Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T18:38:13.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges

Published online by Cambridge University Press:  16 June 2007

Konstantin N. Kudin  and
Gustavo E. Scuseria
Konstantin N. Kudin
Affiliation:
Department of Chemistry and Princeton Institute for Science and Technology of Materials (PRISM), Princeton University, Princeton, NJ 08544, USA.
Gustavo E. Scuseria
Affiliation:
Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.
Get access

Abstract

This paper reviews popular acceleration techniques to converge the non-linear self-consistent field equations appearing in quantum chemistry calculations with localized basis sets. The different methodologies, as well as their advantages and limitations are discussed within the same framework. Several illustrative examples of calculations are presented. This paper attempts to describe recent achievements and remaining challenges in this field.

Keywords

Hartree-Fock equationsself-consistent fieldconvergence acceleration algorithmslevel shiftdirect inversion of the iterative subspaceDIISgeneralized minimum residueGMRESrelaxed constraints algorithmRCAenergy DIISEDIISdensity functional theoryDFT.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007 , pp. 281 - 296
Copyright
© EDP Sciences, SMAI, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bacskay, G.B., A quadratically convergent Hartree-Fock (QC-SCF) method - application to closed shell systems. Chem. Phys. 61 (1981) 385–404. CrossRef
Bhattacharyya, S.P., Accelerated convergence in SCF calculations and level shifting technique. Chem. Phys. Lett. 56 (1978) 395–398. CrossRef
Boys, S.F., Electronic wave functions. 1. A general method of calculation for the stationary states of any molecular system. Proc. R. Soc. Lond. A 200 (1950) 542–554. CrossRef
E. Cancés, in Mathematical Models and Methods for ab initio Quantum Chemistry, M. Defranceschi and C. Le Bris Eds., Lecture Notes in Chemistry 74, Springer, Berlin (2000).
Cancés, E., Self-consistent field algorithms for Kohn-Sham models with fractional occupation numbers. J. Chem. Phys. 114 (2001) 10616–10622. CrossRef
Cancés, E. and Le Bris, C., On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM: M2AN 34 (2000) 749–774. CrossRef
Cancés, E. and Le Bris, C., Can we outperform the DIIS approach for electronic structure calculations? Int. J. Quantum Chem. 79 (2000) 82–90. 3.0.CO;2-I>CrossRef
Cancès, E., Kudin, K.N., Scuseria, G.E. and Turinici, G., Quadratically convergent algorithm for fractional occupation numbers in density functional theory. J. Chem. Phys. 118 (2003) 5364–5368. CrossRef
Daniels, A.D. and Scuseria, G.E., Converging difficult SCF cases with conjugate gradient density matrix search. Phys. Chem. Chem. Phys. 2 (2000) 2173–2176. CrossRef
de Andrade, M.D., Mundim, K.C. and Malbouisson, L.A.C., GSA algorithm applied to electronic structure: Hartree-Fock-GSA method. Int. J. Quant. Chem. 103 (2005) 493–499. CrossRef
R.M. Dreizler and E.K.U. Gross, Density functional theory. Springer, Berlin (1990).
Fouqueau, A., Mer, S., Casida, M.E., Daku, L.M.L., Hauser, A., Mineva, T. and Neese, F., Comparison of density functionals for energy and structural differences between the high-[T-5(2g) : (t(2g))(4)(e(g))(2)] and low-[(1)A(1g) : (t(2g))(6)(e(g))(0)] spin states of the hexaquoferrous cation [ Fe(H2O)(6)] (2+). J. Chem. Phys. 120 (2004) 9473–9486. CrossRef
Francisco, J.B., Martinez, J.M. and Martinez, L., Globally convergent trust-region methods for self-consitent field electronic structure calculations. J. Chem. Phys. 121 (2004) 10863–10878. CrossRef
M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, and J.A. Pople, Gaussian 03, Revision C.02. Gaussian Inc., Wallingford CT (2004).
D.R. Hartree, The calculation of atomic structures. Wiley (1957).
Helgaker, T., Larsen, H., Olsen, J. and Jorgensen, P., Direct optimization of the AO density matrix in Hartree-Fock and Kohn-Sham theories. Chem. Phys. Lett. 327 (2000) 397–403. CrossRef
Hohenberg, P. and Kohn, W., Inhomogeneous electron gas. Phys. Rev. 136 (1964) 864B–B871. CrossRef
H. Hsu, E.R. Davidson and R.M. Pitzer, SCF method for hole states.J. Chem. Phys. 65 (1976) 609–613.
Johnson, B.G., Gill, P.M.W. and Pople, J.A., The performance of a family of Density Functional methods. J. Chem. Phys. 98 (1993) 5612–5626. CrossRef
Karlstrom, G., Dynamical damping based on energy minimization for use in ab initio molecular-orbital SCF calculations. Chem. Phys. Lett. 67 (1979) 348–350. CrossRef
Kohn, W. and Sham, L.J., Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133–A1138. CrossRef
Kudin, K.N., Scuseria, G.E. and Cancès, E., A black-box self-consistent field convergence algorithm: One step closer. J. Chem. Phys. 116 (2002) 8255–8261. CrossRef
Lions, P.L., Solutions of Hartree-Fock equations for coulomb-systems. Comm. Math. Phys. 109 (1987) 33–97. CrossRef
Mitin, A.V., The dynamic level shift method for improving the convergence of the SCF procdure. J. Comput. Chem. 9 (1988) 107–110. CrossRef
Natiello, M.A. and Scuseria, G.E., Convergence properties of Hartree-Fock SCF molecular calculations. Int. J. Quantum Chem. 26 (1984) 1039–1049. CrossRef
Pulay, P., Convergence acceleration of iterative sequences - the case of SCF iteration. Chem. Phys. Lett. 73 (1980) 393–398. CrossRef
Pulay, P., Improved SCF convergence acceleration. J. Comp. Chem. 3 (1982) 556–560. CrossRef
Rabuck, A.D. and Scuseria, G.E., Improving self-consistent field convergence by varying occupation numbers. J. Chem. Phys. 110 (1999) 695–700. CrossRef
Ramek, M. and Fritzer, H.P., New aspects of dynamical damping in ab initio molecular SCF calculations. Comput. Chem. 6 (1982) 165–168. CrossRef
Roothan, C.C.J., New developments in molecular orbital theory. Rev. Mod. Phys. 23 (1951) 69–89. CrossRef
Saad, Y. and Schultz, M.H., GMRES - a generalized minimal residual algorithm for solving nonsymmetric linear-systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856–869. CrossRef
Saunders, V.R. and Hillier, I.H., Level-shifting method for converging closed shell Hartree-Fock wave-functions. Int. J. Quant. Chem. 7 (1973) 699–705. CrossRef
Schultz, N.E., Zhao, Y. and Truhlar, D.G., Databases for transition element bonding: Metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations. J. Phys. Chem. A 109 (2005) 4388–4403. CrossRef
Scuseria, G.E., Linear scaling density functional calculations with Gaussian orbitals. J. Phys. Chem. A 103 (1999) 4782–4790. CrossRef
Thogersen, L., Olsen, J., Yeager, D., Jorgensen, P., Salek, P. and Helgaker, T., The trust-region self-consistent field method: Towards a black-box optimization in Hartree-Fock and Kohn-Sham theories. J. Chem. Phys. 121 (2004) 16–27. CrossRef
Thogersen, L., Olsen, J., Kohn, A., Jorgensen, P., Salek, P. and Helgaker, T., The trust-region self-consitent field method in Kohn-Sham density-functional theory. J. Chem. Phys. 123 (2005) 074103. CrossRef
Voorhis, T.V. and Head-Gordon, M., A geometric approach to direct minimization. Mol. Phys. 100 (2002) 1713–1721. CrossRef
Yazyev, O.V., Kudin, K.N. and Scuseria, G.E., Efficient algorithm for band connectivity resolution. Phys. Rev. B 65 (2002) 205117. CrossRef
Zerner, M.C. and Hehenberger, M., Dynamical damping scheme for converging molecular SCF calculations. Chem. Phys. Lett. 62 (1979) 550–554. CrossRef