High molecular weight "ROOR'" dimers, likely formed in the gas phase through self- and cross-reactions of complex peroxy radicals (RO2), have been suggested to play a key role in forming ultrafine aerosol particles in the atmosphere. However, the molecular-level reaction mechanism producing these dimers remains unknown. Using multireference quantum chemical methods, we explore one potentially competitive pathway for ROOR' production, involving the initial formation of triplet alkoxy radical (RO) pairs, followed by extremely rapid intersystem crossings (ISC) to the singlet surface, permitting subsequent recombination to ROOR'. Using CH3OO + CH3OO as a model system, we show that the initial steps of this reaction mechanism are likely to be very fast, as the transition states for both the formation and the decomposition of the CH3O4CH3 tetroxide intermediate are far below the reactants in energy. Next, we compute ISC rates for seven different atmospherically relevant 3(RO···R'O) complexes. The ISC rates vary significantly depending on the conformation of the complex and also exhibit strong stereoselectivity. Furthermore, the fastest ISC process is usually not between the lowest-energy triplet and singlet states but between the triplet ground state and an exited singlet state. For each studied (RO···R'O) system, at least one low-energy conformer with an ISC rate above 108 s-1 can be found. This demonstrates that gas-phase dimer formation in the atmosphere very likely involves ISCs originating in relativistic quantum mechanics.