Orbital orientation

As orbitals spread into bands, orbitals oriented for a or a bonds spread into the widest bands. 7t orbitals form narrower bands and 5 bonding orbitals form the narrowest bands. 

We saw in Chapter 1 that the carbon-carbon double bond can be described in two ways. In valence bond language (Section 1.8), the carbons are sp2-hybridized and have three equivalent hybrid orbitals that lie in a plane at angles of 120° to one another. The carbons form a cr bond by head-on overlap of sp2 orbitals and a tt bond by sideways overlap of unhybridized p orbitals oriented... 

Electron Pairs Orbitals Orbitals Orientation Examples... 

The tertiary-secondary 1,2-H shift O itlO is not rate-determining in the interconversion of 5 and 6, but may become so in a conformationally fixed system. It has been found for the interconversion of tertiary and secondary adamantyloxocarbonium ions that <10" sec at 70°C (Hogeveen and Roobeek, 1971a) as compared with k= 1-5 x 10 sec at 20°C for the reaction 5 6. The absence of interconversion between tertiary and secondary adamantyloxocarbonium ions is due to the circumstance that 1,2-H shifts do not occur in the tertiary adamantyl ion as a result of the effect of orbital orientation (Brouwer and Hogeveen, 1970 Schleyer etal., 1970). That the secondary adamantyloxocarbonium ion can lose CO is demonstrated by the reaction with isopropyl cation in SbFs—SO2CIF solution at 0°C with formation... 

The water complexes are high spin, whereas the cyanide and phen complexes are low spin. In the case of the cyanide and phen complexes, the interconversion of the 2g iron(ii) and /2g iron(iii) states simply involves the loss or gain of an electron from the 2g level. Since these are the orbitals oriented between the ligand donor atoms. 

The magnetic quantum number derives its name from the fact that different orbital orientations generate different behaviors in... 

As mentioned in Section Wl, an electron has magnetism associated with a property called spin. Magnetism is directional, so the spin of an electron is directional, too. Like orbital orientation, spin orientation is quantized Electron spin has only two possible orientations, up or down. The spin orientation quantum number )... 

Each of the carbon atoms in butadiene has a p orbital oriented to overlap with those on neighboring carbon atoms, generating a set of four MOs, of which one is shown. 

Band structure for a chain of p orbitals oriented head-on... 

What would the band structure of a chain of p orbitals oriented head-on (Fig. 10.5) look like... 

The outer most levels in C60 are due to rc orbitals . These are formed by 2p electrons which have their orbitals oriented along the radius of the molecule. The different environment inside and outside the spherical molecule causes the double-peaked structure in the momentum densities. In graphite the n band is formed by 2p orbitals oriented perpendicular to the sheets of carbon atoms. Using single-crystal graphite films we have a unique opportunity to study the effects of the orientation of these 2p orbitals in detail. 

In view of the clear correlation of local ring geometry with methyl rotor barrier height in the S0 and D0 states, the strong effects of S, <— S0 excitation on rotor potentials seem to indicate substantial distortion of the ring away from hexagonal symmetry in the S, state as well. There is little clear evidence of this from molecular spectroscopy. We have speculated that such a n-molecular orbital orientation effect in the S j state (similar to that in the cation) might explain the observed characteristic... 

The interaction of the metal s and dzi orbitals with those of the cyclopentadienyl anion can be illustrated as follows. We begin by placing the metal orbital between the two ligands that have the orbitals oriented to match the sign of the wave function of the metal orbital. Therefore, for the s and dzi orbitals, the combinations are shown in Figure 21.16. 

But it was not really until 1931, when Slater and Pauling independently developed methods to explain directed chemical valence by orbital orientation that it can truly be said that a chemical quantum mechanics, rather than an application of quantum mechanics to chemistry, had been created. In a study of Slater, S. S. Schweber notes the distinction between the Heitler-London-Pauling-Slater theory and the Heitler-London theory. Heitler and London successfully explained the electron-valence pair on the basis of the Goudsmit-Uhlenbeck theory of spin. Slater and Pauling explained the carbon tetrahedron. This second explanation distinguishes quantum chemistry from quantum physics.2... 

The Third Quantum Number Describing Orbital Orientation... 

There is also a third type of reactive species that we shall discuss in detail in Chapter 9, namely radicals. Briefly, radicals are uncharged entities that carry an unpaired electron. A methyl radical CH3 results from the fission of a C-H bond in methane so that each atom retains one of the electrons. In the methyl radical, carbon is sp hybridized and forms three CT C-H bonds, whilst a single unpaired electron is held in a 2/ orbital oriented at right angles to the plane containing the ct bonds. The unpaired electron is always shown as a dot. The simplest of the radical species is the other fission product, a hydrogen atom. 

The principal quantum number n is the most important determinant of the radius and energy of the electron atomic orbital. The orbital shape quantum number I determines the shape of the atomic orbital. When / = 1, the atomic orbital is called an s orbital there are two s orbitals for each value of n, and they are spherically symmetric in space around the nucleus. When I = 2, the orbitals are called the p orbitals there are six p orbitals, and they have a dumbbell shape of two lobes that are diametrically opposed. When I = 3 and 4, we have 10 d orbitals and 14 f orbitals. The orbital orientation quantum number m controls the orientation of the orbitals. For the simplest system of a single electron in a hydrogen atom, the most stable wave function Is has the following form ... 

Since the d orbitals have quadrupolar character, this distortion must be modelled using a point electric quadrupole with the shape of the d i orbital oriented with a negative pole along the z axis and the positive pole in the x-y equatorial plane (Fig. 8.7(a)). No fluxes have been calculated for Jahn-Teller distorted cations, either with or without the quadrupolar contribution but, as in the other cases, the experimental bond valences are expected to provide a good approximation to the bond fluxes. 

Figure 5.1 The CNDO formalism for estimating repulsive two-electron interactions fails to distinguish in one-center cases between different orbitals (top example for the case of methylene) and in two-center cases either between different orbitals or different orbital orientations (bottom example for the case of hydrazine)...

---