[1,5]H sigmatropic shift
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If one of the numbers in the square brackets is '1' it means the sigma bond stays attached to one atom. Hence we can expect this atom to physically 'shift' or migrate. The [1,5]H abbreviation tells you which atom is moving. We expect a six membered transition state ring (remember: just sum the numbers), with the H atom shifting to a new position. This is still a sigmatropic rearrangement since one sigma bond breaks and another forms. Other examples are [1,3]H and [1,7]H shifts.
Richard Windsor - Undergraduate Final Year Project 2008
Other pages of interest to do with Animated Molecular Orbitals are