Anti-parallel spins

In the ground state of a covalent bond, the molecular orbital is occupied by at least one, usually two electrons with anti-parallel spins. This is said to be the HOMO level that is, the highest occupied molecular orbital. If the bond is slightly sheared, the kinetic energies of its electrons is not affected, but the... 

In the case of iron, magnetism is due to the unpaired electrons in the 3d-orbitals, which have all parallel spin. These electrons interact with all other electrons of the atom, also the s-electrons that have overlap with the nucleus. As the interaction between electrons with parallel spins is slightly less repulsive than between electrons with anti parallel spins, the s-electron cloud is polarized, which causes the large but also highly localized magnetic field at the nucleus. The field of any externally applied magnet adds vectorially to the internal magnetic field at the nucleus. 

The exact high- and low-density limits can be found from arguments given in Ref. [57]. For = 0 in the high-density limit (where the random phase approximation becomes exact), the parallel-spin and anti-parallel-spin correlation energies are equal [57], so... 

What he does not seem to realize is that a perfectly good explanation existed for chemical bonding prior to the advent of the quantum mechanical explanation, namely Lewis s theory whereby pairs of electrons form the bonds between the various atoms in a covalently bonded molecule. Although the quantum mechanical theory provides a more fundamental explanation in terms of exchange energy and so on is undeniable but it also retains the notion of pairs of electrons even if this notion is now augmented by the view that electrons have anti-parallel spins within such pairs. 

Since /3 is negative, these are in increasing order of magnitude. The lowest level is orbitally non-degenerate and can accommodate two 77-electrons with anti-parallel spins, each electron having energy a+ 2/3. 

A positron in an electronic media can pick up an electron and form a neutral atom called Positronium (Ps) [9], The existence of Ps and its chemical reaction with molecules was detected from annihilation photons in 1951 [10], Ps is formed in most molecular systems. Due to the different combinations of positron and electron, there are two states of Ps the para-Ps (p-Ps) from the anti-parallel spin, and the ortho-Ps (o-Ps) from the parallel spin combination. The lifetime and the annihilation events for p-Ps and o-Ps are very different from each other, as given by electromagnetic theory. Figure 1.1 shows basic physical properties of Ps and compares them with the H atom, although it should not be considered an isotope of H (see problems 1.5 and 1.6 and answers at the end of this chapter). 

The p-Ps has a shorter lifetime than o-Ps and it annihilates into two photons, while o-Ps annihilates into three photons. The intrinsic lifetime is 0.125 ns and 142 ns for the free p-Ps and o-Ps, respectively. In ordinary molecular media, the electron density is low enough so that Ps can pick off electrons from the media that have anti-parallel spin to that of the positron, and undergo two-photon annihilation. This is called the pick-off annihilation of Ps. The pick-off annihilation of o-Ps not only occurs in the form of two-photon annihilation, it also shortens the o-Ps lifetime from 142 ns (free o-Ps) to a few ns. The pick-off annihilation lifetime of o-Ps in molecular systems is about one order of magnitude greater than in crystalline or metallic media. Experimental determination of o-Ps lifetime is one of the most useful methods for positron and positronium chemistry. This is because o-Ps lifetime contains information about electron density, which governs the basic properties of chemical bonding in molecules. It is also controlled by the physical structure of molecules. 

This is characteristic of a metal and occurs because, in the presence of a magnetic field, the energy of spins parallel to the magnetic field is lowered and that of anti-parallel spins is raised. With a constant Fermi energy this means that anti-paraiiel spin electrons above F will flip their spins and occupy the empty parallel spin states below EF. There is then a preponderance of parallel spins that renders the metal paramagnetic. 

Fig. 8.13. Illustration of the spin singlet exeiton model in the undoped Cu—O plane. The exeiton eonsists of a vaeaney at a Cu site and a Cu—O spin singlet at the neighboring site. The latter is represented by a solid line with two anti-parallel spins.

Spin symmetry constraints a two-electron single determinant may have the electrons with parallel or anti-parallel spins. In the first case the variation principle will find the lowest triplet, in the second the lowest singlet. 

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