Grundei, Martin (2023): Application of density functional theory and the random phase approximation under periodic boundary conditions employing Gaussian-type basis functions. Dissertation, LMU München: Faculty of Chemistry and Pharmacy |

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**DOI**: 10.5282/edoc.31976

### Abstract

This work presents a robust Random-Phase-Approximation (RPA) method to compute ground state energies not only for molecules but also for solids. A translation symmetry adapted Hartree kernel under periodic boundary conditions is derived using Bloch functions of local, atom-centered Gaussian-type basis functions and resolution of the identity (RI) factorization. Long-range Coulomb sums are evaluated in direct space using an adapted fast continuous multipole method (CFMM), which works for defined points in reciprocal space apart from Γ. The computational cost of this method scales as O(N hoch 4 log(N)) with system size N and as O(N hoch 2 _k) with the number of sampled points k in reciprocal space N_k . Explicit treatment of 1D and 2D periodic materials avoids the need of full 3D calculations for chains or films. This method is implemented in the quantum chemistry package TURBOMOLE and adapts sparse density matrix storage and pre-screening of shell pairs to achieve further speedup. As an addendum to these results a parallel implementation of the periodic electrostatic potential (ESP) is provided. This ESP implementation adopts the evaluation of the Coulomb lattice sums from density fitting (DF) accelerated CFMM present in the RIPER Code in TURBOMOLE. CPU parallelisation of the code yields a speedup of about 13 times for 16 cores compared to single core calculations. This main part is accompanied by studies on the triphenyl triazin thiazole covalent organic framework (TTT-COF). COFs distinguish themselves from other polymers by their covalent connectivity, porosity, and crystallinity. The challenge of COF synthesis is to both yield a stable and a highly crystalline product with a minimum amount of structural defects. Therefore, a two step process is established for the synthesis of the TTT-COF. First, the trihphenyl triazine imine COF (TTI-COF) is formed via a thermodynamically reversible order inducing step. Second, a post-synthetic topochemical conversion with elemental sulfur forms the aromatic sulfur rings of the TTT-COF. The TTT-COF exhibits enhanced chemical and electron stability compared to its precursor, allowing for an in-depth structural study via transmission electron microscopy (TEM). In particular, the TTT-COF displays one-dimensional defects, such as edge dislocations and grain dislocations introduced during the TTT-COF formation.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | RPA, DFT, ACFDT |

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: | 24. May 2023 |

1. Referee: | Ochsenfeld, Christian |

MD5 Checksum of the PDF-file: | 0e900acaf9561d0e06b52cd045a6ea62 |

Signature of the printed copy: | 0001/UMC 29699 |

ID Code: | 31976 |

Deposited On: | 07. Jul 2023 10:40 |

Last Modified: | 07. Jul 2023 10:41 |