Born-Oppenheimer approximation tunneling effects

Below we will use Eq. (16), which, in certain models in the Born-Oppenheimer approximation, enables us to take into account both the dependence of the proton tunneling between fixed vibrational states on the coordinates of other nuclei and the contribution to the transition probability arising from the excited vibrational states of the proton. Taking into account that the proton is the easiest nucleus and that proton transfer reactions occur often between heavy donor and acceptor molecules we will not consider here the effects of the inertia, nonadiabaticity, and mixing of the normal coordinates. These effects will be considered in Section V in the discussion of the processes of the transfer of heavier atoms. 

KINETIC ISOTOPE EFFECTS BORN-OPPENHEIMER APPROXIMATION HYDROGEN TUNNELING EQUILIBRIUM ISOTOPE EFFECT... 

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. 

Quantum effects are most important for the lightest particles, and, correspondingly, they are often included solely for the electrons when studying molecular systems, whereas the nuclei are considered so heavy that a classical treatment is sufficiently accurate. This is the physical basis for the Born-Oppenheimer approximation discussed in Section 2. There are, however, cases where a quantum treatment of the nuclei can become important. Such cases occur first of all for the lightest nuclei, i.e. most notably for hydrogen atoms, but also for systems where small energy barriers between different isomers can lead to tunneling effects. 

All the models are more complicated than before. One accounts for the breakdown of the Born-Oppenheimer approximation. Another shows the possibility of proton transfer by tunnel effect. We see that the role of the solvent cavity size and electron coupling was no longer negligible. It was shown that the water molecule ionisation and hydrogen bonding polarisation play an important role in the ionic equilibrium of water. 

It is very important to remember that this definition of a PES is based on the assumption that the atomic positions can be exactly specified, which is the ultimate condition for the structure or shape of a molecule. This means adoption of the Born-Oppenheimer (B.O.) approximation, in which the nuclei are viewed as stationary point charges, whereas the electrons are described quantum mechanically [5]. This approximation is justified by the fact that the electrons are much lighter than the nuclei and hence are moving faster. The classical nature of the atomic nuclei is usually a valid approximation, but the zero-point vibrational energy of molecules or the tunneling effect, for example, make it evident that it does not always hold. 

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