Logo Logo
Help
Contact
Switch language to German
Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory
Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory
One of the major goals of quantum chemistry is to develop electronic-structure methods, which are not only highly accurate in the evaluation of electronic ground-state 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 linear-scaling electronic-structure methods. A scheme combining an elegant way to introduce local orbitals and multi-node 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 quadratic-scaling self-consistent minimization of the total RPA energy with respect to the one-particle density matrix in the atomic-orbital 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 self-correlation inherent in the RPA functional, range-separation of the electron-electron interaction is exploited for atomic-orbital RPA, yielding a linear-scaling range-separated RPA method with consistent performance over a broad range of chemical problems. As a natural extension, the concepts including local orbitals, self-consistency, and range-separation are further combined in a RPA-based 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 self-correlation error within RPA lies in the neglect of exchange-effects in the calculation of the interacting density-density response functions. While range-separation is a reasonable approach to counteract this shortcoming — since self-correlation is pronounced at short interelectronic distances — a more rigorous but computationally sophisticated approach is to introduce the missing exchange-effects, 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 linear-scaling RPA with exchange methods. The developments presented in this work, however, are not only limited to RPA and beyond-RPA methods. The connection between RPA and many-body perturbation theory is further used to present a second-order Møller–Plesset perturbation theory method, which combines the tools to obtain low- and linear-scaling RPA and beyond-RPA methods with efficient linear-algebra routines, making it highly efficient and applicable to large molecular systems comprising several thousand of basis functions.
Not available
Graf, Daniel
2021
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Graf, Daniel (2021): Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory. Dissertation, LMU München: Faculty of Chemistry and Pharmacy
[img]
Preview
PDF
Graf_Daniel.pdf

9MB

Abstract

One of the major goals of quantum chemistry is to develop electronic-structure methods, which are not only highly accurate in the evaluation of electronic ground-state 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 linear-scaling electronic-structure methods. A scheme combining an elegant way to introduce local orbitals and multi-node 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 quadratic-scaling self-consistent minimization of the total RPA energy with respect to the one-particle density matrix in the atomic-orbital 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 self-correlation inherent in the RPA functional, range-separation of the electron-electron interaction is exploited for atomic-orbital RPA, yielding a linear-scaling range-separated RPA method with consistent performance over a broad range of chemical problems. As a natural extension, the concepts including local orbitals, self-consistency, and range-separation are further combined in a RPA-based 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 self-correlation error within RPA lies in the neglect of exchange-effects in the calculation of the interacting density-density response functions. While range-separation is a reasonable approach to counteract this shortcoming — since self-correlation is pronounced at short interelectronic distances — a more rigorous but computationally sophisticated approach is to introduce the missing exchange-effects, 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 linear-scaling RPA with exchange methods. The developments presented in this work, however, are not only limited to RPA and beyond-RPA methods. The connection between RPA and many-body perturbation theory is further used to present a second-order Møller–Plesset perturbation theory method, which combines the tools to obtain low- and linear-scaling RPA and beyond-RPA methods with efficient linear-algebra routines, making it highly efficient and applicable to large molecular systems comprising several thousand of basis functions.