Tunneling electron-proton

Protium/deuterium/tritium kinetic isotope effects are often used to support hydride transfer mechanisms over single electron transfer mechanisms. However, sequential electron/proton/electron transfer mechanisms can easily show isotope effects as well. Even though the rate limiting step in the overall two electron reduction of flavin or NADH may be the isotope independent endergonic electron tunneling to form a radical intermediate state, once formed, this radical state can return the electron to recreate the... 

In recent research, the concept of simultaneous electron and proton transfer has been explored. In this process, directly coupled electron and proton transfer result in the formal transfer of a hydrogen atom (Figure 18, path C). In this pathway, two quantum events occur electron tunneling and proton tunneling [56. Whereas electron tunneling is a well-accepted phenomenon, proton tunneling is a far less commonly invoked property. Proton tunneling can be readily understood if we consider... 

Figure 1. A tunnelling particle (proton or positive muon) in a superposition state in a metal hydride, perturbed by phonons and conduction electrons (from Ref. [Karlsson 1998]).

The evidence for the atom is now direct, as it is possible to see atoms directly, using such techniques as electron tunnelling microscopy. If this technique is used to look at the surface of copper metal, the atoms show up as bumps (Figure 2.1). The atom may be defined as the smallest unit of an element that retains the physical and chemical characteristics of the element. Dalton considered that the atom could be treated as a hard sphere that could not be broken down into smaller units, i.e. it had no internal structure, rather like a billiard ball. While this is not quite true, it can be understood in terms of the present knowledge of the structure of the atom. In the late 1800s, J. J. Thompson showed that the atom was built up from much smaller units, namely, electrons, protons and neutrons (Table 2.1). 

Figure 3. Zig-zag tunneling path in a two-dimensional electron-proton tunneling space. The wavy line denotes the electron s tunneling when the proton rearranges to the proper configuration to symmetrize the electron potential energy surface. The straight arrows denote the protons motion for the initial i and final f electron states,...

CERN (Conseil Europeen pour la Recherche Nucleaire) The European Laboratory for Particle Physics, formerly known as the European Organization for Nuclear Research, which is situated close to Geneva in Switzerland and is supported by a number of European nations. It runs the Super Proton Synchrotron (SPS), which has a7-kilometre underground tunnel enabling protons to be accelerated to 400 GeV, and the Lai e Electron-Positron Collider (LEP), in which 50 GeV electron and positron beams are collided. The Large Hadron Collider began operation in September 2008. 

The left-hand part of Figure 3.11 shows electron-proton terms for the initial and the final states. These two curves correspond to different positions of a proton. They are obtained from the sections of paraboloids (see Figure 3.10) by vertical planes R = const (R = R and R = Rof Figure 3.11 shows these two sections projected on the same vertical plane. The right-hand part of this figure shows the electron terms of a proton for different values of q. It can be seen that for q = q the zero energy levels of the proton in the initial and the final states equalize, and proton tunneling becomes possible. 

Thus, for the second model we have two discrete states with two different equilbrium positions of the proton. The lifetime of the final state (adsorbed hydrogen) is sufficiently long and is determined by the tunneling probability for the proton. Although the activation energy of the reverse process is zero, it does not proceed in each oscillation of the solvent polarization in the direction of the initial state. This is so because the system remains on the electron-proton term of the final state until the proton tunnels through to the initial state. 

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. 

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... 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

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... 

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