Evolution-operator method for density functional theory

We describe an implementation of density functional theory that is formulated fully in configuration space, where all wave functions, densities, and potentials are represented on a grid. Central to the method is a fourth-order factorization of the evolution operator for the Kohn-Sham Hamiltonian. Special attention is paid to nonlocal pseudopotentials of the Kleinman-Bylander type, which are necessary for a quantitatively accurate description of molecules, clusters, and solids. It is shown that the fourth-order factorization improves the computational efficiency of the method by about an order of magnitude compared with second-order schemes. We use the Ono-Hirose filtering method to reduce the resolution of the grid used for representing the wave functions. Some care is needed to maintain the fourth-order convergence using filtered projectors, and the necessary precautions are discussed. We apply the method to an isolated carbon atom as well as the carbon-monoxide molecule, the benzene molecule, and the buckminsterfullerene cluster, obtaining quantitative agreement with previous results. The convergence of the method with respect to time step, grid resolution, and filtering method is discussed in detail.

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

[2]  Matthieu Verstraete,et al.  First-principles computation of material properties: the ABINIT software project , 2002 .

[3]  Siu A. Chin,et al.  Symplectic integrators from composite operator factorizations , 1997 .

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

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

[6]  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.

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

[8]  T. Arias.  Multiresolution analysis of electronic structure: semicardinal and wavelet bases , 1998, cond-mat/9805262.

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

[10]  Rochus Schmid,et al.  A general and efficient pseudopotential Fourier filtering scheme for real space methods using mask functions. , 2006, The Journal of chemical physics.

[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]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[13]  V. Eyert.  A Comparative Study on Methods for Convergence Acceleration of Iterative Vector Sequences , 1996 .

[14]  K. Schwarz,et al.  Solid state calculations using WIEN2k , 2003 .

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

[16]  M. Suzuki,et al.  General theory of fractal path integrals with applications to many‐body theories and statistical physics , 1991 .

[17]  S. Pantelides,et al.  Lagrange‐function approach to real‐space order‐N electronic‐structure calculations , 2006 .

[18]  E. Krotscheck,et al.  A fast configuration space method for solving local Kohn–Sham equations , 2005 .

[19]  M. Scheffler,et al.  Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory , 1998, cond-mat/9807418.

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

[21]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

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

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

[24]  A. Zunger,et al.  CORRIGENDUM: Momentum-space formalism for the total energy of solids , 1979 .

[25]  Gregory Beylkin,et al.  Multiresolution quantum chemistry: basic theory and initial applications. , 2004, The Journal of chemical physics.

[26]  Matt Probert,et al.  First-principles simulation: ideas, illustrations and the CASTEP code , 2002 .

[27]  Zhenyu Zhang,et al.  "Lagrange functions": a family of powerful basis sets for real-space order-N electronic structure calculations. , 2004, Physical review letters.

[28]  K. Jacobsen,et al.  Real-space grid implementation of the projector augmented wave method , 2004, cond-mat/0411218.

[29]  Jean-Luc Fattebert,et al.  Linear-scaling first-principles molecular dynamics with plane-waves accuracy , 2006 .

[30]  Warren E. Pickett,et al.  Pseudopotential methods in condensed matter applications , 1989 .

[31]  Daniel Jean Baye,et al.  Lagrange‐mesh method for quantum‐mechanical problems , 2006 .

[32]  T. Arias,et al.  Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .

[33]  Taisuke Ozaki,et al.  Efficient projector expansion for the ab initio LCAO method , 2005 .

[34]  Richard M. Martin.  Electronic Structure: Frontmatter , 2004 .

[35]  Sullivan,et al.  Real-space multigrid-based approach to large-scale electronic structure calculations. , 1996, Physical review. B, Condensed matter.

[36]  Rochus Schmid,et al.  Car–Parrinello molecular dynamics using real space wavefunctions , 2006 .

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

[38]  Siu A. Chin,et al.  A fourth order diffusion monte carlo algorithm for solving quantum many-body problems , 2000, nucl-th/0009068.

[39]  Andrew P. Horsfield,et al.  Efficient AB Initio Tight Binding , 1997 .

[40]  Sullivan,et al.  Large-scale electronic-structure calculations with multigrid acceleration. , 1995, Physical review. B, Condensed matter.

[41]  M. Aichinger,et al.  Fourth-order algorithms for solving local Schrödinger equations in a strong magnetic field , 2005, Comput. Phys. Commun..

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

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