Computation of molecular magnetic properties using cholesky decomposition
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Abstract
This dissertation focuses on the development and application of wavefunction-based methods to enable the efficient computation of molecular magnetic properties for large molecules. The accurate calculation of these molecular properties, such as nuclear magnetic resonance (NMR) chemical shifts and magnetizabilities, is of central importance for interpreting experimental data and predicting future measurements. To obtain precise results, highly accurate quantum chemical methods are required; however, these are associated with substantial computational cost, primarily due to the computation, storage, and processing of two-electron integrals. In this work, the Cholesky decomposition (CD) of the two-electron integral matrix is applied to the unperturbed integrals as well as their first and second derivatives with respect to an external magnetic field, significantly reducing the computational costs. Using the CD-based schemes developed in this work, NMR chemical shifts can be computed at the second-order Møller-Plesset perturbation theory (MP2) level for systems with approximately 1500 basis functions, and magnetizabilities at the Hartree-Fock (HF) level for systems with around 1000 basis functions — system sizes that are practically infeasible using conventional MP2/HF methods without CD. The CD-MP2 scheme was further employed in quantum mechanics/molecular mechanics (QM/MM) calculations to compute NMR shifts of liquid water. The efficiency gains realized through the CD make it possible to treat a large QM region, which is essential for accurately describing hydrogen bonds. Additionally, both CD-MP2 and CD-HF schemes were applied to investigate the aromaticity of bridged annulenes, demonstrating the broad applicability of the CD-based methods.