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.
Mots clés : Hartree-Fock equations, self-consistent field, convergence acceleration algorithms, level shift, direct inversion of the iterative subspace, DIIS, generalized minimum residue, GMRES, relaxed constraints algorithm, RCA, energy DIIS, EDIIS, density functional theory, DFT
@article{M2AN_2007__41_2_281_0,
author = {Kudin, Konstantin N. and Scuseria, Gustavo E.},
title = {Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {281--296},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/m2an:2007022},
zbl = {1135.81381},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007022/}
}
TY - JOUR AU - Kudin, Konstantin N. AU - Scuseria, Gustavo E. TI - Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 281 EP - 296 VL - 41 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007022/ DO - 10.1051/m2an:2007022 LA - en ID - M2AN_2007__41_2_281_0 ER -
%0 Journal Article %A Kudin, Konstantin N. %A Scuseria, Gustavo E. %T Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 281-296 %V 41 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007022/ %R 10.1051/m2an:2007022 %G en %F M2AN_2007__41_2_281_0
Kudin, Konstantin N.; Scuseria, Gustavo E. Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 2, pp. 281-296. doi : 10.1051/m2an:2007022. http://www.numdam.org/articles/10.1051/m2an:2007022/
[1] , A quadratically convergent Hartree-Fock (QC-SCF) method - application to closed shell systems. Chem. Phys. 61 (1981) 385-404.
[2] , Accelerated convergence in SCF calculations and level shifting technique. Chem. Phys. Lett. 56 (1978) 395-398.
[3] , 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. | Zbl
[4] , 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). | MR | Zbl
[5] , Self-consistent field algorithms for Kohn-Sham models with fractional occupation numbers. J. Chem. Phys. 114 (2001) 10616-10622.
[6] and, On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM: M2AN 34 (2000) 749-774. | Numdam | Zbl
[7] and, Can we outperform the DIIS approach for electronic structure calculations? Int. J. Quantum Chem. 79 (2000) 82-90.
[8] ,, and, Quadratically convergent algorithm for fractional occupation numbers in density functional theory. J. Chem. Phys. 118 (2003) 5364-5368.
[9] and, Converging difficult SCF cases with conjugate gradient density matrix search. Phys. Chem. Chem. Phys. 2 (2000) 2173-2176.
[10] , and, GSA algorithm applied to electronic structure: Hartree-Fock-GSA method. Int. J. Quant. Chem. 103 (2005) 493-499.
[11] and, Density functional theory. Springer, Berlin (1990). | Zbl
[12] ,,,,, and, 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 120 (2004) 9473-9486.
[13] , and, Globally convergent trust-region methods for self-consitent field electronic structure calculations. J. Chem. Phys. 121 (2004) 10863-10878. | Zbl
[14] ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, and, Gaussian 03, Revision C.02. Gaussian Inc., Wallingford CT (2004).
[15] , The calculation of atomic structures. Wiley (1957). | MR | Zbl
[16] ,, and, Direct optimization of the AO density matrix in Hartree-Fock and Kohn-Sham theories. Chem. Phys. Lett. 327 (2000) 397-403.
[17] and, Inhomogeneous electron gas. Phys. Rev. 136 (1964) 864B-B871.
[18] , and, SCF method for hole states.J. Chem. Phys. 65 (1976) 609-613.
[19] , and, The performance of a family of Density Functional methods. J. Chem. Phys. 98 (1993) 5612-5626.
[20] , Dynamical damping based on energy minimization for use in ab initio molecular-orbital SCF calculations. Chem. Phys. Lett. 67 (1979) 348-350.
[21] and, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133-A1138.
[22] , and, A black-box self-consistent field convergence algorithm: One step closer. J. Chem. Phys. 116 (2002) 8255-8261.
[23] , Solutions of Hartree-Fock equations for coulomb-systems. Comm. Math. Phys. 109 (1987) 33-97. | Zbl
[24] , The dynamic level shift method for improving the convergence of the SCF procdure. J. Comput. Chem. 9 (1988) 107-110.
[25] and, Convergence properties of Hartree-Fock SCF molecular calculations. Int. J. Quantum Chem. 26 (1984) 1039-1049.
[26] , Convergence acceleration of iterative sequences - the case of SCF iteration. Chem. Phys. Lett. 73 (1980) 393-398.
[27] , Improved SCF convergence acceleration. J. Comp. Chem. 3 (1982) 556-560.
[28] and, Improving self-consistent field convergence by varying occupation numbers. J. Chem. Phys. 110 (1999) 695-700.
[29] and, New aspects of dynamical damping in ab initio molecular SCF calculations. Comput. Chem. 6 (1982) 165-168.
[30] , New developments in molecular orbital theory. Rev. Mod. Phys. 23 (1951) 69-89. | Zbl
[31] and, GMRES - a generalized minimal residual algorithm for solving nonsymmetric linear-systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856-869. | Zbl
[32] and, Level-shifting method for converging closed shell Hartree-Fock wave-functions. Int. J. Quant. Chem. 7 (1973) 699-705.
[33] , and, 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.
[34] , Linear scaling density functional calculations with Gaussian orbitals. J. Phys. Chem. A 103 (1999) 4782-4790.
[35] ,,,, and, 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.
[36] ,,,, and, The trust-region self-consitent field method in Kohn-Sham density-functional theory. J. Chem. Phys. 123 (2005) 074103.
[37] and, A geometric approach to direct minimization. Mol. Phys. 100 (2002) 1713-1721.
[38] , and, Efficient algorithm for band connectivity resolution. Phys. Rev. B 65 (2002) 205117.
[39] and, Dynamical damping scheme for converging molecular SCF calculations. Chem. Phys. Lett. 62 (1979) 550-554.
Cité par Sources :
