Q1(d). Thermal [1,3]- and [1,5]-hydrogen shifts

Reading of the question: the product of (i) is printed as CH₂=CH-CD₂ with an H on the last carbon, i.e. CH₂=CH-CHD₂.

Introduction. A thermal sigmatropic shift of hydrogen is analysed as a hydrogen atom (1s orbital) moving across the HOMO of the radical left behind. H has only one lobe, so it can only move suprafacially (on one face); an antarafacial path for H across a short chain is geometrically impossible. Woodward–Hoffmann: a thermal suprafacial [1,j]-H shift is allowed when j+1 = 4n+2.

Figure: Shaded and open lobes are opposite phases. H bridges the two ends on the top face only.

(i) [1,3]-H shift in 1,1-dideuteriopropene: slow

1. H moves from C-3 (CH₃) to C-1 (CD₂) across a three-carbon allyl unit: a [1,3] shift, 4 electrons (one σ bond + one π bond).
2. The HOMO of the allyl radical, ψ₂, has a node at C-2 and opposite phases at C-1 and C-3 on the same face. A suprafacial shift would need H to bond to both ends with the same lobe: symmetry-forbidden.
3. The allowed path, antarafacial, would need H to reach from the top face of C-3 to the bottom face of C-1: impossible for a three-atom chain.
4. So the thermal reaction is very slow; the label scrambles only at high temperature by non-concerted (radical) routes, or under irradiation (photochemical [1,3] shifts are suprafacially allowed).

(ii) [1,5]-H shift in 7-deuteriocycloheptatriene: ready

1. The C-7 hydrogen moves to C-4, five atoms away round the triene (C7→C1→C2→C3→C4): a [1,5] shift, 6 electrons. C-4 becomes the new CH₂; C-7 becomes sp² and keeps D, as printed.
2. The pentadienyl HOMO, ψ₃, has the same phase at C-1 and C-5 on the same face, so a suprafacial shift is thermally allowed (aromatic, six-electron Hückel transition state).
3. The ring holds the two termini close; the shift goes at moderate temperatures (around 100°C) and repeated shifts walk the label round the ring.
4. H rather than D migrates in the printed product, as the primary kinetic isotope effect (C–H is easier to break than C–D) predicts.

Conclusion. (i) The [1,3]-H shift is suprafacially forbidden and antarafacially impossible: it proceeds slowly. (ii) The [1,5]-H shift is suprafacially allowed (six electrons): it proceeds readily.

Application. Thermal [1,5]-H shifts scramble substituents in cyclopentadienes and cycloheptatrienes and are the step that converts previtamin D into vitamin D (an antarafacial [1,7]-H shift in that open chain).