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Fock Matrix Construction for Large Systems
KTH, School of Biotechnology (BIO).
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This licentiate 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.The methods described are also applicable in Kohn--Sham Density FunctionalTheory calculations, where the Coulomb and exchange matrices areparts of the Kohn--Sham matrix. Screening techniques for reducing the computational complexity of bot Coulomb and exchange computations are discussed, as well as the fast multipole method, used for efficient computation of the Coulomb matrix.

The thesis also discusses how sparsity in the matrices occurring in Hartree--Fock and Kohn--Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them.

As an example of a possible type of application, the thesis includes a theoretical study of Heisenberg exchange constants, using unrestricted Kohn--Sham Density Functional Theory calculations.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , viii, 28 p.
Keyword [en]
quantum chemistry
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:kth:diva-4247ISBN: 978-91-7178-535-0 (print)OAI: oai:DiVA.org:kth-4247DiVA: diva2:11442
Presentation
2006-12-15, FD41, Albanova, Roslagstullsbacken 21, Stockholm, 11:15
Opponent
Supervisors
Note
QC 20101123Available from: 2006-12-19 Created: 2006-12-19 Last updated: 2010-11-23Bibliographically approved
List of papers
1. Efficient implementation of the fast multipole method
Open this publication in new window or tab >>Efficient implementation of the fast multipole method
2006 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 125, no 8, 084106- p.Article in journal (Refereed) Published
Abstract [en]

A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions into branches. Also, a new approach for estimating the error caused by truncation of multipole expansions is presented. It is found that the use of dynamically truncated multipole expansions gives a speedup of a factor of 10 in the work required for multipole interactions, compared to the case when all interactions are computed using a fixed multipole expansion order. Results of benchmark calculations on three-dimensional systems are reported, demonstrating the usefulness of our present implementation of the fast multipole method.

Keyword
Electric charge; Error detection; Matrix algebra; Numerical methods; Probability density function; Coulomb matrix elements; Fast multipole method; Gaussian charge distributions; Computational methods
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-6666 (URN)10.1063/1.2244565 (DOI)000240237000010 ()2-s2.0-33748258300 (Scopus ID)
Note
QC 20100817Available from: 2006-12-19 Created: 2006-12-19 Last updated: 2017-12-14Bibliographically approved
2. A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations
Open this publication in new window or tab >>A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations
2007 (English)In: Journal of Computational Chemistry, ISSN 0192-8651, E-ISSN 1096-987X, Vol. 28, no 16, 2531-2537 p.Article in journal (Refereed) Published
Abstract [en]

A hierarchic sparse matrix data structure for Hartree-Fock/Kohn-Sham calculations is presented. The data structure makes the implementation of matrix manipulations needed for large systems faster, easier, and more maintainable without loss of performance. Algorithms for symmetric matrix square and inverse Cholesky decomposition within the hierarchic framework are also described. The presented data structure is general; in addition to its use in HartreeFock/Kohn-Sham calculations, it may also be used in other research areas where matrices with similar properties are encountered. The applicability of the data structure to ab initio calculations is shown with help of benchmarks on water droplets and graphene nanoribbons.

Keyword
sparse matrix, C plus plus templates, Hartree-Fock, Density Functional Theory, inverse Cholesky decomposition, symmetric matrix square, electronic-structure calculations, approximate inverse preconditioners, conjugate-gradient method, consistent-field theory, density-matrix, diagonalization, search, purification, atoms
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-16288 (URN)10.1002/jcc.20691 (DOI)000250972500003 ()2-s2.0-35948953260 (Scopus ID)
Note
QC 20100817Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
3. Heisenberg Exchange in Dinuclear Manganese Complexes:  A Density Functional Theory Study
Open this publication in new window or tab >>Heisenberg Exchange in Dinuclear Manganese Complexes:  A Density Functional Theory Study
2006 (English)In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 2, no 4, 981-989 p.Article in journal (Refereed) Published
Abstract [en]

This work presents a systematic investigation of the performance of broken symmetry density functional theory for the evaluation of Heisenberg exchange constants. We study dinuclear MnIV-MnIV complexes with bis(μ-oxo), bis(μ-oxo)(μ-carboxylato), and tris(μ-oxo) cores for this purpose, as these are of fundamental biological interest as well as being potential precursors for molecular magnets based on manganese complexes, the so-called Mn12 magnets. The obtained results indicate that quantitative agreement with available experimental data for the Heisenberg exchange constants can be achieved for most of the investigated complexes but also that there are significant failures for some compounds. We evaluate factors influencing the accuracy of obtained results and examine effects of different mappings between broken symmetry and Heisenberg Hamiltonian states in an attempt to formulate a reliable recipe for the evaluation of magnetic coupling in these complexes. An assessment of the bonding situation in the molecular system under investigation is found crucial in choosing the appropriate scheme for evaluation of the Heisenberg exchange constants.

Keyword
TRANSITION-METAL-COMPLEXES, BROKEN SYMMETRY APPROACH, CRYSTAL-STRUCTURE, ELECTRONIC-STRUCTURE, MAGNETIC-PROPERTIES, DFT CALCULATIONS, BASIS-SETS, CLUSTERS, DIMERS, RELEVANCE
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-6668 (URN)10.1021/ct050325b (DOI)000238926400010 ()2-s2.0-33846233085 (Scopus ID)
Note
QC 20100916Available from: 2006-12-19 Created: 2006-12-19 Last updated: 2017-12-14Bibliographically approved

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