Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals.

Electronic structure methods based on density-functional theory, pseudopotentials, and local-orbital basis sets offer a hierarchy of techniques for modeling complex condensed-matter systems with a wide range of precisions and computational speeds. We analyze the relationships between the algorithms for atomic forces in this hierarchy of techniques, going from empirical tight-binding through ab initio tight-binding to full ab initio. The analysis gives a unified overview of the force algorithms as applied within techniques based either on diagonalization or on linear-scaling approaches. The use of these force algorithms is illustrated by practical calculations with the CONQUEST code, in which different techniques in the hierarchy are applied in a concerted manner.

[1]  Li,et al.  Density-matrix electronic-structure method with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[2]  K. Kudin,et al.  Linear scaling density functional theory with Gaussian orbitals and periodic boundary conditions , 2000 .

[3]  Hernández,et al.  Linear-scaling density-functional-theory technique: The density-matrix approach. , 1996, Physical review. B, Condensed matter.

[4]  O. Sankey,et al.  Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems. , 1989, Physical review. B, Condensed matter.

[5]  Peter Pulay,et al.  A low-scaling method for second order Møller–Plesset calculations , 2001 .

[6]  Michael J. Frisch,et al.  A linear scaling method for Hartree–Fock exchange calculations of large molecules , 1996 .

[7]  G. Kresse,et al.  Ab initio molecular dynamics for liquid metals. , 1993 .

[8]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[9]  G. Scuseria,et al.  Analytic energy gradients for the Gaussian very fast multipole method (GvFMM) , 1996 .

[10]  David R. Bowler,et al.  Parallel sparse matrix multiplication for linear scaling electronic structure calculations , 2001 .

[11]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[12]  Hernández,et al.  Self-consistent first-principles technique with linear scaling. , 1995, Physical review. B, Condensed matter.

[13]  Michele Parrinello,et al.  Polarized atomic orbitals for linear scaling methods , 2002 .

[14]  G. Scuseria,et al.  Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals , 2001 .

[15]  Guntram Rauhut,et al.  Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory , 1998 .

[16]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[17]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. IV. Multipole accelerated formation of the exchange matrix , 1999 .

[18]  Hideaki Fujitani,et al.  Transferable atomic-type orbital basis sets for solids , 2000 .

[19]  Christian Ochsenfeld,et al.  Linear and sublinear scaling formation of Hartree-Fock-type exchange matrices , 1998 .

[20]  Eduardo Hernández,et al.  Linear-scaling DFT-pseudopotential calculations on parallel computers , 1997 .

[21]  M. Dewar,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[22]  Kelly,et al.  Theoretical study of the Si(100) surface reconstruction. , 1995, Physical review. B, Condensed matter.

[23]  Martin Head-Gordon,et al.  Closely approximating second-order Mo/ller–Plesset perturbation theory with a local triatomics in molecules model , 2000 .

[24]  R. Hoffmann.  An Extended Hückel Theory. I. Hydrocarbons , 1963 .

[25]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[26]  Philippe Y. Ayala,et al.  Linear scaling coupled cluster and perturbation theories in the atomic orbital basis , 1999 .

[27]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

[28]  Robert G. Parr,et al.  A Method for Estimating Electronic Repulsion Integrals Over LCAO MO'S in Complex Unsaturated Molecules , 1952 .

[29]  Car,et al.  Orbital formulation for electronic-structure calculations with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[30]  C. M. Goringe,et al.  Basis functions for linear-scaling first-principles calculations , 1997 .

[31]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build , 1997 .

[32]  Martin,et al.  Unconstrained minimization approach for electronic computations that scales linearly with system size. , 1993, Physical review. B, Condensed matter.

[33]  C. Wang,et al.  Tight-binding molecular dynamics with linear system-size scaling , 1994 .

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

[35]  Colombo,et al.  Efficient linear scaling algorithm for tight-binding molecular dynamics. , 1994, Physical review letters.

[36]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[37]  Christian Ochsenfeld,et al.  Linear scaling exchange gradients for Hartree–Fock and hybrid density functional theory , 2000 .

[38]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[39]  David R. Bowler,et al.  Recent progress in linear scaling ab initio electronic structure techniques , 2002 .

[40]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[41]  C Filippi,et al.  Role of electronic correlation in the Si(100) reconstruction: a quantum Monte Carlo study. , 2001, Physical review letters.

[42]  Y Ohta,et al.  The tight-binding bond model , 1988 .

[43]  David R. Bowler,et al.  Tight-binding modelling of materials , 1997 .

[44]  Gustavo E. Scuseria,et al.  A fast multipole algorithm for the efficient treatment of the Coulomb problem in electronic structure calculations of periodic systems with Gaussian orbitals , 1998 .

[45]  Peter Pulay,et al.  Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules , 1969 .

[46]  Vanderbilt,et al.  Generalization of the density-matrix method to a nonorthogonal basis. , 1994, Physical review. B, Condensed matter.

[47]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[48]  J. Pople,et al.  Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures , 1965 .

[49]  G. Scuseria,et al.  Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals. III. Comparison with Born–Oppenheimer dynamics , 2002 .

[50]  Michael J. Frisch,et al.  Achieving linear scaling in exchange-correlation density functional quadratures , 1996 .

[51]  Scheffler,et al.  Total-energy gradients and lattice distortions at point defects in semiconductors. , 1985, Physical review. B, Condensed matter.

[52]  N. Mermin.  Thermal Properties of the Inhomogeneous Electron Gas , 1965 .

[53]  M. Gillan,et al.  A first principles study of sub-monolayer Ge on Si(001) , 2002 .

[54]  M. Gillan,et al.  Tight binding studies of strained Ge/Si(001) growth , 2003 .

[55]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

[56]  Harris.  Simplified method for calculating the energy of weakly interacting fragments. , 1985, Physical review. B, Condensed matter.

[57]  Foulkes,et al.  Tight-binding models and density-functional theory. , 1989, Physical review. B, Condensed matter.

[58]  Yihan Shao,et al.  Efficient evaluation of the Coulomb force in density-functional theory calculations , 2001 .