Improving the Scalability and Efficiency of High Accuracy Electronic Structure Methods: Expanding the Reach of Configuration Interaction

Abstract

Computational chemistry methods have been around since the birth of quantum mechanics nearly a century ago, and theoretical methods have become an ever-increasing part of chemical research especially as computational resources have exploded in the last few decades. This thesis addresses developments in high-accuracy electronic structure methods and how modern computational frameworks can be used to solve hitherto intractable chemical problems. One of the key considerations in modern computational chemistry is the balance of computational cost and method accuracy, with more accurate methods generally requiring higher cost. Two novel methods will be described herein which leverage two separate approaches for lowering computational cost of configuration interaction calculations without impacting their accuracy. First, the incremental natural orbital full configuration interaction (iNO-FCI) method uses a novel procedure for screening virtual orbitals thereby reducing computational complexity without a loss in FCI-like accuracy. This method was benchmarked against a series of notorious strong-correlation and multireference systems to showcase its effectiveness. Due to the overall decrease in computational cost, iNO-FCI allows computations in previously prohibitively large basis sets. Second, the many-body basis set amelioration (MBBSA) method allows for near-exact approximations of the most expensive step in the incremental full configuration interaction (iFCI) method. MBBSA performs a series of iFCI calculations to find the basis set correction of considering additional basis functions and the method correction of expanding to a higher n-body level in the iFCI method. These results are combined to approximate the large n-body iFCI calculation in a large basis. Computational cost savings are demonstrated to be between 75 and 95%. This work then seeks to leverage the methodological improvements of iNO-FCI and MBBSA in combination with graph-based reaction discovery tools to investigate the reaction networks of Criegee intermediates. The combination of these reaction discovery methods with iFCI allows for quantitatively and qualitatively accurate treatment of Criegee intermediates which are particularly challenging as they exhibit both zwitterionic and biradical character, where single reference methods are shown to underperform. Finally, this work will demonstrate how CI methods can be integrated with density functional theory (DFT). DFT offers a more favorable balance between cost and accuracy but, despite its exact formalism, often falls short of chemical accuracy. By inverting the exact ground-state density obtained from CI wavefunctions, one can generate exact exchange-correlation potentials, energies, and energy densities. These properties provide a rigorous benchmark for assessing model functionals and serve as high-fidelity training data for the development of CI-informed exchange-correlation functionals. This thesis aims to refine and improve computationally reasonable solutions for complex chemical systems where traditional electronic structure methods fail—either due to insufficient accuracy or intractable computational cost. The CI methods employed in this work offer a practical compromise between such traditional methods by accurately and efficiently modeling such complex chemical phenomena at reasonable cost.