Breathing sphere model

The first system we consider is the solute iodine in liquid and supercritical xenon (1). In this case there is clearly no IVR, and presumably the predominant pathway involves transfer of energy from the excited iodine vibration to translations of both the solute and solvent. We introduce a breathing sphere model of the solute, and with this model calculate the required classical time-correlation function analytically (2). Information about solute-solvent structure is obtained from integral equation theories. In this case the issue of the quantum correction factor is not really important because the iodine vibrational frequency is comparable to thermal energies and so the system is nearly classical. 

The breathing sphere model was enhanced by Garrison and coworkers [59-62] to allow the photons to break a bond in the molecule and to describe subsequent abstraction and recombination reactions. The model was initially applied to chlorobenzene, where good correlation with experimental data was found. 

VT Energy Transfer. Breathing Sphere Model and Infinite Order Sudden Approximation. 

Where cp is a factor correcting for the population of the inodes. The rate of collisions, for exanple in CClhas been calculated by a molecular dynamics simulation (18), and thus we are in the position to calculate the probability factor and to compare it to the theoretical predictions. It has been found that the commonly used calculations based upon the breathing sphere model of the internal degrees of freedom are too rough and cannot reproduce the observed temperature dependence of x If we use instead a mode... 

With the goal of describing some VER experiments on the solute iodine in Xe solvent (1), in this section we specialize to the case of a diatomic solute in an atomic solvent. In fact, we consider a simplified model where the diatomic solute is replaced with a breathing sphere (2). We take the... 

A simple well-known extension of a collinear Landau-Teller model is provided by the breathing sphere (BSP) model of Schwartz, Slawsky and Herzfeld [13] which fully retains the Landau-Teller exponential factor. More consistent treatment, which approximately takes into account the anisotropic character of the atom-molecule interaction, is based on the so-called infinite order sudden approximation (lOSA) [14] with respect to rotational transitions that accompany the vibrational transition. Within this approximation the rotation of the relaxing molecule plays the role of a spectator, which insignificantly modifies the exponent in Eq. (8) through quite unimportant redefinition of a. If, in addition, the quasiclassical correction to the semiclassical Landau-Teller exponent is small and the effect of the attractive part of the potential is weak, one can write the following simple expression for the deactivation rate constant within BSP or lOSA approximation ... 

Quantitative calculations of the rate constants ky y for vibrational transitions are relatively easy if the diatomic molecules are simulated by a harmonic oscillator interacting isotropically with the impinging atom (the so-called breathing sphere or the SSH (Schwartz-Slawsky-Herzfeld) model [3, 192, 339, 395] based on the one-dimensional Landau-Teller model [261]). Then the mean transition probability Py y per one gas-kinetic collision calculated to the first order of the semiclassical perturbation treatment is... 

The nuclear tunnelling factor can be accurately estimated from a 1-mode model based on the high frequency inner-sphere breathing mode (10, Tl)... 

This model has been adopted by a Task Group of the International Commission on Radiological Protection (ICRP) to all available experimental total and regional deposition data and extended for calculating regional deposition of ultrafine particles (3). For oral breathing of unit-density spheres at rest, total and regional depositions calculated with the ICRP model are shown in Fig. 12. 

Figure 12 Total deposition and deposition in extrathoracic, upper and lower bronchial, and alveolar regions estimated with the ICRP semiempirical deposition model (3) for oral breathing of unit-density spheres at the reference resting pattern for an adult Caucasian male sitting awake (9) 15-s breathing-cycle period and flow rate of 300 cm s . ...

Figure 6 Total deposition fraction of unit-density spheres during mouth breathing Data were modeled for a tidal volume of 1000 em and a rate of 15 breaths per minute and for different morphometric models of the human lung. (From Ref. 150.)...

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