Born-Oppenheimer approximation radiationless transitions

In the framework of the Born-Oppenheimer approximation, radiationless transitions from one surface to another are impossible. (See, e.g., Michl and BonaCit -Koutecky, 1990.) It is therefore necessary to go beyond the Born-Oppenheimer approximation and to include the interaction between different electronic molecular states through the nuclear motion in order to be able to describe such transitions. Using the time-dependent perturbation theory for the rate constant of a transition between a pair of states one arrives at... 

Fig. 1. The molecular energy level model used to discuss radiationless transitions in polyatomic molecules. 0O, s, and S0,S are vibronic components of the ground, an excited, and a third electronic state, respectively, in the Born-Oppenheimer approximation. 0S and 0 and 0j are assumed to be allowed, while transitions between j0,j and the thermally accessible 00 are assumed to be forbidden. The f 0n are the molecular eigenstates...

Understand that intermolecular radiationless transitions of excited states are caused by a breakdown of the Born-Oppenheimer approximation. 

Let us assume the availability of a useful body of quantitative data for rates of decay of excited states to give new species. How do we generalize this information in terms of chemical structure so as to gain some predictive insight For reasons explained earlier, I prefer to look to the theory of radiationless transitions, rather than to the theory of thermal rate processes, for inspiration. Radiationless decay has been discussed recently by a number of authors.16-22 In this volume, Jortner, Rice, and Hochstrasser 23 have presented a detailed theoretical analysis of the problem, with special attention to the consequences of the failure of the Born-Oppenheimer approximation. They arrive at a number of conclusions with which I concur. Perhaps the most important is, "... the theory of photochemical processes outlined is at a preliminary stage of development. Extension of that theory should be of both conceptual and practical value. The term electronic relaxation has been applied to the process of radiationless decay. 

Chapter 3 describes radiationless transitions in the tunneling electron transfers in multi-electron systems. The following are examined within the framework of electron Green s function approach the dependence on distance, the influence of crystalline media, and the effect of intermediate particles on the tunneling transfer. It is demonstrated that the Born-Oppenheimer approximation for the wave function is invalid for longdistance tunneling. 

Diabatic photoreaction Within the Born-Oppenheimer approximation, a reaction beginning on one excited state potential-energy surface and ending, as a result of radiationless transition, on another surface, usually that of the ground state. Also called non-adiabatic. 

Radiationless transitions (IC and ISC) represent a conversion of electronic energy of an initial, excited state to vibrational energy in a lower-energy electronic state (cf. Figure 2.1). Within the Born Oppenheimer approximation (Section 1.3), radiationless... 

There are molecules which, in the Born-Oppenheimer approximation, can be bound only in excited states, such as the "excimer" molecules (HeH), (NeH), (ArH), and (HeF). These excited bound states decay to the dissociative continuum of the ground state either via radiative transitions or via radiationless transitions, each having its characteristic probability. Suppose we look at the collision of the (ground repulsive state) free atoms in the... 

The Born-Oppenheimer approximation is generally a good one and is used in most molecular problems. However, it breaks down in many cases such as in avoided crossing regions, where transitions between potential energy surfaces can occur. The neglected interactions in this approximation are responsible for many physical processes of interest e.g. predissociation, coilisions or radiationless transitions. It is still possible to use this approximation if we take into account the neglected terms. The first theoretical calculation of the adiabatic correction was performed for the hJ molecule [45] in 1941. For the heteronuclear molecules, the first theoretical calculation of the adiabatic correction for the HeH+ molecuie [30,31] with two eiectrons, then for more compiex systems such as LiH, KH, RbH and CsH... 

The Born-Oppenheimer (BO) description is not exact. The deviation from the BO approximation can be treated as an additional nonadiabatic interaction. This interaction does not depend on time and can be the origin of radiationless transitions. Moreover, the nonadiabatic interaction is a main mechanism for one kind of indirect photodissociation, namely, photopredissociation of Type I (electronic predissociation). 

This section briefly introduces the generalized coupled master equation within the Born-Oppenheimer adiabatic (BOA) approximation. In this case, the non-adiabatic processes are treated as the vibronic transitions between the vibronic manifolds. Three types of the rate constant are then introduced to specify the nature of the transitions depending on whether the electronically excited molecular system achieves its vibrational thermal equilibrium or not. The radiationless transitions can occur between two... 

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch." In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Born-Oppenheimer states. Henry and Kasha > and Jortner and co-workers< > have pointed out that the Born-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

---