Aims: Interstellar molecules form early in the evolutionary sequence of interstellar material that eventually forms stars and planets. To understand this evolutionary sequence, it is important to characterize the chemical composition of its first steps. Methods: In this paper, we present the result of a 2 and 3 mm survey of five cold clumps identified by the Planck mission. We carried out a radiative transfer analysis on the detected lines in order to put some constraints on the physical conditions within the cores and on the molecular column densities. We also performed chemical models to reproduce the observed abundances in each source using the gas-grain model Nautilus. Results: Twelve molecules were detected: H2CO, CS, SO, NO, HNO, HCO+, HCN, HNC, CN, CCH, CH3OH, and CO. Here, CCH is the only carbon chain we detected in two sources. Radiative transfer analyses of HCN, SO, CS, and CO were performed to constrain the physical conditions of each cloud with limited success. The sources have a density larger than $10^4$ cm$^{-3}$ and a temperature lower than 15 K. The derived species column densities are not very sensitive to the uncertainties in the physical conditions, within a factor of 2. The different sources seem to present significant chemical differences with species abundances spreading over one order of magnitude. The chemical composition of these clumps is poorer than the one of Taurus Molecular Cloud 1 Cyanopolyyne Peak (TMC-1 CP) cold core. Our chemical model reproduces the observational abundances and upper limits for 79 to 83% of the species in our sources. The best times for our sources seem to be smaller than those of TMC-1, indicating that our sources may be less evolved and explaining the smaller abundances and the numerous non-detections. Also, CS and HCN are always overestimated by our models.
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