Diffusion coefficients quantum calculations

The classical equation for 7 sis provided in Section VII.A of Chapter 2. It depends only on the spin quantum number S, on the molar concentration of paramagnetic metal ions, on the distance d, and on a diffusion coefficient D, which is the sum of the diffusion coefficients of both the solvent molecule (Dj) and the paramagnetic complex (Dm), usually much smaller. The outer-sphere relaxivity calculated with this equation at room temperature and in pure water solution, by assuming d equal to 3 A, is shown in Pig. 25. It appears that the dispersions do not have the usual Lorentzian form. 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

The rate of diffusive separation, k, was determined from separate experimental measurements of iodine radical diffusion rates in the high pressure diffusion limited regime (19). The rate of excited state deactivation, k i, was calculated from the measured quantum yields at high densities where G> = kd/k i (18). It was assumed that k i is proportional to the inverse diffusion coefficient, D 1 (19,23) as both properties are related to the collision frequency. 

Section II provides a summary of Local Random Matrix Theory (LRMT) and its use in locating the quantum ergodicity transition, how this transition is approached, rates of energy transfer above the transition, and how we use this information to estimate rates of unimolecular reactions. As an illustration, we use LRMT to correct RRKM results for the rate of cyclohexane ring inversion in gas and liquid phases. Section III addresses thermal transport in clusters of water molecules and proteins. We present calculations of the coefficient of thermal conductivity and thermal diffusivity as a function of temperature for a cluster of glassy water and for the protein myoglobin. For the calculation of thermal transport coefficients in proteins, we build on and develop further the theory for thermal conduction in fractal objects of Alexander, Orbach, and coworkers [36,37] mentioned above. Part IV presents a summary. 

Transition state theory, combined with ab initio quantum mechanics, provides a means of calculating kp (and other rate coefficients which are not diffusion-controlled) from first principles. The starting point is the transition state expression (e.g., [4]) ... 

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