Electron degeneracy

Here, AS° = AS i + AS n, but since identical vibrational levels have been assumed for the two electronic levels, AS jb = 0. In addition, AS j is related to the electronic degeneracies of the two levels by ASei = K In ( l/ h)- Finally, if the transformation takes place at constant pressure, AH° = NAE where AE is defined as above. Consideration of the Gibbs free energy for an assembly of N molecules thus produces the same relation for the HS fraction Uh as the potential energy for the isolated molecule, if only the interaction between the molecules is neglected. 

The above results mainly apply to the Longuet-Higgins E x e problem, but this historical survey would be incomplete without reference to early work on the much more challenging problems posed by threefold or higher electronic degeneracies in molecules with tetrahedral or octahedral symmetry [3]. For example, tetrahedral species, with electronic symmetry T or T2, have at least five Jahn-Teller active vibrations belonging to the representations E and T with individual coordinates (Qa,Qb) and (Qx. Qx. Q ) say. The linear terms in the nine Hamiltonian matrix elements were shown in 1957 [3] to be... 

Using transition state theory, find the temperature dependence of the pre-exponential factor in the Arrhenius expression for the reaction NO + NO3 —> NO2 + NO2. In other words for A (X Tn, find n. Assume that both NO3 and the activated complex are nonlinear. Furthermore assume that hv << kgT and that the electronic degeneracies are all one. 

Originally, the Jahn-Teller (JT) theorem was formulated as a prediction of a symmetry break for any non-linear polyatomic molecule with an orbital degeneracy in its ground state. However, as we understand it now, the real meaning of the JT theorem is a non-zero slope of the adiabatic potential energy surface (APES) at the point of electron degeneracy. This does not necessarily result in a lowering of... 

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