Kassel integral

These Kassel integrals may be evaluated numerically by elementary methods. 

The rate coefficient at lower pressures must be evaluated by the quantum equivalent of the Kassel integral, Eq. (32), which may be written... 

Numerical evaluation of the Kassel integral permitted a comparison between theoretical and experimental fall-off behaviour . With an average molecular diameter of 5.5 A the calculated rate coefficient-azoethane pressure curve showed the best agreement with experiment at an effective number of oscillators of 18, somewhat less than half of the maximum 2N— 6. Because of the complexity of the reaction the experimental curve is probably in error, rendering comparison unreliable. Similar calculations for azomethane using the earlier uninhibited kinetic data showed best agreement with experiments at a molecular diameter of 4.7 A and an effective number of oscillators of 12, one half of the total normal modes of vibrations. 

One thus obtains the apparent rate constants k g and kg3 by evaluation of the rate constants for the elementary steps (k , kr> kjj, and kg) and using tables of the Kassel integral (13) to estimate the degree of fall-off (I) from the limiting high pressure rate constant, k. k can be taken to be the high pressure recombination rate constant kg is the collisional stabilization rate constant k and kjj are the unimolecular rate constants corresponding to N-N and N-H bond fission, respectively, of the collision complex. These decay rate constants were estimated from the RRK expression. 

Figure 13 Reduced strong-collision fall-off curves for thermal unimolecular reactions. Full curves RRKM caladatUms from ref. 33 dashed curves reduced Kassel integrals from ref. IB for CH3NC, both curves coinckk...

Use equation (5.14) to evaluate the rate constant, but form the decay rate constants according to the Kassel prescription (1.7) show that this is the same result as that obtained by using the tabulated values of Kassel integrals [72.E] for the same value of s. 

Rourick, R. A., Jenkins, K. M., Walsh, J., Xu, R., Cai, Z. and Kassel, D. B., Integration of Custom LC/MS Automated Data Processing Strategies for the Rapid Assessment of Metabolic Stability and Metabolic Identification in Drug Discovery, American Society for Mass Spectrometry 2002 Conference Abstract, Orlando, FL, USA, 2002. 

Kariv, I., Rourick, R.A., Kassel, D.B., and Chung, T.D.Y. Improvement of hit-to-lead optimization by integration of in vitro HTS experimental models for early determination of pharmacokinetic properties. Comb. Chem. High Throughput Screen. 2002, 5, 459-472. 

The int rated molecular transform (FT ) is a molecular descriptor calculated from the square ofthe molecular transform, by integrating the squared molecular transform in a selected interval of the scattering parameter s to obtain the area under the curve and finally taking the square root of the area [King, Kassel et al., 1990, 1991]. The square root of the integrated molecular transform, called SQRT index, was also proposed as molecular descriptor [Famini, Kassel et al., 1991]. 

Applications of integrated molecular transforms found in literature are ]King and Kassel, 1992 King, 1993, 1994 Molnar and King, 1995, 1998 King and Molnar, 1996, 1997, 2000]. 

King, J.W. and Kassel, R.J. (1991) Dimensional response ofthe integrated molecular transform. Int. J. Quantum Chem. Quant. Biol Symp., 18, 289-297. 

Schmitt, B. (2014) Integration of solar heating plants for supply of process heat in industrial companies (in German language). Dissertation University of Kassel, Shaker Verlag, Aachen, Germany. 

Here, most quantities are defined above and k(e + Ei) = k(E ) is the unimolecular dissociation rate constant, evaluated using modern statistical theories, such as Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Note that Equation (8) combines the distribution of deposited energies (Equation (5)) with the probability that the complex dissociates in time r (term in square brackets), and a summation over the internal energy available to the reactants. Importantly, the integration recovers Equation (2) when the dissociation rate, A ( ), is faster than the experimental time scale, such that the term in brackets is unity. 

Field tests to evaluate the feasibility and the effectiveness of a geotechnical reinforcement to improve the stability of a slope failure and to decrease the failure speed were carried out at an old mining site in Zimmersrode, located about 50 km south of Kassel, Germany (see Figure 13.13). Two types of multi-functional geotextiles (MFCs) were considered an optical fibre sensor integrated in geogrids and three optical fibre... 

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