-
3
-
-
35949007371
-
-
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).
-
(1993)
Phys. Rev. B
, vol.47
, pp. 10891
-
-
Li, X.P.1
Nunes, R.W.2
Vanderbilt, D.3
-
4
-
-
0001554805
-
-
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
-
10
-
-
0842341771
-
-
M. J. S. Dewar, E. G. Zoebisch, E. F. Hearly, and J. P. Stewart, J. Am. Chem. Soc. 107, 3902 (1985).
-
(1985)
J. Am. Chem. Soc.
, vol.107
, pp. 3902
-
-
Dewar, M.J.S.1
Zoebisch, E.G.2
Hearly, E.F.3
Stewart, J.P.4
-
11
-
-
0003912310
-
-
Gaussian, Inc., Pittsburgh, PA
-
GAUSSIAN 95, Development Version (Revision G.3), M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, G. A. Petersson, P. Y. Ayala, A. D. Rabuck, K. Raghavachari, Q. Cui, K. Morokuma, J. B. Foresman, J. Cioslowski, J. V. Ortiz, V. Barone, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. M. W. Gill, B. Johnson, and J. Pople. Gaussian, Inc., Pittsburgh, PA, 1998.
-
(1998)
GAUSSIAN 95, Development Version (Revision G.3)
-
-
Frisch, M.J.1
Trucks, G.W.2
Schlegel, H.B.3
Scuseria, G.E.4
Robb, M.A.5
Cheeseman, J.R.6
Zakrzewski, V.G.7
Montgomery, J.A.8
Stratmann, R.E.9
Burant, J.C.10
Dapprich, S.11
Millam, J.M.12
Daniels, A.D.13
Kudin, K.N.14
Strain, M.C.15
Farkas, O.16
Petersson, G.A.17
Ayala, P.Y.18
Rabuck, A.D.19
Raghavachari, K.20
Cui, Q.21
Morokuma, K.22
Foresman, J.B.23
Cioslowski, J.24
Ortiz, J.V.25
Barone, V.26
Stefanov, B.B.27
Liu, G.28
Liashenko, A.29
Piskorz, P.30
Chen, W.31
Wong, M.W.32
Andres, J.L.33
Replogle, E.S.34
Gomperts, R.35
Martin, R.L.36
Fox, D.J.37
Keith, T.38
Al-Laham, M.A.39
Nanayakkara, A.40
Challacombe, M.41
Peng, C.Y.42
Gill, P.M.W.43
Johnson, B.44
Pople, J.45
more..
-
14
-
-
0040323749
-
-
R. C. Bingham, M. J. S. Dewar, and D. H. Lo, J. Am. Chem. Soc. 97, 1285,1294,1302,1307 (1975).
-
(1975)
J. Am. Chem. Soc.
, vol.97
, pp. 1285
-
-
Bingham, R.C.1
Dewar, M.J.S.2
Lo, D.H.3
-
16
-
-
85034534647
-
-
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
-
-
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
-
-
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
-
21
-
-
0003851780
-
-
SIAM Publications, Philadelphia
-
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).
-
(1998)
ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
-
-
Lehoucq, R.1
Sorensen, D.C.2
Yang, C.3
-
22
-
-
0000322706
-
-
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
-
24
-
-
0003474751
-
-
Cambridge University Press, Cambridge
-
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and W. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge University Press, Cambridge, 1992).
-
(1992)
Numerical Recipes in Fortran, 2nd Ed.
-
-
Press, W.H.1
Teukolsky, S.A.2
Vetterling, W.T.3
Flannery, W.P.4
-
26
-
-
85034537953
-
-
note
-
i. In addition, it requires 2 matrix multiplications to determine the form of the matrices, and 2 for DIIS.
-
-
-
-
28
-
-
85034533104
-
-
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
-
-
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
-
-
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
-
-
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.
-
-
-
-
38
-
-
0030498830
-
-
S. E. Lietzke, V. E. Carperos, and C. E. Kundrot, Acta Crystallogr., Sect. D: Biol. Crystallogr. 52, 687 (1996).
-
(1996)
Acta Crystallogr., Sect. D: Biol. Crystallogr.
, vol.52
, pp. 687
-
-
Lietzke, S.E.1
Carperos, V.E.2
Kundrot, C.E.3
|