Dephasing vibrational

Loring R F and Mukamel S 1985 Selectivity in coherent transient Raman measurements of vibrational dephasing in liquids J. Chem. Phys. 83 2116-28... 

Vanden Bout D, Fretas J E and Berg M 1994 Rapid, homogeneous vibrational dephasing in ethanol at low temperatures determined by Raman echo measurements Chem. Phys. Lett. 229 87-92... 

Vos M H, Jones M R, Breton J, Lambry J-C and Martin J-L 1996 Vibrational dephasing of long- and short-lived primary donor states in mutant reaction centers ot Rhodobacter sphaeroides Biochemistry 35 2687-92... 

Berg M and Vanden Bout D A 1997 Ultrafast Raman echo measurements of vibrational dephasing and the nature of solvent-solute interactions Acc. Chem. Res. 30 65-71... 

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

Tokmakoff A, Kwok A S, Urdahl R S, Franois R S and Fayer M D 1995 Multilevel vibrational dephasing and vibrational... 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

Condition (3.19) is usually satisfied in processes of vibrational dephasing [41, 130, 131, 132], Because of this condition the dephasing is weak and the effect of rotational structure narrowing is pronounced. A much more important constraint is imposed by inequality (3.18). It shows that perturbation theory must be applied to a rather dense medium and even then only the central part of the spectrum (at Aa> < 1/t , 1/tc) is Lorentzian. 

The quasi-classical description of the Q-branch becomes valid as soon as its rotational structure is washed out. There is no doubt that at this point its contour is close to a static one, and, consequently, asymmetric to a large extent. It is also established [136] that after narrowing of the contour its shape in the liquid is Lorentzian even in the far wings where the intensity is four orders less than in the centre (see Fig. 3.3). In this case it is more convenient to compare observed contours with calculated ones by their characteristic parameters. These are the half width at half height Aa)i/2 and the shift of the spectrum maximum ftW—< > = 5a>+A, which is usually assumed to be a sum of the rotational shift 5larger scale A determined by vibrational dephasing. 

Fig. 3.5. The shift of oxygen Q-branch [137]. The contribution of vibrational dephasing A that is linear in density is shown as a straight line. The initial deviation of this line reproduces the theoretical behaviour of 5(n) shown in Fig. 4.4(b). The experiment was performed at a few temperatures higher than the critical one 7.87 K (A), 0.95 K (o) and 0.12 K ( ).

Fig. 3.8. The Q-branch Raman width alteration with condensation of nitrogen. The theoretical results for the strong (A) and weak (B) collision limits are shown together with experimental data for gaseous [89] ( ) and liquid nitrogen [145] ( ) (point a is taken from the CARS experiment of [136]). The broken curves in the inset are A and B limits whereas the intermediate solid curve presents the rotational contribution to line width at y = 0.3. The straight line estimates the contribution of vibrational dephasing [143], and the circles around it are the same liquid data but without rotational contribution.

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Vibrational broadening in [162] was taken into account under the conventional assumption that contributions of vibrational dephasing and rotational relaxation to contour width are additive as in Eq. (3.49). This approximation provides the largest error at low densities, when the contour is significantly asymmetric and the perturbation theory does not work. In the frame of impact theory these relaxation processes may be separated more correctly under assumption of their statistical independence. Inclusion of dephasing causes appearance of a factor... 

The relaxation operator f carries out rotational broadening as well as vibrational dephasing between 0 and 1 states. 

As can be seen from the above, the shape of the resolved rotational structure is well described when the parameters of the fitting law were chosen from the best fit to experiment. The values of estimated from the rotational width of the collapsed Q-branch qZE. Therefore the models giving the same high-density limits. One may hope to discriminate between them only in the intermediate range of densities where the spectrum is unresolved but has not yet collapsed. The spectral shape in this range may be calculated only numerically from Eq. (4.86) with impact operator Tj, linear in n. Of course, it implies that binary theory is still valid and that vibrational dephasing is not yet... 

It was underlined twice in [251] that the use of fitting laws ties in with the validity of the impact theory, and the present results have to be interpreted cautiously . At high pressure nonlinear increase of rates of energy relaxation and vibrational dephasing with gas density must be... 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

The algorithm proposed above may be also realized in the presence of vibrational dephasing, exactly in the same way as is done in Chapter 3 for spherical tops. For this the following substitution should be made ... 

Knaap E. W. Vibrational dephasing of diatomic molecules in liquids role of anharmonicity of the diatom, Chem. Phys. Lett. 58, 221-4 (1978). 

Kroon R., Baggen M., Lagendijk A. Vibrational dephasing in liquid nitrogen at high densities studied with time-resolved stimulated Raman gain spectroscopy, J. Chem. Phys. 91, 74-8 (1989). 

Valiev-Ivanov model 219, 275 vibrational broadening 123 vibrational dephasing 111, 113-15, 123 vibrational relaxation, and angular momentum relaxation 92 vibrational transition, adiabatic dephasing 92... 

Iwata K, Ozawa R, Hamaguchi H (2002) Analysis of the solvent- and temperature-dependent Raman spectral changes of S1 trans-stilbene and the mechanism of the trans to cis isomerization dynamic polarization model of vibrational dephasing and the C=C double-bond rotation. J Phys Chem A 106 3614—3620... 

Figure 3. Field-matter interactions for a pair of electronic states. The zero and first excited vibrational levels are shown for each state (A). The fields are resonant with the electronic transitions. A horizontal bar represents an eigenstate, and a solid (dashed) vertical arrow represents a single field-matter interaction on a ket (bra) state. (See Refs. 1 and 54 for more details.) A single field-matter interaction creates an electronic superposition (coherence) state (B) that decays by electronic dephasing. Two interactions with positive and negative frequencies create electronic populations (C) or vibrational coherences either in the excited (D) or in the ground ( ) electronic states. In the latter cases (D and E) the evolution of coherence is decoupled from electronic dephasing, and the coherences decay by the vibrational dephasing process.

The observations of vibrational coherence in optically initiated reactions described above clearly show that the standard assumption of condensed-phase rate theories—that there is a clear time scale separation between vibrational dephasing and the nonadiabatic transition—is clearly violated in these cases. The observation of vibrational beats has generally been taken to imply that vibrational energy relaxation is slow. This viewpoint is based on the optical Bloch equations applied to two-level systems. In this model, the total dephasing rate is given by... 

The flow of energy from the ground state can also be calculated when it is assumed that the rate of electronic dephasing is small (i.e., L%Pg = 0) and/or the rate of pure vibrational dephasing is small (i.e., L%Hg = 0). These conditions apply when the rate of relaxation to equilibrium is small relative to the rate of loss of phase coherence. Under these conditions... 

H. Hamaguchi I would like to comment on the stilbene photoisomerization in solution. We recently found an interesting linear relationship between the dephasing time of the central double-bond stretch vibration of Si franj-stilbene, which was measured by time-resolved Raman spectroscopy, and the rate of isomerization in various solutions. Although the linear relationship has not been established in an extensive range of the isomerization rate, I can point out that the vibrational dephasing time measured by Raman spectroscopy is an important source of information on the solvent-induced vibrational dynamics relevant to the reaction dynamics in solution. 

XVII. Subquadratic Quantum Number Dependence of the Overtone Vibrational Dephasing in Molecular Liquids... 

XVII. SUBQUADRATIC QUANTUM NUMBER DEPENDENCE OF THE OVERTONE VIBRATIONAL DEPHASING IN MOLECULAR LIQUIDS... 

This is a subject of great interest to the physical chemistry/chemical physics community. In this section we discuss how the mode coupling theory calculation of the friction on atoms connected by a chemical bond can lead to a better understanding of vibrational dephasing in dense liquids. In particular, the application of MCT is shown to provide a possible explanation of an old ill-understood problem. 

Vibrational dephasing provides us with a powerful method to probe the interaction of a chemical bond with the surrounding medium. Over the years, many experimental techniques have been developed to study dephasing of bonds in many molecular systems at various temperatures, pressures, and concentrations [122-124]. One popular experimental technique is the isotropic Raman lineshape. The other methods involve a coherent excitation of the vibration with a laser pulse and monitoring the decay of the phase coherence,... 

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