Graf, Daniel (2021): Development of efficient electronicstructure methods based on the adiabaticconnection fluctuationdissipation theorem and Møller–Plesset perturbation theory. Dissertation, LMU München: Faculty of Chemistry and Pharmacy 

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Abstract
One of the major goals of quantum chemistry is to develop electronicstructure methods, which are not only highly accurate in the evaluation of electronic groundstate properties, but also computationally tractable and versatile in their application. A theory with great potential in this respect, however, without being free from shortcomings is the random phase approximation (RPA). In this work, developments are presented, which address the most important of these shortcomings subject to the constraint to obtain low and linearscaling electronicstructure methods. A scheme combining an elegant way to introduce local orbitals and multinode parallelism is put forward, which not only allows to evaluate the RPA correlation energy in a fraction of the time of former theories, but also enables a scalable decrease of the high memory requirements. Furthermore, a quadraticscaling selfconsistent minimization of the total RPA energy with respect to the oneparticle density matrix in the atomicorbital space is introduced, making the RPA energy variationally stable and independent of the quality of the reference calculation. To address the slow convergence with respect to the size of the basis set and the selfcorrelation inherent in the RPA functional, rangeseparation of the electronelectron interaction is exploited for atomicorbital RPA, yielding a linearscaling rangeseparated RPA method with consistent performance over a broad range of chemical problems. As a natural extension, the concepts including local orbitals, selfconsistency, and rangeseparation are further combined in a RPAbased generalized Kohn–Sham method, which not only shows a balanced performance in general main group thermochemistry, kinetics, and noncovalent interactions, but also yields accurate ionization potentials and fundamental gaps. The origin of the selfcorrelation error within RPA lies in the neglect of exchangeeffects in the calculation of the interacting densitydensity response functions. While rangeseparation is a reasonable approach to counteract this shortcoming — since selfcorrelation is pronounced at short interelectronic distances — a more rigorous but computationally sophisticated approach is to introduce the missing exchangeeffects, at least to some extent. To make RPA with exchange methods applicable to systems containing hundreds of atoms and hence a suitable choice for practical applications, a framework is developed, which allows to devise highly efficient low and linearscaling RPA with exchange methods. The developments presented in this work, however, are not only limited to RPA and beyondRPA methods. The connection between RPA and manybody perturbation theory is further used to present a secondorder Møller–Plesset perturbation theory method, which combines the tools to obtain low and linearscaling RPA and beyondRPA methods with efficient linearalgebra routines, making it highly efficient and applicable to large molecular systems comprising several thousand of basis functions.
Item Type:  Theses (Dissertation, LMU Munich) 

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:  26. March 2021 
1. Referee:  Ochsenfeld, Christian 
MD5 Checksum of the PDFfile:  476823afdcd9d7fd6e73f8d5c9b2e1fb 
Signature of the printed copy:  0001/UMC 27866 
ID Code:  27791 
Deposited On:  19. Apr 2021 10:15 
Last Modified:  19. Apr 2021 10:16 