Correlation Energy and Exact Exchange for Periodic Systems with Numerical Atomic Orbitals

This thesis presents the development and validation of advanced electronic structure methods for molecular and periodic systems. In Chapter 2, MP2 theory was implemented in the BAND code using Gaussian numerical atomic orbitals and benchmarked against Psi4 results for the S66 dataset, with additional tests using Slater-type orbitals showing agreement between codes. The projector method was employed to regularize atomic orbitals and the exact exchange matrix, preventing correlation energy collapse and variational instabilities, and a new NAO fit set generation algorithm was introduced. Chapter 3 describes a periodic RPA implementation with Coulomb damping and augmented reciprocal grids, validated against molecular results and lattice models. A dual-grid approach improved Γ-point convergence, applied to CO adsorption on MgO. Chapter 4 presents a periodic Hartree–Fock implementation using density matrix localization and real-space exchange, with a multipole approximation to reduce computational cost. Benchmarking against common crystals and the Crowley dataset showed excellent agreement. This work provides a robust framework for accurate electronic structure calculations in molecular and periodic systems.