Spin statistics greatly limits the efficiency of OLEDs, which might be largely improved upon conversion of triplet into singlet-excited (and thus light-emitting) states via a Thermally Activated Delayed Fluorescence (TADF) process. We theoretically investigate here the combination of some real-life donor (D) and acceptor (A) moieties with the connectivity D-A and D-A-D. We selected phenoxazine (PXZ) and phenylthiazine (PTZ) as electron-donating groups, and 2,5-diphenyl-1,3,4-oxadiazole (OXD), 3,4,5-triphenyl-4H-1,2,4-triazole (TAZ), and 2,5-diphenyl-1,3,4-thiadiazole (TDZ) as their electron-accepting partners. The systematic Tamm-Dancoff Approximation-Density Functional Theory calculations performed allowed us to calculate accurately not only the energy levels of low-lying singlet and triplet-excited states, but also to characterize their Charge-Transfer (CT) or Locally Excited (LE) nature, since the energy difference and the coupling between the 3 CT, 3 LE, and 1 CT states become key to understanding the molecular mechanism involved in this process. We have also studied the role played by the conformational landscape, arising from the thermally accessible range of D-A(-D) torsion angles, in the singlet-triplet energy gap as well as its influence on oscillator strengths. Overall, we rationalize the origin of the higher efficiencies found in real devices for D-A-D molecules, disclosing the underlying structure-property relationships and thus anticipating successful design strategies.