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On the efficiency of algorithms for solving Hartree-Fock and Kohn-Sham response equations
2011 (English)In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 7, no 6, 1610-1630 p.Article in journal (Refereed) Published
Abstract [en]

The response equations as occurring in the Hartree-Fock, multiconfigurational self-consistent field, and Kohn-Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors are split into symmetric and antisymmetric components. Numerical examples are given to compare the performance of the algorithms. The calculations show that the standard response equation for frequencies smaller than the highest occupied molecular orbital-lowest unoccupied molecular orbital gap is best solved using the preconditioned conjugate gradient or conjugate residual algorithms where trial vectors are split into symmetric and antisymmetric components. For larger frequencies in the standard response equation as well as in the damped response equation in general, the preconditioned iterative subspace approach with symmetrized trial vectors should be used. For the response eigenvalue equation, the Davidson algorithm with either paired or symmetrized trial vectors constitutes equally good options. © 2011 American Chemical Society.

Place, publisher, year, edition, pages
American Chemical Society (ACS), 2011. Vol. 7, no 6, 1610-1630 p.
National Category
Theoretical Chemistry
URN: urn:nbn:se:kth:diva-198751DOI: 10.1021/ct100729tISI: 000291500400005ScopusID: 2-s2.0-79959188600OAI: diva2:1059062

References: Olsen, J., Jørgensen, P., (1985) J. Chem. Phys., 82, pp. 3235-3264; Casida, M.E., Chong, D.P., (1995) Recent Advances in Density Functional Methods, 1, pp. 155-192. , In, Part 1;, Ed.; World Scientific: Singapore,; Vol.; Chapter 5, pp; Norman, P., Bishop, D.M., Jensen, H.J.Aa., Oddershede, J., (2001) J. Chem. Phys., 115, pp. 10323-10334; Norman, P., Bishop, D.M., Jensen, H.J.Aa., Oddershede, J., (2005) J. Chem. Phys., 123, pp. 194103-194120; Kristensen, K., Kauczor, J., Kjærgaard, T., Jørgensen, P., (2009) J. Chem. Phys., 131, p. 04411233; Orr, B.J., Ward, J.F., (1971) Mol. Phys., 20, pp. 513-526; Boyd, R.W., (2008) Nonlinear Optics, pp. 155-157. , 3rd ed.; Academic Press: Burlington, MA; Bunch, J.R., Hopcroft, J.E., (1974) Math. Comp., 28, pp. 231-236; Atkinson, K.A., (1989) An Introduction to Numerical Analysis, pp. 511-525. , 2nd ed.; John Wiley & Sons: New York; Trefethen, L.N., Iii, B.D., (1997) Numerical Linear Algrebra, pp. 172-178. , SIAM: Philadelphia, PA; Jørgensen, P., Linderberg, J., (1970) Int. J. Quantum Chem., 4, pp. 587-602; Pople, J.A., Krishnan, R., Schlegel, H., Binkley, J.S., (1979) Int. J. Quantum Chem., 13, pp. 225-241; Purvis, G.D., Bartlett, R.J., (1981) J. Chem. Phys., 75, pp. 1284-1292; Wormer, P.E.S., Visser, F., Paldus, J., (1982) J. Comput. Phys., 48, pp. 23-44; Hestenes, M.R., Stiefel, E., (1952) J. Res. Natl. Bur. Stand., Sect. A, 49, pp. 409-436; Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., (2007) Numerical Recipes in C++: The Art of Scientific Computing, pp. 87-92. , 3rd ed.; Cambridge University Press: Cambridge, U.K; Shewchuk, J.R., (1994) An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, , Carnegie Mellon University: Pittsburgh, PA; Saad, Y., (2003) Iterative Methods for Sparse Linear Systems, pp. 187-194. , SIAM: Philadelphia, PA; Stiefel, E., (1955) Comment. Math. Helv., 29, pp. 157-179; Niklasson, A.M.N., Challacombe, M., (2004) Phys. Rev. Lett., 92, p. 1930014; Coriani, S., Høst, S., Jansík, B., Thøgersen, L., Olsen, J., Jørgensen, P., Reine, S., Sałek, P., (2007) J. Chem. Phys., 126, p. 15410811; Davidson, E.R., (1975) J. Comput. Phys., 17, pp. 87-94; Flament, J.P., Gervais, H.P., (1979) Int. J. Quantum Chem., 16, pp. 1347-1356; Hansen, A.E., Voigt, B., Rettrup, S., Bouman, T.D., (1983) Int. J. Quantum Chem., 23, pp. 595-611; Olsen, J., Jensen, H.J.A., Jørgensen, P., (1988) J. Comput. Phys., 74, pp. 265-282; Olsen, J., Jørgensen, P., Simons, J., (1990) Chem. Phys. Lett., 169, pp. 463-472; Saue, T., Schwerdtfeger, P., (2002) Relativistic Electronic Structure Theory - Part 1: Fundamentals, pp. 332-400. , In;, Ed.; Elsevier, Amsterdam, The Netherlands,; Chapter 7, pp; Saue, T., Jensen, H.J.A., (2003) J. Chem. Phys., 118, pp. 522-536; Bast, R., Jensen, H.J.A., Saue, T., (2009) Int. J. Quantum Chem., 109, pp. 2091-2112; Villaume, S., Saue, T., Norman, P., (2010) J. Chem. Phys., 133, p. 06410510; Kjærgaard, T., Jørgensen, P., Olsen, J., Coriani, S., Helgaker, T., (2008) J. Chem. Phys., 129, p. 05410623; Cíaek, J., Paldus, J., (1967) J. Chem. Phys., 47, pp. 3976-3985; Larsen, H., Jørgensen, P., Olsen, J., Helgaker, T., (2000) J. Chem. Phys., 113, pp. 8908-8917; Axelsson, O., (1996) Iterative Solution Methods, pp. 252-254. , Cambridge University Press: Cambridge, U.K; Helgaker, T., Jørgensen, P., Olsen, J., (2000) Molecular Electronic-Structure Theory, pp. 543-548. , Wiley: Chichester, U.K; Parlett, B.N., (1980) The Symmetric Eigenvalue Problem, pp. 75-80. , Prentice Hall: Englewood Cliff, New Jersey; MacDonald, J.K.L., (1933) Phys. Rev., 43, pp. 830-833; Ziółkowski, M., Weijo, V., Jørgensen, P., Olsen, J., (2008) J. Chem. Phys., 128, p. 20410512; Helgaker, T., Jensen, H.J.A., Jørgensen, P., (2005) DALTON An Ab Initio Electronic Structure Program, ,, release 2.0; Hehre, W.J., Ditchfield, R., Pople, J.A., (1972) J. Chem. Phys., 56, pp. 2257-2261; NIST Standard Reference Database Number 69, ,, NIST: Gaithersburg, MD; (2008) Maestro, ,, v. 8.5; Schrodinger, LLC: Cambridge, MA; Becke, A.D., (1993) J. Chem. Phys., 98, pp. 5648-5652; Stephens, P.J., Devlin, F.J., Chabalowski, C.F., Frisch, M.J., (1994) J. Phys. Chem., 98, pp. 11623-11627; Dunning, T.H., (1989) J. Chem. Phys., 90, pp. 1007-1023; Genick, U.K., Soltis, S.M., Kuhn, P., Canestrelli, I.L., Getzoff, E.D., (1998) Nature, 392, pp. 206-209; Yanai, T., Tew, D.P., Handy, N.C., (2004) Chem. Phys. Lett., 393, pp. 51-57; Pulay, P., (1980) Chem. Phys. Lett., 73, pp. 393-398; Pulay, P., (1982) J. Comput. Chem., 3, pp. 556-560. QC 20170118

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