With the advancement of artificial intelligence-embedded methodologies, their application to predict fundamental molecular properties has become increasingly prevalent. In this study, a graph convolutional neural network fingerprint-enabled artificial neural network (GCN-ANN) was utilized to probe the relationship between the chemical hardness of neurochemicals and their affinities for neuroreceptors. The GCN-ANN model was derived using a training set of B3LYP-calculated HOMO and LUMO energies of >110,000 molecules. A benchmark study of 45 neurochemicals produced consistent hardness and electronegativity values across the three density functionals, namely, B3LYP, ωB97XD, and M06-2X. However, the computed energetics varied significantly when the Hartree-Fock theory was used. The scrutiny of binding affinities, hardness, and GCN-ANN-derived substructures of neurochemicals reinforces the notion that human brain receptors interact with neurochemicals based on Pearson's Hard-Soft Acid-Base (HSAB) principle. In summary, this machine-learning-embedded study offers physical insights into the interactions between neurochemicals and neuroreceptors, which could lead to the development of more targeted and effective antidepressants, thereby addressing anxiety and depression with greater precision and immediacy.