Local ab initio methods for calculating optical bandgaps in periodic systems. II. Periodic density fitted local configuration interaction singles method for solids.

We present a density fitted local configuration interaction singles (CIS) method for calculating optical bandgaps in 3D-periodic systems. We employ an Ewald technique to carry out infinite lattice summations for the exciton-exciton interaction, and robust product-density specific local density fitting in direct space for the electron-hole interaction. Moreover, we propose an alternative to the usual cyclic model with Born-von Karman periodic boundary conditions, the so called Wigner-Seitz supercell truncated infinite model, which exhibits much improved convergence of the CIS excitation energy with respect to the size of the supercell. Test calculations on a series of prototypical systems demonstrate that the method at the present stage can be used to calculate the excitonic bandgaps of 3D periodic systems with up to a dozen atoms in the unit cell, ranging from wide-gap insulators to semiconductors.

[1]  Bartolomeo Civalleri,et al.  Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: the case of LiH. , 2011, The Journal of chemical physics.

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

[3]  Lucia Reining,et al.  Efficient ab initio calculations of bound and continuum excitons in the absorption spectra of semico , 2007, 0705.3140.

[4]  Š. Varga,et al.  Density fitting of Coulomb integrals in electronic structure calculations of solids , 2005 .

[5]  Scarontefan Varga.  Long-range analysis of density fitting in extended systems† , 2008 .

[6]  G. Kresse,et al.  Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections. , 2007, Physical review letters.

[7]  J. Noga,et al.  Accuracy of density fitting in calculation of two-electron repulsion integrals in periodic systems , 2007 .

[8]  Cesare Pisani,et al.  Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications , 2008, J. Comput. Chem..

[9]  P. Fulde.  Method of increments for excitations in correlated electron systems , 2005 .

[10]  Miller,et al.  Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. , 1985, Physical review. B, Condensed matter.

[11]  Jozef Noga,et al.  Density fitting of two-electron integrals in extended systems with translational periodicity: the Coulomb problem. , 2006, The Journal of chemical physics.

[12]  J. Nicholas,et al.  Basis sets for ab initio periodic Hartree—Fock studies of zeolite/adsorbate interactions: He, Ne, and Ar in silica sodalite , 1996 .

[13]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg , 2011 .

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

[15]  L. Maschio,et al.  Fitting of local densities in periodic systems , 2008 .

[16]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[17]  R. Dovesi,et al.  A general method to obtain well localized Wannier functions for composite energy bands in linear combination of atomic orbital periodic calculations , 2001 .

[18]  Koichi Kobayashi,et al.  Optical spectra and electronic structure of ice , 1983 .

[19]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[20]  Christof Hättig,et al.  CC2 excitation energy calculations on large molecules using the resolution of the identity approximation , 2000 .

[21]  Manabu Oumi,et al.  A doubles correction to electronic excited states from configuration interaction in the space of single substitutions , 1994 .

[22]  H. Katagiri.  Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition. , 2005, The Journal of chemical physics.

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

[24]  Asbjörn M. Burow,et al.  Resolution of identity approximation for the Coulomb term in molecular and periodic systems. , 2009, The Journal of chemical physics.

[25]  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 .

[26]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[27]  N. Marzari,et al.  Maximally localized Wannier functions for entangled energy bands , 2001, cond-mat/0108084.

[28]  R. Dovesi,et al.  On the electrostatic potential in crystalline systems where the charge density is expanded in Gaussian functions , 1992 .

[29]  A. Kolmakov,et al.  REFLECTION SPECTRA OF LITHIUM HYDRIDE CRYSTALS IN 4-25 eV RANGE AT 5 K , 1987 .

[30]  M. Schütz,et al.  Second Order Local Møller-Plesset Perturbation Theory for Periodic Systems: the CRYSCOR Code , 2010 .

[31]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[32]  M. Preuss,et al.  Optical absorption of water: coulomb effects versus hydrogen bonding. , 2005, Physical review letters.

[33]  Brett I. Dunlap,et al.  Robust and variational fitting , 2000 .

[34]  Martin Schütz,et al.  A multistate local coupled cluster CC2 response method based on the Laplace transform. , 2009, The Journal of chemical physics.

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

[36]  R. Evarestov,et al.  The hartree-fock method and density-functional theory as applied to an infinite crystal and to a cyclic cluster , 2002 .

[37]  W. C. Walker,et al.  Exciton thermoreflectance of MgO and CaO , 1973 .

[38]  F. Harris.  Hartree-Fock Studies of Electronic Structures of Crystalline Solids , 1975 .

[39]  G. H. Reiling,et al.  Fundamental Optical Absorption in Magnesium Oxide , 1958 .

[40]  J. Mintmire,et al.  Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations , 1982 .

[41]  Denis Usvyat,et al.  Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers. , 2011, The Journal of chemical physics.

[42]  M. Albrecht,et al.  Ab initio Green's function formalism for band structures , 2004, cond-mat/0409078.

[43]  U. Birkenheuer,et al.  Multireference configuration interaction treatment of excited-state electron correlation in periodic systems: the band structure of trans-polyacetylene , 2004, cond-mat/0407382.

[44]  Bartolomeo Civalleri,et al.  CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals , 2005 .

[45]  Georg Kresse,et al.  Second-order Møller-Plesset perturbation theory applied to extended systems. II. Structural and energetic properties. , 2010, The Journal of chemical physics.

[46]  Localization of Wannier functions for entangled energy bands , 2004, cond-mat/0409337.

[47]  G. Scuseria,et al.  Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree-Fock-type exchange introduce excitonic effects? , 2008, The Journal of chemical physics.

[48]  A. Savin,et al.  Density Functionals for Correlation Energies of Atoms and Molecules , 1985 .

[49]  A Marini,et al.  The Bethe–Salpeter equation: a first-principles approach for calculating surface optical spectra , 2004 .

[50]  Peter Pulay,et al.  Local configuration interaction: An efficient approach for larger molecules , 1985 .

[51]  Kim Julia Hintze,et al.  Periodic calculations of excited state properties for solids using a semiempirical approach. , 2012, Physical chemistry chemical physics : PCCP.

[52]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[53]  M. Schütz,et al.  On the physisorption of water on graphene: a CCSD(T) study. , 2011, Physical chemistry chemical physics : PCCP.

[54]  P. Knowles,et al.  Poisson equation in the Kohn-Sham Coulomb problem. , 2001, Physical review letters.

[55]  Claudia Ambrosch-Draxl,et al.  Lowest optical excitations in molecular crystals: bound excitons versus free electron-hole pairs in anthracene. , 2004, Physical review letters.

[56]  Cesare Pisani,et al.  CRYSCOR: a program for the post-Hartree-Fock treatment of periodic systems. , 2012, Physical chemistry chemical physics : PCCP.

[57]  R. Bartlett,et al.  Many-body Green's-function calculations on the electronic excited states of extended systems , 2000 .

[58]  W. C. Walker,et al.  Electronic spectrum of crystalline lithium fluoride. , 1967 .

[59]  S. Tomić,et al.  First-principles optical response of semiconductors and oxide materials , 2011 .

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

[61]  Frederick R. Manby,et al.  The Poisson equation in density fitting for the Kohn-Sham Coulomb problem , 2001 .

[62]  Stoll,et al.  Correlation energy of diamond. , 1992, Physical review. B, Condensed matter.

[63]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[64]  H Germany,et al.  Correlation-induced corrections to the band structure of boron nitride: a wave-function-based approach. , 2009, The Journal of chemical physics.

[65]  V. Plekhanov.  Wannier-Mott excitons in isotope-disordered crystals , 1998 .

[66]  D. Lynch,et al.  Thermoreflectance of LiF between 12 and 30 eV , 1976 .

[67]  Lu J. Sham,et al.  Local-field and excitonic effects in the optical spectrum of a covalent crystal , 1975 .

[68]  Hans W. Horn,et al.  Fully optimized contracted Gaussian basis sets for atoms Li to Kr , 1992 .

[69]  Cesare Pisani,et al.  Symmetry-adapted Localized Wannier Functions Suitable for Periodic Local Correlation Methods , 2006 .