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Volumn 134, Issue , 2007, Pages 61-91

Chapter 4: The lower bound method for density matrices and semidefinite programming

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EID: 34247396641     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (14)

References (23)
  • 1
    • 36149015994 scopus 로고
    • The structure of fermion density matrices
    • A. J. Coleman, The structure of fermion density matrices. Rev. Mod. Phys. 35, 668-687 (1963).
    • (1963) Rev. Mod. Phys , vol.35 , pp. 668-687
    • Coleman, A.J.1
  • 4
    • 34247400212 scopus 로고    scopus 로고
    • R. M. Erdahl and B. Jin, On calculating approximate and exact density matrices, in Chapter 4 of Many-Electron Densities and Density Matrices (J. Cioslowski, ed.), Kluwer, Boston, 2000.
    • R. M. Erdahl and B. Jin, On calculating approximate and exact density matrices, in Chapter 4 of Many-Electron Densities and Density Matrices (J. Cioslowski, ed.), Kluwer, Boston, 2000.
  • 5
    • 0242295588 scopus 로고    scopus 로고
    • Uncertainty relations and reduced density matrices: Mapping many-body quantum mechanics onto four particles
    • D. A. Mazziotti and R. M. Erdahl, Uncertainty relations and reduced density matrices: mapping many-body quantum mechanics onto four particles. Phys. Rev. A 63, 042113 (2001).
    • (2001) Phys. Rev. A , vol.63 , pp. 042113
    • Mazziotti, D.A.1    Erdahl, R.M.2
  • 6
    • 1442282174 scopus 로고    scopus 로고
    • The reduced density matrix method for electronic structure calculations and the role of three-index representability
    • Z. Zhao, B. J. Braams, M. Fukuda, M. L. Overton, and J. K. Percus, The reduced density matrix method for electronic structure calculations and the role of three-index representability. J. Chem. Phys. 120, 2095 (2004),
    • (2004) J. Chem. Phys , vol.120 , pp. 2095
    • Zhao, Z.1    Braams, B.J.2    Fukuda, M.3    Overton, M.L.4    Percus, J.K.5
  • 8
    • 36749112377 scopus 로고
    • The variational approach to the two-body density matrix
    • C. Garrod, M.V. Mihailovic, and M. Rosina, The variational approach to the two-body density matrix. J. Math. Phys. 16, 868-874 (1975).
    • (1975) J. Math. Phys , vol.16 , pp. 868-874
    • Garrod, C.1    Mihailovic, M.V.2    Rosina, M.3
  • 9
    • 84987142241 scopus 로고
    • A density matrix variational calculation for atomic Be
    • C. Garrod and M. A. Fusco, A density matrix variational calculation for atomic Be. Int. J. Quantum Chem. 10, 495 (1976).
    • (1976) Int. J. Quantum Chem , vol.10 , pp. 495
    • Garrod, C.1    Fusco, M.A.2
  • 10
    • 0000450455 scopus 로고
    • Two algorithms for the lower bound method of reduced density matrix theory
    • R. M. Erdahl, Two algorithms for the lower bound method of reduced density matrix theory. Reports Math. Phys. 15, 147-162 (1979).
    • (1979) Reports Math. Phys , vol.15 , pp. 147-162
    • Erdahl, R.M.1
  • 11
    • 0001110772 scopus 로고
    • On minimizing the maximum eigenvalue of a symmetric matrix
    • M. L. Overton, On minimizing the maximum eigenvalue of a symmetric matrix. SIAM J. Matrix Anal. Appl. 9, 256-268 (1988).
    • (1988) SIAM J. Matrix Anal. Appl , vol.9 , pp. 256-268
    • Overton, M.L.1
  • 12
    • 0035872736 scopus 로고    scopus 로고
    • Variational calculations of fermion second-order reduced density matrices by semi-definite programming algorithm
    • M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, Variational calculations of fermion second-order reduced density matrices by semi-definite programming algorithm. J. Chem. Phys. 114, 8282-8202 (2001).
    • (2001) J. Chem. Phys , vol.114 , pp. 8282-8202
    • Nakata, M.1    Nakatsuji, H.2    Ehara, M.3    Fukuda, M.4    Nakata, K.5    Fujisawa, K.6
  • 13
    • 0036599956 scopus 로고    scopus 로고
    • Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix
    • D. A. Mazziotti, Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix. Phys. Rev. A 65, 062511 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 062511
    • Mazziotti, D.A.1
  • 16
    • 0000538731 scopus 로고
    • The variational approach to the density matrix for light nuclei
    • M.V. Mihailovic and M. Rosina, The variational approach to the density matrix for light nuclei. Nucl. Phys. A 237, 221-228 (1975).
    • (1975) Nucl. Phys. A , vol.237 , pp. 221-228
    • Mihailovic, M.V.1    Rosina, M.2
  • 17
    • 33748313131 scopus 로고    scopus 로고
    • Variational reduced-density-matrix method using three-particle N-representability conditions with application to many-electron molecules
    • D. A. Mazziotti, Variational reduced-density-matrix method using three-particle N-representability conditions with application to many-electron molecules. Phys. Rev. A 74, 032501 (2006).
    • (2006) Phys. Rev. A , vol.74 , pp. 032501
    • Mazziotti, D.A.1
  • 18
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite optimization
    • M. J. Todd, Semidefinite optimization. Acta Numer. 10, 515 (2001).
    • (2001) Acta Numer , vol.10 , pp. 515
    • Todd, M.J.1
  • 20
    • 37649028080 scopus 로고    scopus 로고
    • Realization of quantum chemistry without wave functions through first-order semidefinite, programming
    • D. A. Mazziotti, Realization of quantum chemistry without wave functions through first-order semidefinite, programming. Phys. Rev. Lett. 93, 213001 (2004).
    • (2004) Phys. Rev. Lett , vol.93 , pp. 213001
    • Mazziotti, D.A.1
  • 21
    • 11144324409 scopus 로고    scopus 로고
    • First-order semidefinite programming for the direct determination of two-electron reduced density matrices with application to many-electron atoms and molecules
    • D. A. Mazziotti, First-order semidefinite programming for the direct determination of two-electron reduced density matrices with application to many-electron atoms and molecules. J. Chem. Phys. 121, 10957 (2004).
    • (2004) J. Chem. Phys , vol.121 , pp. 10957
    • Mazziotti, D.A.1
  • 22
    • 28844460348 scopus 로고    scopus 로고
    • 2 condition through first-order semidefinite programming
    • 2 condition through first-order semidefinite programming. Phys. Rev. A 72, 032510 (2005).
    • (2005) Phys. Rev. A , vol.72 , pp. 032510
    • Mazziotti, D.A.1


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