Protons quantum mechanical model

Molecular modeling treatments of electron transfer kinetics for reactions involving bond breaking were developed much earlier than the continuum theories originated by Weiss in 1951. Gurney in 193l published a landmark paper (the foundation of quantum electrochemistry) on a molecular and quantum mechanical model of proton and electron transfer... 

The enzyme mechanism, however, remains elusive. Quantum mechanical models generally disfavor C6-protonation, but 02, 04, and C5-protonation mechanisms remain possibilities. Free energy computations also appear to indicate that C5-protonation is a feasible mechanism, as is direct decarboxylation without preprotonation O-protonation mechanisms have yet to be explored with these methods. Controversy remains, however, as to the roles of ground state destabilization, transition state stabilization, and dynamic effects. Because free energy models do take into account the entire enzyme active site, a comprehensive study of the relative energetics of pre-protonation and concerted protonation-decarboxylation at 02, 04, and C5 should be undertaken with such methods. In addition, quantum mechanical isotope effects are also likely to figure prominently in the ultimate identification of the operative ODCase mechanism. 

We can use the quantum mechanical model of the atom to show how the electron arrangements in the atomic orbitals of the various atoms account for the organization of the periodic table. Our main assumption here is that all atoms have orbitals similar to those that have been described for the hydrogen atom. As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these atomic orbitals. This is called the aufbau principle. 

MuUiken (140) has given a simple quantum-mechanical model of molecular complexes involving acids and bases (acceptors and donors) and points out that a loose complex of A and B should attract an additional A or B molecule additively. He gives a mechanism by which a weak Lewis acid like HCl may be transformed into a functioning proton... 

It has been shown by quantum mechanical modelling, that in dehydration the alcohol is activated by interaction of the oxygen atom with the electrophilic species, namely a proton, and that the most activated of the /3-hydrogens is that which is awft -periplanar with respect to the hydroxyl-group. ... 

The main challenge in the present type of quantum mechanical modeling is to estimate the protonation cost The proton needed for the substrate reaction is ultimately provided by the solvent, a part that cannot be included in the model. To be able to work with a limited model, it is assumed that the resting state of the proton is the position of lowest energy in the quantum chemical model. For most models this position turns out to be the carboxyl-ate. This does not mean that the proton actually comes from the carboxylate or that the mechanism requires that the carboxylate is protonated in the reactant. The procedure simply gives a lower limit for the energy required to protonate the base. 

The above results, using extended quantum mechanical models for the active site of ODCase, indicate that the base protonation mechanism has a decarboxylation barrier that is too high to be compatible with the experi-... 

Dogonadze and Kuznetsov showed for the first time the way to take into account the processes of transfer of heavy particles for reactions in liquids. This work was the basis for the first simplest quantum mechanical model of the electrochemical proton transfer process which was proposed by Dogonadze, Kuznetsov, and Levich in 1967 (see also Ref. 33). The expressions and conclusions of Dogonadze and Kuznetsov s work were used in a number of subsequent papers (also in some recent works, see, e.g.. Ref. 34). Therefore, it is necessary to consider this approach in more detail. 

Gurney s Quantum Mechanical Model of Proton Transfer... 

An example of such an approximation may be found in the applied mathematical field of quantum mechanics, by which the behavior of electrons in molecules is modeled. The classic quantum mechanical model of the behavior of an electron bound to an atomic nucleus is the so-called particle-in-a-box model. In this model, the particle (the electron) can exist only within the confines of the box (the atomic orbital), and because the electron has the properties of an electromagnetic wave as well as those of a physical particle, there are certain restrictions placed on the behavior of the particle. For example, the value of the wave function describing the motion of the electron must be zero at the boundaries of the box. This requires that the motion of the particle can be described only by certain wave functions that, in turn, depend on the dimensions of the box. The problem can be solved mathematically with precision only for the case involving a single electron and a single nuclear proton that defines the box in which the electron is found. The calculated results agree extremely well with observed measurements of electron energy. 

Think, for a moment, how remarkable this is. Mendeleev and Meyer developed their periodic tables from the physical and chemical properties of the elements. They knew nothing of electrons, protons, nuclei, wave functions, or quantized energy levels. Yet, when these things were found some 60 years later, the match between the first periodic tables and the quantum mechanical model of the atom was nearly perfect. 

The main difference between the new and the old theories of an elementary act lies in the interpretation of the mechanism of proton transfer, in particular, of the discharge of proton donors. This question is elucidated in the fourth chapter where a considerable amount of experimental data has been given to demonstrate the advan tage of the new, quantum-mechanical model of an elementary act. 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

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