P-orbital introduced

Flipping this one p orbital introduces two more nodes... 

This is an example of a Mobius reaction system—a node along the reaction coordinate is introduced by the placement of a phase inverting orbital. As in the H - - H2 system, a single spin-pair exchange takes place. Thus, the reaction is phase preserving. Mobius reaction systems are quite common when p orbitals (or hybrid orbitals containing p orbitals) participate in the reaction, as further discussed in Section ni.B.2. 

Neighboring group participation (a term introduced by Winstein) with the vacant p-orbital of a carbenium ion center contributes to its stabilization via delocalization, which can involve atoms with unshared electron pairs (w-donors), 7r-electron systems (direct conjugate or allylic stabilization), bent rr-bonds (as in cyclopropylcarbinyl cations), and C-H and C-C [Pg.150]

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

The case of boron as a network former cation is somewhat specific in that this element has no available d orbitals. However, a p orbital is available when the boron has a coordination number of 3, which allows stabilisation of an electronic doublet of the oxygen or sulphur introduced by the modifier. This oxygen or sulphur giving up a doublet to another boron atom increases the cross-linking by the formation of two BO4 tetrahedra. In hybridisation terms, the boron is altered from the sp configuration to the sp configuration. The coordination change of boron has been especially well observed by NMR (Bray and O Keefe, 1963 Muller-Warmuth and Eckert, 1982). 

Consider one beautifully symmetrical shape predicted by VSEPR theory the tetrahedron. Four equivalent pairs of electrons in the valence shell of an atom should distribute themselves into such a shape, with equal angles and an equal distance between each pair. But what sort of atom has four equivalent electron pairs in its valence shell Aren t valence electrons distributed between different kinds of orbitals, like s and p orbitals (We introduce these orbitals in Chapter 4.)... 

The axially symmetric metal carbonyl fragments M(CO)n (n = 1, 3, 4) have three outpointing hybrid orbitals with a high proportion of s and p orbital character, which are suitable for forming cluster skeletal molecular orbitals (77, 78, 238). The number and radial characteristics of these frontier molecular orbitals, which are illustrated schematically in Fig. 26a, are reminiscent of the frontier orbitals of a main group diatomic hydride fragment E—H, where E = C or B (Fig. 26b). To describe this similarity the term isolobal has been introduced (77). Molecular orbital... 

It is by no means easy to say whether d polarization orbitals are needed in the quantum-chemical description of phosphorus and sulphur compounds. Because of the variational principle, one has to be exceptionally unlucky not to ameliorate an approximate P when introducing a new free parameter. But the question is whether the d polarization orbitals are an essential aspect of the unknown (and somewhat Platonic) true St. This is a very profound question related to the problem whether the natural spin-orbitals (introduced by Lowdin) having occupation numbers closely below 1 are those which define the preponderant configuration. It is now known... 

If overlap is neglected, the destabilization due to the antibonding electron is exactly equal to the stabilization conferred by the bonding electron. However, the destabilizing effects become greater when overlap is introduced [cf. Equations (2.11) and (2.14)]. When the p orbitals are orthogonal, the overlap is zero and the destabilization disappears. As a result, this conformation is adopted in the ethylene excited state. 

Carbenes, having a low-lying vacant p orbital and a lone pair, can react with nucleophiles and electrophiles alike. Introducing very bulky substituents is one obvious way to diminish its reactivity. A more interesting solution is electronic stabilization. For example, the following carbene has indefinite stability in the solid state 41... 

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