Born-Oppenheimer approximation Failure

Fig. 3. Vibrational population distributions of N2 formed in associative desorption of N-atoms from ruthenium, (a) Predictions of a classical trajectory based theory adhering to the Born-Oppenheimer approximation, (b) Predictions of a molecular dynamics with electron friction theory taking into account interactions of the reacting molecule with the electron bath, (c) Born—Oppenheimer potential energy surface, (d) Experimentally-observed distribution. The qualitative failure of the electronically adiabatic approach provides some of the best available evidence that chemical reactions at metal surfaces are subject to strong electronically nonadiabatic influences. (See Refs. 44 and 45.)...

The Keiec value for an isotopic exchange reaction resulting from a failure of the Born-Oppenheimer approximation is sometimes referred to as Kboele. With the notation employed above A AC is the value of AEeiec for the reaction (see Fig. 2.1). 

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. 

Waschewsky, Gabriela C. G., Kash, Philip W., Myers, Tanya L., Kitchen, David C., Butler, Laurie J. 1994. "What Woodward and Hoffmann Didn t Tell Us The Failure of the Born-Oppenheimer Approximation in Competing Reaction Pathways." Journal of the Chemical Society, Faraday Transactions 90 1581-1598,... 

G. C. Waschewsky, P. W. Kash, T. L. Myers, D. C. Kitchen, and L. J. Butler, What Woodward and Hoffmann didn t tell us the failure of the Born-Oppenheimer approximation in competing reaction pathways, J. Chem. Soc. Faraday Trans. 90 1581 (1994). 

It is usually assumed that the electronic coupling matrix element is a constant across the reaction coordinate. Since the electronic wavefunction is a function of both the electronic and nuclear coordinates, even in the Born-Oppenheimer approximation, it is not surprising that in some systems the assumption that the nuclear and electronic coordinates are independent (the Condon approximation) is not appropriate. The most obvious example of the failure of this approximation is for a system in which the matrix element is dominated by superexchange contributions, since the vertical energies, Adb and Eba. vary with the nuclear coordinates. There are other, probably less obvious kinds of such vibronic coupling ... 

Fig. 7.6. Failure of the Born-Oppenheimer approximation for HD. The shaded circle on the left represents the deuterium nucleus, the shaded circle on the right the proton. The frozen electron distribution is indicated by an ellipse.

The purpose of this review article is to present a comprehensive account of what is generally known as the Born-Oppenheimer approximation, its meaning, its implications, its properties, and very importantly also its limitations and how to cure them. This approximation and the underlying idea have been a milestone in the theory of molecules and actually also of electronic matter in general. Still today this approximation is basic to all molecular quantum mechanics and even in those cases where it fails, it remains the reference to which we compare and in terms of which we discuss this failure. 

The electric dipole moment of HD failure of the Born-Oppenheimer (adiabatic) approximation... 

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