Molecular Geometry & Bonding
what the shape decides
Concept

Ring current — where it appears

The circulation a magnetic field induces in a cyclic conjugated system, and the field that circulation produces in return. It is one of the two computable criteria for aromaticity, and in a fused system it does not divide between the rings the way a current divides between resistors.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

A length that keeps growing, and one that stops. The fitted decay length of the ring-current response, against the number of rings. The bare acene's runs 1.397, 1.669, 1.896, 2.104, 2.302 — up by a factor of 1.65 and still climbing — while its own gap falls from 0.590 to 0.1102. With a gap held open the same measurement gives 0.678, 0.642, 0.636, 0.636, 0.639, which has stopped moving by the third molecule. There is a magnetic reach, and an acene is too nearly gapless to have one.

A reach that has no length

A ring current's response to a neighbouring ring falls with distance, which invites asking for the length. Every acene computed gives a longer one — 1.397, 1.669, 1.896, 2.104, 2.302 rings — because the gap that would set the length is closing at the same time. Give the same molecule a gap that stays open and the number settles at 0.636 by the third one and does not move.

symmetry · Aromaticity 6 rings fused two ways. Two catacondensed chains of 6 hexagons: the linear one, where every fusion continues the line, and the angular one, where the fusions alternate. They have the same formula and the same number of bonds and they are not the same graph. Ring centres are numbered; in the linear molecule two rings k steps apart have centres 1.7321k units apart and in the angular one they do not, which is the whole reason this pair can be asked the question.

Neither of the two separations

A linear acene cannot pose the question, because the number of fusions between two rings and the distance between their centres are the same variable there. Bending the molecule pulls them apart — and the response follows neither. Two pairs of rings the same distance apart differ by two thirds, and the larger one is at the greater distance.

symmetry · Aromaticity The end pair against the deepest pair, at each separation. For each separation, the response of the pair that touches an end divided by the response of the pair at the same separation sitting deepest in the molecule. A straight chain is below one at every separation and a zigzag is above one at every separation, so the end effect has opposite signs on the two shapes. The third chain — two straight arms meeting at one angular ring — is above two at three separations and below one at the fourth, which is a third behaviour and not an intermediate one.

An end effect with two signs

Neither of two separations accounts for the scatter in a fused ring system's response, and the natural guess is the end: pairs with more molecule outboard should behave differently from pairs at an edge. They do. In a straight chain an end pair responds a third less than an interior one, in a zigzag a quarter more, and in a chain of two straight arms meeting at one angular ring the anomaly is in the middle.

symmetry · Aromaticity One turned fusion, moved along the chain. Chains of 9 rings differing in one integer: which fusion's direction is turned. Turned at the first or last fusion, that leaves one angular ring beside an end; anywhere between, it leaves two adjacent angular rings whose turns cancel. The widest ratio between two pairs at the same separation, against which fusion is turned. A straight chain gives 1.520 and every bent one gives more — from 3.052 to 4.600. The two ends of the curve are the one-ring members; every interior point is a two-ring step.

One integer, and everything it changes

Eight molecules with the same rings, the same carbons and the same graph distance between every pair, differing in which fusion's direction is turned — one angular ring when the turned fusion is at an end, two adjacent ones anywhere else. The scatter within a separation class runs from three to four and a half times, against a straight chain's one and a half — and the two ends of one molecule disagree by up to a factor of four.

symmetry · Aromaticity The one-bend family was one angular ring at its ends and two everywhere else. Filled circles: the worst spread within a separation class for the eight nine-ring chains built by bending one fusion, placed at the angular rings each actually has. The chains bent at the first and last fusions have one angular ring, next to an end; the six bent in between have two adjacent angular rings whose turns cancel. The lower line is a single angular ring at each interior position, running 3.05, 3.66, 3.46, 3.03, 3.46, 3.66, 3.05; the upper line is two adjacent ones, running 4.30, 4.60, 4.06, 4.06, 4.60, 4.30. Every published point lies on one line or the other.

The scatter counts angular rings

Eight nine-ring chains built by turning one fusion looked like one bend moved along a molecule. They were two families: one angular ring when the turned fusion is at an end, two adjacent angular rings everywhere else. Built from stated angular rings instead, twenty-seven chains show the ring-current scatter ignores which way a ring turns, does not grow with how many turn, and is mostly explained by one count per pair — each angular ring between two rings multiplies their response by 0.60, each one under them by 0.65.

bonding · Aromaticity

Named alongside it

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

AromaticityConventionDelocalisationHückel theoryLeast-squaresModel limitApproximationBand gapClosed formDegeneracyPerturbationReference state

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