  (Abridged) The chemical composition of planetary atmospheres has long been
thought to store information regarding where and when a planet accretes its
material. Predicting this chemical composition theoretically is a crucial step
in linking observational studies to the underlying physics that govern planet
formation. As a follow-up to a study of hot Jupiters in our previous work, we
present a population of warm Jupiters (semi-major axis between 0.5-4 AU)
extracted from the same planetesimal formation population synthesis model as
used in our previous work. We compute the astrochemical evolution of the
protoplanetary disks included in this population to predict the
carbon-to-oxygen (C/O) and nitrogen-to-oxygen (N/O) ratio evolution of the disk
gas, ice, and refractory sources, the accretion of which greatly impacts the
resulting C/O and N/O in the atmosphere of giant planets. We confirm that the
main sequence (between accreted solid mass and atmospheric C/O) we found
previously is largely reproduced by the presented population of synthetic warm
Jupiters. And as a result, the majority of the population fall along the
empirically derived mass-metallicity relation when the natal disk has solar or
lower metallicity. Planets forming from disks with high metallicity ([Fe/H] $>$
0.1) result in more scatter in chemical properties which could explain some of
the scatter found in the mass-metallicity relation. Combining predicted C/O and
N/O ratios shows that Jupiter does not fall among our population of synthetic
planets, suggesting that it likely did not form in the inner 5 AU of the solar
system before proceeding into a Grand Tack. This result is consistent with
recent analysis of the chemical composition of Jupiter's atmosphere which
suggests that it accreted most of its heavy element abundance farther than tens
of AU away from the Sun.
