(7) mode was observed to be strongly coupled to the nu(7) mode and essential to its relaxation. The two isopropionate side chains of the heme were found to play an essential role in the VER mechanism for both nu(4) and nu(7) modes, providing the mode-specific level explanation to previous observations. Comparison of the results for VER in iron porphine (FeP) to results for the imidazole-ligated porphine model (FeP-Im) demonstrates that the axial Im ligand has little effect on the nu(4) or nu(7) mode relaxation processes. By considering the VER process as a multistep reaction and the third order Fermi resonance parameters the reaction rate constants, the VER kinetics of FeP was examined by solving the master equation.

Prevention of decoherence by two femtosecond chirped pulse trains

We study the vibrational energy relaxation (VER) and collisional dephasing as channels of coherence loss in a vibrational mode that is selectively excited using chirped pulse adiabatic passage in the Raman configuration. Based on the dressed state picture analysis we propose a method to reduce decoherence using femtosecond chirped pulse trains. When applied with a period close to the VER time, the pulse trains allow one to sustain high coherence in the selected vibrational mode.

Ultrafast vibrational dynamics and solvation complexes of methyl acetate in methanol studied by sub‐picosecond infrared spectroscopy

AbstractThe vibrational dynamics of the CO stretching mode of methyl acetate (MA) in methanol was studied by time‐resolved infrared (IR) pump‐probe spectroscopy. The vibrational energy relaxation (VER) process includes two components with time constants of 1.3 ± 0.1 and 4.0 ± 0.2 ps. These components result from the vibrational excitations of the hydrogen‐bonding complex of MA with one methanol and the MA monomer, respectively. The difference in the VER time is explained by the increase of the vibrational density of states (VDOS) by the intermolecular hydrogen bond. The time constants and the decay‐associated spectra are almost identical between the CH3OH and the CH3OD solutions. The vibrational modes localized in the intramolecular OH/OD bond of the solvent methanol have little effect on the vibrational dynamics of MA. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Initial heating mechanism of fluids after photoexcitation of molecules in various phases

Heating rates after photoexcitation of several organic molecules have been studied by the transient grating spectroscopy with sub-picosecond laser pulses in solution and supercritical fluids. The rise time of the acoustic signal produced by the energy dissipation process of the hot ground state molecule was monitored. The acoustic signal was analyzed by an equation including the acoustic damping. The solvent temperature rise times in various media have been determined. The temperature rise times in solutions were longer than the vibrational energy relaxation times of the solutes determined by the transient absorption measurements. The difference was discussed in terms of the contribution of vibrational states in the energy transfer pathways from the solute to the solvent. It was found that the hydrogen-bonding between the solute and solvent play important roles in determining the energy transfer pathway from the solute to the solvent.

Study on the vibrational energy relaxation of p-nitroaniline, N,N-dimethyl-p-nitroaniline, and azulene by the transient grating method

The vibrational energy dissipation processes of the electronic ground states of p-nitroaniline and N,N-dimethyl-p-nitroaniline have been studied by transient grating spectroscopy with subpicosecond laser pulses. The rise time of the acoustic signal produced by the energy dissipation process of the hot ground state molecule was monitored. The acoustic signal was analyzed by an equation including the acoustic damping. The solvent temperature rise times in various solvents have been determined. The acoustic signals of azulene in previous papers [Y. Kimura et al., J. Chem. Phys. 123, 054512 (2005); 123, 054513 (2005)] were also reanalyzed using this equation. The temperature rise times in all cases are longer than the vibrational energy relaxation times of the solutes determined by the transient absorption measurements. The difference is discussed in terms of the energy transfer pathways from the solute to the solvent. We concluded that both the hydrogen bonding between the solute and the solvent and the lower frequency modes of the solutes play important roles in determining the energy transfer pathway from the solute to the solvent.