We report chamber measurements of secondary organic aerosol (SOA) formation from isoprene photochemical oxidation, in which radical concentrations were systematically varied and the molecular composition of semi- to low-volatility gases and SOA were measured online. Using a detailed chemical kinetics box model, we find that to explain the behavior of low-volatility products and SOA mass yields relative to input H₂O₂ concentrations, the second-generation dihydroxy hydroperoxy peroxy radical (C₅H₁₁O₆·) must undergo an intramolecular H-shift with a net forward rate constant of order 0.1 s^-1 or higher. This finding is consistent with quantum chemical calculations that suggest a net forward rate constant of 0.3-0.9 s^-1. Furthermore, these calculations suggest that the dominant product of this isomerization is a dihydroxy hydroperoxy epoxide (C₅H₁₀O₅), which is expected to have a saturation vapor pressure ∼2 orders of magnitude higher, as determined by group-contribution calculations, than the dihydroxy dihydroperoxide, ISOP(OOH)₂(C₅H₁₂O₆), a major product of the peroxy radical reacting with HO₂. These results provide strong constraints on the likely volatility distribution of isoprene oxidation products under atmospheric conditions and, thus, on the importance of nonreactive gas-particle partitioning of isoprene oxidation products as an SOA source.