A Rigorously Spin-Adapted and Spin-Complete Coupled Cluster Method for Arbitrary High-Spin Open-Shell States

One of the most prominent approaches in wave function theory is the coupled cluster (CC) method. Standard -- spin orbital based -- CC wave functions of open-shell references are known to be spin-contaminated. A promising technique to remove spin contamination and reduce computational efforts is the employment of spin-free -- also called spin-adapted -- substitution operators. This thesis covers the (I) conceptualization and derivation, (II) analysis, and (III) implementation of a general spin-adapted and spin-complete (SASC) CC approach for arbitrary high-spin states. In comparison to literature-known approaches and implementations, the presented scheme is guaranteed to span complete spin spaces for arbitrary spin quantum numbers and truncated cluster operators. The thesis is divided according to parts (I) to (III). Part (I) covers the generation of general sets of SASC substitution operators. It introduces a scheme based on Löwdin's projection operator method for spin eigenfunction generation to ensure both linear independence and completeness of the generated operators. In part (II), the quality of the operators in consecutive configuration interaction (CI) and CC calculations in terms of the amount of recovered correlation energy and the wave function overlap to full CI is analyzed. It was found that the generated operators produce optimal results compared to (i) different operator sets spanning identical linear spaces, (ii) orthogonalized operator sets, and (iii) operator sets of different spin completeness levels. Therefore, the operators were used to derive correctly scaling (factorized) equations throughout part (III). These equations were generated in a black box procedure using Wick's theorem and Goldstone diagrams specially adapted to the SASC framework. An implementation of SASC-CCSD is successfully applied to several small molecular systems. These show a small beneficial impact on the correlation energy compared to spin orbital CCSD.