Red and near-infrared (NIR) thermally activated delayed fluorescence (TADF) molecules show excellent potential applications in organic light-emitting diodes (OLEDs). Due to the lack of systematic studies on the relationship between molecular structures and luminescence properties, both the species and amounts of red and NIR TADF molecules are far from meeting the requirements for practical applications. Herein, four new efficient molecules (DQCN-2spAs, TPCN-2spAs, DPCN-2spAs and BPCN-2spAs) are proposed and their photophysical properties are theoretically predicted based on first-principles calculations and thermal vibration correlation function (TVCF) theory. The results show that all molecules exhibit red or NIR emissions and they have fast radiative decay rates and reverse intersystem crossing (RISC) rates, and the excellent TADF luminescence properties are predicted. Moreover, based on spiro-acridine (spAs) as the donor unit, the combination with different acceptors can change the dihedral angle between the ground state and the excited state, the bending degree of the donor is positively correlated with the reorganization energy, and this feature can have a great influence on the non-radiative process. Furthermore, based on these theoretical predictions, experimental verifications are performed and the synthesized BPCN-2spAs is confirmed to be an efficient NIR TADF molecule. Thus, the relationships between basic molecular structures and photophysical properties are revealed, a feasible design strategy is applied and four promising red and NIR TADF molecules are proposed. All these results could contribute to the development of red and NIR TADF emitters and OLEDs.