In this work, three computational methods (Hatree-Fock (HF), Møller–Plesset 2 (MP2), and Density Functional Theory (DFT)) using a variety of basis sets are used to determine the atomic and molecular properties of dihydrothiouracil-based indenopyridopyrimidine (TUDHIPP) derivatives. Reactivity descriptors of this system, including chemical potential (µ), chemical hardness (η), electrophilicity (ω), condensed Fukui function and dual descriptors are calculated at B3LYP/6-311++ G (d,p) to identify reactivity changes of these molecules in both gas and aqueous phases. We determined the molecular electrostatic surface potential (MESP) to determine the most active site in these molecules. Molecular docking study of TUDHIPP with topoisomerase II α and β is performed, predicting binding sites and binding energies with amino acids of both proteins. Docking studies of TUDHIPP versus etoposide suggest their potential as antitumor candidates. We have applied Lipinski, Veber’s rules and analysis of the Golden triangle and structure activity/property relationship for a series of TUDHIPP derivatives indicate that the proposed compounds exhibit good oral bioavailability. The comparison of the drug likeness descriptors of TUDHIPP with those of etoposide, which is known to be an antitumor drug, indicates that TUDHIPP can be considered as an antitumor drug. The overall study indicates that TUDHIPP has comparable and even better descriptors than etoposide proposing that it can be as effective antitumor drug, especially 2H, 6H and 7H compounds.