Depression affects millions worldwide, with the effectiveness of antidepressants often linked to interactions between medication and neuroreceptors. Laboratory testing and clinical studies of these interactions are extremely expensive and time consuming, which makes the computational approach an increasingly important step for drug discovery. The relationship between frontier molecular orbitals (HOMO-LUMO) and ligand-protein interactions is not well understood. In the present study, the interactions of neurotransmitters and antidepressants with several neuroreceptors are thoroughly examined using classical mechanical, quantum chemical, and machine learning methods. The quantum chemistry-based computations use electronic structure theory to compute molecular orbitals, while the machine learning architecture utilizes a large volume of pre-computed data and a deep learning architecture involving graph convolutional neural networks resulting in a faster and accurate prediction of molecular properties. The binding of these molecules has been simulated in selected neuroreceptors using docking and classical physics-based calculations. Our initial results suggest correlations between molecular hardness, substructures, HOMO-LUMO energy gaps, and binding affinity, potentially offering a cost-effective approach to predict drug-receptor interactions and accelerate antidepressant development.