Mapping Ab Initio Physical Theories to Computational Chemistry Methods: The Contributions of Classical Mechanics, Thermodynamics and Statistical Mechanics, Electromagnetism, Relativity, Quantum Mechanics, and Quantum Field Theory

Ab initio quantum chemistry aims to predict molecular properties solely from fundamental physical constants and system composition, without empirical parameterization. This review elucidates how this endeavor is built upon an interdependent hierarchy of physical theories, each contributing essential concepts and introducing inherent approximations. We trace the foundational role of classical mechanics in the Born-Oppenheimer approximation, which separates nuclear and electronic motion, and the establishment of the molecular Hamiltonian through the synergy of quantum mechanics and classical electromagnetism. We detail how thermodynamics and statistical mechanics provide the critical link between microscopic quantum states and macroscopic observables through the partition function. The review further examines the essential integration of relativistic effects for heavy elements, governed by the Dirac equation, and the formal power of quantum field theory, which provides the second quantization formalism underpinning high-accuracy methods like coupled cluster theory. The emerging frontier of integrating Quantum Electrodynamics (QED) in chemistry, where the electromagnetic field itself is quantized, is also explored. Lastly, the discussion is framed by the central trade-off between the rigorous inclusion of physical effects—from electron correlation to relativistic and QED corrections—and the associated computational cost. This synthesis demonstrates that the ongoing evolution of ab initio methods is a systematic effort to replace the convenience-driven classical approximations with rigorously derived, unified physical theories, thereby extending the domain of first-principles prediction.