Real-space electronic-structure calculations with a time-saving double-grid technique

We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve norm-conserving pseudopotentials, solving Poisson equations, and treating models which have specific periodicities, while keeping a high degree of accuracy. Since real-space methods are inherently local, they have a lot of advantages in applicability and flexibility compared with the conventional plane-wave approach, and promise to be well suited for large and accurate {\it ab initio} calculations. In order to demonstrate the potential power of these techniques, we present several applications for electronic structure calculations of atoms, molecules and a helical nanotube.

[1]  Tomoya Ono,et al.  First-Principles Calculations In Real-Space Formalism: Electronic Configurations And Transport Properties Of Nanostructures , 2005 .

[2]  First-principles study on field evaporation of surface atoms from W(0 1 1) and Mo(0 1 1) surfaces , 2004, cond-mat/0410034.

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

[4]  David Vanderbilt,et al.  First-principles approach to insulators in finite electric fields. , 2002, Physical review letters.

[5]  Yoshitaka Fujimoto,et al.  First-principles treatments of electron transport properties for nanoscale junctions , 2003 .

[6]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[7]  D. Hamann,et al.  Norm-Conserving Pseudopotentials , 1979 .

[8]  First-principles study on field evaporation for silicon atom on Si(001) surface , 2003, cond-mat/0307683.

[9]  L. Kleinman,et al.  Self-consistent calculations of the energy bands and bonding properties of B sub 12 C sub 3 , 1990 .

[10]  First-principles study of dielectric properties of bulk NaCl and ultrathin NaCl films under a finite external electric field , 2004, cond-mat/0410182.

[11]  Martins,et al.  Efficient pseudopotentials for plane-wave calculations. , 1991, Physical review. B, Condensed matter.

[12]  S. Okada,et al.  Three-dimensional crystalline carbon: Stable polymers of C20 fullerene , 2001 .

[13]  H.-W. Lee,et al.  Towards unified understanding of conductance of stretched monatomic contacts , 2003 .

[14]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[15]  Comparison of variational real-space representations of the kinetic energy operator , 2001, cond-mat/0112141.

[16]  N. N. Medvedev,et al.  The algorithm for three-dimensional Voronoi polyhedra , 1986 .

[17]  James R. Chelikowsky,et al.  Real-space pseudopotential method for computing the electronic properties of periodic systems , 2004 .

[19]  Riichiro Saito,et al.  Electronic structure of chiral graphene tubules , 1992 .

[20]  Tomoya Ono,et al.  Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations , 1999 .

[21]  Leonard Kleinman,et al.  Efficacious Form for Model Pseudopotentials , 1982 .

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

[23]  K. Kobayashi.  Norm-conserving pseudopotential database (NCPS97) , 1999 .

[24]  Allan,et al.  Solution of Schrödinger's equation for large systems. , 1989, Physical review. B, Condensed matter.

[25]  Dawn A. Yarne,et al.  Ab initio molecular dynamics calculations with simple, localized, orthonormal real-space basis sets , 2003 .

[26]  Kikuji Hirose,et al.  First-principles calculations in real-space formalism , 2005 .

[27]  J. Mintmire,et al.  First-principles band structures of armchair nanotubes , 1998 .

[28]  Sawada,et al.  New one-dimensional conductors: Graphitic microtubules. , 1992, Physical review letters.

[29]  T. Torsti,et al.  Multigrid method for electronic structure calculations , 2001, cond-mat/0101233.

[30]  Y. Saad,et al.  Finite-difference-pseudopotential method: Electronic structure calculations without a basis. , 1994, Physical review letters.

[31]  White,et al.  Are fullerene tubules metallic? , 1992, Physical review letters.

[32]  T. Beck.  Real-space mesh techniques in density-functional theory , 2000, cond-mat/0006239.

[33]  Galli,et al.  Real-space adaptive-coordinate electronic-structure calculations. , 1995, Physical review. B, Condensed matter.

[34]  Andrew G. Glen,et al.  APPL , 2001 .

[35]  Geert Brocks,et al.  Real-space finite-difference method for conductance calculations , 2004 .

[36]  D. R. Hamann,et al.  Pseudopotentials that work: From H to Pu , 1982 .

[37]  K. Chang,et al.  Even-odd behavior of conductance in monatomic sodium wires. , 2001, Physical review letters.

[38]  A. Becke.  A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[39]  Wu,et al.  Higher-order finite-difference pseudopotential method: An application to diatomic molecules. , 1994, Physical review. B, Condensed matter.

[40]  Hyun-Woo Lee,et al.  Even-odd behavior and quantization of conductance in monovalent atomic contacts , 2002 .

[41]  J. Mintmire,et al.  Electronic structure simulations of carbon nanotubes , 1996 .

[42]  Ville Havu,et al.  Nonequilibrium electron transport in two-dimensional nanostructures modeled using Green's functions and the finite-element method , 2003, cond-mat/0308105.

[43]  T. Ono,et al.  Geometry and Conductance of Al Wires Suspended between Semi-Infinite Crystalline Electrodes , 2003, cond-mat/0307684.

[44]  Lawrence T. Scott,et al.  Gas-phase production and photoelectron spectroscopy of the smallest fullerene, C20 , 2000, Nature.