Thermally activated delayed fluorescence (TADF) is a current promising route for generating highly efficient light-emitting devices. However, the design process of new chromophores is hampered by the complicated underlying photophysics that requires a number of different pathways to be optimised simultaneously. In this work, four closely related donor-pi-acceptor-pi-donor systems have been investigated, two of which were synthesised previously, with the aim of elucidating their varying effectiveness for TADF. We, first, outline that neither the frontier orbitals nor the singlet-triplet gaps are sufficient in discriminating between the molecules. Subsequently, a detailed analysis of the excited states, performed at a correlated ab initio level, is shown highlighting the presence of a number of closely spaced singlet and triplet states of varying character. Five density functionals are benchmarked against this reference revealing dramatic changes in, both, excited state energies and wavefunctions following variations in the amount of Hartree-Fock exchange included. Excited-state minima are optimised in solution showing the crucial role of structural variations for stabilising locally excited and CT states and of symmetry breaking for producing a strongly emissive S1 state. More generally, this work shows how a detailed analysis of excited-state wavefunctions can provide critical new insight into excited-state electronic structure, helping to reveal the photophysics of existing push-pull chromophores and ultimately guiding the design of new ones.