Chalcones are polyphenolic secondary metabolites of plants, many of which have antioxidant activity. Herein, a set of 26 synthetic chalcone derivatives with alkyl substituted pyrazine heterocycle A and four types of the monophenolic ring B, were evaluated for the potential radical scavenging and antioxidant cellular capacity influencing the growth of cells exposed to H₂O₂. Before that, compounds were screened for cytotoxicity on THP-1 and HepG2 cell lines. Most of them were not cytotoxic in an overnight MTS assay. However, three of them, 4a, 4c and 4e showed 1,1-diphenyl-2-picrylhydrazyl (DPPH●) radical scavenging activity, through single electron transfer followed by a proton transfer (SET-PT) mechanism as revealed by density functional theory (DFT) modeling. DFT modeling of radical scavenging mechanisms was done at the SMD//(U)M052X/6-311++G** level. The in vitro effects of 4a, 4c and 4e on the growth of THP-1 cells during four days pre- or post-treatment with H₂O₂ were examined daily with the trypan blue exclusion assay. Their various cellular effects reflect differences in their radical scavenging capacity and molecular lipophilicity (clogP) and depend upon the cellular redox status. The applied simple in vitro-in silico screening cascade enables fast identification and initial characterization of potent radical scavengers.