Development of downfolded configuration interaction algorithm for molecular electronic structure calculation

Abstract

Accurately calculating the electronic structure of strongly correlated molecular systems, such as transition metal complexes, actinides, lanthanides, and extended $\pi$-conjugated organic molecules, is a significant challenge in the field of quantum chemistry. In these systems, strong electron correlations are crucial, and their accurate description is essential for predicting and understanding the properties and reactivity, which includes but is not limited to bond breaking, charge transfer, and excited states. Traditional methods often have difficulties in accurately capturing the intricate electron correlations in these systems, which limits their capacity to produce reliable results. Furthermore, the scaling of high-level methods has significant limitations on their practical use when the system correlation size becomes large, making them computationally prohibitive. As a result, there is a need to develop efficient approximate techniques that can maintain high accuracy while reducing computational cost.

In an exact diagonalization of benzene in the cc-pVDZ basis, the Hilbert space contains over $10^{45}$ determinants. However, the molecular Hamiltonian in real systems is very sparse, with the vast majority of matrix elements being negligible. This sparsity can be exploited to reduce the effective dimension dramatically. This thesis presents the development and application of the Downfolded Configuration Interaction (dCI) algorithm for accurate and efficient calculations of molecules with strong correlations. The dCI, as a branch of the selected CI method, constructs a compact, effective Hamiltonian through an iterative process that captures the essential electron correlations. This is accomplished by carefully selecting significant configurations and applying a local treatment to the model subspace. Building upon the dCI algorithm, the extended-dCI (ext-dCI) method has been developed to further increase the applicability to larger molecular systems by approximating effective Hamiltonian expansion truncation. Detailed benchmarks demonstrate the accuracy and efficiency of ext-dCI in calculating challenging systems such as benzene and chromium dimer. Utilizing the sparsity and locality of the electronic structure, the dCI and ext-dCI methods provide an in-depth description of both static and dynamic electron correlation effects. The dCI approach opens new possibilities for studying complex chemical phenomena governed by strong electron correlations.