Vibrational lifetime

Within physical chemistry, the long-lasting interest in IR spectroscopy lies in structural and dynamical characterization. Fligh resolution vibration-rotation spectroscopy in the gas phase reveals bond lengths, bond angles, molecular symmetry and force constants. Time-resolved IR spectroscopy characterizes reaction kinetics, vibrational lifetimes and relaxation processes. 

Laubereau A, von der Linde D and Kaiser W 1972 Direst measurement of the vibrational lifetimes of moleoules in liquids Phys. Rev. Lett. 28 1162-5... 

Beokerle J D, Casassa M P, Cavanagh R R, Heilweil E J and Stephenson J C 1990 Ultrafast infrared response of adsorbates on metal surfaoes vibrational lifetime of CO/Pt(111) Phys. Rev. Lett. 64 2090-3... 

Comparing the vibrational A lifetimes issued from both decay mechanisms (Tables 7 - 8), it is readily seen that the eleetric dipolar transition decay is always slightly favoured. A similar eonclusion holds for the A n state but, as expected, the vibrational transition probabilities are much larger for the dipolar decay which lead to mueh smaller vibrational lifetimes with respect to those via the cascade mode of decay, the differences amounting to five to six powers of ten (Table 7 - 8). 

The system of dilute HOD in H20 is equally good for probing the structure and dynamics of water with an isolated chromophore (in this case the OD stretch), and it may be even better for two reasons. First, in this case the solvent is water, not heavy water and second, the excited state vibrational lifetime of the OD stretch is somewhat longer (1.45 ps [55]) than that of the OH stretch in HOD/ D20, providing a wider dynamic window before effects of local heating due to energy deposition from population relaxation occur. 

Another, less straightforward way to determine the vibrational lifetime is by studies of the infrared absorption peak shape. Consider a single adsorbed molecule at 0 K. The width of the peak is then determined by the lifetime broadening and in the first approximation it has a Lorentaan shape with a full width at half maximum (FWHM) A = (2nct), t then being the lifetime. However, as usual we have to consider an ensemble of molecules at finite temperatures and then there exist other peak broadening mechanisms that must be taken into account. 

Table 1. The central frequency Wo, width Aw, vibrational lifetime T and spectral diffusion time tc of the O-H stretch vibration of different hydrogen-bonded O-H groups.

The values of rc of the solvation shells are surprisingly long in comparison to the value of rc of 500 100 fs of the O-H- -O hydrogen bond in bulk liquid water, but are quite comparable to the recently calculated residence time of 18 ps of water in the solvation shell of Br- [10]. However, one should be very careful with this comparison since the characteristic time of the fluctuations of the hydrogen bond is not the same as the residence time in the solvation shell because the breaking of the hydrogen bond does not automatically mean that the water molecule really leaves the shell. The narrow width and long rc of the O-H- Y absorption component imply that the first solvation shell forms a stable and well-defined structure. The solvation shells of F and of the cations likely show similar dynamics, but unfortunately these dynamics could not be measured because the O-H stretch vibrational lifetime of the water molecules in these solvation shells is comparable to that of bulk HDO D20. 

In Fig. 5, the measured decay of R for solutions of 0 M. 1 M, and 3 M Mg(C104)2 in HD0 H20 is shown. In these measurements, the OD- -0 band was pumped and probed at the 0—>1 transition using pump and probe pulses at 2500 cm-1. We used the O-D vibration to probe, the bulk water orientational dynamics, because, due to its long vibrational lifetime of 2 ps, this vibration allows us to measure the anisotropy decay over a much longer delay time interval than when the O-H vibration is probed. 

The latter is determined by the oscillation frequency, decaying coefficient, and vibration lifetime. This nonrigid dipole moment stipulates a Lorentz-like addition to the correlation function. As a result, the form of the calculated R-band substantially changes, if to compare it with this band described in terms of the pure hat-curved model. Application to ordinary and heavy water of the so-corrected hat-curved model is shown to improve description (given in terms of a simple analytical theory) of the far-infra red spectrum comprising superposition of the R- and librational bands. 

The solid curve in Fig. 31 shows the frequency dependence of absorption [Eq. (255)]. We see the shoulder in the R-band region (at x 2) and the main (librational) absorption peak at x 5.5. This dependence (solid curve) agrees with the experimental data [42, 51] (a more detailed analysis is given in the next section). If the vibration lifetime r b were twice as large, we would get an unreasonably large and narrow R-peak (dashed curve). On the other hand, if the parameter, v were twice as large, the intensity of the R-band would increase unreasonably (dash-and-dotted curve). This example shows convincingly that the form of the FIR water spectra sharply determines the parameters (25 lb) of our polarization model. 

To measure the departure from an Arrhenius-like behavior and to decrease the ambiguity in the use of fragility as a quantitative probe of the liquid state, the so-called F1/2 metric has been introduced. It is defined as the value of Tg/T at the midway of the relaxation time on a log scale, specifically, between the high-temperature phonon vibration lifetimes 10 14 s and the relaxation time at Tg, namely, i Tg), which is generally taken to be 102s [37], An advantage of this definition is that the midway values for the relaxation time are readily and accurately accessible by viscosimetric and by dielectric measurements [37,43], Let T /2 be temperature at which x = 10 6s. Now define a quantity Fx /2 as follows [37,43] ... 

Low current regime the time between tunneling electrons should be much larger than the vibrational lifetime. The theory only assumes one excitation at a time. 

Connection with vibrational lifetime on surfaces. The decay of molecular vibrations in the excitation of the electron-hole pairs of metallic surfaces have been identified with the mechanisms of vibration excitation by tunneling electrons [42]. Intuitively this may seem so. Indeed, an excited vibration may couple to the surface electronic excitations through the same electron-vibration matrix elements of Eqs. (2) and (4). The surface... 

The first time-resolved investigations on vibrational dephasing and vibrational lifetimes of molecules in the liquid phase were reported in 1971 and 1972 by Kaiser et al. utilizing nonlinear Raman scattering (3,4). A combination of infrared excitation with spontaneous Raman probing... 

Ethanol Oligomers in Solution Spectral Holes and Vibrational Lifetime Shortening... 

All data are taken at room temperature besides the one shown for methanol diluted in C5CI6 (T = 333 K). vc peak position of the OH stretch Ar>h, AV12 spectral width of the transient hole and the excited-state absorption, respectively anharmonic shift vc — V12 Ti, T10, ror time constants for the vibrational lifetime of the OH, ground state filling and reorientation, respectively. 

Measurements of the free acid Ti vibrational lifetimes were also monitored as a function of base concentration (e.g., pyrrole with acetonitrile) to determine the effect of collisions and hydrogen-bond formation rates. Stern-Volmer plots of 1 /T1 rates versus base concentration enabled extraction of a bimolecular rate constant (kbm) for pyrrole acetonitrile of 2.5 0.2 x 1010 dm3/mol-s, which is slightly larger than the estimated Stokes-Einstein diffusion coefficient (0.73 x... 

Woutersen S, Emmerichs U, Nienhuys HK, Bakker HJ. Anomalous temperature dependence of vibrational lifetimes in water and ice. Phys Rev Lett 1998 81 1106-1109. 

Myers DJ, Urdahl RS, Cherayil BJ, Fayer MD. Temperature dependence of vibrational lifetimes at the critical density in supercritical mixtures. J Phys Chem 1997 107 9741-9748. 

Myers DJ, Chen S, Shigeiwa M, Cherayil BJ, Fayer MD. Temperature dependent vibrational lifetimes in supercritical fluids near the critical point. J Chem Phys 1998 109 5971-5979. 

Fendt A, Fischer SF, Kaiser W. Vibrational lifetime and Fermi resonance in polyatomic molecules. Chem Phys 1981 57 55-64. 

The lifetime (Ti) of a vibrational mode in a polyatomic molecule dissolved in a polyatomic solvent is, at least in part, determined by the interactions of the internal degrees of freedom of the solute with the solvent. Therefore, the physical state of the solvent plays a large role in the mechanism and rate of VER. Relaxation in the gas phase, which tends to be slow and dominated by isolated binary collisions, has been studied extensively (11). More recently, with the advent of ultrafast lasers, vibrational lifetimes have been measured for liquid systems (1,4). In liquids, a solute molecule is constantly interacting with a large number of solvent molecules. Nonetheless, some systems have been adequately described by isolated binary collision models (5,12,13), while others deviate strongly from this type of behavior (14-18). The temperature dependence of VER of polyatomic molecules in liquid solvents can show complex behavior (16-18). It has been pointed out that a change in temperature of a liquid solute-solvent system also results in a change in the solvent s density. Therefore, it is difficult to separate the influences of density and temperature from an observed temperature dependence. 

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