Electron Correlation Methods for Sustainable Energy Solutions

The accurate description of electron correlation in crystalline materials is essential for understanding and predicting the properties of complex functional solids. This PhD thesis investigates a range of solid-state systems using quantum-chemical approaches, with particular emphasis on periodic and local post-Hartree–Fock (post-HF) methods. The work combines applications to energy-related and technologically relevant materials with the development and implementation of new computational tools within the CRYSCOR code. The first part of the thesis addresses several problems in solid-state chemistry and materials science. Lithium-ion diffusion in layered LiNiO2 was investigated by combining DFT-based metadynamics and path sampling with periodic and post-HF calculations. The calculated migration barriers showed that electrostatic effects dominate the diffusion process and that DFT provides a reliable description, while correlated methods offer valuable benchmarks. The anomalous melting behaviour of transition-metal hexafluorides was analysed through periodic local MP2 calculations with embedded-fragment CCSD(T) corrections, together with a study of vibrational energy levels. The results showed that the different melting points of MoF6 and WF6 cannot be explained by lattice energies alone, but arise mainly from differences in vibrational and entropic contributions. A comprehensive computational study was also performed on the main allotropes of elemental phosphorus, combining periodic DFT and local correlated calculations to investigate their structural, vibrational and thermodynamic properties. The results reproduce the experimental vibrational spectra and relative stability trends, confirming the lower stability of white phosphorus with respect to the condensed red and black forms and revealing the close energetic competition between violet and black phosphorus. Additional work concerned the structural and vibrational characterization of sodium amide, including the investigation of a possible low-temperature symmetry breaking, as well as the development of computational tutorials within the VISUENERGY project. These studies motivated the development of correlated methods capable of treating spin-polarized periodic systems. The second part of the thesis therefore focuses on extending CRYSCOR to open-shell systems. A fully periodic local unrestricted MP2 (ULMP2) formulation was implemented on top of a periodic unrestricted HF reference. The method treats the α and β spin spaces separately and distinguishes same-spin and opposite-spin electron pairs, while exploiting localized Wannier functions, projected atomic orbitals, local density fitting and multipole approximations to preserve the favourable scaling of local correlation methods. In parallel, the embedded-fragment approach was extended to unrestricted HF references, allowing correlated calculations on localized regions of spin-polarized materials while retaining the periodic mean-field environment. The new implementations were extensively validated on one-, two- and three-dimensional periodic systems constructed from ammonia and molecular oxygen. Comparisons between closed- and open-shell formulations and with canonical molecular UMP2 calculations showed excellent numerical agreement. Domain-size and finite-fragment effects were identified and characterized, providing guidelines for improving convergence towards the periodic limit