Interest in HDAC3 inhibitors (HDAC3i) for pharmacological applications outside of cancer is growing. However, concerns regarding the possible mutagenicity of the commonly used hydroxamates (zinc-binding groups, ZBGs) are also increasing. Considering these concerns, non-hydroxamate ZBGs offer a promising alternative for the development of non-mutagenic HDAC3 inhibitors. Unfortunately, the quantum chemical space of non-hydroxamates has not been studied in detail. This study has three primary goals: (i) to perform semiempirical quantum chemical calculations, examining AM-1 model parameters relevant to zinc binding, (ii) to develop supervised mathematical learning models to train a diverse set of non-hydroxamate-based HDAC3i, and (iii) to apply fragment-based approaches to identify sub-structural fragments (fingerprints) that promote or hinder HDAC3 inhibitory activity through classification-based QSARs. In addition, flexible molecular docking analysis, 200 ns MD simulation, and free energy landscape (FEL) analysis further established the importance of identified fingerprints in the modulation of HDAC3 inhibitory activity. This comprehensive analysis of structural variations among non-hydroxamate HDAC3i provides valuable insights, contributing to the design of potential non-mutagenic HDAC3i.