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Volumn 110, Issue 3, 1999, Pages 1321-1328

What is the best alternative to diagonalization of the Hamiltonian in large scale semiempirical calculations?

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Indexed keywords


EID: 0000725931     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.478008     Document Type: Article
Times cited : (120)

References (38)
  • 4
    • 0001554805 scopus 로고
    • X. P. Li, R. W. Nunes, and D. Vanderbilt, Phys. Rev. B 47, 10 891 (1993); R. W. Nunes and D. Vanderbilt, ibid. 50, 17611 (1994).
    • (1994) Phys. Rev. B , vol.50 , pp. 17611
    • Nunes, R.W.1    Vanderbilt, D.2
  • 16
    • 85034534647 scopus 로고    scopus 로고
    • note
    • During each SCF iteration between 2 to 4 CG-DMS iterations are needed to produce a sufficiently converged density matrix. During each CG-DMS step 5 matrix multipications are required to form the gradient and 3 to calculate the step size. 2 more matrix multiplications are required to perform each purification transformation. To calculate the form of the matrix to be used in the CG-DMS step, 2 matrix multiples are needed and 2 matrix multiples are needed for the DIIS step. Thus, a calculation with 2 CG-DMS steps per SCF iteration and 2 purification cycles per CG-DMS step requires a total of 28 matrix multiples per SCF cycle.
  • 18
    • 85034561078 scopus 로고    scopus 로고
    • note
    • ov, and 1 more to rotate the orbitals. (The rotation is similar to a matrix multiplication in CPU cost.) Every SCF iteration 1 more matrix multiplication is required to form estimates for the eigenvalues of the matrix, 1 to form ρ, and 2 for DIIS. Hence, a calculation taking 2 PD steps per SCF cycle requires 10 matrix multiplications per SCF cycle.
  • 20
    • 0003668665 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ
    • B. N. Bartlett, The Symmetric Eigenvalue Problem (Prentice-Hall, Englewood Cliffs, NJ, 1980). R. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, Philadelphia, 1998); D. C. Sorensen, SIAM J. Matrix Anal. Appl. 13, 357 (1992).
    • (1980) The Symmetric Eigenvalue Problem
    • Bartlett, B.N.1
  • 22
    • 0000322706 scopus 로고
    • B. N. Bartlett, The Symmetric Eigenvalue Problem (Prentice-Hall, Englewood Cliffs, NJ, 1980). R. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, Philadelphia, 1998); D. C. Sorensen, SIAM J. Matrix Anal. Appl. 13, 357 (1992).
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 357
    • Sorensen, D.C.1
  • 26
    • 85034537953 scopus 로고    scopus 로고
    • note
    • i. In addition, it requires 2 matrix multiplications to determine the form of the matrices, and 2 for DIIS.
  • 28
    • 85034533104 scopus 로고    scopus 로고
    • note
    • PDM requires 2 matrix multiplications per purification cycle. It also requires 2 matrix multiplications to determine the form of the matrices, and 2 for DIIS. So a PDM step using 9 purification transformations requires 22 matrix multiplications per SCF cycle.
  • 31
    • 85034549079 scopus 로고    scopus 로고
    • note
    • The polyglycine chains are similar to those described in Refs. 1, 29, and 30. Coordinates for these molecules are available from us.
  • 34
    • 85034555569 scopus 로고    scopus 로고
    • note
    • The water clusters up to 150 water molecules are those used in Ref. 32. We obtained the coordinates from the authors of Ref. 32. Coordinates for the larger water molecule clusters are available from us.
  • 36
    • 85034545020 scopus 로고    scopus 로고
    • note
    • The 368 and 1576 atom RNA molecules are from Refs. 26 and 35, respectively. The 651 atom DNA molecule is from Ref. 34 with sodium atoms added to balance the charge. Hydrogens were added with XPLOR. All larger RNA molecules were made from replicating the 1576 atom RNA molecule.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.