Sökning: "Density Matrix Purification"

Visar resultat 1 - 5 av 11 avhandlingar innehållade orden Density Matrix Purification.

1. 1. Matrix Algebra for Quantum Chemistry

   Författare :Emanuel H. Rubensson; Pawel Salek; Stefan Goedecker; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; linear scaling; reduced complexity; electronic structure; density functional theory; Hartree-Fock; density matrix purification; congruence transformation; inverse factorization; eigenvalues; eigenvectors; numerical linear algebra; occupied subspace; canonical angles; invariant subspace; Theoretical chemistry; Teoretisk kemi;

   Sammanfattning : This thesis concerns methods of reduced complexity for electronic structure calculations.  When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. LÄS MER

3. 2. Sparse Matrices in Self-Consistent Field Methods

   Författare :Emanuel Rubensson; Pawel Salek; Hans Ågren; Anders Niklasson; Axel Ruhe; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; sparse matrix; self-consistent field; Hartree-Fock; Density Functional Theory; Density Matrix Purification; Theoretical chemistry; Teoretisk kemi;

   Sammanfattning : This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. LÄS MER

4. 3. Efficient Density Matrix Methods for Large Scale Electronic Structure Calculations

   Författare :Anastasia Kruchinina; Emanuel H. Rubensson; Elias Rudberg; David Bowler; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; electronic structure; linear scaling; density matrix; density functional theory; Hartree-Fock; recursive polynomial expansion; density matrix purification; eigenvectors; molecular orbitals; stopping criteria; inverse factorization; matrix sparsity; parallelization; Scientific Computing; Beräkningsvetenskap;

   Sammanfattning : Efficient and accurate methods for computing the density matrix are necessary to be able to perform large scale electronic structure calculations. For sufficiently sparse matrices, the computational cost of recursive polynomial expansions to construct the density matrix scales linearly with increasing system size. LÄS MER

5. 4. Parallelization of dynamic algorithms for electronic structure calculations

   Författare :Anton G. Artemov; Emanuel H. Rubensson; Maya Neytcheva; Bo Kågström; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; parallelization; task-based programming; matrix algorithms; sparse matrices; inverse factorization; localized computations; density matrix methods; electronic structure calculations; Scientific Computing; Beräkningsvetenskap;

   Sammanfattning : The aim of electronic structure calculations is to simulate behavior of complex materials by resolving interactions between electrons and nuclei in atoms at the level of quantum mechanics. Progress in the field allows to reduce the computational complexity of the solution methods to linear so that the computational time scales proportionally to the size of the physical system. LÄS MER

7. 5. Quantum Chemistry for Large Systems

   Författare :Elias Rudberg; Pawel Salek; Christian Ochsenfeld; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; quantum chemistry; fast multipole method; density matrix purification; sparse matrices; Theoretical chemistry; Teoretisk kemi;

   Sammanfattning : This thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree-Fock calculations. LÄS MER