Vogler, Sigurd (2018): Development of efficient and low-scaling methods to compute molecular properties at MP2 and double-hybrid DFT levels. Dissertation, LMU München: Faculty of Chemistry and Pharmacy |

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**DOI**: 10.5282/edoc.23073

### Abstract

This thesis introduces new methods to compute molecular properties at the level of second-order Møller-Plesset perturbation theory (MP2) and double-hybrid density functional theory, building on a reformulation in atomic orbitals and exploiting the rank deficiency of the (pseudo-)density matrices, thus reducing the scaling behavior with respect to the size of the basis set. By furthermore employing the resolution-of-the-identity approximation, low-scaling and efficient MP2 energy gradients are presented, where significant two-electron integrals are screened using a distance-including integral estimation technique. With this, the forces and the hyperfine coupling constants of systems larger than previously computable at the MP2-level are obtained. In the second part of this thesis, the locality of the spin density in many molecular systems is exploited in the computation of the hyperfine coupling constants, leading to further speed-ups and allowing for a thorough investigation of the effect of the protein environment on the hyperfine coupling within the core region of a pyruvate formate lyase. With this efficient method, studying the effect of nuclear motion on the accuracy of the computed hyperfine coupling constants is possible. The study presented in this thesis demonstrates that both electron correlation and vibrational motion are crucial for an accurate theoretical description. When calculating magnetic properties, the dependence on the choice of gauge origins needs to be considered. This effect is studied systematically, and in detail, in a fourth project of this thesis for the computation of electronic g-tensors, for which it was previously assumed that the computation is largely independent of the choice of the gauge-origin. The study clearly contradicts this assumption and motivates the use of gauge including atomic orbitals in future work on electronic g-tensors. In a last part, this work transfers the algorithmic developments on the computation of analytic gradients to the computation of nuclear magnetic resonance (NMR) shieldings at the MP2-level. Though a sublinear scaling ansatz to compute the NMR shielding tensor per nucleus is available, the lack of an efficient implementation and the large dependency on the size of the basis sets prohibits the accurate computation of the shielding tensor of medium- to large-sized molecules. Furthermore, while this ansatz in theory scales linearly when all nuclei in a system are computed, it is inefficient due to the dependence of the rate-determining steps on the nuclear magnetic moments. This thesis therefore presents a new all-nuclei ansatz and introduces the methodology for the efficient computation of the energy gradients developed in this thesis, highlighting significant computational savings.

Item Type: | Theses (Dissertation, LMU Munich) |
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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: | 29. October 2018 |

1. Referee: | Ochsenfeld, Christian |

MD5 Checksum of the PDF-file: | e021ad266758bce7629633e546c3fe17 |

Signature of the printed copy: | 0001/UMC 27509 |

ID Code: | 23073 |

Deposited On: | 09. Nov 2020 15:12 |

Last Modified: | 09. Nov 2020 15:12 |