CC2 response method using local correlation and density fitting approximations for the calculation of the electronic g-tensor of extended open-shell molecules

In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen. Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem.This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem

Efficient treatment of three-body interactions in transcorrelated methods

An efficient implementation for approximate inclusion of the three-body operator arising in transcorrelated methods via exclusion of explit three body correlation (xTC) is presented and tested against results in the ``HEAT'' benchmark set [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)]. Using relatively modest basis sets and computationally simple methods, total, atomization, and formation energies within near-chemical accuracy from HEAT results were obtained. The xTC ansatz reduces the nominal scaling of the three-body part of transcorrelation by two orders of magnitude to O(N^5) and can readily be used with almost any quantum chemical correlation method

Transcorrelated coupled cluster methods. II. Molecular systems

We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at the level of singles and doubles excitations. Our results show that already with the cc-pVTZ basis the transcorrelated distinguishable cluster method gets close to complete basis limit and near full configuration interaction quality values for relative energies of over thirty atoms and molecules. To gauge the performance in different correlation regimes we also investigate the breaking of the nitrogen molecule with transcorrelated coupled cluster methods. Numerical evidence is presented to further justify an efficient way to incorporate the major effects coming from the three-body integrals without explicitly introducing them into the amplitude equations.Comment: peer-reviewed and accepted manuscript (J. Chem. Phys.