  Gas-phase methanol was recently detected in a protoplanetary disk for the
first time with ALMA. The peak abundance and distribution of methanol observed
in TW Hya differed from that predicted by chemical models. Here, the chemistry
of methanol gas and ice is calculated using a physical model tailored for TW
Hya with the aim to contrast the results with the recent detection in this
source. New pathways for the formation of larger complex molecules (e.g.,
ethylene glycol) are included in an updated chemical model, as well as the
fragmentation of methanol ice upon photodesorption. It is found that including
fragmentation upon photodesorption improves the agreement between the peak
abundance reached in the chemical models with that observed in TW Hya ($\sim
10^{-11}$ with respect to \ce{H2}); however, the model predicts that the peak
in emission resides a factor of $2-3$ farther out in the disk than the ALMA
images. Reasons for the persistent differences in the gas-phase methanol
distribution between models and the observations of TW Hya are discussed. These
include the location of the ice reservoir which may coincide with the compact
mm-dust disk ($\lesssim 60$~au) and sources of gas-phase methanol which have
not yet been considered in models. The possibility of detecting larger
molecules with ALMA is also explored. Calculations of the rotational spectra of
complex molecules other than methanol using a parametric model constrained by
the TW Hya observations suggest that the detection of individual emission lines
of complex molecules with ALMA remains challenging. However, the
signal-to-noise ratio can be enhanced via stacking of multiple transitions
which have similar upper energy levels.
