GW method with the self-consistent Sternheimer equation

We propose an approach to quasiparticle GW calculations which does not require the computation of unoccupied electronic states. In our approach the screened Coulomb interaction is evaluated by solving self-consistent linear-response Sternheimer equations and the noninteracting Green's function is evaluated by solving inhomogeneous linear systems. The frequency dependence of the screened Coulomb interaction is explicitly taken into account. In order to avoid the singularities of the screened Coulomb interaction the calculations are performed along the imaginary axis, and the results are analytically continued to the real axis through Pad\'e approximants. As a proof of concept we implemented the proposed methodology within the empirical pseudopotential formalism and we validated our implementation using silicon as a test case. We examine the advantages and limitations of our method and describe promising future directions.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  L. Hedin.  NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[3]  Marvin L. Cohen,et al.  Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures , 1966 .

[4]  Richard M. Martin,et al.  Microscopic theory of force constants in the adiabatic approximation , 1970 .

[5]  John P. Walter,et al.  Wave-Vector-Dependent Dielectric Function for Si, Ge, GaAs, and ZnSe , 1970 .

[6]  D. R. Hamann,et al.  Self-Consistent Pseudopotential for Si , 1973 .

[7]  James R. Chelikowsky,et al.  ELECTRONIC STRUCTURE OF SILICON , 1974 .

[8]  H. J. Vidberg,et al.  Solving the Eliashberg equations by means ofN-point Padé approximants , 1977 .

[9]  Alfonso Baldereschi,et al.  Mean-value point and dielectric properties of semiconductors and insulators , 1978 .

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

[11]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

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

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  E. Tosatti,et al.  "Direct" evaluation of the inverse dielectric matrix in semiconductors , 1984 .

[15]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[16]  D. Vanderbilt,et al.  Optimally smooth norm-conserving pseudopotentials. , 1985, Physical review. B, Condensed matter.

[17]  Resta,et al.  Dielectric matrices in semiconductors: A direct approach. , 1985, Physical review. B, Condensed matter.

[18]  D. A. H. Jacobs,et al.  A Generalization of the Conjugate-Gradient Method to Solve Complex Systems , 1986 .

[19]  Louie,et al.  Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies. , 1986, Physical review. B, Condensed matter.

[20]  Baroni,et al.  Ab initio calculation of the macroscopic dielectric constant in silicon. , 1986, Physical review. B, Condensed matter.

[21]  Testa,et al.  Green's-function approach to linear response in solids. , 1987, Physical review letters.

[22]  Louie,et al.  Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators. , 1987, Physical review. B, Condensed matter.

[23]  Johnson,et al.  Modified Broyden's method for accelerating convergence in self-consistent calculations. , 1988, Physical review. B, Condensed matter.

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

[25]  V. Anisimov,et al.  Band theory and Mott insulators: Hubbard U instead of Stoner I. , 1991, Physical review. B, Condensed matter.

[26]  Ortega,et al.  Inverse-photoemission study of Ge(100), Si(100), and GaAs(100): Bulk bands and surface states. , 1993, Physical review. B, Condensed matter.

[27]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[28]  Godby,et al.  GW Gamma approximation for electron self-energies in semiconductors and insulators. , 1994, Physical review. B, Condensed matter.

[29]  S deGironcoli,et al.  Lattice dynamics of metals from density-functional perturbation theory. , 1995 .

[30]  R. Needs,et al.  Space-time method for ab initio calculations of self-energies and dielectric response functions of solids. , 1995, Physical review letters.

[31]  Andreoni,et al.  Ab initio calculations of the quasiparticle and absorption spectra of clusters: The sodium tetramer. , 1995, Physical review letters.

[32]  Analytic continuation of the dynamic response function using an N-point Padé approximant. , 1996, Physical review. B, Condensed matter.

[33]  ELIMINATION OF UNOCCUPIED-STATE SUMMATIONS IN AB INITIO SELF-ENERGY CALCULATIONS FOR LARGE SUPERCELLS , 1997, cond-mat/9803228.

[34]  Xavier Gonze,et al.  First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm , 1997 .

[35]  SYSTEMATIC VERTEX CORRECTIONS THROUGH ITERATIVE SOLUTION OF HEDIN'S EQUATIONS BEYOND THE GW APPROXIMATION , 1997, cond-mat/9710295.

[36]  Steven G. Louie,et al.  Excitonic Effects and the Optical Absorption Spectrum of Hydrogenated Si Clusters , 1998 .

[37]  Stefan Albrecht Lucia Reining Rodolfo Del Sole Giovanni Onida.  Ab Initio Calculation of Excitonic Effects in the Optical Spectra of Semiconductors , 1998 .

[38]  F. Aryasetiawan,et al.  The GW method , 1997, cond-mat/9712013.

[39]  Steven G. Louie,et al.  Electron-Hole Excitations in Semiconductors and Insulators , 1998 .

[40]  W. Aulbur,et al.  Quasiparticle calculations in solids , 2000 .

[41]  S. Louie,et al.  Electron-hole excitations and optical spectra from first principles , 2000 .

[42]  Anomalous quasiparticle lifetime in graphite: band structure effects. , 2001, Physical review letters.

[43]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[44]  C. Spataru,et al.  Anomalous Quasiparticle Lifetime in Graphite , 2001 .

[45]  L. Reining,et al.  Electronic excitations: density-functional versus many-body Green's-function approaches , 2002 .

[46]  Andreas Frommer,et al.  BiCGStab(ℓ) for Families of Shifted Linear Systems , 2003, Computing.

[47]  S. Lebègue,et al.  Implementation of an all-electron GW approximation based on the projector augmented wave method without plasmon pole approximation: Application to Si, SiC, AlAs, InAs, NaH, and KH , 2003, cond-mat/0301320.

[48]  S. Louie,et al.  Excitonic effects and optical spectra of single-walled carbon nanotubes. , 2003, Physical review letters.

[49]  Steven G. Louie,et al.  Effect of semicore orbitals on the electronic band gaps of Si, Ge, and GaAs within the GW approximation , 2004 .

[50]  Matthias Scheffler,et al.  Combining GW calculations with exact-exchange density-functional theory: an analysis of valence-band photoemission for compound semiconductors , 2005, cond-mat/0502404.

[51]  Takao Kotani,et al.  Quasiparticle self-consistent GW theory. , 2006, Physical review letters.

[52]  Steven G. Johnson,et al.  A Modified Split-Radix FFT With Fewer Arithmetic Operations , 2007, IEEE Transactions on Signal Processing.

[53]  Valeria Simoncini,et al.  Recent computational developments in Krylov subspace methods for linear systems , 2007, Numer. Linear Algebra Appl..

[54]  Lucia Reining,et al.  Understanding correlations in vanadium dioxide from first principles. , 2007, Physical review letters.

[55]  James R. Chelikowsky,et al.  Real-space pseudopotential method for first principles calculations of general periodic and partially periodic systems , 2008 .

[56]  X. Gonze,et al.  Accurate GW self-energies in a plane-wave basis using only a few empty states: Towards large systems , 2008 .

[57]  A. Alavi,et al.  Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential , 2008 .

[58]  Angel Rubio,et al.  Conserving GW scheme for nonequilibrium quantum transport in molecular contacts , 2007, 0710.0482.

[59]  L. Kronik,et al.  Orbital-dependent density functionals: Theory and applications , 2008 .

[60]  Stefano Baroni,et al.  Optimal representation of the polarization propagator for large-scale GW calculations , 2009 .

[61]  F. Gygi,et al.  Iterative calculations of dielectric eigenvalue spectra , 2009 .

[62]  S. Baroni,et al.  GW quasiparticle spectra from occupied states only , 2009, 0910.0791.