  Despite its relevance for chemistry, the electronic structure of free
carbenes throughout chemical space has not yet been studied in a systematic
manner. We explore a large and systematic carbene chemical space consisting of
eight thousand diverse and common carbene scaffolds in their singlet and
triplet state computed at controlled accuracy (higher order multireference
level of theory) and with verified carbene character in the electronic
structure. Originating in strong electron correlation, a hard upper limit for
the singlet-triplet gap is found to emerge at around 30 kcal/mol for all the
carbene classes in this chemical space. We also observe large vertical and
adiabatic spin gap ranges within many carbene classes ($>$100 and $>$60
kcal/mol, respectively), and we report novel relationships between
compositional, structural, and electronic degrees of freedom. Our QMspin data
base includes numerical results for $\approx$13'000 MRCI calculations on
randomly selected carbene scaffolds.
