States of identity

Off-diagonal interaction elements between half-filled shell states of identical (C/) parity will be zero if //,)f is symmetric under time reversal. 

Non-radiative processes can also be distinguished on the basis of the spin multiplicity of the initial and final electronic states. Internal conversion (IC) is the non-radiative crossover between two states of identical multiplicity, while intersystem crossing (ISC) is a process in which spin is not conserved. In both instances, crossover between the states is isoenergetic, regardless of the multiplicity. Subsequent vibrational relaxation (VR) occurs to release excess vibrational energy (see Figure 2.12). 

A recent discussion of solvolysis in water in terms of the interaction model (Robertson, 1966) assumes that the transition state of Sjf2 solvolysis will be reached when the initial state solvation shell has been disrupted to such an extent that the remaining solvent-solvent interactions have the same energy as the interactions between solvent molecules and the incipient anion. For Sul reaction the transition state is believed to require a greater breakdown of the initial-state solvation shell and is believed to correspond to the state of identical energies for the remaining solvent-solvent and solvent-cation interactions. These views have been employed for the interpretation of AG but the implications for J/S have not yet been considered. It remains to be seen whether... 

Electrostatic perturbations occur between states of identical electronic symmetry (Fig. 3.4), i.e., those with identical values of A, E and S. In Section 3.1.2, two types of off-diagonal matrix elements were shown to connect these states those of the Hel and TN operators,... 

This latter relation means that the diabatic potential curves associated with these functions can cross. The noncrossing rule between states of identical symmetry applies only for exact solutions of the electronic Hamiltonian. 

This integral has been evaluated ab initio and found equal to 300 cm-1 (Felen-bok and Lefebvre-Brion, 1966). (The one-center part of this integral is approximately the nonzero atomic integral sp 1/ r 12]dp).) This calculated value is in fair agreement with the semiexperimental value of 450 cm-1 found by a deperturbation procedure (Jungen, 1966). Note that this electrostatic interaction is responsible not only for perturbations between states of identical symmetry but also for predissociation (Section 7.8.1) and auto-ionization (Section 8.8). 

States that are the only ones of their type have energies that depend linearly on the crystal field strength, whereas, when there are two or more states of identical designation, their lines will in general show curvature. This is because such states interact with one another as well as with the crystal field. 

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