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Dimethyl ether is one of the most abundant interstellar complex organicmolecules. Yet its formation route remains elusive. In this work, we haveperformed electronic structure and kinetics calculations to derive the ratecoefficients for two ion-molecule reactions recently proposed as a gas-phaseformation route of dimethyl ether in interstellar objects, namely CH$_3$OH +CH$_3$OH$_2^+$ $\rightarrow$ (CH$_3$)$_2$OH$^+$ + H$_2$O followed by(CH$_3$)$_2$OH$^+$ + NH$_3$ $\rightarrow$ CH$_3$OCH$_3$ + NH$_4^+$. Acomparison with previous experimental rate coefficients for the reactionCH$_3$OH + CH$_3$OH$_2^+$ sustains the accuracy of the present calculations andallow a more reliable extrapolation at the low temperatures of interest ininterstellar objects (10-100 K). The rate coefficient for the reaction(CH$_3$)$_2$OH$^+$ + NH$_3$ is, instead, provided for the first time ever. Therate coefficients derived in this work essentially confirm the prediction byTaquet et al. (2016) concerning dimethyl ether formation in hot cores/corinos.Nevertheless, this formation route cannot be efficient in cold objects (likeprestellar cores) where dimethyl ether is also detected, because ammonia has avery low abundance in those environments.

Interstellar dimethyl ether gas-phase formation: a quantum chemistry and kinetics study