The disc around the Herbig Ae/Be star HD 100546 is one of the most extensively studied discs in the southern sky. Although there is a wealth of information about its dust content and composition, not much is known about its gas and large scale kinematics. We detect and study the molecular gas in the disc at spatial resolution from 7.7 to 18.9 using the APEX telescope. The lines 12CO J=7-6, J=6-5, J=3-2, 13CO J=3-2 and [C I] 3P2-3P1 are observed, diagnostic of disc temperature, size, chemistry, and kinematics. We use parametric disc models that reproduce the low-J 12CO emission from Herbig~Ae stars and vary the basic disc parameters - temperature, mass and size. Using the molecular excitation and radiative transfer code RATRAN we fit the observed spectral line profiles. Our observations are consistent with more than 0.001 Msun of molecular gas in a disc of approximately 400 AU radius in Keplerian rotation around a 2.5 Msun star, seen at an inclination of 50 degrees. The detected 12CO lines are dominated by gas at 30-70~K. The non-detection of the [C I] line indicates excess ultraviolet emission above that of a B9 type model stellar atmosphere. Asymmetry in the 12CO line emission suggests that one side of the outer disc is colder by 10-20~K than the other, possibly due to a shadow by a warped geometry of the inner disc. Pointing offsets, foreground cloud absorption and asymmetry in the disc extent are excluded scenarios. Efficient heating of the outer disc ensures that low- and high-J 12CO lines are dominated by the outermost disc regions, indicating a 400 AU radius. The 12CO J=6--5 line arises from a disc layer higher above disc midplane, and warmer by 15-20~K than the layer emitting the J=3--2 line. The existing models of discs around Herbig Ae stars, assuming a B9.5 type model stellar atmosphere overproduce the [CI] 3P2--3P1 line intensity from HD 100546 by an order of magnitude.
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