Cyclohexane conformation

A cyclohexane conformation is any of several three-dimensional shapes that a cyclohexane molecule can assume while maintaining the integrity of its chemical bonds. A cyclohexane conformation is any of several three-dimensional shapes that a cyclohexane molecule can assume while maintaining the integrity of its chemical bonds. The internal angles of a flat regular hexagon are 120°, while the preferred angle between successive bonds in a carbon chain is about 109.5°, the tetrahedral angle. Therefore, the cyclohexane ring tends to assume certain non-planar (warped) conformations, which have all angles closer to 109.5° and therefore a lower strain energy than the flat hexagonal shape. The most important shapes are called chair, half-chair, boat, and twist-boat. The molecule can easily switch between these conformations, and only two of them—chair and twist-boat—can be isolated in pure form. Cyclohexane conformations have been extensively studied in organic chemistry because they are the classical example of conformational isomerism and have noticeable influence on the physical and chemical properties of cyclohexane. In 1890, Hermann Sachse, a 28-year-old assistant in Berlin, published instructions for folding a piece of paper to represent two forms of cyclohexane he called symmetrical and unsymmetrical (what we would now call chair and boat). He clearly understood that these forms had two positions for the hydrogen atoms (again, to use modern terminology, axial and equatorial), that two chairs would probably interconvert, and even how certain substituents might favor one of the chair forms. Because he expressed all this in mathematical language, few chemists of the time understood his arguments. He had several attempts at publishing these ideas, but none succeeded in capturing the imagination of chemists. His death in 1893 at the age of 31 meant his ideas sank into obscurity. It was only in 1918 when Ernst Mohr, based on the molecular structure of diamond that had recently been solved using the then very new technique of x-ray crystallography, was able to successfully argue that Sachse's chair was the pivotal motif. Derek Barton and Odd Hassel shared the 1969 Nobel Prize for work on the conformations of cyclohexane and various other molecules. The carbon-carbon bonds along the cyclohexane ring are sp³ hybrid orbitals, which have tetrahedral symmetry. Therefore, the angles between bonds of a tetravalent carbon atom have a preferred value θ ≈ 109.5°. The bonds also have a fairly fixed bond length λ. On the other hand, adjacent carbon atoms are free to rotate about the axis of the bond. Therefore, a ring that is warped so that the bond lengths and angles are close to those ideal values will have less strain energy than a flat ring with 120° angles.For each particular conformation of the carbon ring, the directions of the 12 carbon-hydrogen bonds (and therefore the positions of the hydrogen atoms) are fixed. There are exactly eight warped polygons with six distinguished corners that have all internal angles equal to θ and all sides equal to λ. They comprise two ideal chair conformations, where the carbons alternately lie above and below the mean ring plane; and six ideal boat conformations, where two opposite carbons lie above the mean plane, and the other four lie below it. In theory, a molecule with any of those ring conformations would be free of angle strain. However, due to interactions between the hydrogen atoms, the angles and bond lengths of the actual chair forms are slightly different from the nominal values. For the same reasons, the actual boat forms have slightly higher energy than the chair forms. Indeed, the boat forms are unstable, and deform spontaneously to twist-boat conformations that are local minima of the total energy, and therefore stable. Each of the stable ring conformations can be transformed into any other without breaking the ring. However, such transformations must go through other states with stressed rings. In particular, they must go through unstable states where four successive carbon atoms lie on the same plane. These shapes are called half-chair conformations. In 2011, Donna Nelson and Christopher Brammer surveyed comprehensive undergraduate organic chemistry textbooks in use at that time, in order to determine and evaluate consistency among the textbooks and with research literature. They recommended changes in introductory organic chemistrytexts. To remedy inconsistencies in nomenclature, they proposed using 'chair, half-chair,twist-boat, and boat' to name cyclohexane conformers. Additionally, for clarity in teaching the half-chair conformation, they recommended the four coplanar carbon structure over the five coplanar carbon form. The two chair conformations have the lowest total energy, and are therefore the most stable, and have D3d symmetry. In the basic chair conformation, the carbons C1 through C6 alternate between two parallel planes, one with C1, C3 and C5, the other with C2, C4, and C6. The molecule has a symmetry axis perpendicular to these two planes, and is congruent to itself after a rotation of 120° about that axis. The two chair conformations have the same shape; one is congruent to the other after 60° rotation about that axis, or after being mirrored across the mean plane. The perpendicular projection of the ring onto its mean plane is a regular hexagon. All C-C bonds are tilted relative to the mean plane, but opposite bonds (such as C1-C2 and C4-C5) are parallel to each other. As a consequence of the ring warping, six of the 12 carbon-hydrogen bonds end up almost perpendicular to the mean plane and almost parallel to the symmetry axis, with alternating directions, and are said to be axial. The other six C-H bonds lie almost parallel to the mean plane, and are said to be equatorial. The precise angles are such that the two C-H bonds in each carbon, one axial and one equatorial, point in opposite senses relative to the symmetry axis. Thus, in a chair conformation, there are three C-H bonds of each kind — axial 'up', axial 'down', equatorial 'up', and equatorial 'down'; and each carbon has one 'up' and one 'down', and one axial and one equatorial. The hydrogens in successive carbons are thus staggered so that there is little torsional strain. This geometry is often preserved when the hydrogen atoms are replaced by halogens or other simple groups. The conversion from one chair shape to the other is called ring flipping or chair-flipping. Carbon-hydrogen bonds that are axial in one configuration become equatorial in the other, and vice versa; but their relative positions—their 'up' or 'down' character—remains the same. In cyclohexane, the two chair conformations have the same energy, and at 25 °C, 99.99% of all molecules in a cyclohexane solution will be in a chair conformation.