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You searched for +publisher:"University of North Dakota" +contributor:("Mark Hoffmann"). Showing records 1 – 2 of 2 total matches.

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1. Timian, Eric. Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems.

Degree: PhD, Chemistry, 2018, University of North Dakota

Electronic structure theory programs strive to be as widely applicable as possible. In order to account for effects exhibited by heavier elements, relativistic considerations must be incorporated into these programs. The methods developed in recent years generally succeed in describing the relativistic nature of systems containing heavier elements with reasonable accuracy, but have limited application due to their complexity and computational demand. Highly correlated systems exhibiting significant relativistic effects remain as a challenge to quantum chemical methods. In this thesis, I present the application of a well-defined relativistic Hamiltonian to a high-level electronic structure theory to generate a relativistic variant of a high-level multireference electronic structure theory capable of obtaining accurate results for highly correlated relativistic systems. This theory applies the exact two-component (X2C) relativistic Hamiltonian and a third-order Douglass-Kroll-Hess (DKH3) transformation for the spin-free and spin-orbit terms, respectively. The spin-orbit integrals are contracted into an effective one-electron Hamiltonian using the atomic mean field (AMFI) approximation, which increases computational efficiency with little loss in accuracy. By applying this scheme to the second-order generalized van Vleck perturbation theory (GVVPT2), which offers appropriate treatment of electron correlation, a theory providing an accurate analysis of chemical systems with strong relativistic effects is obtained. The method developed in this work is used to explore ground and low-lying excited states of the lanthanide dimer systems Gd2 and Dy2. Results from scalar relativistic studies show that GVVPT2 can accurately characterize these systems. The ground electronic states obtained (Gd2: 19Σg- ; Dy2: 11Πg) match literature and theoretical results. The spectroscopic data obtained for the ground state of Gd2 (Re = 2.826 Å; De = 2.48 eV; ωe = 153.0 cm-1) are in excellent agreement with literature values (Re = 2.877 Å; D0 = 2.1 ± 0.7 eV; ωe = 138-149 cm-1). Inclusion of spin-orbit coupling in these studies is expected to improve the results to agree with literature values to within chemical accuracy. Future work is planned to extend this method to transition metal trimers. Advisors/Committee Members: Mark Hoffmann.

Subjects/Keywords: Chemistry; Dimer; Lanthanide; Multireference; Perturbation Theory; Relativistic

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Timian, E. (2018). Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems. (Doctoral Dissertation). University of North Dakota. Retrieved from https://commons.und.edu/theses/2365

Chicago Manual of Style (16th Edition):

Timian, Eric. “Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems.” 2018. Doctoral Dissertation, University of North Dakota. Accessed April 18, 2021. https://commons.und.edu/theses/2365.

MLA Handbook (7th Edition):

Timian, Eric. “Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems.” 2018. Web. 18 Apr 2021.

Vancouver:

Timian E. Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems. [Internet] [Doctoral dissertation]. University of North Dakota; 2018. [cited 2021 Apr 18]. Available from: https://commons.und.edu/theses/2365.

Council of Science Editors:

Timian E. Relativistic Multireference Perturbation Theory With Applications To D And F Block Metal Systems. [Doctoral Dissertation]. University of North Dakota; 2018. Available from: https://commons.und.edu/theses/2365

2. Mahmoud, Mohammed. Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu.

Degree: PhD, Computer Science, 2018, University of North Dakota

Configuration interaction (CI) is a post Hartree–Fock method that is commonly used for solving the nonrelativistic Schrödinger equation for quantum many-electron systems of molecular scale. CI includes instantaneous electron correlation and it can deal with the ground state as well as multiple excited states. The CI matrix is a sparse matrix, and the bigger the CI matrix, the more electron correlation can be captured. However, due to the large size of the CI sparse matrix that is involved in CI computations, a good amount of the time spent on the eigenvalue computations is associated with the multiplication of the CI sparse matrix by numerous dense vectors, which is basically known as Sparse matrix-vector multiplication (SpMV). Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous and varying scientific applications. One of the scientific applications that SpMV is involved in is Configuration Interaction (CI). In this work, we have developed a new hybrid approach to deal with CI sparse matrices. The proposed model includes a newly-developed hybrid format for storing CI sparse matrices on the Graphics Processing Unit (GPU). In addition to the new developed format, the proposed model includes the SpMV kernel for multiplying the CI matrix (proposed format) by a vector using the C language and the CUDA platform. The proposed SpMV kernel is a vector kernel that uses the warp approach. We have gauged the newly developed model in terms of two primary factors, memory usage and performance. Our proposed kernel was compared to the cuSPARSE library and the CSR5 (Compressed Sparse Row 5) format and already outperformed both. Our proposed kernel outperformed the CSR5 format by 250.7% and the cuSPARSE library by 395.1% Keywords— CI, SpMV, Linear System, GPU, Kernel, CUDA. Advisors/Committee Members: Mark Hoffmann, Hassan Reza.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Mahmoud, M. (2018). Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu. (Doctoral Dissertation). University of North Dakota. Retrieved from https://commons.und.edu/theses/2415

Chicago Manual of Style (16th Edition):

Mahmoud, Mohammed. “Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu.” 2018. Doctoral Dissertation, University of North Dakota. Accessed April 18, 2021. https://commons.und.edu/theses/2415.

MLA Handbook (7th Edition):

Mahmoud, Mohammed. “Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu.” 2018. Web. 18 Apr 2021.

Vancouver:

Mahmoud M. Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu. [Internet] [Doctoral dissertation]. University of North Dakota; 2018. [cited 2021 Apr 18]. Available from: https://commons.und.edu/theses/2415.

Council of Science Editors:

Mahmoud M. Developing A New Storage Format And A Warp-Based Spmv Kernel For Configuration Interaction Sparse Matrices On The Gpu. [Doctoral Dissertation]. University of North Dakota; 2018. Available from: https://commons.und.edu/theses/2415

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