Crossing of potential energy curves for diatomics

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

FIGURE 3.8 Potential energy curves for the ground state and two electronically excited states in a hypothetical diatomic molecule. Predissociation may occur when the molecule is excited into higher vibrational levels of the state E and crosses over to repulsive state R at the point C (from Okabe, 1978). 

Historically the first application of symmetry to potential energy surfaces was to prove the so-called non-crossing rule. In its simplest form this may be stated as potential energy curves for states of diatomic molecules of the same symmetry do not cross . We have already seen in section 2 that this should be qualified to apply to adiabatic curves, as in some situations it may be convenient to define diabatic curves wdiich do cross. 

Hydroxyl radical (OH) is a key reactive intermediate in combustion and atmospheric chemistry, and it also serves as a prototypic open-shell diatomic system for investigating photodissociation involving multiple potential energy curves and nonadiabatic interactions. Previous theoretical and experimental studies have focused on electronic structures and spectroscopy of OH, especially the A2T,+-X2n band system and the predissociation of rovibrational levels of the M2S+ state,84-93 while there was no experimental work on the photodissociation dynamics to characterize the atomic products. The M2S+ state [asymptotically correlating with the excited-state products 0(1 D) + H(2S)] crosses with three repulsive states [4>J, 2E-, and 4n, correlating with the ground-state fragments 0(3Pj) + H(2S)[ in... 

Figure 5.7. Franck-Condon factors for radiationless transitions between different potential energy curves of a diatomic molecule a) for a large and b) for a small energy gap, such as those observed, for instance, between S and S, or between S, and S respectively, and c) for the case that the potential energy curves (e.g., S, and T,) cross.

For N > 2 these relations constitute a system of two equations in the 3N — 6 real scalar variables represented by q, i.e., three variables for = 3 and 6 variables for N = 6, and intersections between PESs are common. For N = 2, however, q is a single scalar variable, the internuclear distance, and diatomic potential energy curve crossings for adiabatic electronic states of the same symmetry and spin multiplicity are very rare, because their existence requires that this distance satisfy two independent conditions [14]. This leads to the noncrossing rule of such curves. 

Quite frequently, potential energy curves (surfaces) cross and these crossings have very important consequences. One of the simplest examples for potential curve interaction is predissociation of a diatomic molecule. The key points are ... 

Fig. 6.4. Ground- and excited-state potential energy curves illustrating possible dissociation pathways. For a diatomic molecule r is the internuclear distance in a polyatomic molecule r is a normal mode displacement. Vibrational separations are greatly exaggerated. The vertical arrows correspond to Franck-Condon allowed transitions. Where possible, molecular examples are indicated, (a) Repulsive excited state—immediate dissociation, (b) Crossing of bound and repulsive excited states—intersystem crossing leads to predissociation. (c) Metastable excited state—tunneling leads to dissociation, (d) Bound state— excitation energy greater than dissociation limit.

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