Evaluation of matrix elements of operators lies at the core of all post-Hartree-Fock ab initio theories for the accurate computation of energies and molecular properties. Among the available methods — commutation algebra, Wick’s theorem, and diagrammatic techniques — Wick’s theorem occupies a central role, finding application across configuration interaction, coupled cluster (CC), and many-body perturbation theories. CC theory, however, is the primary focus here, owing to its unique combination of size extensivity, size consistency, and rapid convergence toward full-CI results within an elegant mathematical framework. In its simplest form, the CC cluster operator contains single and double replacements from the reference determinant (CCSD); augmenting these with perturbative triples yields the gold-standard CCSD(T). Deriving and implementing equations beyond this level becomes increasingly intractable by hand. This thesis presents an automatic code generator environment (AGE), based on Wick’s theorem and implemented within the ORCA quantum chemistry package, capable of generating arbitrary-order parallelized CC programs — currently realized up to CCSDTQ for UHF and up to CCSDT for RHF references. As an illustrative application, the High-Accuracy Extrapolated Thermochemistry (HEAT) protocol was implemented in ORCA (introduced as ORCA-HEAT) via its compound job workflow engine, requiring CC correlation energies at the CCSD(T), CCSDT, and CCSDTQ levels. While single-reference Wick’s theorem efficiently underpins high-order ab initio theories, multireference theories demand the generalized Wick’s theorem (GWT) — an indispensable tool for internally contracted multireference CC (ic-MRCC) and driven similarity renormalization group (DSRG)-based MRCC and MRPT theories. The algebraic complexity of these frameworks, compounded by the requirement of a spin-free formulation, has long posed a formidable theoretical and implementation challenge. A pragmatic route proceeds through spinorbital-based GWT, with subsequent conversion to spin-free equations. The Wick a Python code generator for fully parallelized C++ output was implemented up to singles and doubles excitations. The resulting spin-free ric-MRCC is fully size-extensive, highly affordable — only 40% slower than the optimized NEVPT2 code in ORCA for CAS(14,14) — and promisingly accurate. On the computational front, non-covalent interactions (NCIs) were investigated using state-of-the-art methods. NCIs govern a remarkably broad domain — stereochemical outcomes in asymmetric reactions, pre-reactive intermediate formation, protein and nucleic acid secondary and tertiary structure, and conformational stability in gas and solution phases. Reliable computational protocols must satisfy three simultaneous criteria: accuracy, efficiency, and broad applicability. Implicit solvation methods typically incur errors exceeding the magnitude of the interactions themselves, while explicit embedding of solute in a solvent sphere, though physically sound, becomes cost-prohibitive at the post-HF level. Approximate CC methods — DLPNO-CCSD(T) and Hartree-Fock plus London dispersion (HFLD) — were deployed alongside DFT-based approaches to capture long-range dynamic correlation. Additionally, an iterative explicit solvent-addition strategy was employed to compute van der Waals interactions, enabling both qualitative and quantitative insight into the role of dispersion effects in homogeneous catalysis, specifically the IDPi-catalyzed olefin activation reaction.
Riya Kayal (Wed,) studied this question.