Electronic-state Crossings

A simple method for predicting electronic state crossing transitions is Fermi s golden rule. It is based on the electromagnetic interaction between states and is derived from perturbation theory. Fermi s golden rule states that the reaction rate can be computed from the first-order transition matrix and the density of states at the transition frequency p as follows ... 

Going back to expression (1.12) for the coupling term, we shall now elucidate the situation that occurs when the potential energy surfaces belonging to different electronic states cross. This is easily obtained on introducing the following expressions [27] ... 

For an initial approximation of the activation energy, the energies of the various substrates and transition structure should be detemined. This enables the reaction rate to be determined in an intuitive way so as to describe the reaction mechanisms. However, set out in this way relatively low accuracy is achieved for most reactions. Other methods exist to determine the degree of incident response (e.g., electronic state crossings—Fermi s golden rule). 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

By examining the expression for Q ( equation (B1.16.4)). it should now be clear that the nuclear spin state influences the difference in precessional frequencies and, ultimately, the likelihood of intersystem crossing, tlnough the hyperfme tenn. It is this influence of nuclear spin states on electronic intersystem crossing which will eventually lead to non-equilibrium distributions of nuclear spin states, i.e. spin polarization, in the products of radical reactions, as we shall see below. 

Thennal dissociation is not suitable for the generation of beams of oxygen atoms, and RF [18] and microwave [19] discharges have been employed in this case. The first excited electronic state, 0( D), has a different spin multiplicity than the ground 0( P) state and is electronically metastable. The collision dynamics of this very reactive state have also been studied in crossed-beam reactions with a RF discharge source which has been... 

Equations (C3.4.5) and (C3.4.6) cover the common case when all molecules are initially in their ground electronic state and able to accept excitation. The system is also assumed to be impinged upon by sources F. The latter are usually expressible as tlie product crfjo, where cr is an absorjition cross section, is tlie photon flux and ftois tlie population in tlie ground state. The common assumption is tliat Jo= q, i.e. practically all molecules are in tlie ground state because n n. This is tlie assumption of linear excitation, where tlie system exhibits a linear response to tlie excitation intensity. This assumption does not hold when tlie extent of excitation is significant, i.e. 

FIGURE 17.2 Illustration of the reaction coordinate for a reaction with a change in the electronic state, (a) Potential energy curves for the two electronic states of the system. (A) Avoided crossing that can be seen in single-detenninant calculations. 

Energy level diagram for a molecule showing pathways for deactivation of an excited state vr Is vibrational relaxation Ic Is Internal conversion ec Is external conversion, and Isc Is Intersystem crossing. The lowest vibrational energy level for each electronic state Is Indicated by the thicker line. 

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