New insights into molecular structure

The two carbon saturated hydrocarbon, ethane, of chemical formula C{-2}H{-6} has two CH{-3} groups. This molecule has an equilibrium structure in which the CH{-3} groups are stacked over each other so that the hydrogens are separated at a maximum distance, although a single bond as existing in ethane can be rotated. This equilibrium state called the staggered conformation and is the most stable one.

The molecule has a least stable state called the eclipsed conformation in which the hydrogens come in close contact. Reason for the existence of staggered conformation is central to an understanding of the structure of all organic molecules. In a chemistry beginners' textbook, the answer to this question would be stated as "steric repulsion", meaning the repulsion of atoms or groups in close contact.

This hypothesis of steric repulsion is good to explain conformations of small molecules, but macromolecular conformations cannot be fully accounted for by this alone. One of the challenges before structural biologists is to understand how proteins fold quickly and correctly. The forces responsible for hindering rotations about a single bond are the important controlling factors of structure and dynamics of polymeric molecules, including proteins. Therefore, it is necessary to look back into the factors controlling C-C single bond rotations.

The simplest model one can choose for studying C-C single bond rotation is ethane, the molecule with which we began this note. The energy difference between staggered and eclipsed conformations of ethane is calculated to be around 3 kcal/mol. Here arises the question, what causes the internal energy to rise when a staggered conformation turns to eclipsed?

Recently, Pophristic and Goodman came forward with a new explanation for the question with the help of computational techniques and this work was published recently in Nature.

Pophristic and Goodman considered three factors, which are supposed to control the structural preference of ethane, "exchange, electrostatic and hyperconjugative interactions". Exchange interactions, which can act only in short-ranges, arise from Pauli's exclusion principle, one of the central concepts of molecular quantum mechanics which states that, "pairs of electrons cannot occupy the same spatial region".

Hyper conjugation involves charge transfer from an occupied to unoccupied orbital, leading to stabilisation of electrons via delocalisation, just means that there is more space for electrons to move so the system has less energy. The electrostatic term arises from the interactions between charged particles within the molecule. Hyper conjugation as well as the exchange interactions are quantum mechanical properties, while electrostatic interactions can be accounted for by classical Newtonian mechanics.

Conjugation is the energy stabilisation of a set of potentially mobile electrons separated by a single bond distance by delocalisation. The stabilisation of benzene can be attributed to the conjugative interaction between the electrons present on all the six carbon atoms (these are actually the electrons).

Hyperconjugation can be defined as the stabilisation of partially filled or vacant orbitals by overlap with a filled bonding orbital of the type. Here the interaction is not between the filled orbitals, unlike in the case of conjugation.

Pophristic and Goodman performed a series of calculations on different ethanes after eliminating one or other of the above- mentioned effects to find out what exactly leads ethane to the staggered conformation.

First they considered the steric factor which is the combined effect of exchange and electrostatic interactions. To find out the role of exchange interactions, they did calculations on real ethane and on a hypothetical ethane molecule in which no exchange interactions are present. They observed that the potential energy curves for both the ethanes look similar. Therefore, it is clear that exchange interaction does not have a major role in determining ethane's conformational preferences.

Next they looked into the effect of Coulombic interactions on the ethane structure. They have calculated electrostatic repulsion energy for three different models of ethane, which are

(a) rigid rotational (all skeletal rotations are frozen while rotation) (b) partially relaxed rotational (C-C lengthening is included) and (c) fully relaxed rotational (all skeletal rotations are included) models. The potential energy curves for both electron-electron and nuclear-nuclear repulsions of the rigid rotation mode show an increase as the molecule is approaching eclipsed conformation.

When they introduced the central bond flexibility as a part of C- C rotation, both the electronic and nuclear Coulomb repulsions got decreased. They concluded that the central bond stretching reduces the strain that is accumulated in the molecule by rotation alone, leading to a large decrease in electrostatic repulsion energies. It is sure that Coulombic interaction alone cannot result such a behaviour since in both the cases the electrostatic interactions are almost similar.

Finally they calculated the effect of hyper conjugation on the barrier of C-C bond rotation by examining the internal rotation induced change in nuclear-electron attraction (V{-n}{-e}), since V{-n}{-e} mostly originates from inherent electron transfers in hyper conjugative interactions. They found that the rotational freedom of the C-C bond will help in effective overlap of (C-H) and *(C-H) through the central C-C bond. This result shows importance of hyper conjugation on the structure of ethane.

In ethane there are two types of hyper conjugations, one is geminal (within in a methyl group) and the other is vicinal (between two methyl groups). Natural bond orbitals (NBO) analysis can provide a better understanding of hyper conjugation. Pophristic and Goodman performed NBO calculations by deleting different hyper conjugative interactions.

They found that when they are deleting the vicinal hyper conjugation, the ethane prefers eclipsed conformation, even though there exists Coulombic interactions. They concluded that it is the hyperconjugation, not steric repulsion that makes ethane staggered.

This result is surely a landmark in the history of structural chemistry. It may, however, be pointed out that the importance of orbital interactions in describing the molecular structure was recognised long ago (F. A. Cary and R. J. Sundberg, Advanced Organic Chemistry, Plenum Press, New York, 1984, page 54).

T. K. Manoj Kumar & T. Pradeep

IIT, Chennai

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