8-17 Extension to Heteroatomic Molecules
Chapter 8 The Simple H ¨uckel Method and Applications average for acyclics. The very different bond orders in these two molecules is fully consistent with the energy argument based on the 4n + 2 rule described earlier.16 To summarize, the π bonds in acyclic polyenes exhibit delocalization in the sense that bond orders are not transferable from one molecule to another, additivity in effective
bond energies, immobility in formal bonds. Cyclic molecules do not exhibit additivity of effective energies or immobility of formal bonds. Their energy deviations from energy calculated assuming additivity and immobility are good indicators of kinetic and thermodynamic stability. Aromatic molecules possess extra stability because their π electrons17 are more bonding than those in acyclic polyenes. Antiaromatics are unstable because their π electrons are less bonding.
From a consideration of experimental heats of atomization, Schaad and Hess have evaluated β to be −1.4199 eV. The physical processes involved in dissociating a gasphase molecule into constituent atoms are quite different from those involved in adding or removing a π electron from a molecule in a solvent. Therefore, it is not surprising that the β value obtained from heats of atomization differs substantially from values obtained from redox experiments. Indeed, it is this variability of β as we compare HMO theory with different types of experiment that compensates for many of the oversights and simplifications of the approach. It is remarkable that, with but one such parameter, HMO theory does as well as it does.
8-17 Extension to Heteroatomic Molecules
The range of application of the HMO method could be greatly extended if atoms other than carbon could be treated. Consider pyridine as an example (XV). A π electron at a carbon atom contributes an energy α to Eπ . The contribution due to a π electron at nitrogen is presumably something different. Let us take it to be α = α + hβ, where h is a parameter that will be fixed by fitting theoretical results to experiment. If the π electron is attracted more strongly to nitrogen than to carbon, h will be a positive 16It has been noted that bond length equalization associated with bond mobility results in it energy lowering when the C–C–C angles are near 120◦. When the angle is very different from this, π energies are higher than expected. This has led to suggestions that “strain energy” may be an important factor in aromaticity. Because of the present lack of a quantum mechanical quantity equivalent to strain energy, and because the HMO method may include effects of σ electrons in an implicit but poorly understood way, it is very hard to know whether such suggestions are at variance with other statements or are simply equivalent to them but stated from a different viewpoint.
17It is not necessarily true that all the “extra” stability of aromatic molecules is attributable to π-electron effects; σ -electron energies also depend on bond lengths and bond angles. Hence, we may be seeing, once again, a situation where the π -electron treatment includes other effects implicitly. Schaad and Hess [18] indicate that σ energies and π energies are indeed simply related over the bond-length range of interest.
Section 8-17 Extension to Heteroatomic Molecules number. In a similar spirit, we will take the energy of a π electron in a C–N bond to be β = kβ and evaluate k empirically. Not surprisingly, the values of h and k appropriate for various heteroatoms depend somewhat on which molecules and properties are used in the evaluation procedure. A set of values compiled and critically discussed by Streitwieser [7] is given in Table 8-3. Other sets have been published.18
The dots over each symbol indicate the number of π electrons contributed by the atom. In pyridine, the formal bond diagram indicates a six π -electron system, implying that the nitrogen atom contributes one π electron. We also can argue that, of the five TABLE 8-3 Parameters for Heteroatoms in the H¨uckel Methoda Heteroatom
h
Heteroatomic bond
k
˙N
0.5
C . . .
— ¨
N
1.0
¨N
1.5 C— ¨
N
0.8
+
N
2.0
˙O
1.0
C—
— ˙
O
1.0
¨O
2.0 C— ¨
O
0.8
+
O
2.5 N— ¨
O
0.7
¨F
3.0 C— ¨
F
0.7
¨
Cl
2.0 C— ¨
Cl
0.4
¨
Br
1.5 C— ¨
Br
0.3
Sb
0.0
C—S
0.8
S
0.0
C—S
0.8 S— S
1.0
Methyl (inductive ˙ Cα—Me)−0.5 hC = −0.5
none
—
α
Methyl (heteroatom ˙ Cα— ¨
Me)0.2 hMe = 0.2
Cα—Me
0.7
Methyl (conjugative ˙ Cα—C ¨
—H3)
hC = −0.1
C
α α —C
0.8
hc = −0.1
C—H3
3.0
hH = −0.5
3
a Consistent with the philosophy of this approach is a distinction between single, double, and intermediate C—C bonds. Streitwieser recommends kC−C = 0.9, kC... −C = 1.0, kC=C = 1.1.
b Sulfur is treated as a pair of AOs with a total of two π electrons, i.e., a sulfur in an aromatic ring is formally treated as two adjacent atoms S and S with the indicated parameters.
18See McGlynn et al. [24, p. 87].
Chapter 8 The Simple H ¨uckel Method and Applications valence electrons of nitrogen, two are involved in σ covalent bonds with neighboring carbons, two more are in a σ lone pair, leaving one for the π system. Therefore, the atom parameter to use for this molecule is h = 0.5. The pyridine ring, like benzene, admits two equivalent structural formulas, and so the C–N bonds should be intermediate between double and single, symbolized C... – ˙ N in Table 8-3. Since k = 1.0 in this case, β = β, and pyridine will have an HMO determinant differing from the benzene determinant only in the diagonal position corresponding to the nitrogen atom–the 1, 1 position according to our (arbitrary) numbering scheme. For this position, instead of x, we will have x = (α − E)/β = (α + 0.5β − E)/β = (α − E)/β + 0.5β/β = x + 0.5
(8-64)
The pyrrole molecule has a nitrogen atom of the type ¨ N(XVI). Since three valence electrons of nitrogen are in covalent σ bonds, two remain for inclusion in the π system.
Therefore, pyrrole has a total of six π electrons. The unique structural formula indicates that the C– ¨ N bond is formally single, and k = 0.8, h = 1.5 are the appropriate parameters here. Also, the carbon–carbon bonds are now formally single or double. If we choose to distinguish among these bonds using the parameters in note a of Table 8-3, the resulting HMO determinant is
x + 1.5 0.8
0
0
0.8
0
.8
x
1.1
0
0
0
1.1
x
0.9
0
0
0
0.9
x
1.1
0.8
0
0
1.1
x
The methyl group can also be incorporated into the HMO method.
Several approaches have been suggested. One is simply to modify the coulomb integral α for the carbon to which the methyl group is attached. A methyl group is thought to release sigma electrons to the rest of the molecule as compared to a substituent hydrogen. This suggests that an atom having a methyl group attached to it will be a bit electron rich and hence will be less attractive to π electrons. Use of a negative h parameter for this carbon is appropriate. This method is called the inductive model. Use of the inductive model does not add any new centers or any more π electrons to the conjugated system to which the methyl group is attached: The carbon to which the methyl is bonded is merely treated as a less attractive atom. A second approach is to treat the methyl group itself as a heteroatom. As we shall see shortly, the methyl group has two electrons that