Exchange-repulsion

It is now considered that this type of behaviour is caused by the selftrapping of ortho-positronium in bubbles in the low temperature gas. The bubbles are thought to form because the ortho-positronium-atom interaction at low energies is dominated by repulsive exchange forces, and this effect results in a lowering of the annihilation rate the bubble is so rarified in some cases that (q)p approaches zero. 

It was mentioned earlier that the dispersion interaction energy (DIS) is the most important attractive term of the correlation energy (CORR) it is usually attributed to the van der Waals interactions, physical meaning of the latter is usually the sum of attraction (DIS) and the repulsive exchange energy (EX). 

It indicates that, the physical sense of the 2-body SCF energy in trimers is the same as the SCF interaction energy in dimers it is predominantly the exchange interactions which are repulsive for two interacting atoms with closed subshells. The attractive contributions from the electrostatic and induction energies are less than the repulsive exchange contribution. This is the reason that CF(A3) is positive for the alkaline trimers in all calculated distance regions [22]. 

Note the somewhat imconventional choice, at least for surface and solid state physics, of Hartree atomic units h = qeiectnm = fneiectmn = i> 1 Ejj = 27.2116 eV). The local potential Vgff[ne r)] contains electron-electron Coulomb repulsion, exchange-correlation ( XC ), and nuclear-electron attraction terms that are the functional derivatives of the corresponding terms. Egg, Exc, and E e, in the density functional [/te]... 

Finally we note the existence of repulsive exchange forces which arise when the electron clouds of the two molecules begin to overlap. These occur because of the exclusion principle which forbids two electrons to occupy the same orbital unless their spins are antiparallel. Since all orbitals are already occupied by electron pairs, any overlap means that some electrons must be transferred to anti-bonding orbitals of higher energy, which implies a repulsive interaction. This interaction, being of very short range, depends upon the exact relative positions of the two molecules and it is not worth while to consider the almost endless possibilities involved until we can deal with molecules fixed in a crystal lattice. 

Where, tfi and if2 are charges of ions, r - the distance between ions, A - the coefficient that characterizes the energy of repulsive exchange interactions of the electron orbitals and p is... 

The reason for the rotation at the dimerization of the PIC molecules is the influence of the two forces the Coulomb interaction of the two cations and anions which try to bring the particles together and repulsive exchange interaction of the molecules in the ground state. The overlap integral of the external. -electron orbitals of the carbon atoms and cr-electron... 

The first term is the kinetic energy of non-interacting electrons and the remaining terms are classical Coulomb repulsion, exchange correlations, and external potential, respectively. <, (r) are Kohn-Sham orbitals whose density... 

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