[i,j] notation is the shorthand Organic Chemistry uses to name a sigmatropic rearrangement by the positions of the atoms involved in the shift. It helps you track how a sigma bond migrates across a conjugated pi system.
[i,j] notation is the naming system Organic Chemistry uses for sigmatropic rearrangements. The two numbers tell you how far a group or sigma bond moves through a conjugated pi system, so you can describe the reaction without redrawing the whole mechanism every time.
The first number, i, and the second number, j, mark the positions connected by the migration. In a [3,3] rearrangement, for example, the bond shifts across a six-atom framework in a way that changes which atoms are bonded, but the reaction still happens in one concerted step. That is why you often see [3,3] attached to named reactions like the Cope and Claisen rearrangements.
The notation is not random numbering. It is tied to the carbon or atom count in the pathway being reorganized, and it tells you something about the reaction geometry. Once you know the notation, you can start predicting whether a rearrangement is allowed under orbital symmetry rules and what the product connectivity should look like.
A big idea here is that [i,j] notation describes movement through a pi system, not just movement in space. The migrating group does not drift around in separate steps. Instead, bonds break and form together, so the pattern of electrons has to fit a concerted mechanism. That is why the notation shows up right alongside Woodward-Hoffmann rules, Hückel topology, and orbital symmetry.
A common way to read it is: identify the bond that migrates, count the atoms between the original and new position, then label the shift with the two numbers. If you can do that, you can turn a complicated line drawing into a clean reaction name and usually predict the product more confidently.
[i,j] notation gives you a fast way to classify sigmatropic rearrangements instead of treating every reaction like a new puzzle. In Organic Chemistry, that matters because many rearrangements look messy at first, but the notation tells you the underlying pattern right away.
It also helps you connect mechanism to outcome. A [3,3] shift, for instance, signals a very specific kind of bond reorganization, which means you can check whether the process is concerted, whether the geometry makes sense, and whether the product keeps the right stereochemical relationship. That is especially useful when you are comparing reactions that seem similar on paper but behave differently because the electron flow is different.
The notation becomes even more useful when you study named reactions and exam-style mechanism questions. Instead of memorizing only the final product, you can ask, “What moved, over how many atoms, and does the orbital alignment work?” That is the kind of thinking professors look for when they ask you to justify a rearrangement, not just draw it.
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view galleryConcerted Mechanism
[i,j] notation usually shows up in reactions that happen in one step, not through a carbocation or radical intermediate. If you can recognize that a rearrangement is concerted, the notation starts to make sense as a summary of the whole bond shift. It tells you the reaction path is happening all at once, which affects stereochemistry and product prediction.
Orbital Symmetry
The numbers in [i,j] notation are only part of the story. The rearrangement also has to satisfy orbital symmetry requirements, or the electron movement will not be allowed under the reaction conditions. That is why you use the notation together with orbital analysis, especially when deciding whether a thermal or photochemical path is favorable.
Woodward-Hoffmann Rules
Woodward-Hoffmann rules help you decide whether a given [i,j] sigmatropic shift is allowed. The notation names the rearrangement, while the rules explain whether the electron flow can happen with the correct symmetry. When a problem asks you to predict products, both pieces work together.
Hückel Topology
Hückel topology comes up when you classify the cyclic electron movement in a sigmatropic shift. A [i,j] label alone does not tell you if the reaction is allowed, but the topology of the electron loop does. That makes it a useful next step when you move from naming the rearrangement to analyzing its feasibility.
A mechanism question will often show a rearrangement and ask you to name it or predict the product. That is where [i,j] notation saves time: you identify which bond migrates, count the atom positions, and label the shift before you draw arrows or products. If the problem includes stereochemistry, use the notation as a clue that the reaction is concerted, so the relative placement of substituents may be preserved or reorganized in a specific way.
You may also see it in multiple-choice items that ask which sigmatropic shift matches a given structure change. The fastest move is to match the starting and ending positions of the migrating group, then check whether the bond network fits a [3,3] or similar pattern. On free-response work, you should use the notation to justify why a rearrangement is classified a certain way, not just to name the product.
[i,j] notation names a sigmatropic rearrangement by the positions involved in the bond migration.
The numbers help you see how a sigma bond shifts across a conjugated pi system in one concerted step.
A [3,3] rearrangement is a common example, especially in reactions like the Cope and Claisen rearrangements.
The notation works best when you pair it with orbital symmetry and Woodward-Hoffmann rules.
If you can trace the migrating bond from start to finish, you can usually read the notation and predict the product pattern.
[i,j] notation is the shorthand used to describe a sigmatropic rearrangement by the positions of the atoms involved in the shift. It tells you how a sigma bond migrates through a pi system, which makes it easier to classify the reaction and predict the product. You will see it most often with concerted rearrangements.
A [3,3] notation means the rearrangement involves a bond shift across a six-atom framework in a way that connects positions labeled 3 and 3. In practice, it points you toward reactions like the Cope or Claisen rearrangement. The exact product still depends on the starting structure and orbital alignment.
No. In Organic Chemistry, [i,j] notation has nothing to do with data tables or arrays. It is a reaction label for sigmatropic rearrangements, where the numbers describe the positions of atoms involved in the bond migration.
First identify the sigma bond that moves, then count the atom positions from the starting point to the ending point. After that, check whether the reaction is concerted and whether the electron flow makes sense under orbital symmetry rules. That lets you name the rearrangement and draw the product more confidently.