Minimal orbitals

The most common and also most effective mechanism of radical stabilization involves the resonant delocalization of the unpaired spin into an adjacent 7r system, the allyl radical being the prototype case. A minimal orbital interaction diagram describing this type of stabilization mechanism involves the unpaired electron located in a 7r-type orbital at the formal radical center and the 7r- and tt -orbitals of the n system (Scheme 1). 

Schier and Schmidbaur93 performed a clever experiment that addressed part of this question does the orientation of the carbanion relative to the phosphorus atom play any role Scheme 2 shows two syntheses of ylides involving cyclopropyl substituents. In the first reaction, since the pKa of cyclopropane is considerably below that of propane, the expected product is the cyclopropylide. However, the isopropylide is the only recovered product. The second reaction also demonstrates the avoidance of the cyclopropylide product. The cyclopropylide possesses a very pyramidal carbanion that is directed away from phosphorus, allowing for minimal orbital overlap. The isopropylide is much less pyramidal and phosphorus can better assist in stabilizing the carbanion. While this stabilization does not require explicit orbital overlap (the electrostatic interaction of the carbanion with the onium is expected to be smaller in the cyclopropylide since it is directed away from P), it does suggest that some orbital interactions are involved. Hence, although the ylene contribution is small, it is unlikely that the ylene contribution is nil. 

This so-called stereoelectronic factor operates to maximize or minimize orbital overlap, as the case requires, to obtain the most favorable energy. This was evident from the three- and four-center systems we have discussed by the VB and HMO methods. It was also implicit in favored anti-1,2-additions, 1,3-cyclizations (Fig. 23), fragmentations (e.g. (174)), etc. Here we have selected several reaction types to illustrate the principle. In this and other sections, we show that the tendency for reaction centers to be collinear or coplanar stems largely from orbital symmetry (bonding), but may also derive from steric and electrostatic effects, as well as PLM. 

The Karplus relationship makes perfect sense according to the Dirac model. When the two adjacent C—H cr bonds are orthogonal (a= 90°, perpendicular), there should be minimal orbital overlap, with little or no spin interaction between the electrons in these orbitals. As a result, nuclear spin information is not transmitted, and Vhh = 0- Conversely, when these two bonds are parallel (a= 0°) or antiparallel (a= 180°), the couphng constant should have its greatest magnitude ( hh = max). 

For d-transition-metal ions, the number of water molecules in the primary coordination sphere (A-zone) is in most cases determined by the strength of orbital overlap between the metal ion and H2O molecules, crystal field stabilization effects, and cationic charge. Other species (e.g., alkaline earths, rare earths) interact with solvent molecules via ion-dipole forces with minimal orbital overlap conhibution to the bonding. Their solvation numbers are determined by a combination of coulombic attraction between cations and water molecules, steric fiictors, and van der Waals repulsion between the bound water molecules. The larger size and high charge of the lanthanides combine with the absence of directed valence effects to produce primary-sphere hydration numbers above eight for these metal ions. 

In choosing a basis, one can search for an optimum choice that gives successively the highest overlap of wave functions. Thus, let y(r) 5 and tt(r) e 5 and choose the maximum of l(xln)l with respect to both subspaces moreover, let lx,), Iq,) be the minimizing orbitals under the normalization conditions. By a proper choice of phases so that (xlq) is real, the following can be obtained ... 

If, for instance, p = s = 0 and = 1, the GTO corresponds to the function Py. The minimal orbital basis set in which N Gaussian functions are used to approximate one Slater function is designated as the STO-NG basis set. Usually one sets N = 3, seeing that with the further increase the accuracy improves very slowly. 

---