  A solar-type system starts from an initial molecular core that acquires
organic complexity as it evolves. The so-called prestellar cores that can be
studied are rare, which has hampered our understanding of how organic chemistry
sets in and grows. Aims. We selected the best prestellar core targets from the
cold core catalogue that represent a diversity in terms of their environment to
explore their chemical complexity: 1390 (in the compressed shell of Lambda
Ori), 869 (in the MBM12 cloud), and 4149 (in the California nebula). We
obtained a spectral survey with the IRAM 30 m telescope in order to explore the
molecular complexity of the cores. We carried out a radiative transfer analysis
of the detected transitions in order to place some constraints on the physical
conditions of the cores and on the molecular column densities. We also used the
molecular ions in the survey to estimate the cosmic-ray ionisation rate and the
S/H initial elemental abundance using a gas-phase chemical model to reproduce
their abundances. We found large differences in the molecular complexity
(deuteration, complex organic molecules, sulphur, carbon chains, and ions) and
compared their chemical properties with a cold core and two prestellar cores.
The chemical diversity we found in the three cores seems to be correlated with
their chemical evolution: two of them are prestellar (1390 and 4149), and one
is in an earlier stage (869). The influence of the environment is likely
limited because cold cores are strongly shielded from their surroundings. The
high extinction prevents interstellar UV radiation from penetrating deeply into
the cores. Higher spatial resolution observations of the cores are therefore
needed to constrain the physical structure of the cores, as well as a
larger-scale distribution of molecular ions to understand the influence of the
environment on their molecular complexity.
