Mixing of states

Fig. 5. Energies of S, To and T i states of a radical pair as a function of radical separa-cion. The dotted lines indicate mixing of states.

The rate constant for formation of excited-state S02 was measured by Halstead and Thrush to be 1.7 X 10 12 exp(-2100/T) cm3 molec1 s 1 [28-31], while the overall rate constant for the loss of SO is 3.6 x 10 12 exp(-1100/T) cm3 molec-1 s 1 [11], Thus, at room temperature, S02 constitutes —1.6% of the product channels. This figure can only be considered approximate, however, since mixing of states within the singlet manifold affects the interpretation of the rate constant for formation of the excited state [32],... 

If the rare-earth ion is immersed in a crystal field, the perfect symmetry of the free ion is destroyed, leaving parity in some cases not quite a good quantum number. Under this circumstance, electric-dipole transitions become quite possible. It was Van Vleck (25), in his classic 1937 paper The Puzzle of Rare Earth Spectra, who first pointed out that the weak electric dipole emission was due to this mixing of states of opposite parity by the crystal field. 

In the state basis diagonalizing H0 the mixing of states is due to the coupling operator W. In the P-space one has the ingoing quantum state for the reactant (say,... 

Equation (8.296) shows that as the magnitude of the applied electric field increases, our coupled basis set will become less and less meaningfiil because of the mixing of states with different values for F, F and J. 

Considering the crystal electric field as a first-order perturbation, the mixing of states with higher energy and opposite parity, nla"[S"l"]J"M") may be represented by iff") with A) and Z ) defined as... 

According to Judd and Ofelt, the hypersensitivity of a transition is due to the mixing of the excited states 4f" 1 —< 5d1 and 4f 1 5g1 with 4f" states. Henrie et al. added a partial charge transfer character to the above mixing of states in their covalency model in which... 

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