An Information-Theoretic Perspective on Molecular Quantum Mechanics

Abstract

Scientists often refer to matter, energy, and information as the three basic categories, though they are related by various scientific laws. Compared to the concepts of matter and energy, the scientific definition of information is relatively new: it was only in the 1940s that Claude Shannon introduced the definition of information as a reduction of uncertainty, laying the foundation for modern information theory. In molecular electronic structure theory, we routinely encounter nonnegative quantities that sum to unity, forming valid probability distributions. These include properly normalized electron densities, eigenvalues of reduced density matrices, squared wave function coefficients in orthonormal bases, and related quantities. The incorporation of information-theoretic concepts into quantum chemistry has yielded profound insights into electronic system behavior. The two dominant frameworks in electronic structure theory are quantum many-body theory and density functional theory. This thesis systematically integrates these approaches with: classical information theory, yielding the information-theoretic approach, and quantum information theory, generating distinct tools like orbital entanglement measures and quantum fidelity metrics. In this thesis, we subsequently demonstrate applications of these information-theoretic methods in quantum chemistry for analyzing electronic structure and chemical phenomena.