Quantum mechanical integrated reaction

I 6 Single and Multiple Hydrogen/Deuterium Tranter Reactions in Liquids and Solids the quantum mechanical integrated reaction probability by... 

Group theory is also used prior to calculations to determine whether a quantum-mechanical integral of the type /i j, op. % dt is different from zero or not. This is important in such areas as selection rules for electronic transitions, chemical reactions, infrared and Raman spectroscopy, and other spectroscopies. 

Theresultsgivenbelowarebasedonstandardparametervalues Vq = 1-56 x 10 a.u., fl = 1.36 a.u., mass m = 1060 a.u., and reaction coordinate = x. The exact quantum mechanical (QM) rate constant kq for this reaction can be obtained by integrating the exact quantum mechanical cumulative reaction probability, which is known analytically [30,78]. 

Finally, we note that although all of the discussion in this section has applied to a completely classical mechanical treatment of the reaction, the expression for the cumulative reaction probability can be quantized in the usual ad hoc fasion in statistical theory by replacing the classical flux of equation (21) by the quantum mechanical integral density of states... 

London (1928) was first to apply this idea to a chemical reaction. London and Heitler developed a simple quantum mechanical treatment of hydrogen molecule, according to which, the allowed energies for H2 molecules are the sum and differences of two integrals as... 

Contemporary computer-assisted molecular simulation methods and modern computer technology has contributed to the actual numerical calculation of solvent effects on chemical reactions and molecular equilibria. Classical statistical mechanics and quantum mechanics are basic pillars on which practical approaches are based. On top of these, numerical methods borrowed from different fields of physics and engineering and computer graphics techniques have been integrated into computer programs running in graphics workstations and modem supercomputers (Zhao et al., 2000). 

Motion along the reaction coordinate was limited to classical mechanics, whereas the sum and density (or, to be precise, the degeneracy) of states should be evaluated according to quantum mechanics. The integral in Eq. (7.49) should really be replaced by a sum N (E) is not a continuous function of the energy, but due to the quantization of energy, it is only defined at the allowed quantum levels of the activated complex. That is, the sum of states G (E ) should be calculated exactly by a direct count of the number of states ... 

The first exact quantum calculations of integral and differential cross sections on the adiabatic state were reported in 2001 by Honvault and Laimay [15,81]. They have carried out quantum reactive scattering calculations of the title reaction on the DK PES within the Time Independent Quantum Mechanical (HQM) framework using the hyperspherical close-coupling method. 

This estimate of the barrier effectively includes zero-point energy and tunneling effects since it is obtained from experimental data. In typical EVB studies of enzymatic reactions it is usually assumed that these quantum-mechanical effects do not differ significantly between the water and enzyme environments. This assumption has been verified by implementation of the path integral method [51] within the EVB framework [52,53]. 

More recently we described the calculation of differential cross sections (DCSs) for the CI+H2 reaction.[35] These were used in the interpretation of ongoing crossed molecular beam studies. The rationale for this investigation is that DCSs offer, in principle, a far more detailed probe of the dynamics than the integral cross sections (ICSs). This paper [35] marked the first ever fully quantum mechanical determination of reactive DCSs for a set of coupled ab initio PESs. Because of space constraints, no details of the determination of the DCSs were reported.[35] The goal of the present article is to present, for future reference, these details. 

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