Molecular tunneling process

Molecular tunnelling processes have been detected in the recombination of HbCO after flash photolysis at low temperature ( < 10 K) and attempts to analyse the data using non-adiabatic molecular group transfer theory have met with reasonable success. At higher temperatures, (< 20 K) a non-exponential Arrhenius pathway is detected suggesting a distribution of activation enthalpies depend-... 

The development of an ab initio quantum molecular dynamics method is guided by the need to overcome two main obstacles. First, one needs to develop an efficient, yet accurate, method for solving the electronic Schrodinger equation for both ground and excited electronic states. Second, the quantum mechanical character of the nuclear dynamics must be addressed. (This is necessary for the description of photochemical and tunneling processes.) This section provides a detailed discussion of the approaches we have taken to solve these two problems. 

The traditional treatment of molecules relies upon a molecular Hamiltonian that is invariant under inversion of all particle coordinates through the center of mass. For such a molecular Hamiltonian, the energy levels possess a well-defined parity. Time-dependent states conserve their parity in time provided that the parity is well defined initially. Such states cannot be chiral. Nevertheless, chiral states can be defined as time-dependent states that change so slowly, owing to tunneling processes, that they are stationary on the time scale of normal chemical events. [22] The discovery of parity violation in weak nuclear interactions drastically changes this simple picture, [14, 23-28] For a recent review, see Bouchiat and Bouchiat. [29]... 

The next example of molecular tunneling near absolute zero was the rebinding of ligands to heme proteins that I have already mentioned. The typical distances of electron tunneling in various (e.g., radiation-chemical) oxidation reduction processes in solid state at 100 to 140°K are of the order of tens of angstroms. Distances of molecular tunneling at about 4°K are equal to 0.3 to 0.5 A. 

Figure 11. 35 Molecular rectification (a) Flow of electrons, (b) No current unless V is sufficiently large. Steps 1, 2 and 3 are tunnelling processes.

The differences are more serious indeed. Calculations show that even in the case where elastic contributions are negligible, the behavior of molecular excitation by tunneling electrons and molecular de-excitation in electron-hole pairs follow different trends [36], The reason after this discrepancy can be found in the initial and final electronic states (see discussion about Eq. (10) below). In the tunneling process the electron ends up in a state above the Fermi level. In the de-excitation one, the electron ends up in a state above the Fermi level after having left a hole behind. This shows in the difference in the equations leading to the evaluation of both processes [36]. 

During this tunneling process, the nuclear molecular framework is not conserved in between the alternative chiral states (1/ /2 )[ h arise, which do not possess a nuclear structure. Incidentally, for small level splitting (E -E ), the tunneling process is very slow and so we need to ask which of the available chiral states (on the equator of the Bloch sphere) actually arise in a properly chiral molecule. 

A ballistic wavepacket motion is incompatible with a tunneling process of the proton from the enol to the keto site. The transition probability of a single attempt is much smaller than 1 and many tunnel events are necessary for an efficient population transfer leading to a gradual population rise in the product state. However, if the proton itself would move from the enol to the keto site via a barrierless path, the ESIPT would take less than 10 fs because of the small proton mass [18]. This is a first indication that slower motions of the molecular skeleton are the speed determining factors and that the proton mode is not the relevant reaction coordinate [27]. 

The conduction of electrons through single molecules is however in all known cases not an Ohmic conductivity, but rather a tunneling process. Molecular wires facilitate an electron transport relative to the vacuum, but they differ from metallic wires in terms of the order of magnitude as well as the mechanism of the conductivity. 

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