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Development of low-scaling electronic structure methods using rank factorizations and an attenuated Coulomb metric
Development of low-scaling electronic structure methods using rank factorizations and an attenuated Coulomb metric
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.
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Lünser, Arne
2017
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
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
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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.