Incorporating quantum correlation in extended molecular systems using advanced electronic structure methods in quantum chemistry

Abstract

Understanding electronic correlations in biomolecules is critical for advancing quantum chemistry, drug design, and molecular biology. This thesis presents a quantum information theory approach to analyzing electronic correlations in biomolecular systems using Mutual Information (MI), a measure derived from Reduced Density Matrices (RDMs) and orbital entropies. We introduce Atomic Mutual Information (AMI) as a novel metric that quantifies total correlation between atoms by summing MI contributions from all orbital pairs connecting them, enabling detailed characterization of both intra- and inter-molecular interactions.

The methodology is first applied to small systems, including dipeptides. To ensure accuracy, density matrix renormalization group (DMRG) calculations serve as a high-level benchmark against which less computationally demanding methods such as Density Functional Theory (DFT) and restricted Hartree-Fock (RHF) are evaluated. We then extend our approach to larger peptides by introducing Fragment-wise Mutual Information (FMI), a coarse-grained version of AMI that enables inter-fragment correlation analysis. To study dynamic behavior, we analyze the evolution of FMI by extracting snapshots from molecular dynamics (MD) trajectories. The results demonstrate that increases in FMI correlate with folding and stabilization of peptide structures, offering a quantum-informed descriptor of conformational changes that complements classical metrics. Finally, the method is scaled up to small proteins through a cut-wise reconstruction strategy. By stitching together results from overlapping fragments, we approximate full-system FMI with reasonable accuracy. Validation on the insulin protein confirms the method’s ability to capture key features, including hydrogen bonding, secondary structures, and disulfide bridges.

This work introduces scalable and interpretable tools for mapping electronic correlations in biomolecular systems, bridging quantum chemistry and molecular modeling, with broad applications in drug discovery, protein engineering, and force field development.