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  • 1
    Electronic Resource
    Electronic Resource
    Linear scaling computation of the Fock matrix. IV. Multipole accelerated formation of the exchange matrix (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 6223-6229 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new method for the multipole evaluation of contracted Cartesian Gaussian-based electron repulsion integrals is described, and implemented in linear scaling methods for computation of the Hartree–Fock exchange matrix. The new method, which relies on a nonempirical multipole acceptability criterion [J. Chem. Phys. 109, 8764 (1998)], renders the work associated with integral evaluation independent of the basis set contraction length. Benchmark calculations on a series of three-dimensional water molecule clusters and graphitic sheets with highly contracted basis sets indicate that the new method is up to 4.6 times faster than a well optimized direct integral evaluation routine. For calculations involving lower levels of contraction a factor of 2 speedup is typically observed. Importantly, the method achieves these large gains in computational efficiency while maintaining numerical equivalence with standard direct self consistent field theory. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479926
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  • 2
    Electronic Resource
    Electronic Resource
    The solvation of Na+ in water: First-principles simulations (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 4668-4673 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: First-principles molecular dynamics simulations have been performed on the solvation of Na+ in water. Consistent with the available experimental data, we find that the first solvation shell of Na+ contains on average 5.2 water molecules. A significant number of water exchanges between the first and second solvation shells are observed. However, the simulations are not long enough to reliably measure the rate of water exchange. Contrary to several previous studies, we do not find any effect of Na+ on the orientation of water molecules outside of the first solvation shell. Furthermore, the complete set of structural properties determined by first-principles molecular dynamics is not predicted by any of the known classical simulations. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1288688
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  • 3
    Electronic Resource
    Electronic Resource
    A multipole acceptability criterion for electronic structure theory (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 8764-8769 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Accurate and computationally inexpensive estimates of multipole expansion errors are crucial to the success of several fast electronic structure methods. In this paper, a new nonempirical multipole acceptability criterion is described that is directly applicable to expansions of high order moments. Several model calculations typical of electronic structure theory are presented to demonstrate its performance. For cases involving small translation distances, accuracies are increased by up to five orders of magnitude over an empirical criterion. The new multipole acceptance criterion is on average within an order of magnitude of the exact expansion error. Use of the multipole acceptance criterion in hierarchical multipole based methods as well as in traditional electronic structure methods is discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477546
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  • 4
    Electronic Resource
    Electronic Resource
    Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 9708-9717 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473833
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  • 5
    Electronic Resource
    Electronic Resource
    Fast assembly of the Coulomb matrix: A quantum chemical tree code (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 4685-4698 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Fast methods based on a representation of the electron charge density in a Hermite Gaussian basis are introduced for constructing the Coulomb matrix encountered in Hartree-Fock and density functional theories. Simplifications that arise from working in a Hermite Gaussian basis are discussed, translations of such functions are shown to yield rapidly convergent expansions valid in both the near- and far-field, and the corresponding truncation errors are derived in compact form. The relationship of such translations to hierarchical multipole methods is pointed out and a quantum chemical tree code related to the Barnes-Hut method is developed. Novel methods are introduced for the independent thresholding of "bra'' and "ket'' distributions as well as for screening out insignificant multipole interactions. Recurrence relations for computing the Cartesian multipole tensor are used to efficiently calculate far-field electrostatic interactions using high-order expansions. Application of the quantum chemical tree code to assembly of the Coulomb matrix for HF/3-21G calculations on sequences of polyglycine α-helices and water clusters demonstrate scalings as favorable as N1.6, where N is the number of basis functions. Comparisons with a commercial electronic structure program indicate that our method is highly competitive. Speed is obtained without sacrificing precision, truncation errors are controlled with a single parameter, and the method performs equally well with a contracted or uncontracted LCAO basis. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471163
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  • 6
    Electronic Resource
    Electronic Resource
    Linear scaling computation of the Fock matrix (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 5526-5536 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Computation of the Fock matrix is currently the limiting factor in the application of Hartree-Fock and hybrid Hartree-Fock/density functional theories to larger systems. Computation of the Fock matrix is dominated by calculation of the Coulomb and exchange matrices. With conventional Gaussian-based methods, computation of the Fock matrix typically scales as ∼N2.7, where N is the number of basis functions. A hierarchical multipole method is developed for fast computation of the Coulomb matrix. This method, together with a recently described approach to computing the Hartree-Fock exchange matrix of insulators [J. Chem. Phys. 105, 2726 (1900)], leads to a linear scaling algorithm for calculation of the Fock matrix. Linear scaling computation the Fock matrix is demonstrated for a sequence of water clusters at the restricted Hartree-Fock/3-21G level of theory, and corresponding accuracies in converged total energies are shown to be comparable with those obtained from standard quantum chemistry programs. Restricted Hartree-Fock/3-21G calculations on several proteins of current interest are documented, including endothelin, charybdotoxin, and the tetramerization monomer of P53. The P53 calculation, involving 698 atoms and 3836 basis functions, may be the largest Hartree-Fock calculation to date. The electrostatic potentials of charybdotoxin and the tetramerization monomer of P53 are visualized and the results are related to molecular function. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473575
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  • 7
    Electronic Resource
    Electronic Resource
    Linear scaling computation of the Hartree–Fock exchange matrix (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 2726-2734 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Thresholding criteria are introduced that enforce locality of exchange interactions in Cartesian Gaussian-based Hartree–Fock calculations. These criteria are obtained from an asymptotic form of the density matrix valid for insulating systems, and lead to a linear scaling algorithm for computation of the Hartree–Fock exchange matrix. Restricted Hartree–Fock/3-21G calculations on a series of water clusters and polyglycine α-helices are used to demonstrate the O(N) complexity of the algorithm, its competitiveness with standard direct self-consistent field methods, and a systematic control of error in converged total energies. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472135
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  • 8
    Electronic Resource
    Electronic Resource
    A quantum fluid of metallic hydrogen suggested by first-principles calculations (2004)
    [s.l.] : Macmillian Magazines Ltd.
    Nature 431 (2004), S. 669-672 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] It is generally assumed that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models have also suggested that compressed hydrogen may form an unusual two-component (protons and electrons) metallic fluid at low ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/nature02968
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  • 9
    Electronic Resource
    Electronic Resource
    Electronic and structural transitions in dense liquid sodium (2007)
    [s.l.] : Nature Publishing Group
    Nature 449 (2007), S. 448-451 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] At ambient conditions, the light alkali metals are free-electron-like crystals with a highly symmetric structure. However, they were found recently to exhibit unexpected complexity under pressure. It was predicted from theory—and later confirmed by experiment—that lithium and ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/nature06123
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  • 10
    Electronic Resource
    Electronic Resource
    Linear scaling computation of the Fock matrix. III. Formation of the exchange matrix with permutational symmetry (2000)
    Springer
    Theoretical chemistry accounts 104 (2000), S. 344-349 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Linear Scaling ; Exact exchange ; Electron repulsion integrals ; Gaussian basis functions ; Permutational symmetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract.  A direct comparison is made between two recently proposed methods for linear scaling computation of the Hartree–Fock exchange matrix to investigate the importance of exploiting two-electron integral permutational symmetry. Calculations on three-dimensional water clusters and graphitic sheets with different basis sets and levels of accuracy are presented to identify specific cases where permutational symmetry may or may not be useful. We conclude that a reduction in integrals via permutational symmetry does not necessarily translate into a reduction in computation times. For large insulating systems and weakly contracted basis sets the advantage of permutational symmetry is found to be negligible, while for noninsulating systems and highly contracted basis sets a fourfold speedup is approached.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140000127
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