It has been 100 years since sweeping arrows, also known as curved arrows, first appeared in scientific literature. Since then, they’ve made friends and foes alike, going from novelty to organic chemistry staple. While arrows have long been little more than a shortcut unrelated to reality, evidence is beginning to emerge that the electron motion represented by the arrows has an actual, real basis in quantum mechanics.
Today, experienced chemists slide arrows around structures without much thought. The idea is that it allows creativity in rationalizing mechanisms and reactions. But with textbooks still not agreeing on the best way to draw curly arrows, they remain one of the concepts that chemistry students often struggle with.
What are curly arrows?
They’re a shortcut to rationalize what’s happening during a reaction. Mainly used in organic chemistry, they illustrate which bonds are broken and formed or how charges are distributed around molecules by resonance.
Perhaps counterintuitively, the arrows do not illustrate the movement of individual atoms, but rather the movement of electron density – indirectly implying how the atoms move. The arrow’s tail sits at the source of the electron density (like a bond or radical electron), while the arrowhead points to where that density is going. Double arrows are most common as they denote pairs of electrons such as σ or π bonds or lone pairs. Trajectories of individual electrons, for example in radicals, are indicated with single-barbed arrows.
Who developed the concept and why?
The first scientific papers on curly arrows were published in 1922 – one by Robert Robinson and William Kermack and another by Arthur Lapworth. Both used arrows to illustrate why reactions gave specific products rather than random permutations of the constituent atoms of the substrate.
In the 1920s, organic chemistry was still in its infancy. Researchers were just beginning to look into molecular shapes, double bonds, and mechanisms. Robinson and Kermack worked on the hottest topic of their time: aromatics and polyenes. They wanted to answer the question why only 1,2- and 1,4-dibromo products are formed from butadiene in a mixture with bromine and not a mixture of all possible regioisomers. The way electrons jump between adjacent carbon atoms determines which ones bond with the bromine atoms. The duo illustrated this idea by drawing curved arrows in a way that’s surprisingly close to how chemists still use them today.
Robinson’s friend Lapworth took a slightly different approach. He developed his concept of induced alternating polarities to explain why cyanide plus ketones form cyanohydrins. He had realized that the negatively charged cyanide would attack the carbonyl carbon atom because its neighboring oxygen gave it a positive polarity. The carbons next to the carbonyl carbon would then be negative and the nearest hydrogen positive – an alternating chain of polarities. In his work, Lapworth used arrows to shift so-called partial valences, which were thought to have three in covalent bonds. But partial valences eventually fell out of fashion, as did Lapworth’s curly arrows.
How did curly arrows become so popular?
Neither the work of Robinson and Kermack nor that of Lapworth mentions the arrow as a distinct concept. The arrows are almost incidental to understanding how chemical change occurs, which was the hot topic of the 1920s. In fact, it was so hotly debated that for some time the British Society of Chemical Industry refused to publish further correspondence on the subject.
But over the next few years, curly arrows and electron impact won many chemists over, including Robinson’s arch-rival Christopher Ingold. The two were lifelong enemies as both claimed credit for having laid the foundations of mechanistic thought.
In the mid-1920s, Ingold began using curly arrows to explain resonance effects, substitution, and elimination reactions. He did not give credit to Robinson and Kermack’s work – a fact about which Robinson remained bitter for the rest of his life. In 1931, Ingold published a study on directing groups in aromatic nitration with Lapworth. The paper does not contain curly arrows.
How did curly arrows evolve over the last century?
At first there was a bit of confusion as to whether arrows represent movement of single or paired electrons. But in 1926, Robinson used curved arrows in a way that would be very recognizable to chemists today. However, for the next few decades, the explanation of reaction mechanisms with the help of arrows remained in the specialist literature of experts. This began to change in the 1960s when curly arrows made their way into textbooks. Initially they were often used incorrectly or with great hesitation, with one book stating that the arrows in a nucleophilic substitution “tell nothing of the detailed mechanism, which can be very complex”.
The general notation for curly arrows has remained relatively unchanged over the last century: place the end of the arrow on the electron density source and the tip in the direction it’s going. But that’s often where the similarities end. Since there are no Iupac rules for curly arrows, almost every chemist has a slightly different approach to drawing curly arrows. Even student textbooks disagree on the best way to draw arrows. Can you dangle an arrowhead in empty space? Or how about locating the arrowtail on an atom instead of a bond?
Not surprisingly, many chemistry students find the arrows confusing and illogical. Curly arrows should be a tool that allows chemists to get creative with unknown reactions. But students often find them so inscrutable that they feel they have no choice but to memorize them.
Are there alternatives to the curly arrow?
Not really. However, there are ways to draw curly arrows that eliminate ambiguity. These alternatives have been shown to make them more useful for those learning about the concept.
One of the major drawbacks of traditional curly arrows, no matter how they are drawn, is that they say nothing about regioselectivity—the preference for one arrangement over another upon bond formation or bond breaking. For example, the addition of hydrogen bromide to propene follows Markovnikov’s rule, giving the most stable (secondary) carbocation intermediate and thus producing 2-bromopropane. The regiochemistry is indicated by the arrows for experienced chemists, but not for beginners.
In 2009, Suzanne Ruder and colleagues from Virginia Commonwealth University, USA, developed the bouncing arrows that solve this problem. Like conventional darts, their tail sits like a bond at the site of electron density. But with an added curlicue, the dart “bounces” off the atom to which the new bond is formed before heading to its target. Ruder suggests that this is particularly useful for representing regiochemistry in electrophilic additions, electrophilic aromatic substitutions, and carbocation rearrangements.
Another approach is the site-specific curly arrow, a development described in 2015 by the team led by Richard Vaughan Williams of the University of Idaho, USA. Williams credits this style of drawing arrows to Robert Woodward, who championed all types of curly arrows after using them in the 1940s. The arrow runs through the atom to which the new bond is made. This has been shown to work in reactions such as nucleophilic substitutions, electrophilic aromatic substitutions, cyclizations, rearrangements, and Grignard reactions.
Are curly arrows real?
Kind of. For a long time, they were nothing more than a mental shortcut with no basis for what’s really happening during a reaction. More recently, however, evidence has emerged that there is a direct link between quantum chemistry and the electron motion described by arrows.
In 2015, Gerald Knizia and co-workers at Penn State University, USA discovered that changes in intrinsic bond orbitals during nucleophilic attack or Claisen rearrangements correspond directly to what is indicated by curly arrows. And three years later, a team led by Timothy Schmidt from the Australian UNSW Sydney showed for the first time that wave functions calculated from initio in substitutions, additions and Diels-Alder reactions move exactly as curly arrows suggest.
Acknowledgments: Thank you to Kristy Turner for helpful discussions.