Uncorrelated exchange

When Hartree-Fock theory fulfills the requirement that 4 be invarient with respect to the exchange of any two electrons by antisymmetrizing the wavefunction, it automatically includes the major correlation effects arising from pairs of electrons with the same spin. This correlation is termed exchange correlation. The motion of electrons of opposite spin remains uncorrelated under Hartree-Fock theory, however. 

The situation is completely different for mass transfer within the pore network of monolithic compounds. Here mass transfer can occur both on the pore surface or in the pore volume and molecular exchange between these two states of mobility can occur anywhere within the pore system, being completely uncorrelated with the respective diffusion paths. As a consequence, Eq. (3.1.11) is applicable, without any restrictions, to describing long-range diffusion in the pore space. Equation (3.1.14) is thus obtained,... 

The difference between Q(x2 jq) and the uncorrelated probability of finding an electron at x2 describes the change in conditional probability caused by the correction for selfinteraction, exchange and Coulomb correlation, compared to the completely uncorrelated situation ... 

No physical marker was obvious for the enhanced exchange activity (84). A fairly complex ESR signal that had about the proper stability to match the enhanced activity was suggested for this purpose (102), but has not been correlated with catalytic experiments on the same samples. A broad ESR signal (probably at least partly identical with the previously reported one (102)) was found to be uncorrelated with hydrogen-deuterium exchange activity (106), but the catalyst appears to have been a high-temperature-pumped one in which the activity is unaffected... 

A comparison of Equations (2.78) and (2.79) yields that in both approaches, MO (= Hartree-Fock) and VB, the Pauli exchange has been correctly included. The difference between the two is solely given by their amount of electronic correlation. In the MO approach, the electrons are completely uncorrelated (independent), and they may even go into the same atomic orbital, albeit with different spins, thus producing ionic states (H H+). The MO approach therefore does not take care of the energy penalty due to the Coulomb repulsion between the two electrons (see Section 2.9). Because the electronic Coulomb correlation has been completely ignored, the correlation energy may be defined as the difference between the correct energy and that of the Hartree-Fock solution, that is... 

An inherent advantage of mass spectrometric detection of HX processes is the visual distinction between exchange processes occurring via EXl or EX2 kinetics (see Section 1.2.2). The characta--istic evolution of the isotopic envelope as a result of either correlated (EXl) or uncorrelated (EX2) HX is depicted in Figure 1.9. 

MS has a unique advantage in that the two exchange mechanisms can be readily distinguished in the isotope patterns of the deuterated peptides (see also Sections 1.3.1 and 3.2.2). In the EX2 mechanism, the local structure will unfold and refold many times until an exchange event happens. Therefore, the deuterium labeling on each backbone amide site of a peptide will be independent to one another. As a result, the distribution of deuterium across the molecules will be uncorrelated and result in a unimodal isotope distribution. 

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