Parallel electrons, exchange

The breakdown at a pH higher than 10 of the parallelism between the Us(redox) and the redox potential of the redox couple in solution can be explained by assuming that the rate of the dissolution reaction, caused by the attack of H2O or OH- on the surface trapped hole, is so high in this pH range that the electron exchange equilibrium at the interface is no longer achieved. 

Additional experiments related to the influence of the composition of the surface layer in mixed solvents on electrode kinetics were carried out [281] with the V(III)/V(II) system. The electrode kinetics of this system in water-f-butanol mixtures were studied in parallel with the kinetics of the homogeneous electron exchange... 

Exchange energy 11 is a consequence of parallel electron spins in separate orbitals the greater the number of such parallel spins (and consequently the greater the number of exchanges), the lower the energy of the state. 

The simplest case corresponds to the one-electron transfer between the electrode and species that are chemically stable on the time scale of the experiments (Eq. (1.1)). However, electrochemical systems are frequently more complicated and the electroactive species take part in successive electron transfer reactions at the electrode (multistep processes) and/or in parallel chemical reactions in solution such as protonation, dimerisation, rearrangement, electron exchange, nucleophilic/electrophilic addition, disproportionation, etc., the product(s) of which may or may not be electroactive in the potential region under study. The simulation of these cases is described in Chapters 5 and 6. 

Electron-exchange reactions can be regarded as special cases of redox reactions, and in the given case, therefore, the parallel between the electron-exchange reaction of the iron ions and their redox reaction with the Ps atoms is obvious. 

Another important interaction of positronium is the ortho-para conversion. It occurs when the substance contains paramagnetic particles with unpaired electrons. When colliding with such a particle, the orientation of one of the parallel spins of ortho-positronium may be reversed, simultaneously with the reversion of the spin of the unpaired electron of the colliding molecule. This interaction takes place via electron exchange between the molecule and o-Ps. The pflra-positronium formed by this process annihilates very rapidly, according to its short mean lifetime. Consequently, this effect also leads to the decrease of the lifetime of positronium. Ortho-para conversion can be demonstrated by the following reaction scheme (vertical arrows show the directions of the spins) ... 

But there is more than just electron correlation to worry about. We know that each orbital can accommodate a maximum of two electrons, provided they are of opposite spin (denoted a (spin up, ) and (3 (spin down, )). This requirement to pair up electrons of opposite spins, while keeping electrons of parallel spins apart, is known as electron exchange, and must also be included in any accurate molecular description. This is achieved by Fock theory, which makes use of an antisymmetric wavefunction. In this context, antisymmetric means that the wavefunction changes its sign when the coordinates of two electrons are exchanged. We can demonstrate how this is done by considering two electrons, labeled a and b, both with spins up. An antisymmetric wavefunction, for this system would be ... 

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