Coulombic repulsion, spin-paired

This difference between these two carbenes can be attributed to the presence of the lone pair of electrons on nitrogen in 4b. Two-center, three-electron bonding in the molecular plane of 4b, involving the lone pair, produces some unpaired a spin density on nitrogen. Coulombic repulsion between the a and tt electrons of... 

The filled (Is)2 cores lead to additional steric repulsions with the incoming donor hybrid. These combine with nuclear Coulomb repulsions to oppose high electronic overlap. Figure 3.6 displays the calculated increase in steric repulsion as each filled 2s spin-orbital of Li2 collides with the filled core Is of the opposite atom. The paired one-electron steric repulsions shown in Fig. 3.6 are similar to the ionic two-electron steric repulsions of Fig. 2.11, and the wave-mechanical origin of the steric pressure would be analogous to that described in the discussion surrounding Fig. 2.12. 

The operator 2Jj computes the Coulombic repulsion energy between an electron in v[/, and the pair of electrons in /,-, assuming that the electrons in v[/, and in /,- move independently of each other. The operator ICj corrects the Coulombic repulsion energy, computed from 2Jj, for the fact that antisymmetrization of results in correlation between an electron in /,- and the electron of the same spin in v[/,. 

The motion of each electron in the Hartree-Fock approximation is solved for in the presence of the average potential of all the remaining electrons in the system. Because of this, the Hartree-Fock approximation, as discussed earlier, does not provide an adequate description of the repulsion between pairs of electrons. If the electrons have parallel spin, they are effectively kept apart in the Hartree-Fock method by the antisymmetric nature of the wavefunction, producing what is commonly known as the Fermi hole. Electrons of opposite spin, on the other hand, should also avoid each other, but this is not adequately allowed for in the Hartree-Fock method. The avoidance in this latter case is called the Coulomb hole. 

When r-i = r2 the triplet product functions, Eqs. (3.7.4)-(3.7.6), vanish The two electrons cannot be localized in the same spot this is called a "Fermi hole." When r1 = rz, then the singlet spatial wavefunction, Eq. (3.7.3), is finite and nonzero. This consequence of Fermi-Dirac statistics is called "spin pairing" Two electrons with opposite spins attract each other (despite the classical Coulomb repulsion), while two electrons with the same spin repel each other. 

Cr(C6Hii)4 is tetrahedral and a triplet however, square-planar discriminating factor. Another factor at work in these molecules is the spin pairing energies. As indicated previously, 3d valence orbitals are considerably more contracted that 4d and 5d thus the Coulomb repulsion integrals are much larger for first-row transition metal complexes and high-spin states are more favored than is the case for second and third row complexes. 

Other things being equal, for repulsive electronic correlations the ground state of a2, bi pairs is likely to be the triplet state, 3Bi, by Hund s rule. This principle energetically favours the most antisymmetrical space function and symmetrical spin function for a pair by minimising the short range Coulomb repulsion between electrons and is found to be widely applicable [40] in molecular systems. 

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