# Quantum-Tomographic Approaches to the Interpretation of Semi-Empirical Quantum Chemistry Models

Modelling the behavior of correlated electrons in finite systems is at the heart of theoretical chemistry. Many sophisticated techniques have been developed over the past several decades, but first-principles approaches to molecular electronic structure scale very poorly with the size of the molecule. Other approximate methods (e.g. density functional theory) are commonly used, but known to fail for systems of particular interest to optoelectronics research. An alternative is the use of semi-empirical Hamiltonians, which reduce the complexity of the problem by assuming that particular classes of interactions vanish. This project will take an entirely new approach to the interpretation of these approximations by examining the structure of the STATISTICAL state for which these approximations are rigorously true. The results will be of far-ranging consequence to molecular electronic structure and theoretical chemistry. The student will gain experience in modern information-theoretic techniques of quantum state estimation, as well as a thorough training in traditional computational techniques from quantum chemistry and condensed-matter physics.