  A prevailing theory for the interstellar production of complex organic
molecules (COMs) involves formation on warm dust-grain surfaces, via the
diffusion and reaction of radicals produced through grain-surface
photodissociation of stable molecules. However, some gas-phase O-bearing COMs,
notably acetaldehyde(CH$_3$CHO), methyl formate(CH$_3$OCHO), and dimethyl
ether(CH$_3$OCH$_3$), are now observed at very low temperatures, challenging
the warm scenario. Here, we introduce a selection of new non-diffusive
mechanisms into an astrochemical model, to account for the failure of the
standard diffusive picture and to provide a more generalized scenario of COM
formation on interstellar grains. New generic rate formulations are provided
for cases where: (i) radicals are formed by reactions occurring close to
another reactant, producing an immediate follow-on reaction; (ii) radicals are
formed in an excited state, allowing them to overcome activation barriers to
react with nearby stable molecules; (iii) radicals are formed through
photo-dissociation close to a reaction partner, followed by immediate reaction.
Each process occurs without the diffusion of large radicals. The new mechanisms
significantly enhance cold COM abundances, successfully reproducing key
observational results for prestellar core L1544. H-abstraction from
grain-surface COMs, followed by recombination, plays a crucial role in
amplifying chemical desorption into the gas phase. The UV-induced chemistry
produces significant COM abundances in the bulk ices, which are retained on the
grains and may persist to later stages. O$_2$ is also formed strongly in the
mantle though photolysis, suggesting cometary O$_2$ could indeed be
interstellar.
