Laqua, Henryk Sebastian (2022): Development of highly efficient and accurate real-space integration methods for Hartree-Fock and hybrid density functional calculations. Dissertation, LMU München: Faculty of Chemistry and Pharmacy |

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**DOI**: 10.5282/edoc.30648

### Abstract

The central focus of molecular electronic structure theory is to find approximate solutions to the electronic Schrödinger equation for molecules, and as such represents an essential part of any theoretical (in silico) study of chemical processes. However, a steep increase of the computational cost with increasing system size often prevents the application of accurate approximations to the molecules of interest. The main focus of the present work is the efficient evaluation of Fock-exchange contributions, which typically represents the computational bottleneck in Hartree-Fock (HF) and hybrid density functional theory (DFT) calculations. This bottleneck is addressed by means of seminumerical integration, i.e., one electronic coordinate within the 4-center-2-electron integral tensor is represented analytically and one numerically. In this way, an asymptotically linear scaling method for computing the exchange matrix (denoted as sn-LinK) is developed, enabling fast and accurate ab-initio calculations on large molecules, comprising hundreds or even thousands of atoms, even in combination with large atomic orbital basis sets. The novel sn-LinK method comprises improvements to the numerical integration grids, a rigorous, batch-wise integral screening scheme, the optimal utilization of modern, highly parallel compute architectures (e.g., graphics processing units; GPUs), and an efficient combination of single- and double-precision arithmetic. In total, these optimizations enable over two orders of magnitude faster evaluation of Fock-exchange contributions. Consequently, this greatly improved performance allows to perform previously unfeasible computations, which is also demonstrated at the example of an ab initio molecular dynamics simulation (AIMD) study on the hydrogen bond strengths within double-stranded DNA. In addition to Fock-exchange, the other two computational bottlenecks in hybrid-DFT applications – the evaluation of the Coulomb potential and the numerical integration of the semilocal exchange-correlation functional – are also addressed. Finally, more efficient methods to evaluate more accurate post-HF/DFT methods, namely the random-phase approximation (RPA) and the second-order approximate coupled cluster (CC2) method, are also put forward. In this way, the highly efficient methods introduced in this thesis cover some of the most substantial computational bottlenecks in electronic-structure theory – the evaluation of the Coulomb- and the exchange-interactions, the integration of the semilocal exchange-correlation functional, and the computation of post-Hartree-Fock correlation energies. Consequently, computational chemistry studies on large molecules (>100 atoms) are accelerated by multiple orders of magnitude, allowing for much more accurate and thorough in-silico studies than ever before.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | Quantum Chemistry, Electronic Structure Theory, Density Functional Theory, Strong Correlation, Hartree-Fock, F12, Coupled Cluster, Random Phase Approximation, Numerical Integration, Linear Scaling, High Performance Computing, Parallel Computing, Graphics Processing Units, Molecular Dynamics |

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: | 7. July 2022 |

1. Referee: | Ochsenfeld, Christian |

MD5 Checksum of the PDF-file: | ecdc849fa91343471d169352b8665a81 |

Signature of the printed copy: | 0001/UMC 29122 |

ID Code: | 30648 |

Deposited On: | 19. Oct 2022 09:37 |

Last Modified: | 19. Oct 2022 09:37 |