Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

[1]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[2]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[3]  V. R. Saunders,et al.  A “Level–Shifting” method for converging closed shell Hartree–Fock wave functions , 1973 .

[4]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[5]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[6]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

[7]  P. Pulay.  Improved SCF convergence acceleration , 1982 .

[8]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[9]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi , 1985 .

[10]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[11]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[12]  G. A. Petersson,et al.  A complete basis set model chemistry. I. The total energies of closed‐shell atoms and hydrides of the first‐row elements , 1988 .

[13]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[14]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[15]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

[16]  G. A. Petersson,et al.  A complete basis set model chemistry. II. Open‐shell systems and the total energies of the first‐row atoms , 1991 .

[17]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[18]  K N Houk,et al.  Theozymes and compuzymes: theoretical models for biological catalysis. , 1998, Current opinion in chemical biology.

[19]  Alex Zunger,et al.  The inverse band-structure problem of finding an atomic configuration with given electronic properties , 1999, Nature.

[20]  Gustavo E. Scuseria,et al.  IMPROVING SELF-CONSISTENT FIELD CONVERGENCE BY VARYING OCCUPATION NUMBERS , 1999 .

[21]  C. Bris,et al.  Can we outperform the DIIS approach for electronic structure calculations , 2000 .

[22]  P. Mitchell.  A chemist's guide to density functional theory. Wolfram Koch and Max C. Holthausen. Wiley–VCH, Weinheim, 2000. x + 294 pages. £70 ISBN 3‐527‐29918‐1 , 2000 .

[23]  E. Cancès,et al.  On the convergence of SCF algorithms for the Hartree-Fock equations , 2000 .

[24]  E. Cancès,et al.  Self-consistent field algorithms for Kohn–Sham models with fractional occupation numbers , 2001 .

[25]  J. Pople,et al.  Self-consistent molecular orbital methods. 21. Small split-valence basis sets for first-row elements , 2002 .

[26]  G. Scuseria,et al.  A black-box self-consistent field convergence algorithm: One step closer , 2002 .

[27]  W. L. Jorgensen.  The Many Roles of Computation in Drug Discovery , 2004, Science.

[28]  Paweł Sałek,et al.  The trust-region self-consistent field method: towards a black-box optimization in Hartree-Fock and Kohn-Sham theories. , 2004, The Journal of chemical physics.

[29]  Paweł Sałek,et al.  The trust-region self-consistent field method in Kohn-Sham density-functional theory. , 2005, The Journal of chemical physics.

[30]  Weitao Yang,et al.  Designing molecules by optimizing potentials. , 2006, Journal of the American Chemical Society.

[31]  Gustavo E. Scuseria,et al.  Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges , 2007 .

[32]  Shahar Keinan,et al.  Designing molecules with optimal properties using the linear combination of atomic potentials approach in an AM1 semiempirical framework. , 2007, The journal of physical chemistry. A.

[33]  Weitao Yang,et al.  Localization and delocalization errors in density functional theory and implications for band-gap prediction. , 2007, Physical review letters.

[34]  A. M. Efstathiou,et al.  CO adsorption on transition metal clusters: trends from density functional theory , 2008 .

[35]  Weitao Yang,et al.  Fractional spins and static correlation error in density functional theory. , 2008, The Journal of chemical physics.

[36]  Weitao Yang,et al.  Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach. , 2008, The Journal of chemical physics.

[37]  Trygve Helgaker,et al.  A ground-state-directed optimization scheme for the Kohn-Sham energy. , 2008, Physical chemistry chemical physics : PCCP.

[38]  Hao Hu,et al.  Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. , 2008, Annual review of physical chemistry.

[39]  Weitao Yang,et al.  Insights into Current Limitations of Density Functional Theory , 2008, Science.

[40]  Trygve Helgaker,et al.  The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices. , 2008, The Journal of chemical physics.

[41]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.