The Electron Pair Bond and Pauli Repulsion

These level splittings are the essential features that determine the type of chemical interaction, i.e., 2c-le, 2c-2e or 2c-3e bond. However, as discussed in the preceding section, there are not many examples in which these bonds occur in such a pure state. Archetypal representatives of these bonding modes (e.g.,, H2, HeH) are in fact rather atypical for chemical bonds in general. In nearly all other cases, we have to deal with mono- or polyatomic fragments, carrying additional electrons in other orbitals. These electrons will interfere with and affect the nature of the primary frontier orbital interactions. Here we focus on the nature of the electron pair bond and how this bond can be influenced by Pauli repulsion effects due to other fragment orbitals such as lone pairs.54 72 

The nature of the three-electron (2c-3e) bond as well as the relation between 2c-3e and 2c-le bonding will be the subject of the following section. 

In the following, we examine the nature of the central bond between the CX radicals in 4 and 5 (X = N, P). To what extent can this bond be considered to be a simple a electron pair bond Does it bonding make a significant contribution What exactly determines the degree to which the 2c-2e bond interferes with other electrons, and how does this affect molecular structure and bond strength The discussion of these questions is based on our DFT investiga- 

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There is an implicit assumption contained in all of the above The two bonding electrons are of opposite spin. If two electrons are of parallel spin, no bonding occurs, but repulsion instead curve /, Fig. 5.1). This is a result of the Pauli exclusion principle. Because of the necessity for pairing in each bond formed, the valence bond theory is often referred to as the electron pair theory, and it forms a logical quantum-mechanical extension of Lewis s theory of electron pair formation. 

We have already assumed that electron pairs, whether in bonds or as nonbonding pairs, repel other electron pairs. This is manifested in the tetrahedral and trigonal geometry of tetravalent and trivalent carbon compounds. These geometries correspond to maximum separation of the electron-pair bonds. Part of this repulsion is electrostatic, but there is another important factor. The Pauli exclusion principle states that only two electrons can occupy the same point in space and that they must have opposite spin quantum numbers. Equivalent orbitals therefore maintain maximum separation, as found in the sp, sjf, and sp hybridization for tetra-, tri-, and divalent compounds of the second-row elements. The combination of Pauli exclusion and electrostatic repulsion leads to the valence shell electron-pair repulsion rule (VSEPR), which states that bonds and unshared electron pairs assume the orientation that permits maximum separation. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

We discuss below the physics of the classical electrostatic attraction AVe t and the steric or Pauli repulsion AEPauli. Thereafter, we turn to the stabilizing or bonding interactions, both electron-pair bond formation and donor-acceptor interactions, as well as stabilization coming from admixing of (higher) virtual orbitals on one fragment due to the potential field of the other fragment (polarization). Finally, in the last part of this section we discuss some aspects of the mutual influence between the various interactions. 

In n symmetry, there is a stabilizing donor-acceptor interaction involving four electrons between the doubly degenerate nHOMO and itLUMo causing two partial n bonds (8). They are opposed by the Pauli repulsive iHomo - homo two-center four-electron (2c-4e) interaction. Note the difference in nature between c and the n bonds the former is an electron pair bond between singly occupied orbitals, whereas the latter evolves from a donor-acceptor or charge transfer interaction between occupied and unoccupied orbitals. 

In the preceding section, we discussed the electron pair (2c-2e) bond and how it can be influenced by Pauli repulsion of the SOMOs with other electrons. In the three-electron (2c-3e) bond, Pauli repulsion plays an even more fundamental role, as we will see.72 The idea of the three-electron bond was introduced in the early 1930s by Pauling in the context of the valence bond (VB) model of the chemical bond.70 71 Since then, it has been further developed both in VB and in MO theory and has become a standard concept in chemistry.118-129 In VB theory,7°>71 118 123 the two-center, three-electron (2c-3e) bond between two fragments A and B is viewed as arising from a stabilizing resonance between two valence bond structures in which an electron pair is on fragment A and an unpaired electron on B (13a), or the other way around (13b) ... 

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