The p Orbitals

When n is 4 or greater, there are seven equivalent/orbitals (for which / = 3). The shapes of the/orbitals are even more compHcated than those of the d orbitals and are not presented here. As you wiU see in the next section, however, you must be aware of/orbiteds as we consider the electronic structure of atoms in the lower part of the periodic table. 

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UNSUBSTITUTED BUTADIENE. Butadiene anchors were presented in Figures 1(3) and 13. The basic tetrahedral character of the conical intersection (as for H4) is expected to be maintained, when considering the re-pairing of four electrons. Flowever, the situation is more complicated (and the photochemistiy much richer), since here p electrons are involved rather than s electrons as in H4. It is therefore necessary to consider the consequences of the p-orbital rotation, en route to a new sigma bond. 

Table 2.6 shows the electron affinities, for the addition of one electron to elements in Periods 2 and 3. Energy is evolved by many atoms when they accept electrons. In the cases in which energy is absorbed it will be noted that the new electron enters either a previously unoccupied orbital or a half-filled orbital thus in beryllium or magnesium the new electron enters the p orbital, and in nitrogen electron-pairing in the p orbitals is necessary. 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

Figure 7-23. The polarizing effect ofd-orfeitals. a) The energy of the. t-MO can be lowered slightly by shifting the centers of the AOs slightly towards the center of the bond, b) The lobes ca n be directed towards each other by mixing soine d-character into the p-orbitals. The effect is exaggerated for clarity.

We express the bonding n and antibonding ti orbitals in terms of the atomie p-orbitals from whieh they are formed 7i= 2 h2 [ L + R ] and 7i = 2 h2 [ l - R ], where R and L denote the p-orbitals on the left and right earbon atoms, respeetively. 

Section 2 20 Carbon is sp hybridized in ethylene and the double bond has a ct com ponent and a rr component The sp hybridization state is derived by mix mg the 2s and two of the three 2p orbitals Three equivalent sp orbitals result and their axes are coplanar Overlap of an sp orbital of one car bon with an sp orbital of another produces a ct bond between them Each carbon still has one unhybridized p orbital available for bonding and side by side overlap of the p orbitals of adjacent carbons gives a rr bond between them... 

FIGURE 5 1 (a) The planar framework of u bonds in ethylene showing bond distances and angles (b) and (c) The p orbitals of two sp hybridized carbons overlap to produce a tt bond (d) The electrostatic potential map shows a region of high negative potential due to the tt elec trons above and below the plane of the atoms... 

In principle cis 2 butene and trans 2 butene may be mterconverted by rotation about the C 2=C 3 double bond However unlike rotation about the C 2—C 3 single bond in butane which is quite fast mterconversion of the stereoisomeric 2 butenes does not occur under normal circumstances It is sometimes said that rotation about a carbon-carbon double bond is restricted but this is an understatement Conventional lab oratory sources of heat do not provide enough energy for rotation about the double bond m alkenes As shown m Figure 5 2 rotation about a double bond requires the p orbitals of C 2 and C 3 to be twisted from their stable parallel alignment—m effect the tt com ponent of the double bond must be broken at the transition state... 

Effects that arise because one spatial arrangement of electrons (or orbitals or bonds) IS more stable than another are called stereoelectronic effects There is a stereoelec tromc preference for the anti coplanar arrangement of proton and leaving group in E2 reactions Although coplanarity of the p orbitals is the best geometry for the E2 process modest deviations from this ideal can be tolerated In such cases the terms used are syn periplanar and anti periplanar... 

Section 10 7 Conjugated dienes are stabilized by electron delocalization to the extent of 12-16 kJ/mol (3 kcal/mol) Overlap of the p orbitals of four adja cent sp hybridized carbons in a conjugated diene gives an extended tt system through which the electrons are delocalized... 

The two most stable conformations of conjugated dienes are the s cis and s trans The s trans conformation is normally more stable than the s cis Both conformations are planar which allows the p orbitals to overlap to give an extended tt system... 

In orbital terms as represented m Figure 11 10 benzyl radical is stabilized by delo cahzation of electrons throughout the extended tt system formed by overlap of the p orbital of the benzylic carbon with the rr system of the ring... 

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

Geometrical Isomerism. Rotation about a carbon-carbon double bond is restricted because of interaction between the p orbitals which make up the pi bond. Isomerism due to such restricted rotation about a bond is known as geometric isomerism. Parallel overlap of the p orbitals of each carbon atom of the double bond forms the molecular orbital of the pi bond. The relatively large barrier to rotation about the pi bond is estimated to be nearly 63 kcal mol (263 kJ mol-i). 

The sp orbitals are equivalent, coplanar and oriented at 120° to each other and form a bonds by overlap with orbitals of neighbouring atoms, as in the molecule ethene, CjH, Fig. 1, A2. The remaining p orbital on each C atom forms a n bond by overlap with the p orbital from the neighbouring C atom the bonds formed between two C atoms in this way are represented as Csp =Csp, or simply as C=C. 

Some fundamental structure-stability relationships can be employed to illustrate the use of resonance concepts. The allyl cation is known to be a particularly stable carbocation. This stability can be understood by recognizing that the positive charge is delocalized between two carbon atoms, as represented by the two equivalent resonance structures. The delocalization imposes a structural requirement. The p orbitals on the three contiguous carbon atoms must all be aligned in the same direction to permit electron delocalization. As a result, there is an energy barrier to rotation about the carbon-carbon... 

The preferred alignment of orbitals for a 1,2-hydride or 1,2-alkyl shift involves coplanarity of the p orbital at the carbocation ion center and the a orbital of the migrating group. 

The TT component of the C=0 group and the p orbital of the OH oxygen overlap to form an extended tt system that Includes carbon and both oxygens. 

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