Average energy isotope effect

Average energy isotope effect due to difference of average reaction energy. 

Of these isotope effects, (1) moderator isotope effect and (3) average reaction energy isotope effect can be eliminated when experiments are performed at a high concentration of rare gas moderator. Therefore, use of a large amount of rare gas moderator (e.g., 90% Ar) is recommended to observe (2) the probability integral isotope effect, which is the most interesting one for hot atom chemists. 

To the extent that the perturbation is adequately linear, calculating the potential energy at the average CH and CD bond lengths and subtracting the difference thus yields the zero-point energy isotope effect. As noted above, it is rarely possible to know the mathematical form of the potential exactly, so that it is hard to tell just how linear it is over a vibrational amplitude. However, even a purely harmonic perturbation, if its extremum does not coincide with a = 0, will act as if it were of the form ax - - Sample calculations (62) show that for nor-... 

Here E,j, is the energy of the initial state and R is the nuclear geometry. The division by 3 in (14) comes from orientational averaging. In this form, calculation of the absorption cross section requires the initial vibrational wave function, the transition dipole moment surface and the excited state potential. The reflection principle can be employed for direct or near direct photodissociation. It is again an approximation where the ground state wave function is reflected off the upper potential curve or surface. Prakash et al and Blake et al. [84-86] have used this theory to calculate isotope effects in N2O photolysis. 

In symmetric single minimum potential proton as well as deuteron and triton is located in the centre of bridge, but because of lesser energy of zero-point vibrations and lesser distance between heavy nuclei the amplitude of zero-point vibrations for and is less than for H, and average over wave funetions of ground state values of their chemical shift proves to be larger, the isotope effect A5 > 0 [70, 94]. When the minimum moves from the centre of bridge the potential curve becomes asymmetric, the distance ri(AD) becomes less than... 

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