메뉴 건너뛰기




Volumn 231, Issue 6, 2012, Pages 2551-2564

Approximation of the electron density of Aluminium clusters in tensor-product format

Author keywords

Aluminium clusters; Electron density; Finite elements; Multigrid accelerated tensor approximation; Orbital free density functional theory; Tucker type decomposition

Indexed keywords

ALUMINUM; DENSITY FUNCTIONAL THEORY; ELECTRON DENSITY MEASUREMENT; ELECTRONIC STRUCTURE; ELECTRONS; HARTREE APPROXIMATION; NUMERICAL METHODS; QUANTUM CHEMISTRY; TENSORS;

EID: 84856233829     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.12.009     Document Type: Article
Times cited : (11)

References (29)
  • 1
    • 0039030905 scopus 로고    scopus 로고
    • Simplicial grid refinement: on Freudenthal's algorithm and the optimal number of congruence classes
    • Bey J., Aachen R. Simplicial grid refinement: on Freudenthal's algorithm and the optimal number of congruence classes. Numer. Math. 2000, 85:1-29.
    • (2000) Numer. Math. , vol.85 , pp. 1-29
    • Bey, J.1    Aachen, R.2
  • 2
    • 33744691386 scopus 로고
    • Ground state of the electron gas by a stochastic method
    • Ceperly D.M., Alder B.J. Ground state of the electron gas by a stochastic method. Phys. Rev. 1980, 45:566-569.
    • (1980) Phys. Rev. , vol.45 , pp. 566-569
    • Ceperly, D.M.1    Alder, B.J.2
  • 3
    • 0000329960 scopus 로고    scopus 로고
    • Paramagnetic structure for the soliton of the 30° partial dislocation in silicon
    • Csanyi G., Ismail-Beigi S., Arias T.A. Paramagnetic structure for the soliton of the 30° partial dislocation in silicon. Phys. Rev. Lett. 1998, 80:3984-3988.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 3984-3988
    • Csanyi, G.1    Ismail-Beigi, S.2    Arias, T.A.3
  • 8
    • 34047254716 scopus 로고    scopus 로고
    • Non-periodic finite-element formulation of orbital-free density-functional theory
    • Gavini V., Knap J., Bhattacharya K., Ortiz M. Non-periodic finite-element formulation of orbital-free density-functional theory. J. Mech. Phys. Solids 2007, 55:669-696.
    • (2007) J. Mech. Phys. Solids , vol.55 , pp. 669-696
    • Gavini, V.1    Knap, J.2    Bhattacharya, K.3    Ortiz, M.4
  • 9
    • 34047253234 scopus 로고    scopus 로고
    • Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation
    • Gavini V., Bhattacharya K., Ortiz M. Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 2007, 55:697-718.
    • (2007) J. Mech. Phys. Solids , vol.55 , pp. 697-718
    • Gavini, V.1    Bhattacharya, K.2    Ortiz, M.3
  • 10
    • 36248941211 scopus 로고    scopus 로고
    • Tensor-product approximation to operators and functions in high dimension
    • Hackbusch W., Khoromskij B.N. Tensor-product approximation to operators and functions in high dimension. J. Complex. 2007, 23:697-714.
    • (2007) J. Complex. , vol.23 , pp. 697-714
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 11
    • 11744283687 scopus 로고
    • Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of slater-type atomic orbitals
    • Hehre W.J., Stewart R.F., Pople J.A. Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of slater-type atomic orbitals. J. Chem. Phys. 1969, 51:2657-2664.
    • (1969) J. Chem. Phys. , vol.51 , pp. 2657-2664
    • Hehre, W.J.1    Stewart, R.F.2    Pople, J.A.3
  • 12
    • 10644250257 scopus 로고
    • Inhomogeneous electron gas
    • Hohenberg P., Kohn W. Inhomogeneous electron gas. Phys. Rev. 1964, 136:B864-B871.
    • (1964) Phys. Rev. , vol.136
    • Hohenberg, P.1    Kohn, W.2
  • 13
    • 0001045448 scopus 로고    scopus 로고
    • Ab initio study of screw dislocations in Mo and Ta: a new picture of plasticity in bcc transition metals
    • Ismail-Beigi S., Arias T.A. Ab initio study of screw dislocations in Mo and Ta: a new picture of plasticity in bcc transition metals. Phys. Rev. Lett. 2000, 84:1499-1504.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 1499-1504
    • Ismail-Beigi, S.1    Arias, T.A.2
  • 14
    • 85190814428 scopus 로고    scopus 로고
    • Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods. Ph.D. Dissertation. TU Berlin.
    • V. Khoromskaia. Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods. Ph.D. Dissertation. TU Berlin, 2010. http://opus.kobv.de/tuberlin/volltexte/2011/2948/.
    • (2010)
    • Khoromskaia, V.1
  • 15
    • 77955278344 scopus 로고    scopus 로고
    • Fast and accurate tensor approximation of multivariate convolution with linear scaling in dimension
    • Khoromskij B.N. Fast and accurate tensor approximation of multivariate convolution with linear scaling in dimension. J. Comput. Appl. Math. 2010, 234:3122-3139.
    • (2010) J. Comput. Appl. Math. , vol.234 , pp. 3122-3139
    • Khoromskij, B.N.1
  • 16
    • 47849118953 scopus 로고    scopus 로고
    • On tensor approximation of green iterations for Kohn-Sham equations
    • Khoromskij B.N. On tensor approximation of green iterations for Kohn-Sham equations. Comput. Visual. Sci. 2008, 11:259-271.
    • (2008) Comput. Visual. Sci. , vol.11 , pp. 259-271
    • Khoromskij, B.N.1
  • 17
    • 34447513756 scopus 로고    scopus 로고
    • Low rank Tucker tensor approximation to the classical potentials
    • Khoromskij B.N., Khoromskaia V. Low rank Tucker tensor approximation to the classical potentials. Central Euro. J. Math. 2007, 5(3):1-28.
    • (2007) Central Euro. J. Math. , vol.5 , Issue.3 , pp. 1-28
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 18
    • 84897586218 scopus 로고    scopus 로고
    • Multigrid accelerated tensor approximation of function related multi-dimensional arrays
    • Khoromski B.N., Khoromskaia V. Multigrid accelerated tensor approximation of function related multi-dimensional arrays. SIAM J. Sci. Comput. 2009, 31:3002-3026.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 3002-3026
    • Khoromski, B.N.1    Khoromskaia, V.2
  • 19
    • 79952297523 scopus 로고    scopus 로고
    • Numerical solution of the Hartree-Fock equation in the multilevel tensor-structured format
    • Khoromskij B.N., Khoromskaia V., Flad H.-J. Numerical solution of the Hartree-Fock equation in the multilevel tensor-structured format. SIAM J. Sci. Comput. 2011, 33(1):45-65.
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.1 , pp. 45-65
    • Khoromskij, B.N.1    Khoromskaia, V.2    Flad, H.-J.3
  • 20
    • 0042113153 scopus 로고
    • Self-consistent equations including exchange and correlation effects
    • Kohn W., Sham L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140:A1133-A1138.
    • (1965) Phys. Rev. , vol.140
    • Kohn, W.1    Sham, L.J.2
  • 21
    • 85190803709 scopus 로고    scopus 로고
    • Tensor decompositions and applications, Technical Report number SAND2007-6702, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, November 2007.
    • T.G. Kolda, B.W. Bader, Tensor decompositions and applications, Technical Report number SAND2007-6702, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, November 2007.
    • Kolda, T.G.1    Bader, B.W.2
  • 22
    • 2442537377 scopus 로고    scopus 로고
    • Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
    • Kresse G., Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54:11169-11186.
    • (1996) Phys. Rev. B , vol.54 , pp. 11169-11186
    • Kresse, G.1    Furthmüller, J.2
  • 24
    • 24144475862 scopus 로고    scopus 로고
    • Finite element methods in ab initio electronic structure calculations
    • Pask J.E., Sterne P.A. Finite element methods in ab initio electronic structure calculations. Model. Simul. Mater. SC 2005, 13:R71-R96.
    • (2005) Model. Simul. Mater. SC , vol.13
    • Pask, J.E.1    Sterne, P.A.2
  • 25
    • 26144450583 scopus 로고
    • Self-interaction correction to density-functional approximation for many-electron systems
    • Perdew J.P., Zunger A. Self-interaction correction to density-functional approximation for many-electron systems. Phys. Rev. B 1981, 23:5048-5079.
    • (1981) Phys. Rev. B , vol.23 , pp. 5048-5079
    • Perdew, J.P.1    Zunger, A.2
  • 27
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • Tucker L.R. Some mathematical notes on three-mode factor analysis. Psychometrika 1966, 31:279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 28
    • 0001549358 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy density functionals with a density-dependent kernel
    • Wang Y.A., Govind N., Carter E.A. Orbital-free kinetic-energy density functionals with a density-dependent kernel. Phys. Rev. B. 1999, 60:16350-16358.
    • (1999) Phys. Rev. B. , vol.60 , pp. 16350-16358
    • Wang, Y.A.1    Govind, N.2    Carter, E.A.3
  • 29
    • 0001689864 scopus 로고
    • Kinetic-energy functional of the electron-density
    • Wang L.W., Teter M.P. Kinetic-energy functional of the electron-density. Phys. Rev. B 1992, 45:13196-13220.
    • (1992) Phys. Rev. B , vol.45 , pp. 13196-13220
    • Wang, L.W.1    Teter, M.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.