We present a study of the CO isotopologues and the high-density tracers H$_{2}$CO, HCO$^{+}$, and CS in Class 0/I proto-brown dwarfs (proto-BDs). We have used the IRAM 30m telescope to observe the $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1), C$^{17}$O (2-1), H$_{2}$CO (3-2), HCO$^{+}$ (3-2), and CS (5-4) lines in 7 proto-BDs. The hydrogen column density for the proto-BDs derived from the CO gas emission is $\sim$2-15 times lower than that derived from the dust continuum emission, indicating CO depletion from the gas-phase. The mean H$_{2}$CO ortho-to-para ratio is $\sim$3 for the proto-BDs and indicates gas-phase formation for H$_{2}$CO. We have investigated the correlations in the molecular abundances between the proto-BDs and protostars. Proto-BDs on average show a factor of $\sim$2 higher ortho-to-para H$_{2}$CO ratio than the protostars. Possible explanations include a difference in the H$_{2}$CO formation mechanism, spin-selective photo-dissociation, self-shielding effects, or different emitting regions for the ortho and para species. There is a tentative trend of a decline in the HCO$^{+}$ and H$_{2}$CO abundances with decreasing bolometric luminosity, while the CS and CO abundances show no particular difference between the proto-BDs and protostars. These trends reflect the scaled-down physical structures for the proto-BDs compared to protostars and differences in the peak emitting regions for these species. The C$^{17}$O isotopologue is detected in all of the proto-BDs as well as the more evolved Class Flat/Class II BDs in our sample, and can probe the quiescent gas at both early and late evolutionary stages.

Accepted in MNRAS. arXiv admin note: text overlap with arXiv:1809.10164