Variational determination of the twoparticle density matrix: the case of doublyoccupied space
(2015)
 Author
 Ward Poelmans (UGent)
 Promoter
 Dimitri Van Neck (UGent) and Patrick Bultinck (UGent)
 Organization
 Abstract
 The world at the level of the atom is described by the branch of science called quantum mechanics. The crown jewel of quantum mechanics is given by the Schrödinger equation which describes a system of indistinguishable particles, that interact with each other. However, an equation alone is not enough: the solution is what interests us. Unfortunately, the exponential scaling of the Hilbert space makes it unfeasible to calculate the exact wave function. This dissertation concerns itself with one of the many ab initio methods that were developed to solve this problem: the variational determination of the secondorder density matrix. This method already has a long history. It is not considered to be on par with best ab initio methods. This work tries an alternative approach. We assume that the wave function has a Slater determinant expansion where all orbitals are doubly occupied or empty. This assumption drastically reduces the scaling of the Nrepresentability conditions. The downside is that the energy explicitly depends on the used orbitals and thus an orbital optimizer is needed. The hope is that by using this approximation, we can capture the lion's share of the static correlation and that any missing dynamic correlation can be added through perturbation theory. We developed an algorithm based on Jacobi rotations. The scaling is much more favorable compared to the general case. The method is then tested on a array of benchmark systems.
 Keywords
 Nrepresentability, DOCI, v2DM
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU6933577
 Chicago
 Poelmans, Ward. 2015. “Variational Determination of the Twoparticle Density Matrix: The Case of Doublyoccupied Space”. Ghent, Belgium: Ghent University. Faculty of Sciences.
 APA
 Poelmans, W. (2015). Variational determination of the twoparticle density matrix: the case of doublyoccupied space. Ghent University. Faculty of Sciences, Ghent, Belgium.
 Vancouver
 1.Poelmans W. Variational determination of the twoparticle density matrix: the case of doublyoccupied space. [Ghent, Belgium]: Ghent University. Faculty of Sciences; 2015.
 MLA
 Poelmans, Ward. “Variational Determination of the Twoparticle Density Matrix: The Case of Doublyoccupied Space.” 2015 : n. pag. Print.
@phdthesis{6933577, abstract = {The world at the level of the atom is described by the branch of science called quantum mechanics. The crown jewel of quantum mechanics is given by the Schr{\"o}dinger equation which describes a system of indistinguishable particles, that interact with each other. However, an equation alone is not enough: the solution is what interests us. Unfortunately, the exponential scaling of the Hilbert space makes it unfeasible to calculate the exact wave function. This dissertation concerns itself with one of the many ab initio methods that were developed to solve this problem: the variational determination of the secondorder density matrix. This method already has a long history. It is not considered to be on par with best ab initio methods. This work tries an alternative approach. We assume that the wave function has a Slater determinant expansion where all orbitals are doubly occupied or empty. This assumption drastically reduces the scaling of the Nrepresentability conditions. The downside is that the energy explicitly depends on the used orbitals and thus an orbital optimizer is needed. The hope is that by using this approximation, we can capture the lion's share of the static correlation and that any missing dynamic correlation can be added through perturbation theory. We developed an algorithm based on Jacobi rotations. The scaling is much more favorable compared to the general case. The method is then tested on a array of benchmark systems.}, author = {Poelmans, Ward}, isbn = {9789461973030}, language = {eng}, pages = {XX, 225}, publisher = {Ghent University. Faculty of Sciences}, school = {Ghent University}, title = {Variational determination of the twoparticle density matrix: the case of doublyoccupied space}, year = {2015}, }