A Crystal Orbital approach for two‐ and three‐dimensional solids on the basis of CNDO/INDO Hamiltonians. Basis equations

A Hartree–Fock (HF) self-consistent field (SCF) crystal orbital (CO) formalism for two- and three-dimensional (2D/3D) solids on the basis of semiempirical CNDO/INDO (complete neglect of differential overlap; intermediate neglect of differential overlap) Hamiltonians is presented. The employed SCF variants allow for the treatment of atomic species up to bromine under the inclusion of the first (i.e., 3d) transition metal series. Band structure investigations of 2D and 3D materials containing more than 30 atoms per unit cell are feasible by the present SCF HF CO formalism. The theoretical background of the computational scheme is given in this contribution. Special emphasis is placed on physically reliable truncation criteria for the lattice sums, the adaptation of the crystal symmetry in k space, as well as the suitable choice of domains in Brillouin zone (BZ) integrations required in the determination of charge-density matrices. The capability and limitations of the semiempirical SCF HF CO approach is demonstrated for some simpler solids by comparing the present computational results with those of ab initio CO schemes as well as conventional numerical methods in soid-state theory. The employed model solids are graphite and BN (2D and 3D networks for both solids) as well as diamond, silicon, germanium, and TiS2.

[1]  J. G. Fripiat,et al.  On the behaviour of exchange in restricted hartree-fock-roothaan calculations for periodic polymers , 1981 .

[2]  On weighted lowdin orthogonalization , 1986 .

[3]  Michael C. Böhm,et al.  A CNDO/INDO molecular orbital formalism for the elements H to Br. theory , 1981 .

[4]  J. Matthew,et al.  Parameterisation of LCAO calculations in the solid state , 1980 .

[5]  R. Dovesi.  On the role of symmetry in the ab initio hartree‐fock linear‐combination‐of‐atomic‐orbitals treatment of periodic systems , 1986 .

[6]  M. Böhm.  Symmetry Breaking in Organometallic Polymers Due to Interchain Interactions , 1984 .

[7]  Michael C. Böhm,et al.  A method for the calculation of improved band gaps in the crystal orbital formalism , 1983 .

[8]  Jean-Marie André,et al.  L'Étude Théorique des Systèmes Périodiques. II. La Méthode LCAO ? SCF ? CO , 1967 .

[9]  R. Dovesi,et al.  Exact-exchange Hartree-Fock calculations for periodic systems. III. Ground-state properties of diamond , 1980 .

[10]  Michael J. S. Dewar,et al.  The SPO (Split p‐Orbital) Method and Its Application to Ethylene , 1961 .

[11]  J. Delhalle.  On the need of precision in the calculation of the LCAO density matrix of polymers , 1974 .

[12]  F. Bloch.  Über die Quantenmechanik der Elektronen in Kristallgittern , 1929 .

[13]  Michael C. Böhm,et al.  A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations , 1983 .

[14]  H. Vogler,et al.  Band structures of one-dimensional mixed donor-acceptor systems: A semiempirical INDO crystal orbital study , 1983 .

[15]  J. Delhalle.  Convergence of LCAO density matrices in Hartree—Fock calculations on extended model chains , 1984 .

[16]  Roberto Dovesi,et al.  Exact-exchange Hartree–Fock calculations for periodic systems. II. Results for graphite and hexagonal boron nitride† , 1980 .

[17]  S. Rabii,et al.  Electronic properties of graphite: A unified theoretical study , 1982 .

[18]  F. F. Seelig.  Synthesis and Properties of a New Kind of One-Dimensional Conductors. 2. Extended Hückel Calculations on the Energy Band Structure , 1979 .

[19]  A. Zunger,et al.  Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals investigation of the electronic structure and properties of TiS2 , 1977 .

[20]  S. Pantelides,et al.  Correlation effects in energy-band theory , 1974 .

[21]  M. P. Tosi,et al.  Cohesion of Ionic Solids in the Born Model , 1964 .

[22]  M. Böhm,et al.  The two-dimensional band structure of (polyphthalocyaninato)Ni(II) , 1988 .

[23]  O. K. Andersen,et al.  Linear methods in band theory , 1975 .

[24]  M. Bohm.  The band structure of bis-(1,2-benzoquinonedioximato)-nickel(II)-a crystal orbital approach based on the INDO approximation , 1983 .

[25]  R. Dovesi.  Ab initio Hartree–Fock approach to the study of polymers: Application to polyacetylenes , 1984 .

[26]  M. Böhm,et al.  On the accuracy of fourier transformations in crystal orbitat approaches , 1985 .

[27]  D. Ellis,et al.  A comparison of the one‐dimensional band structures of Ni tetrabenzoporphyrin and phthalocyanine conducting polymers , 1986 .

[28]  R. Dovesi,et al.  A periodic ab initio Hartree-Fock calculation on corundum , 1987 .

[29]  D. Papaconstantopoulos.  Self-consistent augmented-plane-wave band-structure calculations of Si and Ge with overlapping spheres , 1983 .

[30]  F. Illas,et al.  MINDO/3 calculations for periodic systems , 1984 .

[31]  M. Böhm,et al.  Hydrogen bonds in ammonium hydrogen‐DL‐malate monohydrate studied by 2H‐NMR, IR, and LCAO‐MO calculations , 1987 .

[32]  Marvin L. Cohen,et al.  Special Points in the Brillouin Zone , 1973 .

[33]  J. Ladik,et al.  On efficient integration techniques for oscillatory integrals in periodic system calculations , 1981 .

[34]  M. Böhm,et al.  Dielectric and Pyroelectric Properties of Ammonium Hydrogen-DL-Malate Monohydrate, NH4(C4H5O5) H2O , 1987 .

[35]  Conyers Herring,et al.  A New Method for Calculating Wave Functions in Crystals , 1940 .

[36]  J. André,et al.  Self‐Consistent Field Theory for the Electronic Structure of Polymers , 1969 .

[37]  M. Kertész,et al.  Electronic Structure of Polymers , 1982 .

[38]  K. Morokuma.  Electronic Structures of Linear Polymers. II. Formulation and CNDO/2 Calculation for Polyethylene and Poly(tetrafluoroethylene) , 1971 .

[39]  R. Nesper,et al.  The solid-state electronic structure and the nature of the chemical bond of the ternary Zintl-phase Li8MgSi6. A tight-binding analysis , 1985 .

[40]  S. Suhai.  A priori electronic structure calculations on highly conducting polymers. I. Hartree–Fock studies on cis‐ and trans‐polyacetylenes (polyenes) , 1980 .

[41]  B. Widom,et al.  Liquid Surface Tension near the Triple Point , 1970 .

[42]  M. Böhm,et al.  An efficient technique for the evaluation of lattice sums in crystal orbital (CO) calculations , 1986 .

[43]  J. Brédas,et al.  Ab initio Hartree—Fock calculations of model polyacetylene chains using a Christoffersen basis set☆ , 1982 .

[44]  M. Böhm.  THE PHOTOELECTRON SPECTRA OF BIS(CYCLOPENTADIENYL)TITANIUM DERIVATIVES - A GREEN′S FUNCTION APPROACH , 1982 .

[45]  R. Evarestov,et al.  Special points of the Brillouin zone and their use in the solid state theory , 1983 .

[46]  D. A. Shirley,et al.  X-ray photoemission studies of diamond, graphite, and glassy carbon valence bands , 1974 .

[47]  C. Umrigar,et al.  The pressure dependences of TiS2 and TiSe2 band structures , 1985 .

[48]  G. Klopman,et al.  A semiempirical treatment of molecular structures. II. Molecular terms and application to diatomic molecules , 1964 .

[49]  D. Beveridge,et al.  INDO and MINDO/2 Crystal Orbital Study of Polyacetylene, Polyethylene, and Polyglycine , 1972 .

[50]  R. Dovesi,et al.  Regular chemisorption of hydrogen on graphite in the crystalline orbital NDO approximation , 1976 .

[51]  M. Böhm.  The band structure of porphyrinatonickel (II). A semiempirical crystal orbital study based on the tight-binding formalism , 1984 .

[52]  M. Böhm.  A semi-empirical self-consistent-field hartree—fock crystal-orbital investigation on highly puckered porphyrinatonickel(II) backbones , 1984 .

[53]  M. Böhm,et al.  The band structure of Ni(H5C3B2). An example for energetic stabilization due to dimerization , 1986 .

[54]  J. Korringa,et al.  On the calculation of the energy of a Bloch wave in a metal , 1947 .

[55]  S. Suhai,et al.  Quasiparticle energy-band structures in semiconducting polymers: Correlation effects on the band gap in polyacetylene , 1983 .

[56]  A. Faessler,et al.  On the electronic structure of hexagonal boron nitride , 1979 .

[57]  H. Teramae.  Abinitio study on the cis–trans energetics of polyacetylene , 1986 .

[58]  M. Böhm,et al.  Simple geometric generation of special points in brillouin‐zone integrations. Two‐dimensional bravais lattices , 1986 .

[59]  W. Kohn,et al.  Solution of the Schrödinger Equation in Periodic Lattices with an Application to Metallic Lithium , 1954 .

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

[61]  A. Zunger,et al.  Ground-state electronic properties of diamond in the local-density formalism , 1977 .

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

[63]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[64]  R. Nesper,et al.  On the validity of formal electron counting rules in lithium silicides , 1987 .

[65]  Frank Szmulowicz,et al.  Self-consistent non-muffin-tin augmented-plane-wave calculation of the band structure of silicon , 1981 .

[66]  D. Hamann.  Semiconductor Charge Densities with Hard-Core and Soft-Core Pseudopotentials , 1979 .

[67]  H. Isomäki,et al.  The self-consistent electronic spectrum of the layer crystal TiS2 , 1975 .

[68]  A. Freeman,et al.  Electronic structure and optical properties of layered dichalcogenides: TiS2 and TiSe2 , 1974 .

[69]  J. Stewart,et al.  An improved LCAO SCF method for three-dimensional solids and its application to polyethylene, graphite, diamond, and boron nitride , 1980 .

[70]  G. Del Re,et al.  Self-Consistent-Field Tight-Binding Treatment of Polymers. I. Infinite Three-Dimensional Case , 1967 .

[71]  R. Nesper,et al.  Tight-binding approach to the solid-state structure of the complex Zintl-phase Li 12 Si 7 , 1984 .

[72]  M. Böhm.  The electronic structure of the one-dimensional tetrahedrally distorted porphyrinatonickel (II) system , 1984 .

[73]  John C. Slater,et al.  Wave Functions in a Periodic Potential , 1937 .

[74]  S. Suhai,et al.  An error analysis for Hartree-Fock crystal orbital calculations , 1982 .

[75]  Richard H. Friend,et al.  Electronic properties of intercalation complexes of the transition metal dichalcogenides , 1987 .

[76]  M. Böhm.  A simple self-consistent electrostatic field approximation for neighbour strand interactions in band structure calculations , 1982 .

[77]  Ajit Banerjee,et al.  The coupled‐cluster method with a multiconfiguration reference state , 1981 .

[78]  S. Alvarez,et al.  Symmetry constraints to the electrical conductivity of partially oxidized stacks of metal bis(dioximates) , 1984 .