User:2008chem540rigidrotor/Sandbox

Effect of hyperconjugation on chemical properties

a) Bond length: Hyperconjugation is suggested as a key factor in shortening of σ bonds in such systems. For example, the single C-C bonds in 1,3-butadiene and methylacetylene are approximately 1.46 angstrom in length, much less than the value (1.54 angstrom) found in saturated hydrocarbons. This is due mainly to hyperconjugation that gives partial double-bond character of the bond.
b) Dipole moments: The large increase in dipole moment of methyl chloroform as compared with chloroform can be attributed to hyperconjugated structures.
c) The heats of formation of such molecules are greater than sum of their bond energies; and the heats of hydrogenation per double bond are less than the heat of hydrogenation of ethylene.
d) Stability of carbocations:
(CH3)3C+ > (CH3)2CH+ > (CH3)CH2+ > CH3+
The C-C σ bond adjacent to the cation is free to rotate, and as it does so, the three C-H σ bonds of the methyl group in turn undergoes the stabilization interaction. The more adjacent C-H bonds are, the larger hyperconjugation stabilization is.

Conjugation and hyperconjugation stabilization in 1,3-butadiyne and 1,3-butadiene

The conjugation of 1,3-butadiene was first evaluated by Kistinkowsky, a conjugative contribution of 3.5 kcal/mol was found based on the energetic comparison of hydrogenation between conjugated species and unconjugated analogues. Rogers et al., who used the method first applied by Kistinkowsky, reported that the conjugation stabilization of 1,3-butadiyne was zero, as the difference of ∆hydH between first and second hydrogenation was zero. The heats of hydrogenation (∆hydH) were obtained by computational MP2 quantum chemistry method.
Another group led by Houk et al., suggested the methods employed by Rogers and Kistinkowsky was inappropriate, because that comparisons of heats of hydrogenation evaluate not only conjugation effects but also other structural and electronic differences. They obtained -70.6 kcal/mol and -70.4 kcal/mol for the first and second hydrogenation respectively by ''ab initio'' calculation, which confirmed Rogers’ data. However, they interpreted the data differently by taking into account the hyperconjugation stabilization. To quantify hyperocnjugation effect, they designed bellowing isodesmic reactions in 1-butyne and 1-butene.
Deleting the hyperconjugative interactions gives virtual states which have energies that are 4.9 and 2.4 kcal/mol higher than those of 1-butyne and 1-butene, respectively. Employment these virtual states results in a 9.6 kcal/mol conjugative stabilization for 1,3-butadiyne and 8.5 kcal/mol for 1,3-butadiene.

Recent Debate on Existence of Hyperconjugation: Gronert vs. Scheleyer

Gronert proposed a 1,3 repulsive interaction, otherwise known as a geminal repulsion in place of hyperconjugation. This model explains differences in bond strengths based on differential steric strain relief as a result of bond cleavage. The key point of Gronert’s model is that 1,3 repulsions are the major factor in determining stability of C-C of C-H bonds in alkanes. This broad overarching supposition is based on several already existing assumptions:
1. The heats of formation of alkanes are only determined by 1,2 bonding interactions and 1,3 repulsive interactions.
2. All C-H bonding interactions provide the same stabilization.
3. All C-C bonding interactions provide the same stabilization.
4. The 1,3 repulsive interactions can be grouped into C-C-C, C-C-H, and H-C-H interactions.

Gronert’s work is a logical step from work done 50 years ago by Dunitz, Schomaker, Bauld, Wiberg, Bikelhaupt, Ziegler and Scheleyer. From the results of these groups, Gronert makes a leap of faith to assume that 1,3 repulsive interactions are not uniform and vary in magnitude based on what groups are involved.

Gronert’s Method for Evaluating Alkane, Cycloalkane, Alkene and Alkyl radical heats of formation:
where n = number of each type of interaction or atom, E = stabilization/destabilization per interaction, and Ec = free parameter (correction term for electron pairing in atomic carbon). The final term converts to heat of formation from values that are fundamentally atomization energies (gaseous carbon = 170.6 kcal/mole and hydrogen atoms = 52.1 kcal/mole).

There are several important justifications for Gronert’s model:
1. Significant geminal repulsion is already expected because groups are separated by less than the combination of their van der Waals radii and there are no bonding interactions. Computational methods also agree that they are important and of the proper magnitude.
2. It’s already well-accepted that 1,3 repulsive interactions are important in determining structure.
3. Branching has a strong effect on stabilities of alkanes, not just the BDE. No current evidence that differences in bond strengths are only controlled by factors exclusive to the resulting radical. His method addresses the stability of the alkane and alkyl radical.
4. Model depends on interactions observed in many systems and affects both structure and reactivity. This is based on the theory that close-range, nonbonding interactions are repulsive, ie. Steric strain.

The ultimate question is: does Gronert’s model hold up? Gronert claims that his model successfully reproduces accepted data without invoking hyperconjugation and can perhaps explain well-established trends. His conclusion comes with a disclaimer, however: geminal repulsion can absolutely replace hyperconjugation. He only means to give a reasonable alternative explanation.

Scheleyer’s model has several marked differences fromn. He uses new isodesmic addivity design that faithfully reproduces heats of formation for many alkanes, alkenes, alkynes and alkyl radicals. All 1,3 interactions are stabilizing so they support branching and hyperconjugation. All adjustable parameters originate from assumption that the magnitude of stabilizations effects at a specific carbon are eased when more than one substituent contributes.

Scheleyer’s Criticism of Gronert:
1. Gronert’s method arbitrarily set parameters and adjusted the others as best fit averages of experimental hydrocarbon heats of formation.
2. Gronert’s derived C-C and C-H bond energy values are higher than those accepted in the literature.
3. His model only uses 4 adjustable parameters (minimum chemically plausible) while Gronert’s uses 7 – less is more?
4. 1 attractive geminal term that can alone reproduce data satisfactorily.
5. Well-established theories of branching, hyperconjugation and attenuation.
6. Depends only on energetic relationships between the simplest hydrocarbon molecules.

Rotational barrier of ethane

An instance where hyperconjugation may be overlooked as a possible chemical explanation is in rationalizing the rotational barrier of ethane. It had been accepted as early as the 1930’s that the staggered conformations of ethane were more stable than the eclipsed. Wilson had proven that the energy barrier between any pair of eclipsed and staggered conformations was approximately 3 kcal/mol, and the generally accepted rationale for this was the unfavorable steric interactions between hydrogen atoms. In their 2001 paper, however, Pophristic and Goodman revealed that this explanation may be too simplistic.

The work of Goodman and Pophristic:
Goodman focused on three principle physical factors: hyperconjugative interactions, exchange repulsion defined by the Pauli exclusion principle, as well as electrostatic interactions (Coulomb interactions). By comparing a traditional ethane molecule and a hypothetical ethane molecule with all exchange repulsions removed, potential curves were prepared by plotting torsional angle versus energy for each molecule. The analysis of the curves determined that the staggered conformation had no connection to the amount of electrostatic repulsions within the molecule. These results demonstrate that Coulombic forces do not explain the favored staggered conformations, despite the fact that central bond stretching decreases electrostatic interactions.

Goodman also conducted studies to determine the contribution of vicinal (between two methyl groups) vs. geminal (between the atoms in a single methyl group) is interactions to hyperconjugation. In separate experiments, the geminal and vicinal interactions were removed, and the most stable conformer for each interaction was deduced.

Deleted Hyperconjugative interaction	Torsional Angle(°)	Corresponding Conformer
No deletion	60.0	Staggered
No hyperconjugation	0	Eclipsed
No vicinal hyperconjugation	0	Eclipsed
No geminal hyperconjugation	60.0	Staggered

From the experiments, it can be concluded that hyperconjugative effects delocalize charge and stabilize the molecule. Further, it is the vicinal hyperconjugative effects that keep the molecule in the staggered conformation. Thanks to this work, the following model of the stabilization of the staggered conformation of ethane is now more accepted:

Hyperconjugation can also explain several other phenomena whose explanations may also not be as intuitive as that for the rotational barrier of ethane. One such example is the explanations for certain Lewis structures. The Lewis structure for an ammonium ion indicates a positive charge on the nitrogen atom. In reality, however, the hydrogens are more electropositive than is nitrogen, and thus are the actual carriers of the positive charge. We know this intuitively because bases remove the protons as opposed to the nitrogen atom.

Experiments leading to and involving hyperconjugation

Hyperconjugatin in unsaturated compounds

Early studies in hyperconjugation were performed by Kistiakowsky et. al. Their work, first published in 1937, was intended as a preliminary progress report of thermochemical studies of energy changes during addition reactions of various unsaturated and cyclic compounds. This pioneering work would lead many to investigate the group’s puzzling findings.
Kistiakowsky and fellow researchers collected heats of hydrogenation data during gas-phase reactions of various species containing one double bond. When comparing the addition of hydrogen to propylene, 1-butene, 1-heptene, t-butylethylene, neopentylethylene, and finally isopropylethylene the respective methyl, ethyl, n-amyl, isopropyl, t-butyl, and neopentyl groups are equally effective in decreasing the want of the double bond for the addition of hydrogen. The -∆H of values of three compounds in the form of R2C=CH2 were found to be equal (within 0.2 Cal/mol).

A portion of Kistiakowsky’s work involved a comparison of other unsaturated compounds in the form of CH2=CH(CH2)n-CH=CH2 (n=0,1,2). These experiments revealed an important result; when n=0, there is an effect of conjugation to the molecule where the -∆H value is lowered by 3.5 Cal. This is likened to the addition of two alkyl groups into ethylene. Kistiakowsky also investigated open chain systems, where the largest value of heat liberated was found to be during the addition to a molecule in the 1,4-position. Cyclic molecules proved to be the most problematic, as it was found that the strain of the molecule would have to be considered. The strain of five-membered rings increased with a decrease degree of unsaturation. This was a surprising result that was further investigated in later work with cyclic acid anhydrides and lactones. Cyclic molecules like benzene and its derivatives were also studied, as their behaviors were different from other unsaturated compounds.

Despite the thoroughness of Kistiakowsky’s work, it was not complete and needed further evidence to back up his findings. His work was a crucial first step to the beginnings of the ideas of hyperconjugation and conjugation effects.

Conjugation and hyperconjugation stabilization in 1,3-butadiyne and 1,3-butadiene

The conjugation of 1,3-butadiene was first evaluated by Kistinkowsky, a conjugative contribution of 3.5 kcal/mol was found based on the energetic comparison of hydrogenation between conjugated species and unconjugated analogues. Rogers et al., who used the method first applied by Kistinkowsky, reported that the conjugation stabilization of 1,3-butadiyne was zero, as the difference of ?hydH between first and second hydrogenation was zero. The heats of hydrogenation (?hydH) were obtained by computational MP2 quantum chemistry method.
Another group led by Houk et al., suggested the methods employed by Rogers and Kistinkowsky was inappropriate, because that comparisons of heats of hydrogenation evaluate not only conjugation effects but also other structural and electronic differences. They obtained -70.6 kcal/mol and -70.4 kcal/mol for the first and second hydrogenation respectively by ''ab initio'' calculation, which confirmed Rogers’ data. However, they interpreted the data differently by taking into account the hyperconjugation stabilization. To quantify hyperocnjugation effect, they designed bellowing isodesmic reactions in 1-butyne and 1-butene.
Deleting the hyperconjugative interactions gives virtual states which have energies that are 4.9 and 2.4 kcal/mol higher than those of 1-butyne and 1-butene, respectively. Employment these virtual states results in a 9.6 kcal/mol conjugative stabilization for 1,3-butadiyne and 8.5 kcal/mol for 1,3-butadiene.

Trends in hyperconjugation

A relatively recent work (2006) by Fernández and Frenking (2006) summarized the trends in hyperconjugation among various groups of acyclic molecules, using energy decomposition analysis or EDA. For this type of analysis, the formation of bonds between various molecular moieties is comprised of 3 component terms. ∆Eelstat represents what Fernández and Frenking call a molecule’s “quasiclassical electrostatic attractions.” The second term, ∆E_Pauli, represents the molecule’s Pauli repulsion. ∆E_orb, the third term, represents stabilizing interactions between orbitals. The total energy of interaction, ∆E_int, is the result of the sum of the previous 3 terms. A term used often in the paper is ∆E_pi, which appears to represent the pi conjugation for each molecule, and thus is treated as a component of ∆E_orb

One prominent group under study was the series of the four conjugated polyenes, trans-1,3-butadiene, trans-1,3,5-hexatriene, all-trans-1,3,5,7-octaquadraene, and all-trans-1,3,5,7,9-decapentaene. For this group, both interactions of each terminal vinyl group with the rest of the molecules and interactions between the vinyl units of each molecule were studied.

The results from analysis of this group indicate that pi conjugation (∆E_pi) is stronger for each added C=C unit. Fernández and Frenking observed increasing ∆E_pi with increasing C=C units until a value of around six or eight C=C units.5 Another group whose ∆E_pi values were very thoroughly analyzed were a group of enones that varied in substituent.

Fernández and Frenking reported that the methyl, hydroxyl and amino substituents resulted in a decrease in ∆E_pi from the parent 2-propenal. Conversely, halide substituents of increasing atomic mass resulted in increasing ∆E_pi. Because both the enone study and Hammett analysis study substituent effects, Fernández and Frenking felt that comparing the two to investigate possible trends might prove interesting. They observed a linear relationship between the ∆E_pi values for the substituted enones and the corresponding Hammett constants.