In reviewing the literature, we were only able to locate two experimental gas-phase studies on Hf(CO)n systems, which are related to infrared spectra analysis. Work by Zhou and Andrews provides evidence for the existence of all Hf(CO)1-4 and Hf(CO)2 -species. They also report the stretching frequency of CO of HfCO to be 1869 cm -1 (obtained from laser-ablated hafnium in solid neon) and a trend of greater d → π* back-donation going from TiCO to HfCO. This trend is consistent with the spectroscopic study of M(CO)6-8 + (M = Ti-Hf) by Brathwaite and Duncan. Computational modelling is vital in understanding the chemistry of systems that are challenging to handle under laboratory conditions. For example, Hf compounds are known to be highly toxic, motivating theoretical studies. 17, 18 However, selection of appropriate computational tools is crucial to make accurate predictions. In general, unsaturated TM(CO)n complexes have several close-lying electronic states, which make them challenging to model accurately with computation. High-level multi-reference theories provide a platform for predictions of systems with many low-lying electronic states. The gold-standard coupled cluster level of theory can also deliver predictions with higher precision relative to most computationally tractable MR methods as long as the targeted states are sufficiently singlereference in nature. However, both multi-reference and coupled cluster levels of theory require a great deal of quantum chemical expertise and computing power, which makes them less widely used, especially in larger systems. On the other hand, density functional theory (DFT) is widely popular due to its black box nature and reasonable accuracy at low computational cost. However, a practitioner must select an appropriate exchange-correlation functional because the best-performing functional depends on the system and property. In this work, we probe the interactions between between Hf and CO with high-level multireference configuration interaction theory (MRCI), coupled cluster singles doubles and perturbative triples [CCSD(T)], as well as with DFT. Specifically, numerous low-lying electronic states of HfCO are analysed with MRCI and their potential energy profiles, equilibrium electronic configurations, corresponding chemical bonding patterns, and various energy-related properties are reported. The single-reference electronic states are investigated with CCSD(T) and used as benchmarks for evaluating DFT errors associated with 23 exchange-correlation functionals that span multiple rungs of "Jacob's ladder". We assess whether performance trends are transferable to solid-state systems by studying the chemisorption of one CO on a Hf surface with a set of DFT functionals.