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Quantum Chemistry for Large Systems
KTH, School of Biotechnology (BIO).
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

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. Density matrix purification, which is a method used to construct the density matrix for a given Fock matrix, is also discussed.

The methods described are not only applicable in the Hartree-Fock case, but also in Kohn-Sham Density Functional Theory calculations, where the Coulomb and exchange matrices are parts of the Kohn-Sham matrix. Screening techniques for reducing the computational complexity of both Coulomb and exchange computations are discussed, including 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.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , xi, 56 p.
Series
Trita-BIO-Report, ISSN 1654-2312 ; 2007:13
Keyword [en]
quantum chemistry, fast multipole method, density matrix purification, sparse matrices
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:kth:diva-4561ISBN: 978-91-7178-797-2 (print)OAI: oai:DiVA.org:kth-4561DiVA: diva2:12865
Public defence
2007-12-12, FA32, Albanova, Roslagstullsbacken 21, 106 91 Stockholm, 13:00
Opponent
Supervisors
Note
QC 20100817Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2010-08-17Bibliographically 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. Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons
Open this publication in new window or tab >>Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons
2007 (English)In: Nano letters (Print), ISSN 1530-6984, E-ISSN 1530-6992, Vol. 7, no 8, 2211-2213 p.Article in journal (Refereed) Published
Abstract [en]

Band gap studies of zigzag-edge graphene ribbons are presented. While earlier calculations at LDA level show that zigzag-edge graphene ribbons become half-metallic when cross-ribbon electric fields are applied, our calculations with hybrid density functional demonstrate that finite graphene ribbons behave as half-semiconductors. The spin-dependent band gap can be changed in a wide range, making possible many applications in spintronics.

Keyword
Electric fields; Energy gap; Ion exchange; Molecular interactions; Semiconductor materials; Graphenes; Nanoribbons; Nonlocal exchange; Zigzag-edge graphene; Nanostructures; carbon; nanotube
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-7740 (URN)10.1021/nl070593c (DOI)000248657800008 ()17602536 (PubMedID)2-s2.0-34548168661 (Scopus ID)
Note
QC 20100817Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2017-12-14Bibliographically approved
4. A linear scaling study of solvent-solute interaction energy of drug molecules in aqua solution
Open this publication in new window or tab >>A linear scaling study of solvent-solute interaction energy of drug molecules in aqua solution
2007 (English)In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 111, no 34, 10320-10328 p.Article in journal (Refereed) Published
Abstract [en]

Solvent-solute interaction energies for three well-known drug molecules in water solution are computed at the Hartree-Fock and B3LYP density functional theory levels using a linear scaling technique, which allows one to explicitly include in the model water molecules up to 14 A away from the solute molecule. The dependence of calculated interaction energies on the amount of included solvent has been examined. It is found that it is necessary to account for water molecules within an 8 A radius around the drug molecule to reach the saturated solvent interaction level. Effects of electron correlation and basis set on solvent-solute interaction energies are discussed.

Keyword
Density functional theory; Electron correlations; Solutions; Solvents; Water
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-7741 (URN)10.1021/jp072621l (DOI)000248929900035 ()2-s2.0-34548558980 (Scopus ID)
Note

QC 20100630

Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2017-06-14Bibliographically approved
5. Basis set dependence of solute-solvent interaction energy of benzene in water: a HF/DFT study
Open this publication in new window or tab >>Basis set dependence of solute-solvent interaction energy of benzene in water: a HF/DFT study
2008 (English)In: Journal of Computational Chemistry, ISSN 0192-8651, E-ISSN 1096-987X, Vol. 29, no 11, 1725-1732 p.Article in journal (Refereed) Published
Abstract [en]

Solute-solvent interaction energies for the benzene molecule dissolved in water are computed using Hartree-Fock and B3LYP density functional theories. Explicit solvent molecules up to 14-angstrom away from the dissolved benzene molecule are included in the calculation of interaction energies. Both basis set dependence and basis Set Superposition errors are carefully examined. It is found that the use of a larger basis set for the region near the solute together with a smaller basis set for the outer region gives results very close to what would have been obtained if the larger basis set had been used for the whole system. It is also shown that a correction for the basis Set superposition error is a necessary component in this kind of calculations. With this correction, results obtained with different tested basis sets converge to within 1 kcal/mol.

Keyword
Ab-initio; Basis set; Benzene; BSSE; Solution; Benzene; Density functional theory; Dissolution; Error correction; Molecules; Probability density function; Solvents; B3LYP density functional; Basis set superposition error (BSSE); Basis sets; Hartree Fock (HF); Interaction energies; Solute solvent interactions; Solvent molecules; Flow interactions
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-7742 (URN)10.1002/jcc.20930 (DOI)000258358100003 ()2-s2.0-47149098003 (Scopus ID)
Note
QC 20100817. Uppdaterad från Submitted till Published 20100817.Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2017-12-14Bibliographically approved
6. Rotations of occupied invariant subspaces in self-consistent field calculations
Open this publication in new window or tab >>Rotations of occupied invariant subspaces in self-consistent field calculations
2008 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 3, 032103- p.Article in journal (Refereed) Published
Abstract [en]

In this article, the self-consistent field (SCF) procedure as used in Hartree-Fock and Kohn-Sham calculations is viewed as a sequence of rotations of the so-called occupied invariant subspace of the potential and density matrices. Computational approximations are characterized as erroneous rotations of this subspace. Differences between subspaces are measured and controlled by the canonical angles between them. With this approach, a first step is taken toward a method where errors from computational approximations are rigorously controlled and threshold values are directly related to the accuracy of the current trial density, thus eliminating the use of ad hoc threshold values. Then, the use of computational resources can be kept down as much as possible without impairment of the SCF convergence. (C) 2008 American Institute of Physics.

Keyword
Electronic-structure calculations; density-matrix search; fast multipole method; convergence acceleration; expansion methods; large systems; hartree-fock; diagonalization; optimization; purification
National Category
Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-14313 (URN)10.1063/1.2884588 (DOI)000254537500003 ()2-s2.0-41549132179 (Scopus ID)
Note
QC 20100803Available from: 2010-08-03 Created: 2010-08-03 Last updated: 2017-12-12Bibliographically approved
7. Estimation of errors in Coulomb and exchange matrix construction
Open this publication in new window or tab >>Estimation of errors in Coulomb and exchange matrix construction
(English)Manuscript (Other academic)
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-7745 (URN)
Note
QC 20100817Available from: 2007-12-04 Created: 2007-12-04 Last updated: 2010-08-17Bibliographically approved
8. Density matrix purification with rigorous error control
Open this publication in new window or tab >>Density matrix purification with rigorous error control
2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, no 7Article in journal (Refereed) Published
Abstract [en]

Density matrix purification, although being a powerful tool for linear scaling construction of the density matrix in electronic structure calculations, has been limited by uncontrolled error accumulation. In this article, a strategy for the removal of small matrix elements in density matrix purification is proposed with which the forward error can be rigorously controlled. The total forward error is separated into two parts, the error in eigenvalues and the error in the occupied invariant subspace. We use the concept of canonical angles to measure and control differences between exact and approximate occupied subspaces. We also analyze the conditioning of the density matrix construction problem and propose a method for calculation of interior eigenvalues to be used together with density matrix purification. (C) 2008 American Institute of Physics.

Keyword
Electronic-structure calculations; linear scaling computation; consistent-field theory; fast multipole method; chebyshev expansion methods; binding molecular-dynamics; conjugate-gradient method; hartree-fock; tight-binding; parallel computation
National Category
Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-14325 (URN)10.1063/1.2826343 (DOI)000253336800008 ()2-s2.0-39749201822 (Scopus ID)
Note
QC 20100803Available from: 2010-08-03 Created: 2010-08-03 Last updated: 2017-12-12Bibliographically approved
9. Hartree-Fock calculations with linearly scaling memory usage
Open this publication in new window or tab >>Hartree-Fock calculations with linearly scaling memory usage
2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, no 18Article in journal (Refereed) Published
Abstract [en]

We present an implementation of a set of algorithms for performing Hartree-Fock calculations with resource requirements in terms of both time and memory directly proportional to the system size. In particular, a way of directly computing the Hartree-Fock exchange matrix in sparse form is described which gives only small addressing overhead. Linear scaling in both time and memory is demonstrated in benchmark calculations for system sizes up to 11 650 atoms and 67 204 Gaussian basis functions on a single computer with 32 Gbytes of memory. The sparsity of overlap, Fock, and density matrices as well as band gaps are also shown for a wide range of system sizes, for both linear and three-dimensional systems. (C) 2008 American Institute of Physics.

Keyword
Electronic-structure calculations; fast multipole method; consistent-field theory; density-matrix search; convergence acceleration; parallel computation; expansion methods; exchange matrix; coulomb matrix; large systems
National Category
Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-14334 (URN)10.1063/1.2918357 (DOI)000255983500013 ()2-s2.0-43949128760 (Scopus ID)
Note
QC 20100803Available from: 2010-08-03 Created: 2010-08-03 Last updated: 2017-12-12Bibliographically approved
10. Truncation of Small Matrix Elements Based on the Euclidean Norm for Blocked Data Structures
Open this publication in new window or tab >>Truncation of Small Matrix Elements Based on the Euclidean Norm for Blocked Data Structures
2009 (English)In: Journal of Computational Chemistry, ISSN 0192-8651, E-ISSN 1096-987X, Vol. 30, no 6, 974-977 p.Article in journal (Refereed) Published
Abstract [en]

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.

Keyword
sparsity, linear scaling, Hartree-Fock, DFT, density functional theory, blocked data structure, Euclidean norms, Lanczos, sparse matrix, Frobenius norm, electronic-structure calculations, consistent-field theory, density-matrix, expansion methods, diagonalization, minimization, purification, search
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-18301 (URN)10.1002/jcc.21120 (DOI)000264651200015 ()2-s2.0-65449174900 (Scopus ID)
Note
QC 20100817Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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