  We present a detailed observational and modeling study of the hot core VLA 3
in the high-mass star-forming region AFGL 2591, which is a target region of the
NOrthern Extended Millimeter Array (NOEMA) large program CORE. Using NOEMA
observations at 1.37 mm with an angular resolution of ~0."42 (1 400 au at 3.33
kpc), we derived the physical and chemical structure of the source. We modeled
the observed molecular abundances with the chemical evolution code MUSCLE
(MUlti Stage ChemicaL codE). Results. With the kinetic temperature tracers
CH3CN and H2CO we observe a temperature distribution with a power-law index of
q = 0.41+-0.08. Using the visibilities of the continuum emission we derive a
density structure with a power-law index of p = 1.7+-0.1. The hot core spectra
reveal high molecular abundances and a rich diversity in complex molecules. The
majority of the molecules have an asymmetric spatial distribution around the
forming protostar(s), which indicates a complex physical structure on scales <
1 400 au. Using MUSCLE, we are able to explain the observed molecular abundance
of 10 out of 14 modeled species at an estimated hot core chemical age of ~21
100 years. In contrast to the observational analysis, our chemical modeling
predicts a lower density power-law index of p < 1.4. Reasons for this
discrepancy are discussed. Conclusions. Combining high spatial resolution
observations with detailed chemical modeling allows us to derive a concise
picture of the physical and chemical structure of the famous AFGL 2591 hot
core. The next steps are to conduct a similar analysis for the whole CORE
sample, and then use this analysis to constrain the chemical diversity in
high-mass star formation to a much greater depth.
