Spin-pair repulsion

Redress can be obtained by the electron localization function (ELF). It decomposes the electron density spatially into regions that correspond to the notion of electron pairs, and its results are compatible with the valence shell electron-pair repulsion theory. An electron has a certain electron density p, (x, y, z) at a site x, y, z this can be calculated with quantum mechanics. Take a small, spherical volume element AV around this site. The product nY(x, y, z) = p, (x, y, z)AV corresponds to the number of electrons in this volume element. For a given number of electrons the size of the sphere AV adapts itself to the electron density. For this given number of electrons one can calculate the probability w(x, y, z) of finding a second electron with the same spin within this very volume element. According to the Pauli principle this electron must belong to another electron pair. The electron localization function is defined with the aid of this probability ... 

The remaining two are the unchanged 2py and orbitals. There are six electrons to be placed in these orbitals, and for the linear structure, the lowest two, A and B, will be filled, and the Ipy, and 2p will have a single electron each. Hund s rule suggests that the triplet state with parallel spins will be lower in energy than the singlet state (Fig. 7.1). For an related, alternative valence-shell electron-pair repulsion (VESPR) theory treatment see Chapter 11 by Platz in this volume. 

In broad outline, our shape-prediction approach will assume that the valence electrons of the central atom (M) are all spin-paired (that is, their axes are parallel but spinning in opposite directions), and that these pairs of electrons will repel each other in such a way that they occupy positions of minimum repulsion (that is, positions of minimum potential energy). The electron pairs will try to get as far away from each other as they can and still stay in the molecule. The central atom s valence electron pairs will fall into one of two... 

An alternative two-step mechanism involving a spin-paired diradical intermediate has also been considered for 1,3-cycloadditions.18,68,69 However, ab initio calculations70-72 on a wide variety of 1,3-dipoles and dipolarophiles are found to coincide essentially with a synchronous 1,3-cycloaddition mechanism.15,17 On the other hand, a two-step mechanism passing through two transition states separated by an intermediate has been derived using the MINDO/3 method, and found to be compatible with substituent and solvent effects as well as stereospecificity observed in 1,3-cycloadditions.73 However, several factors beyond FMO interactions, such as closed shell repulsions, geometrical distortions, polarization, and secondary orbital interactions, all influence mechanisms, rates, and regioselectivities in cycloaddition reactions.74... 

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