Molecular Geometry & Bonding
what the shape decides
Concept

Torsion — where it appears

The angle between two planes sharing a bond, which fixes how substituents on either end line up. Its energy is threefold for a single bond and is what selects a ring's conformer out of the family the bond angles allow.

Named by 6 essays across one field — each of them below, with the objects they name alongside it.

The twist the ring forces on the bond. For each ring size, the largest torsion about the double bond that the ring will close on — 180° being a flat trans arrangement and 90° being a π bond broken outright. The six-ring will not close at any torsion tested. The eight-ring reaches 139.3°, against 136° measured in trans-cyclooctene by diffraction: a model with bond lengths and bond angles in it and no energy anywhere agrees with the crystal to a few degrees.

The double bond a ring cannot hold

A trans double bond needs a ring of nine carbons to sit flat, and the eight-ring will hold one twisted by 40.7 degrees — against 136 degrees measured in trans-cyclooctene. The same eight-ring threshold, applied by counting ring sizes, sorts nine bridgehead alkenes correctly with no bridgehead anywhere in the argument.

shape · Strain Flat rings: the angles, the torsions and what is measured. For each ring from three to eight, held flat: its interior angle, how far that is from tetrahedral, the angle strain that follows, the torsional strain of having every bond eclipsed, and the measured strain energy. The five-ring is the row the essay is about — its angles are almost ideal and it is strained.

The strain that is not in the angles

Cyclopentane's flat bond angles are 108°, a degree and a half from tetrahedral, and its angle strain computed from a standard bending constant is 0.4 kJ mol⁻¹. Its measured strain is twenty-six. The missing sixty kilojoules are torsional — one ethane barrier for every bond in the ring, which no account built on bond angles mentions.

shape · Strain The same angles, the same torsions, and not the same molecule. twelve closed conformers of a ring of 10 at a bond angle of 111.5 degrees. Every one has exactly the same bond angles, so an account built from angles and torsions places them all on the horizontal axis alone. The vertical axis is the closest approach of two atoms four or more bonds apart, which no term in that account mentions: two of these differ by 0.08 kilojoules in torsional energy and by 0.75 ångström in how close they come.

The atoms that meet across a ring

Twelve closed conformers of a ten-membered ring at one bond angle, so every one has identical angle strain by construction. Two of them differ by 0.026 kilojoules a mole in torsional energy and by 0.80 ångström in how close two atoms on opposite sides of the ring come — 2.331 against 3.131, where two carbons are in contact at about 3.4. An account built from angles and torsions calls those two structures the same.

shape · Strain The 6-ring at 111.5°: the alternating form and what a search finds. The alternating ring — every atom displaced above or below the plane in turn — with its dihedral angles and its two strain terms, beside the lowest-torsion member a search constrained only by bond angles and closure returns. Both satisfy every geometric constraint; only one of them is staggered.

The explanation with the wrong sign

Two methyl groups on one carbon make a ring easier to close, by up to eleven thousand-fold, and the textbook reason is that they compress the ring's internal angle. Computed from a standard bending term, that compression helps a three-ring and a four-ring and hinders every ring from five up — predicting a slowing of 0.754-fold for the five-ring measured to speed up 250-fold. The account with the right sign is about rotations rather than angles, and it has a ceiling of 36.5 that the measurement is already above.

shape · Strain The two rows of a table, and the curve between them. The rotamer ceiling of a closure freezing 4 rotations, against how hard each of a stated number of them is to turn. The top curve is the free-rotor row and the right-hand end of the bottom curve is the absent-rotor row; everything else is what a real hindered tether does. The measured acceleration of 10-fold is drawn across it. It falls below that line when 3 of the 4 are hindered by 4.09 kJ/mol, or when 4 of the 4 are hindered by 2.70 kJ/mol.

The curve between two rows

A rotation a ring closure has to freeze was treated as free or as absent, and the two answers sat in adjacent rows of a table. A real hindered rotor is neither. The factor one rotor contributes runs from 3.316 to one along a curve nobody had drawn, and where it matters is between one and eight kilojoules a mole — which is a torsional barrier rather than a conformational preference.

shape · Strain The two sides of a verdict, with error bars. The computed ceiling for the six-membered closure — 10.9945 — with the band a gauche energy of 3.8 ± 0.4 kJ/mol puts on it, against the measured tenfold rate ratio with an assumed 20 per cent uncertainty. The two bands overlap over most of their length, and the nine per cent margin the verdict was decided by sits inside both of them.

A verdict inside its own error bar

The tightest comparison in the rotamer argument is a computed 10.99 against a measured 10 — a nine per cent margin, offered as a verdict. The computed side is built on one quoted energy known to ±0.4 kJ/mol, and that alone puts a band of twenty-three per cent on it. The verdict turns on four tenths of one standard deviation of a number nobody had put an error bar on.

shape · Strain

Named alongside it

The objects these essays reach for when they reach for this one.

Model limitBond angleConformationApproximationClosed formElastic energyLocal minimumMinimisationReference stateBoltzmann distributionClosureConformer

All concepts