  Recent astronomical observations have shown that interstellar complex organic
molecules (COMs) exist even in cold environments ($\sim$10 K), while various
interstellar COMs have conventionally been detected in the hot gas ($\gtrsim$
100 K) in the vicinity of high-mass and low-mass protostars. However, the
formation pathway of each interstellar COM remains largely unclear. In this
work, we demonstrate that an automated reaction path search based on transition
state theory, which does not require predetermined pathways, is helpful for
investigating the formation pathways of interstellar COMs in the gas phase. The
exhaustive search within electronic ground states helps elucidate the complex
chemical formation pathways of COMs at low temperatures. Here we examine the
formation pathways of dimethyl ether (CH$_3$OCH$_3$) and methyl formate
(HCOOCH$_3$), which are often detected in the cold and hot gas of star-forming
regions. We have identified a barrierless and exothermic formation path of
CH$_3$OCH$_3$ by reaction between neutral species; CH$_3$O + CH$_3$
$\rightarrow$ H$_2$CO $\cdots$ CH$_4$ $\rightarrow$ CH$_3$OCH$_3$ is the most
efficient path in the large chemical network constructed by our automated
reaction path search and is comparable with previous studies. For HCOOCH$_3$,
we obtain complex pathways initiated from reactions between neutral species;
HCOO and CH$_3$ generate HCOOCH$_3$ and its isomers without external energy.
However, we also identified the competing reaction branches producing CO$_2$ +
CH$_4$ and CH$_3$COOH, which would be more efficient than the formation of
HCOOCH$_3$. Then the gas-phase formation of HCOOCH$_3$ through reactions
between neutral species would not be efficient compared to the CH3OCH$_3$
formation.
