Vitamin C (VC) is an essential antioxidant, but its application is limited because of its unstable chemical properties. Hence, a variety of VC derivatives have emerged in practical antioxidant applications. To explore the relationship between the antioxidant properties and the chemical structures of vitamin C and its derivatives, density functional theory (DFT) was used in this work to calculate the reaction enthalpies of the mechanisms related to radical scavenging activity. The structures were optimized at the B3LYP-D3(BJ)/6-31G* level of theory. Single point calculations (SPE) were performed at the PWPB95-D3 (BJ)/def2-QZVPP level. To estimate the solvent effect on antioxidant properties, the SMD (solvation model based on density) method was used. The results showed that in the process of optimizing the chemical structure of vitamin C, the antioxidant capacity of its derivatives decreased slightly in aqueous solvents. In the calculation process, it is also found that in the choice of antioxidant mechanism, these compounds are more inclined to the hydrogen atom transfer (HAT) mechanism, and from the chemical structure point of view, the double bond of the lactone ring is essential for its free radical scavenging activity. In general, it is necessary to continue to optimize the structure of VC to obtain derivatives with better oxidation resistance and more practical value.