Localization Scheme for Relativistic Spinors and Optimized Electron Repulsion Integral Evaluation and Transformation
Published on 23. December 2013
Book
Paperback/Softback
189 pages
978-3-8439-1364-5 (ISBN)
Description
This work is divided into two parts. The first part deals with the development and implementation of a localization scheme for relativistic complex-valued spinors. The localization scheme makes use of the approximate joint diagonalization (AJD) method, frequently used in the field of signal processing, which aims at transforming a set of matrices as close as possible to diagonality. With the proposed scheme, widely used localization criteria such as the one of Foster and Boys or the one of Pipek and Mezey can be employed for relativistic complex-valued spinors in the same manner as for real-valued orbitals. Furthermore, the usage is in principle possible with every many-component wave function. The scheme has been interfaced to the Kramers-restricted two-component pseudopotential (PP) Hartree-Fock SCF program of the Quantum Objects Library (QOL) program package of the Theoretical Chemistry groups at the university of Cologne. Test calculations show that in many cases localized spinors can be obtained which closely resemble their non-relativistic counterparts. However, in case of large spin-orbit coupling, the local relativistic spinors are considerably different to the local orbitals. This fact justifies the need for a localization scheme for relativistic spinors.
The second part of this work is concerned with the code-generated generation and transformation of electron repulsion integrals (ERIs). Numerical problems which are inherent in the code-generated Cartesian integral generation based on the Obara-Saika scheme have been analyzed and and cured to a certain extent. Besides that, a code-generated angular transformation has been developed and implemented which proofed in theoretical considerations and actual calculations to be superior to the existing implementation in QOL. The second part concludes with a presentation of a matrix multiplication and shuffling based ERI contraction module. Especially for generally contracted basis sets containing high angular momentum functions, the contraction module displayed good performance.
The second part of this work is concerned with the code-generated generation and transformation of electron repulsion integrals (ERIs). Numerical problems which are inherent in the code-generated Cartesian integral generation based on the Obara-Saika scheme have been analyzed and and cured to a certain extent. Besides that, a code-generated angular transformation has been developed and implemented which proofed in theoretical considerations and actual calculations to be superior to the existing implementation in QOL. The second part concludes with a presentation of a matrix multiplication and shuffling based ERI contraction module. Especially for generally contracted basis sets containing high angular momentum functions, the contraction module displayed good performance.