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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 92 (1995), S. 13-47 
    ISSN: 1432-2234
    Keywords: Zero differential overlap ; Semiempirical MO methods ; Löwdin transformation ; Overlap density ; Mulliken approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Some systematic errors of the zero differential overlap (ZDO) approximation in semiempirical molecular orbital (MO) methods are discussed. In π electron methods, a power series expansion of the inverse square rootS −1/2 of the overlap matrix and application of the Mulliken approximation to the two-electron integrals show that the ZDO Hamiltonian coincides with the Hamiltonian obtained by explicit performance of the Löwdin transformation up to first-order terms of diatomic overlap densities. Higher than first-order terms lead to a systematic up-shift of the canonical MO energies. Although a power series expansion ofS −1/2 is no longer possible in all-valence-electron methods, the MO levels resulting from the ZDO approximation are also systematically placed at too low energies, especially the low-lying occupied and the virtual MOs. A method based on explicit performance of the Löwdin transformation and retaining the simplicity of the ZDO approach for the calculation of Fock matrix elements is developed. The parameters of this method are obtained by very simple manipulations of the original ZDO parameters. Numerical calculations show that a considerable improvement of the MO energy spectrum in the inner valence region can be obtained in this way
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 939-970 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The magnitude of reorganization energies in the photoelectron (PE) spectra of various transition metal compounds with Mn, Fe, and Ni as 3d center is studied by means of a variable INDO Hamiltonian. The Koopmans defects are analyzed as a function of the one-electron resonance integral βμνAB and as function of the one- and two-center electron-electron interaction integrals. βμνAB has the property of an inverse coupling constant; reorganization effects are enlarged with reduced βμνAB values. In the limit of very small resonance integrals a reduction of the calculated Koopmans defects due to modified localization properties of the orbital wave function is encountered. The two-center electron-electron interaction integrals γμνAB have been calculated via an exponential formula with a variable range parameter. In the limit of long-range potentials with flattened γ;μνAB gradients a significant reduction of relaxation and correlation is diagnozed; large defects are predicted in the short-range limit with steep gradients in the repulsion potential. The one-center Coulomb and exchange integrals (γμνAA, KμνAA) have been modified by a multiplicative factor. With enlarged one-center integrals enhanced Koopmans defects are encountered. The reorganization energies are determined by means of a Green's function approach with a renormalized approximation for the self-energy part.
    Additional Material: 8 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 25 (1984), S. 817-851 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The band structure of porphyrinatonickel(II) (2) has been studied by means of crystal orbital calculations that are based on the tight-binding approximation; the computational framework is a recently developed INDO model for transition metal compounds of the 3d series. The porphyrinato polymer has been studied in an eclipsed arrangement (2a) and in a staggered conformation (2b) where neighboring layers are rotated by 41°. The total energy of the metallomacrocycle has been decomposed into one- and two-center contributions; the latter interaction parameters have been fragmented into physically feasible resonance, exchange, and classical electrostatic (electron-electron, electron-core, core-core) interactions. It is shown that individual two-center potentials between atoms in neighboring layers are prevailingly determined by the electrostatic interaction energy. The NiNi coupling in the chain is highly repulsive; important stabilizing interactions are predicted between the 3d center of one cell and the electronegative N atoms in the neighboring layers. Stabilizing and destabilizing electrostatic interaction potentials largely compensate each other; the net stabilization in the polymer comes from the accumulation of resonance and exchange increments. The unoxidized Ni(II) porphyrinato polymer is an insulator. Several ligand bands (π, σ, and lone-pair) are predicted on top of bands with significant Ni 3d admixtures; the conduction band of the unoxidized strand is of ligand π* character. The dense manifold of ligand states in the vicinity of the Ni 3d states (3dz2, 3dx2-y2, 3dxz/3dyz) prevents the formation of bands in the polymer that are strongly localized at the 3d center. Ni 3dz2 and 3dx2-y2 interact strongly with ligand lone-pair and σ states. Avoided crossings between ∊(k) curves in k space lead to compositions in the various bands that differ significantly at the bottom and the top. The INDO crystal orbital formalism predicts a partial oxidation of ligand bands in derivatives of 2 that contain oxidants (e.g., halides). The theoretical findings derived for 2 are compared with available experimental data on highly conducting porphyrinatonicke(II) polymers (tetrabenzo and octamethyltetrabenzo derivatives of 2).
    Additional Material: 15 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 47-71 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 571-594 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A systematic collection of spatial domains for reciprocal space integrations is derived for all possible crystal symmetries. This set can be used as a simpler alternative to the conventional Brillouin zones. The analysis is restricted to integrations where the function in the integrand satisfies inversion symmetry in k space. In this case only 24 different spatial domains have to be defined in order to allow for k space integrations in the 230 different crystal symmetries. A graphic representation of the asymmetric unit for each of the 24 integration domains is given. Special positions and the associated weighting factors required for numerical integrations in theoretical solid-state approaches are tabulated.
    Additional Material: 11 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 73-84 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF) Hartree-Fock (HF) crystal orbital (CO) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a1u combination (D4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ∊v of 2.92 eV. This value is close to the Δ∊v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at -4.9 eV; they are predicted between -12.2 and -16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.
    Additional Material: 5 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 391-411 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A clear tabulation of sets of special points in numerical integrations over Brillouin zones (BZ) is given for the five two-dimensional Bravais lattices. The special points derived on the basis of plain geometrical criteria coincide with a special case of the large unit cell (LUC) method. This similarity is also found for other generation procedures of k-grids reported in the literature; that is, the corresponding techniques have their common origin in the LUC approach. The underlying integration procedure of the described scheme is based on the discrete summation, which implies that the weighting factors at the k-points are only determined by the point symmetry in reciprocal space not by details of the adopted numerical integration formalism. The method can be applied to semiconducting and insulating solids - that is, to materials with finite band gaps. Grids in reciprocal space are generated on the basis of simple geometric criteria. The numerical effort of the present geometrical approach is negligible in comparison to the computational steps necessary in generation procedures of optimized k-grids that have been published in the literature. The application of the suggested integration procedure is extremely simple; the generation of the k-grids is only based on a few definitions and plain geometrical formulas. Modifications of the grid size are possible without difficulties. A collection of weighting factors ωi and special and general positions in the BZ is given; different grids are tabulated together with their geometrical efficiencies. The generated integration domains are compared with the results of elaborate schemes of finding grids with maximal efficiency.
    Additional Material: 7 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 185-237 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The validity of the Hartree-Fock (HF) approximation in bis(π-pentadienyl)dinickel (1) and in cyclopentadienyl-allyl-cyclobutadiene-dinickel (2) has been investigated by means of the Thouless instability conditions in the computational framework of a variable model Hamiltonian. Singlet, nonsinglet (triplet), and nonreal instabilities in 1 and 2 have been studied as a function of the one-electron resonance integral βμvAB and as a function of the one- and two-center elements of the electron-electron interaction. The one-center integrals of Coulomb (γμvAA) and exchange-type (KμvAA) have been modified by a multiplicative factor; the two-center integrals (γμvAB) have been calculated by means of an exponential interpolation formula with a variable decay amplitude. Additionally the Thouless conditions have been studied for nuclear deformations. The stability domain of the HF solution in the model space spanned by the variable INDO Hamiltonian has been analyzed. The nature of the many-body interactions in the unstable region depends strongly on the parametrization of the model operator. HF instabilities in the high-density region (long-range forces) of 1 have their origin in individual particle-hole fluctuations while negative roots for short-range forces (low-density region) are similar to collective excitations in many-body systems (strong off-diagonal coupling). The opposite behavior is encountered in the Ni complex 2. The physical origin of these different types of correlation processes are analyzed in a simple two-electron two-orbital model. The nature of the HF fluctuations in 1 and 2, the importance of spatial and spin correlation, and the coupling of symmetry breaking of the electronic wave function with nuclear deformations are compared with the nature of phase transitions in solid-state systems.
    Additional Material: 28 Ill.
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  • 9
    ISSN: 0040-5744
    Keywords: Key words: Zero differential overlap ; Semiempirical MO methods ; Löwdin transformation ; Overlap density ; Mulliken approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  Some systematic errors of the zero differential overlap (ZDO) approximation in semiempirical molecular orbital (MO) methods are discussed. In π electron methods, a power series expansion of the inverse square root S -1/2 of the overlap matrix and application of the Mulliken approximation to the two-electron integrals show that the ZDO Hamiltonian coincides with the Hamiltonian obtained by explicit performance of the Löwdin transformation up to first-order terms of diatomic overlap densities. Higher than first-order terms lead to a systematic up-shift of the canonical MO energies. Although a power series expansion of S -1/2 is no longer possible in all-valence-electron methods, the MO levels resulting from the ZDO approximation are also systematically placed at too low energies, especially the low-lying occupied and the virtual MOs. A method based on explicit performance of the Löwdin transformation and retaining the simplicity of the ZDO approach for the calculation of Fock matrix elements is developed. The parameters of this method are obtained by very simple manipulations of the original ZDO parameters. Numerical calculations show that a considerable improvement of the MO energy spectrum in the inner valence region can be obtained in this way
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