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.