The computationally assisted, accelerated design of inorganic functional materials often relies on the ability of a given electronic structure method to return the correct electronic ground state of the material in question. Outlining difficulties with current density functionals and wave function-based approaches, we highlight why double hybrid density functionals represent promising candidates for this purpose. In turn, we show that PBE0-DH (and PBE-QIDH) offers a significant improvement over its hybrid parent functional PBE0 [as well as B3LYP* and coupled cluster singles and doubles with perturbative triples (CCSD(T))] when computing spin-state splitting energies, using high-level diffusion Monte Carlo calculations as a reference. We refer to the opposing influence of Hartree-Fock (HF) exchange and MP2, which permits higher levels of HF exchange and a concomitant reduction in electronic density error, as the reason for the improved performance of double-hybrid functionals relative to hybrid functionals. Additionally, using 16 transition metal (Fe and Co) complexes, we show that low-spin states are stabilised by increasing contributions from MP2 within the double hybrid formulation. Furthermore, this stabilisation effect is more prominent for high field strength ligands than low field strength ligands.