Electronic Structure Calculations under Periodic Boundary Conditions Based on the Gaussian and Fourier Transform (GFT) Method.

We developed the Gaussian and Fourier transform method for crystalline systems. In this method, the Hartree (Coulomb) term of valence electron contribution is taken into account by solving the Poisson equation based on Fourier transform technique. We compared the band structures obtained by the Hartee-Fock (HF) approximation and the density functional theory (DFT). We used three different types of density functional approximations such as the local density approximation (LDA), generalized gradient approximation (GGA), and hybrid density functional. In this paper, we confirm that our calculation technique yields similar results to previous studies.

[1]  G. Scuseria,et al.  The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals. , 2007, The Journal of chemical physics.

[2]  Philippe Y. Ayala,et al.  Atomic orbital Laplace-transformed second-order Møller–Plesset theory for periodic systems , 2001 .

[3]  Jürgen Wieferink,et al.  First-principles study of acetylene adsorption onβ−SiC(001)−(3×2) , 2007 .

[4]  Bernard Delley,et al.  FAST CALCULATION OF ELECTROSTATICS IN CRYSTALS AND LARGE MOLECULES , 1996 .

[5]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

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

[7]  Soler,et al.  Self-consistent order-N density-functional calculations for very large systems. , 1996, Physical review. B, Condensed matter.

[8]  Richard L. Martin,et al.  Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional. , 2005, The Journal of chemical physics.

[9]  M. Head‐Gordon,et al.  Configuration interaction singles, time-dependent Hartree-Fock, and time-dependent density functional theory for the electronic excited states of extended systems , 1999 .

[10]  Frederick R. Manby,et al.  Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms , 2007 .

[11]  Kimihiko Hirao,et al.  Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals. , 2007, The Journal of chemical physics.

[12]  Michael J Frisch,et al.  Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems. , 2006, The Journal of chemical physics.

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

[14]  Artur F Izmaylov,et al.  Influence of the exchange screening parameter on the performance of screened hybrid functionals. , 2006, The Journal of chemical physics.

[15]  Chen,et al.  Dual-space approach for density-functional calculations of two- and three-dimensional crystals using Gaussian basis functions. , 1995, Physical review. B, Condensed matter.

[16]  K. Hirao,et al.  Adaptive density partitioning technique in the auxiliary plane wave method , 2006 .

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

[18]  Saunders,et al.  Static lattice and electron properties of MgCO3 (magnesite) calculated by ab initio periodic Hartree-Fock methods. , 1993, Physical review. B, Condensed matter.

[19]  Michele Parrinello,et al.  Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach , 2005, Comput. Phys. Commun..

[20]  Roberto Dovesi,et al.  Exact-exchange Hartree–Fock calculations for periodic systems. I. Illustration of the method† , 1980 .

[21]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[22]  L. Piela,et al.  Multipole expansion in tight-binding Hartree-Fock calculations for infinite model polymers , 1980 .

[23]  Harold Basch,et al.  Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms , 1984 .

[24]  Artur F Izmaylov,et al.  Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems. , 2008, Physical chemistry chemical physics : PCCP.

[25]  G. Scuseria,et al.  Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems. , 2007, The Journal of chemical physics.

[26]  N. Harrison,et al.  On the prediction of band gaps from hybrid functional theory , 2001 .

[27]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[28]  Matthias Krack,et al.  All-electron ab-initio molecular dynamics , 2000 .

[29]  Peter Pulay,et al.  The Fourier transform Coulomb method: Efficient and accurate calculation of the Coulomb operator in a Gaussian basis , 2002 .

[30]  G. Scuseria,et al.  Assessment of a Middle-Range Hybrid Functional. , 2008, Journal of chemical theory and computation.

[31]  P. Krüger,et al.  Structural, elastic, and electronic properties of SiC, BN, and BeO nanotubes , 2007 .

[32]  Krishnan Raghavachari,et al.  Gaussian‐1 theory of molecular energies for second‐row compounds , 1990 .

[33]  Michele Parrinello,et al.  The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations , 1999 .

[34]  S. Hirata,et al.  Density functional crystal orbital study on the normal vibrations of polyacetylene and polymethineimine , 1997 .

[35]  J. C. Slater.  A Simplification of the Hartree-Fock Method , 1951 .

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

[37]  Edward N Brothers,et al.  Accurate solid-state band gaps via screened hybrid electronic structure calculations. , 2008, The Journal of chemical physics.

[38]  Jürgen Wieferink,et al.  Improved hybrid algorithm with Gaussian basis sets and plane waves: First-principles calculations of ethylene adsorption on β-SiC(001)-(3×2) , 2006 .

[39]  Michele Parrinello,et al.  A hybrid Gaussian and plane wave density functional scheme , 1997 .

[40]  Harold Basch,et al.  Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms , 1992 .

[41]  M. Schlüter,et al.  Self-energy operators and exchange-correlation potentials in semiconductors. , 1988, Physical review. B, Condensed matter.

[42]  Svane.  Hartree-Fock band-structure calculations with the linear muffin-tin-orbital method: Application to C, Si, Ge, and alpha -Sn. , 1987, Physical review. B, Condensed matter.

[43]  S. Massidda,et al.  Hartree-Fock LAPW approach to the electronic properties of periodic systems. , 1993, Physical review. B, Condensed matter.

[44]  J. Ladik.  Polymers as solids: a quantum mechanical treatment , 1999 .

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