Relaxation of molecules

Weston R E and Flynn G W 1992 Relaxation of molecules with chemically significant amounts of vibrational energy the dawn of the quantum state resolved era Ann. Rev. Rhys. Chem. 43 559-89... 

Fig. 1. Relaxation of molecule-medium system subsequent to photoexcitation where Sq is the singlet ground state the fkst excited singlet state and...

If the resolving capacity of the instruments is ideal then vibrational-rotational absorption and Raman spectra make it possible in principle to divide and study separately vibrational and orientational relaxation of molecules in gases and liquids. First one transforms the observed spectrum of infrared absorption FIR and that of Raman scattering FR into spectral functions... 

For the proton (/= 1/2, AE = 2pB o) in a magnetic field of 9.39 T (tesla)— resonance frequency of 400 MHz—and at a temperature of 300 K, the quantity 2 iBo/ kT has a value of about 6 x 1 () 5. In words, the excess population in the lower energy state is extremely small, approximately one nucleus in 300,000. As will be seen in the following, the NMR experiment monitors the relaxation of molecules from an excited state to a ground state. This is in contrast to the EPR technique and many other instrumental techniques that detect absorption of energy in a species moving from a ground state to an excited state. 

H. Pfeifer, Nuclear Magnetic Resonance and Relaxation of Molecules Adsorbed on Solids in NMR - Basic Principles and Progress, Springer, Berlin, 7 (1972) pp. 105-115. 

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

Bauer DR, Braumann JI, Pecora R. Depolarized Rayleigh scattering and orientational relaxation of molecules in solution. IV. Mixtures of hexafluorobenzene with benzene and mesitylene. I Chem Phys 1975 63 53-60. 

A third general issue regards the dynamic coupling between solute and solvent. To accurately model excited states formation and relaxation of molecules in solution, the electronic states have to be coupled with a description of the dynamics of the solvent relaxation toward an equilibrium solvation regime. The formulations of continuum models which allow to include a time dependent solvation response can be formulated as a proper extension of the time-independent solvation problem (of equilibrium or of nonequilibrium). In the most general case, such an extension is based on the formulation of the electrostatic problem in terms of Fourier components and on the use of the whole spectrum of the frequency dependent permittivity, as it contains all the informations on the dynamic of the solvent response [10-17],... 

E.E.Nikitin, Effect of rotation on vibrational relaxation of molecules, Teor. Eksp. Khim. 3,185 (1967)... 

The VT relaxation of molecules with vibrational energy E and vibrational quantum ftco, considered diffusion along the vibrational energy spectrum, is characterized by the flux... 

Pfeifer H (1972) NMR and relaxation of molecules adsorbed on solids. In NMR— Basic principles progress, Vol 7. Springer, Berlin Heidelberg New York, p 53... 

When a gas in an absorption cell is first irradiated at a transition frequency there is a transient imbalance in the population of the two levels as molecules absorb the radiation and the upper level becomes over-populated. Thermal relaxation processes may not be sufficiently fast to repopulate the lower level. Subsequent power absorption will become less than expected from LTE considerations. This effect will be greater at the line centre where the absorption coefficient is greatest and can lead to complete saturation of the transition. The rate of absorption of radiation is then dictated solely by the rate of relaxation of molecules from the upper to the lower state. This is more noticeable at low pressures where the thermalisation processes are less rapid and the line widths narrower. 

We shall discuss here the macroscopic dynamics of liquid crystals that is an area of hydrodynamics or macroscopic properties related to elasticity and viscosity. With respect to the molecular dynamics, which deals, for example, with NMR, molecular diffusion or dipolar relaxation of molecules, the area of hydrodynamics is a long scale, both in space and time. The molecular dynamics deals with distances of about molecular size, a 10 A, i.e., with wavevectors about 10 cm , however, in the vicinity of phase transitions, due to critical behaviour, characteristic lengths of short-range correlations can be one or two orders of magnitude larger. Therefore, as a limit of the hydrodynamic approach we may safely take the range of wavevectors q 10 cm and corresponding frequencies (O c q 10 - 10 = 10"s (c is sound velocity). 

While theoretical prediction of rate coefficients for vibrational and rotational relaxation in a number of atom-diatom systems has been made, comparable experimental results are not available for the majority of these systems. The first measurements of vibrational relaxation of molecules at temperatures below 1K were reported by Weinstein and colleagues [48]. In their study, CaH molecules slowed down by elastic collisions with He buffer gas atoms were trapped in an inhomogeneous magnetic... 

The gaseous and solid phases of weakly bound molecules in an optical lattice are metastable. As well as in the gas of such molecules in free space, the main decay channels are the relaxation of molecules into deep bound states and the formation of trimer states by one light and two heavy atoms. The relaxation into deeply bound states turns out to be rather slow, with a relaxation time exceeding 10 sec even at two-dimensional densities of 10 cm [68]. 

State, which exhibits significant anisotropy in the lab frame. It is the manipulation of the rotational wavefunction by the helium interaction that governs collision-induced Zeeman relaxation of molecules. 

Concerning the vibrational temperature, there is some experimental error (+ 0.05 eV) that is primarily caused by the fitting procedure. The vibrational temperature is much higher than the rotational temperature, since the vibrational kinetics is considerably determined by the electron impact excitation. The vibrational temperature decreased with increasing discharge pressure. It is considered that the collisional relaxation of molecules proceeds rapidly at higher discharge pressure (Sakamoto et al., 2006, 2007). 

The vibrational relaxation of molecules is an important process in non-equilibrium chemical kinetics. Out of the many different relaxation phenomena the simplest one involves diatomic molecules for which there is no complicated intramolecular energy transfer. If the degree of vibrational excitation is not too high, the most important processes correspond to one-quantum transitions. This results in considerable simplification of relaxation kinetics which simplifies even further under the condition of a constant translational temperature T. 

Another interesting case corresponds to a low relative concentration of molecules B, [A] [B]. Neglecting the last term in Eq. (15.9), which describes the direct VT relaxation of molecules B, we get the relaxation equation for n... 

The real-time observation of the structural relaxation of molecules after an electron has been detached by means of an ultrashort laser pulse, by applying a newly developed experimental method based on a charge reversal process. Structural relaxation times of optically excited clusters are determined. Here, the silver trimer acts as a model system. 

When polymers are extruded or calendered the cross-sectional area of the extrudate or the calendered sheet is usually greater than the cross-sectional area of the extruder die or the space between the calender rolls. Known as die swell and calender swell these effects are due to relaxation of molecules that had been oriented during shear. As a general rule die swell is found, like viscosity, to increase with molecular weight and decrease with a rise in temperature. 

Since 1992 and the first success of combining laser techniques with the CRESU apparatus, a good number of neutral-neutral processes have been studied.These include bimolecular reactions, three-body reactions, and inelastic collisions, such as spin orbit relaxation of atoms (Al, Si and C), rotational relaxation of molecules such as NO and CO, and even for some specific cases vibrational relaxation (CH, NO and toluene). In this section we will only concentrate on reactive processes. 

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