Second-order mixing

SECOND-ORDER (MIXED) AND MIXED BIMOLECULAR REACTIONS... 

By this stage, it will be apparent that even the sign of the spin-rotation parameter contains valuable information on the electronic structure of the molecule. To appreciate this point fully, let us consider a3 state which arises from a 2 electron configuration. The effective spin rotation interaction arises from second-order mixing with3 n states. Let us assume that there is only one such state which lies higher in energy so that the... 

The addition of this term is more than intuition the A-doubling in a n state arises from second-order mixing with a state, A-doubling in a A state involves fourth-order mixing with, successively, a n and a state, so that in a state the A-doubling must involve sixth-order spin orbit coupling to a A, n and state in turn. 

The most interesting aspect of these constants is the much larger spin rotation constant observed for the upper state, which undoubtedly arises because of second-order mixing with other nearby electronic states. 

The other particularly interesting feature of the data in table 11.3 is the very large vibrational dependence of the spin-rotation constant y. There is no doubt that this dependence arises because the spin-rotation interaction is dominated by the second-order mixing of excited electronic states with the ground state specifically we may write... 

Case 2. In the second case the secondary steps include one or more processes which are second-order (mixed or pure) with respect to intermediates. 

Johnston and Yost have studied the reaction O3 + NO2 and found it to be very fast, second-order mixed, with a rate constant given by... 

Holmberg showed that optically active alkyl halides are racemized in solution at rates which are second-order mixed with respect to halide ion and alkyl halide. By using 2-octyl iodide, Hughes and coworkcrs showed that the rate of exchange with radioactive 1 in acetone solution is precisely equal to the rate of inversion, both rates being mixed second-order. This, of course, is quite reasonable on the assumption that both reactions proceed by Sn2 mechanisms with inversion of configuration ... 

The distinction between the SnI and jSat2 mechanisms is not necessarily always a sharp one, and if the attacking group Y can facilitate the departure of X, an intennediate case may occur. Such intermediate cases seem to arise in reactions in which the nucleophilic reagent is a solvent molecule, when, unfortunately, kinetic order with respect to solvent is almost impossible to clarify. It is important to note that where the attacking group Y is an ion such as a halide, X"", or Oil or RO the displacement reaction usually follows fairly clean second-order mixed kinetics. The confusion that arises when Y is a solvent molecule is readily understood when we consider that the mechanism of ionization will involve very strong ion-solvent interactions. In fact ionization is not possible without such interactions. 

Modified Huron-Vidal Second-Order Mixing Rule (MHV2)... 

Therefore, the reaction is first-order in both A and B and second-order overall. Such a reaction is referred to as a second-order mixed case, since the... 

In Sec. 2.1, we worked through the details of a second-order mixed reaction, which is first-order in each of two components. We wiU consider briefly here the various third-order cases (those involving reactants of multiple types are worked out in detail by Benson (I960)). The simplest case involves only one reactant for which the rate law can be written as... 

It should be apparent that this equation is very similar to that for the second-order mixed rate law shown in Eq. (2.6). Following the procedure illustrated in that case, separating the fractions gives... 

The 8a and 3n molecular orbitals result from coupling the N 2po and 2j9 i orbitals with the Cr 3do and 3d i orbitals respectively. The 9a molecular orbital is a Apo + 4 hybrid pointing away from the N atom, whilst the 15 is essentially a 3d 2 atomic-like orbital. The Cr Fermi contact interaction is, of course, dependent on the i -orbital spin density. The spin-spin and spin-rotation constants are determined by the second-order mixing of low-lying electronic states with the ground state there are, however, a large number of possible excited states, so that an unambiguous quantitative interpretation is difficult without recourse to ab initio calculations. 

TABLE 3.1. Coefficients Signs of Second-Order Mixing ... 

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