Ethane-Preferred Conformation (Nanotechnology)

INTRODUCTION

In chemistry (as well as biology and medicine), the concept of molecular structure is axiomatic; its status is essentially that of a cornerstone for predicting and understanding diverse molecular phenomena. Consequently, a lot of attention has been paid to developing molecular geometry predictive computational methods.[1] Despite the ability of modern large-scale ab initio calculations to accurately predict molecular geometries (in small-size and medium-size molecules), the forces that control the preferred conformer shape remain only partially appreciated.

ETHANE

Single bonds allow facile rotation around the bond, leading to an abundance of conformations for molecules with many such bonds (e.g., alkanes, sugars, and polymers). It is noteworthy that the formulation of fundamental chemical concepts, including that of molecular structure, originated in the framework of carbon chemistry. The simplest model molecule for studying C—C bond rotation is ethane (C2H6). It is the textbook example of a molecule that can rotate internally around one or more of its bonds so that during a full 360° rotation, it changes between unstable and relatively stable conformations. The equilibrium structure is the staggered (S) structure in which the two methyl (CH3) groups are stacked so that the hydrogen atoms are maximally separated (Fig. 1a). As one of its two methyl groups rotates once around the central carbon—carbon bond, the molecule will alternate three times between the preferred staggered conformation (Fig. 1a) and a ~ 3-kcal/mol[2,3] higher-energy unstable eclipsed (E) conformation (Fig. 1b). Schreiner[4] has given a careful account of the rich history behind the conviction for hindered rotation in ethane. Ebert and Wagner[6] appear to have been the first to propose ethane-hindered rotation in 1929 and 1931, respectively. Their molar heat capacity measurements led to recogni-tion—in the early years of quantum theory—by Nielson[5] and Teller and Weigert[6] of the quantum mechanical nature of internal rotation. However, the magnitude of the barrier remained in dispute and it was not until 1936 that Kemp and Pitzer[7] established definitively, from precise thermodynamic measurements, that the rotational barrier is appreciable, close to the now-accepted 3 kcal/mol. Wilson,[8] realizing that elucidation of rotational barrier origins would lead to an in-depth understanding of the relationship between electronic and molecular structures, published many papers (ethane included) on this topic. More details of the ethane internal rotation history, with additional references, have been given by Payne and Allen[9] and Veillard.[10]


Early work on the staggered structural preference focussed on the change in exchange repulsion (basically the Pauli principle leading to a tendency of electrons to avoid occupying the same space).[11] In this intuitively satisfying model, while ethane rotates toward an eclipsed structure, the electrons in C—H bonds on the different carbon atoms draw closer to each other (Fig. 1b) and experience increased repulsion, which destabilizes the eclipsed structure. Other conjectures included classical electrostatics, van der Waals (dispersion) forces, d-orbital and f-orbital participation, and hyperconjugation.[12] A more recent proposal involves quadrupole polarization of the C—C bond density in the eclipsed conformation.[13] Hyperconjugation is the term given to stabilizing delocal-ization effects caused by a-a* interactions, analogous to the p-conjugation present in unsaturated molecules.a Mulliken,[15] as early as 1939, concluded that aCH-aCH* hyperconjugation plays a role in the torsional potential of ethanelike molecules. However, Mulliken’s estimate of the hyperconjugation effect at that time was necessarily crude, seeming to suggest that it was too small to account for the observed 3.0-kcal/mol staggered-eclipsed energy difference. This idea was largely forgotten until the simple Huckel molecular orbital (MO) studies of Lowe,[16,17] and the analysis in terms of semilocalized orbitals, by England and Gordon[18] in the early 1970s, rekindled interest in hyperconjugation as a factor in the ethane torsional barrier.

Ethane internal rotation.

Fig. 1 Ethane internal rotation.

Building on England and Gordon’s finding that overlap between the tails of incompletely localized CH bond orbitals is important in energy analysis, Brunck and Weinhold,[19] using semiempirical MOs, showed how the staggered-eclipsed energy difference can arise simply from the change in the overlap of vicinal aCH and aCH* orbitals in the anti and syn arrangements of the staggered and eclipsed conformers (Fig. 2). It is clear that the donor-acceptor interactions are sharply reduced in the syn arrangement compared to anti because of unfavorable cancellation in the latter case, as the nodal plane of the CH antibond cuts through the main lobe of the CH bond orbital. This visual estimate is confirmed by the overlap integral magnitudes shown in Fig. 2, which strongly favor larger hyperconjugative stabilization in the staggered conformer.

Thus by the turn of the century (i.e., 21st century), the two surviving models for the ethane staggered preference were: 1) lower steric and electrostatic repulsion; and 2) higher hyperconjugative stabilization than for the eclipsed structure. The latter model, although advocated by a substantial segment of the theoretical chemistry community, remained controversial and virtually every undergraduate organic chemistry textbook in 2000 favored the intuitively seductive steric repulsion model. Almost all omitted any mention of the hyperconjugation explanation.b Even so, a key step had been made in 1980, which had the potential for allowing a decisive choice to be made between the two models: Brunck and Weinhold’s formulation of natural bond orbital (NBO) theory.[19] Lowdin[21] defined a set of ”natural orbitals” describing a system as the unique complete set of orthonormal maximum occupancy orbitals possible within the general double occupancy Pauli restriction. Natural bond orbitals represent an extension of natural orbitals: they are two-centered transforms of MOs into almost doubly occupied bonding orbitals (bonds) and nearly unoccupied antibonding orbitals (antibonds), which fulfill the natural orbital restrictions. They retain the energetic accuracy of MOs; however, they have the desirable property of being able to describe properties of a system in localized terms that are well hidden in the complex forms of MOs.

Leading vicinal aCH-aCH* hyperconjugative donor-acceptor interaction in the staggered (S) and eclipsed (E) conformers of ethane. Dark shading: antibonding orbitals; light shading: bonding orbitals.

Fig. 2 Leading vicinal aCH-aCH* hyperconjugative donor-acceptor interaction in the staggered (S) and eclipsed (E) conformers of ethane. Dark shading: antibonding orbitals; light shading: bonding orbitals.

The NBO scheme allowed a-a* delocalization effects, essentially buried in the ethane MOs, to be pinpointed.

Table 1 Conformational dependence on hyperconjuga-tive interactionsa

Deleted hyperconjugative interactions

Torsional angle (°)

Corresponding conformer

No deletion

60.0

S

No hyperconjugation

0.0

E

No vicinal

0.0

E

hyperconjugation

No geminal

60.0

S

hyperconjugation

Torsional angle dependencies of energy of real ethane (solid curve) and hypothetical ethane with exchange repulsion absent (dashed curve). Zero degrees denotes the staggered con-former; ±60° denotes the eclipsed conformer.

Fig. 3 Torsional angle dependencies of energy of real ethane (solid curve) and hypothetical ethane with exchange repulsion absent (dashed curve). Zero degrees denotes the staggered con-former; ±60° denotes the eclipsed conformer.

The resulting energetic analysis favored the hyperconju-gative model,[22] but a complication arises in evaluating the steric and electrostatic interactions. Steric energetics inherently involve a collective response of the entire N-electron system to the spatial region and, consequently, is sensitive to the details of the staggered! eclipsed torsional coordinate.1-23-1 Thus a central point in eliminating repulsive interactions as a factor in determining the staggered structure is including skeletal expansion, explicitly C—C bond lengthening (i.e., torsion in ethane is not pure rotation).[24] Wanting to get away from the pitfalls of energy analysis, Pophristic and Goodman[25] carried out a series of ethane geometry optimizations by successive removal of hyperconjugative, Pauli exchange, and repulsive electrostatic interactions (with and without the skeletal relaxations).

Because an individual hyperconjugative interaction is expressed as a charge (electron) transfer between selected bond and antibonds in the NBO description, specific hyperconjugative interactions that influence structural preference can be pinpointed. Table 1 shows the result of geometry optimization with selected charge transfers absent. If the inversion of conformational preference occurs on removal of a specific charge transfer interaction, the controlling factor for ethane’s staggered structure has been identified. The ”no hyperconjugation” entry in Table 1 shows that preference for the staggered conformation is lost on removal of all charge transfers. Furthermore, the equilibrium conformer of ethane with only the vicinal hyperconjugation (i.e., charge transfer between NBOs on adjacent carbon atoms) removed (”no vicinal hyperconjugation” entry) is eclipsed. If only the geminal hyperconjugation (i.e., charge transfers between the orbitals originating on the same carbon atom) is deleted, the inversion of conformational preference does not occur. The conclusion is that vicinal charge transfer interactions are the ones that keep the molecule in the staggered conformation. By this argument, it is the hyperconjugatively induced preferential stabilization that controls the ethane structure.

Where does this leave the repulsion model? Repulsion involves two types of interactions: exchange, necessarily a short-range effect because of the orbital overlap requirement, and electrostatic or Coulomb involving classical 1/R repulsion between charges. Taken together, these are frequently regarded as ”steric repulsion.” Fig. 3 considers two cases: the real ethane molecule with all interactions present, and a hypothetical one with all of the exchange repulsions removed. One potential curve (with all interactions present) represents the energy of the real molecule; the other curve represents the energy of the hypothetical molecule with exchange repulsion absent. The conclusion from Fig. 3 is that the minima of both curves coincide at the staggered conformation, establishing that the staggered conformation is preferred regardless of the presence of exchange repulsion.

The effect of electrostatic repulsion can be understood by comparing its torsional angle dependence for three cases: rigid rotation (i.e., pure rotation, all skeletal relaxations frozen), partially relaxed rotation (only C—C bond lengthening included), and fully relaxed rotation (all skeletal flexings taken into account). Fig. 4 shows that for rigid rotation, both electron and nuclear Coulomb repulsions increase as the torsional angle incrementally increases to the eclipsed conformer. However, when C—C bond lengthening is included as part of the rotational process as it is in fully relaxed rotation, both repulsions decrease, agreeing with Bader et al.[13] Thus the central bond stretching that is an intrinsic part of the rotational coordinate, which takes ethane from the staggered structure to eclipsed, reduces the strain that is accumulated in the molecule by rotation alone. The 0.014-A C—C bond lengthening leads to a large decrease in Coulomb repulsion energies. Therefore electrostatic repulsion does not explain the staggered structural preference in ethane.

Torsional dependence of nuclear-nuclear (NN; full line), electron-electron (EE; long dash line) repulsion, and nuclear-electron (NE; short dash line) attraction energy changes for rigid (RR) and fully relaxed (FR) rotation in ethane. Corresponding curves for the partially relaxed model (C—C bond lengthening included) are indistinguishable from the FR ones on the figure scale.

Fig. 4 Torsional dependence of nuclear-nuclear (NN; full line), electron-electron (EE; long dash line) repulsion, and nuclear-electron (NE; short dash line) attraction energy changes for rigid (RR) and fully relaxed (FR) rotation in ethane. Corresponding curves for the partially relaxed model (C—C bond lengthening included) are indistinguishable from the FR ones on the figure scale.

Table 2 MP2/6-311G(3df,2p) optimized geometries of ethane, disilane, and digermane conformers

X—X bond lengthab

X—H bond lengthab

<HXHa,b

Ethane

S

1.523

1.089

107.6

E

1.537

1.088

107.1

Disilane

S

2.344

1.479

108.7

E

2.358

1.479

108.5

Digermane

S

2.444

1.539

108.7

E

2.454

1.539

108.5

The conclusion is that ethane adopts the eclipsed conformation when the vicinal charge transfers are absent, and no inversion of structure occurs on the removal of Coulombic and exchange repulsions. This shows decisively that it is hyperconjugation, not repulsive forces, that determines the staggered equilibrium structure of ethane. A central point in eliminating repulsive interactions as a factor in determining the staggered structure is the necessity to take into account skeletal expansion, explicitly C—C bond lengthening (i.e., internal rotation is not pure rotation).

DISILANE AND DIGERMANE

The interest in silicon and germanium group IV analogs of ethane, disilane (SiH3SiH3), and digermane (GeH3GeH3) stems from a combination of two factors. One is the increased separation of the rotating groups (the central Si—Si and Ge—Ge bonds are 0.84 and 0.92 A, respectively, longer than in ethane; Table 2) and the other is the X-H (X=Si and Ge, respectively) polarity reversal from ethane. These changes are expected to cause hyperconju-gative interactions between the XH3 groups to become small, if not negligible. An analysis of these ethane congener interactions allows a deepening of the hyper-conjugative conformational preference conclusion drawn for ethane itself. Although experiments have not established their equilibrium conformer structure (H atoms contribute little to electron diffraction patterns),[26] all calculations conclude that both digermane and disilane exhibit a staggered conformational preference. As expected from the hyperconjugative diminution, the rotational barriers are strongly reduced (Table 3).[27-32] As pointed out, these molecules can be thought of as stretched ethanes enriched by additional electrons.

Fig. 5 illustrates that hyperconjugative stabilization, the principal barrier forming interaction in ethane, falls to a small fraction of the ethane value (Table 3), as seen from the related reduced overlap between the a-a* hypercon-jugating orbitals. The absence of significant backside lobe overlap with the middle lobe of the antibond is particularly conspicuous. Is the barrier attenuation primarily because of the larger Si—Si and Ge—Ge bond lengths, or because of the X-H polarity reversal? That the attenuation is mostly because of the larger bond lengths can be seen from the barrier energies in two phantom molecules created by expanding ethane to the more open structures of disilane and digermane, respectively, without any electron configuration change (Table 4). These phantom molecules have C—H bonds instead of the Si-H and Ge-H ones in the real molecules. The calculated barrier energies are reduced to even lower values than those found for real disilane and digermane.[31,32]

The effect of hyperconjugation alone is sufficient to keep disilane from exhibiting free rotation (Table 2).[31] However, the 0.3-kcal/mol hyperconjugation energy, by itself, is insufficient to prevent digermane from going into free rotation. Nevertheless, the role that hyperconjugation plays in rigidizing the digermane equilibrium conformer is shown clearly by the internal rotation potential curves with and without this interaction given in Fig. 6. The 0.3-kcal/mol delocalization energy is substantially smaller than the Boltzmann energy at 300 K. The total energy is actually only greater than the Boltzmann energy when the torsional angle exceeds 40°. Thus digermane is expected to exhibit large amplitude (~ 80°) torsional oscillations at room temperature. If vicinal hyperconjugation is removed (dashed curve in Fig. 6), digermane is predicted to go into free rotation at this temperature.

Table 3 Internal rotation barriers and delocaliza-tion energy changes in ethane,[31] disilane,[31] and digermane[32] (kcal/mol)a

tmp1C-177 tmp1C-178 tmp1C-179

Ethane

3.03

6.61

Disilane

1.03

0.68

Digermane

0.74

0.32

 

C—H/C—H*, Si—H/Si—H*, and Ge—H/Ge—H* bond/antibond overlaps for the anti (staggered conformer) and syn (eclipsed conformer) arrangements in ethane (a), disilane (b), and digermane (c).

Fig. 5 C—H/C—H*, Si—H/Si—H*, and Ge—H/Ge—H* bond/antibond overlaps for the anti (staggered conformer) and syn (eclipsed conformer) arrangements in ethane (a), disilane (b), and digermane (c).

Table 4 Barrier energies for ethane and phantom molecules (kcal/mol)a’b'c

A^barrier

Ethane

3.17

(ET)ds

0.28

(ET)dg

0.23

CONCLUSION

The weight of evidence (particularly direct structural optimizations with missing interactions) indicates that vicinal hyperconjugation controls the staggered structure of ethane. A central point in eliminating repulsive interactions as a factor in determining the staggered structure is the effect of the C—C bond lengthening that accompanies internal rotation (i.e., internal rotation in ethane is not pure rotation). The group IV congeners, disilane and diger-mane, show greatly attenuated hyperconjugative interactions. In digermane, hyperconjugation stabilization is predicted to be so weakened that it is insufficient to give much rigidity to the molecule at room temperature.

Torsional potential curves for real digermane (full curve) and hypothetical digermane with hyperconjugation absent (dashed curve). Zero degrees denotes the staggered conformer; ±60° denotes the eclipsed conformer.

Fig. 6 Torsional potential curves for real digermane (full curve) and hypothetical digermane with hyperconjugation absent (dashed curve). Zero degrees denotes the staggered conformer; ±60° denotes the eclipsed conformer.

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