Implementation of the cyclic cluster model in Hartree-Fock LCAO calculations of crystalline systems

The cyclic cluster model combines advantages of periodic and molecular cluster models for the quantum chemical treatment of perfect and defective crystalline solids. Implementations of this model into molecular codes have so far been realized for semiempirical and local density functional methods only. Due to the occurrence of four-center integrals in ab initio Hartree-Fock methods, the cyclic cluster model is difficult to realize for this case. This study presents a simple procedure for the extraction of cyclic cluster models from periodic Hartree-Fock calculations, based on the idempotency relations of the density matrix. The dependence of calculated results for bulk properties of defect-free titanium dioxide (rutile) from the size and shape of the cyclic clusters is investigated. It is demonstrated that by a proper choice of cyclic clusters where full spheres of nearest neighbor atoms are taken into account, relatively small cyclic clusters can reproduce results for total energies and one-electron energies obtained with full band structure calculations.

[1]  Karl Jug,et al.  Extension of SINDO1 to transition metal compounds , 1992 .

[2]  G. Pacchioni,et al.  Cluster and periodic ab-initio calculations on K/TiO2(110) , 1998 .

[3]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[4]  Karl Jug,et al.  SINDO1. A semiempirical SCF MO method for molecular binding energy and geometry I. Approximations and parametrization , 1980 .

[5]  R. Orlando,et al.  Near-Hartree–Fock wave functions for solids: The case of crystalline silicon , 1992 .

[6]  N. Harrison,et al.  The physical and electronic structure of the rutile (001) surface , 2000 .

[7]  Mauro Causà,et al.  Density functional theory in periodic systems using local Gaussian basis sets , 1996 .

[8]  Ching,et al.  Electronic and optical properties of three phases of titanium dioxide: Rutile, anatase, and brookite. , 1995, Physical review. B, Condensed matter.

[9]  Snyder,et al.  Evaluation of semiempirical quantum-chemical methods in solid-state applications. II. Cyclic-cluster calculations of silicon. , 1987, Physical review. B, Condensed matter.

[10]  C. Pisani.  Quantum-mechanical treatment of the energetics of local defects in crystals: A few answers and many open questions , 1994 .

[11]  M. Causà,et al.  ELECTRONIC AND GEOMETRICAL STRUCTURE OF BULK RUTILE STUDIED WITH HARTREE-FOCK AND DENSITY FUNCTIONAL METHODS , 1996 .

[12]  Karl Jug,et al.  Consistent modifications of SINDO1: I. Approximations and parameters , 1999 .

[13]  Thomas Bredow,et al.  Theoretical investigation of water adsorption at rutile and anatase surfaces , 1995 .

[14]  V. A. Veryazov,et al.  Local characteristics of crystal electronic structure in the Hartree-Fock method , 1999 .

[15]  C. Pisani,et al.  Density matrix of crystalline systems. I. Long-range behavior and related computational problems , 1990 .

[16]  V. A. Lovchikov,et al.  Large unit cell calculations of solids in the CNDO approximation , 1977 .

[17]  Alexander L. Shluger,et al.  Modification of the INDO Calculation Scheme and Parametrization for Ionic Crystals , 1990 .

[18]  Gerald Geudtner,et al.  Development of the cyclic cluster approach for ionic systems , 2001, J. Comput. Chem..

[19]  Roberto Dovesi,et al.  The Periodic Hartree‐Fock Method and Its Implementation in the CRYSTAL Code , 2000 .

[20]  R. Orlando,et al.  Convergence properties of the supercell approach in the study of local defects in solids , 1994 .

[21]  Zhukovskii,et al.  Ab initio modeling of metal adhesion on oxide surfaces with defects , 2000, Physical review letters.

[22]  Stashans,et al.  Theoretical study of lithium intercalation in rutile and anatase. , 1996, Physical review. B, Condensed matter.

[23]  W. Mackrodt.  The nature of valence band holes in pure and Fe‐doped NiO: An ab initio Hartree‐Fock study , 1997 .

[24]  R. Orlando,et al.  Trapped-hole centres containing lithium and sodium in MgO, CaO and SrO. An ab initio supercell study , 1998 .

[25]  Steven G. Louie,et al.  Self-consistent electronic states for reconstructed Si vacancy models , 1976 .

[26]  D. Lin,et al.  Electron states of iron group impurities in doped rutile (TiO2) , 1994 .

[27]  J. W. Halley,et al.  Self-consistent tight-binding atomic-relaxation model of titanium dioxide , 1998 .

[28]  K. Jug,et al.  MSINDO study of the adsorption of water molecules at defective MgO(100) surfaces , 1999 .

[29]  A. M. Dobrotvorskii,et al.  The Quasi‐Molecular Large Unit Cell Model in the Theory of Deep Levels in Imperfect Crystals: Point Defects in Graphitic Boron Nitride , 1974 .

[30]  T. Bredow,et al.  MgO(100) surface relaxation and vacancy defects: a semi-empirical quantum-chemical study , 1999 .

[31]  R. Evarestov,et al.  Supercell Model of V-Doped TiO2: Unrestricted Hartree-Fock Calculations , 1999 .

[32]  R. A. Evarestov,et al.  The translational symmetry in the molecular models of solids , 1975 .

[33]  J. E. Szymanski,et al.  A reformulation of the LUC CNDO approach to the properties of solids. I. General theory , 1985 .

[34]  V. A. Lovchikov,et al.  Hartree‐fock exchange and LCAO approximation in the band structure calculations of solids , 1983 .

[35]  Shah,et al.  Periodic boundary conditions in ab initio calculations. II. Brillouin-zone sampling for aperiodic systems. , 1996, Physical review. B, Condensed matter.

[36]  Timothy Hughbanks,et al.  Structural-electronic relationships in inorganic solids: powder neutron diffraction studies of the rutile and anatase polymorphs of titanium dioxide at 15 and 295 K , 1987 .

[37]  C. Catlow,et al.  Pseudopotential periodic hartree-fock study of rutile TiO2 , 1991 .

[38]  Chelikowsky,et al.  Structural and electronic properties of titanium dioxide. , 1992, Physical review. B, Condensed matter.

[39]  Adaptive-coordinate electronic structure of 3d bands: TiO 2 , 1997 .

[40]  P. Deák.  Choosing Models for Solids , 2000 .

[41]  R. Evarestov,et al.  Symmetry Groups of Cyclic Systems in Crystals , 1985, March 1.

[42]  R. Dovesi,et al.  Non-empirical pseudopotentials in the HF-LCAO approach to crystalline solids: comparison to all-electron results , 1989 .

[43]  R. Nieminen,et al.  First-principles calculations of interstitial boron in silicon , 2000 .

[44]  A. Stashans,et al.  Periodic INDO calculations of organic adsorbates on a TiO2 surface , 1998 .

[45]  R. Grimes,et al.  Theoretical study of perfect and defective TiO2 crystals , 1996 .

[46]  Karl Jug,et al.  Development and parametrization of sindo1 for second‐row elements , 1987 .

[47]  M. Causà,et al.  Theoretical analysis of the structures of titanium dioxide crystals. , 1993, Physical review. B, Condensed matter.

[48]  Roman Boča,et al.  Approaching bulk limit for three‐dimensional solids via the cyclic cluster approximation: Semiempirical INDO study , 1999 .