2-Cyanopyrimidine (2-CN-Pym), pyrimidine-2-carboximidamide (Pym-2-cia) and 2,4,6-tris(2-pyrimidyl)-1,3,5-triazine (TPymT), which are related to each other through chemical transformations from 2-CN-Pym through Pym-2-cia to TPymT, were computationally studied. The structures of all the reported compounds were optimized by the DFT calculations to reveal their fine features (electronic and optical). ADMET properties of 2-CN-Pym, Pym-2-cia and TPymT were also predicted using a set of online tools (SwissADME, BOILED-Egg and ProTox-II). Potential inhibition activity of 2-CN-Pym, Pym-2-cia and TPymT toward a series of the SARS-CoV-2 proteins was studied using a molecular docking approach, which revealed that for the applied proteins, both 2-CN-Pym and Pym-2-cia are the best inhibitors of RdRp-RNA, while TPymT exhibits the best activity toward nonstructural protein 14 (N7-MTase).