Quantum Mechanical Justification for Invariant Binding Affinity in Coordinate Transformations

Molecular docking, pharmacological modelling, and quantum chemistry calculations frequently involve coordinate transformations, like the conversion between PDB (Protein Data Bank) and SMILES (Simplified Molecular Input Line Entry System) formats. This paper presents a rigorous quantum mechanical justification for why the binding affinity and molecular interaction properties of a ligand remain invariant under such transformations. Using the Quantum Mechanics, including the invariance of the Schrodinger equation under translation, the Born Oppenheimer approximation, molecular orbital theory, and electrostatic potential analysis, we demonstrate a mathematical framework that makes sure the conservation of molecular interactions.