Development of low-scaling electronic structure methods using rank factorizations and an attenuated Coulomb metric

Lünser, Arne (2017): Development of low-scaling electronic structure methods using rank factorizations and an attenuated Coulomb metric. Dissertation, LMU München: Faculty of Chemistry and Pharmacy

Abstract

Novel low-scaling techniques for molecular electronic structure and property calculations are introduced. Through the use of rank-revealing matrix factorizations, overheads compared to canonical molecular orbital-based formulations are virtually eliminated. Asymptotic computational complexity is linear or sub-linear (depending on the property) through the use of sparsity-preserving transformations throughout. For electron correlation energy calculations within the random phase approximation, these techniques are combined with an attenuated Coulomb metric in the resolution-of-the-identity to improve the accuracy over existing low-scaling methods and to reduce the scaling compared to existing canonical methods. For the resolution-of-the-identity itself, a novel method for the compression of auxiliary bases is introduced, powered by removal of the particle-hole-interaction nullspace through projection. Furthermore, efficient schemes for the calculation of molecular response properties at the Hartree–Fock and density functional theory levels are introduced: For the linear scaling calculation of vibrational frequencies, the exact cancellation of different long-range operator derivatives is employed in combination with Laplace-transformed and Cholesky-decomposed coupled-perturbed self-consistent field theories. Using related techniques, calculations of indirect nuclear spin-spin coupling constants with asymptotically constant time complexity are demonstrated and used to explore the dependence of spin-spin couplings in a peptide on the size of a surrounding solvent environment.

• Item Type: Theses (Dissertation, LMU Munich)
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 540 Chemistry and allied sciences
• Faculties: Faculty of Chemistry and Pharmacy
• Language: English
• Date of oral examination: 1. June 2017
• 1. Referee: Ochsenfeld, Christian
• Signature of the printed copy: 0001/UMC 24748