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Alzheimer’s disease (AD) is a neurological disease, and its signs and symptoms appear slowly over time. Although current Alzheimer’s disease treatments can alleviate symptoms, they cannot prevent the disease from progressing. To accurately diagnose and treat Alzheimer’s disease, it is therefore necessary to establish effective methods for diagnosis. Apolipoprotein E4 (ApoE4), the most frequent genetic risk factor for AD, is expressed in more than half of patients with AD, making it an attractive target for AD therapy. We used molecular docking simulations, classical molecular mechanics optimizations, and ab initio fragment molecular orbital (FMO) calculations to investigate the specific interactions between ApoE4 and the naturally occurring compounds found in the plant Moringa Oleifera. According to the FMO calculations, quercetin had the highest binding affinity to ApoE4 among the sixteen compounds because its hydroxyl groups generated strong hydrogen bonds with the ApoE4 residues Trp11, Asp12, Arg15, and Asp130. As a result, we proposed various quercetin derivatives by introducing a hydroxyl group into quercetin and studied their ApoE4 binding properties. The FMO data clearly showed that adding a hydroxyl group to quercetin improved its binding capacity to ApoE4. Furthermore, ApoE4 Trp11, Asp12, Arg15, and Asp130 residues were discovered to be required for significant interactions between ApoE4 and quercetin derivatives. They had a higher ApoE4 binding affinity than our previously proposed epicatechin derivatives. Accordingly, the current results evaluated using the ab initio FMO method will be useful for designing potent ApoE4 inhibitors that can be used as a candidate agent for AD treatment.