Local correlation methods for periodic systems

Thesis

Wavefunction-based electronic structure methods, which accurately evaluate the electronic energy of chemical systems, have been increasingly applied to periodic or crystalline materials. Here, the requirement to simulate the in-principle infinite extent of the bulk material significantly exacerbates the computational cost of employing these methods, necessitating the development of reduced-cost algorithms specifically for periodic systems. Domain-based pair natural orbital local correlation (DLPNO) theory has been widely adopted in molecular contexts, and achieves near-linear scaling of computational effort with system size with only modest loss in accuracy by replacing Hamiltonian integrals and excitation amplitudes with low-rank approximations that exploit the inherent locality of electron correlation within non-conducting systems.

In this thesis, we extend DLPNO theory to periodic systems, in order to obtain accurate unit cell electronic energies using Møller–Plesset second order perturbation theory (DLPNO-MP2). Using the existing machinery within the TURBOMOLE quantum chemistry package, we present two complementary implementations for periodic DLPNO-MP2, which arise from different choices to account for the infinite summation of lattice images contained within periodic Coulomb integrals. Proof-of-concept calculations, demonstrating the correct convergence to the infinite bulk limit are shown for both schemes, using a range of one-, two- and three-dimensional systems, and further analysis is conducted comparing the rate of convergence and the computational scaling. The pilot approach of one scheme, in particular, already demonstrates linear and sub-linear scaling with respect to supercell size.

Localised occupied orbitals are an essential starting input to fully leverage the computational savings afforded through DLPNO theory. This thesis also outlines a novel scheme to generate localised Wannier functions, by adapting the molecular intrinsic atomic orbital approach to periodic systems. Finally, in an effort to demonstrate the computational efficiency afforded by periodic DLPNO-MP2, we apply our approach to study surface adsorption interactions, involving calculations with up to 30000 basis functions within the correlation treatment.

Authors: Zhu, A

• DOI: 10.5287/ora-av76e7xgq
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: theoretical chemistry; electronic structure theory; condensed-phase quantum chemistry
• Subjects: Chemistry, Physical and theoretical