Proton tunneling quantum mechanical

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

Concept of quantum-mechanical tunnelling in proton-uansfer reactions introduced (without experimental evidence) by several authors. 

First, we shall discuss reaction (5.7.1), which is more involved than simple electron transfer. While the frequency of polarization vibration of the media where electron transfer occurs lies in the range 3 x 1010 to 3 x 1011 Hz, the frequency of the vibrations of proton-containing groups in proton donors (e.g. in the oxonium ion or in the molecules of weak acids) is of the order of 3 x 1012 to 3 x 1013 Hz. Then for the transfer proper of the proton from the proton donor to the electrode the classical approximation cannot be employed without modification. This step has indeed a quantum mechanical character, but, in simple cases, proton transfer can be described in terms of concepts of reorganization of the medium and thus of the exponential relationship in Eq. (5.3.14). The quantum character of proton transfer occurring through the tunnel mechanism is expressed in terms of the... 

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

Quantum-mechanical tunnelling has been recognized as a possible contributor to the rate of a chemical reaction for many years. For instance, the theory of tunnelling for proton transfer reactions was developed by Bell (1959) in his famous book The Proton in Chemistry. Later, Bell (1980a) published a more thorough treatment of tunnelling in his book The Tunnel Effect in Chemistry. 

Quantum mechanical tunneling is a fertile idea with many applications in chemistry. It will be seen that in practice calculations using its concepts make a significant difference with very light particles, e.g., electrons and (to a much lesser degree) protons. But these are exactly the particles that hold center stage in interfacial electrochemistiy. Indeed, without quantum mechanical tunneling, no electric currents across interfaces could occur.11... 

The picture begins to come somewhat into focus. Starting off with some basic mechanics of electrons, one was able to define the quantum mechanical condition for the tunneling of electrons from a metallic donor to electron acceptors through an electron-energy barrier. The tunneling condition could be expressed in terms of an energy barrier for ion movement, e.g., the movement of protons toward the metal in the reaction ... 

Totally deuterated aromatic hydrocarbons yield measured phosphorescence lifetimes greater than their protonated analogs.182 This behavior is ascribed to the closer spacing of vibrational levels in deuterated compounds with a consequent decrease in probability for nonradiative T -> S0 transitions. Quantum mechanical tunnelling may also contribute to the rate of the radiationless process with the normal compounds. 

Cui Q, M Karplus (2002) Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions Effect of geometry and tunneling on proton-transfer rate constants. J. Am. Chem. Soc. 124 (12) 3093-3124... 

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