Extrapolation of real-space quantum chemical calculations from finite-size super cells to the ideal infinite system. I. Theory

A method is proposed how to calculate the correct density matrix of an infinite polymeric chain from that of a standard finite supercell calculation. The density matrix of the finite supercell is transformed into k-space for all k-values allowed by the periodic boundary conditions. The k-dependent matrices are then unitarily transformed, with each unitary matrix being represented by a set of complex rotation matrices. It is shown that the corresponding angles can be interpolated and extrapolated toward the zone boundaries in a straghtforward manner and that this extrapolation can be done from any finite supercell with reasonable accuracy. This gives rise to an infinite system density matrix for which all fundamental properties are guaranteed by construction. This infinite system density matrix may be used to construct a corrected density matrix for the finite supercell calculation. © 1994 John Wiley & Sons, Inc.     

Extrapolation of real-space quantum chemical calculations from finite-size super cells to the ideal infinite system. II. Application to one-dimensional polymers

Calculations of finite atomic clusters based on the Hartree–Fock self-consistent field theory are modified to model more closely the ideal behavior of the infinite system. The density matrix of the standard finite supercell calculation is extrapolated to an infinite supercell so that it contains information from a continuum of k points in the first Brillouin zone. This modification is incorporated into the self-consistency loop of the MOPAC quantum chemistry program and leads to improved results compared to a standard finite supercell calculation. Heats of formation, bond lenghts, and electronic properties converge more quickly to the correct ground-state values. For polyacetylene, we obtain a reduced bond-length alternation of Δr = 0.084 Å, which is in agreement with more sophisticated calculations containing electron correlation effects. © 1994 John Wiley & Sons, Inc.     

Semiempirical calculations on WO3 and MXWO3 crystals (M = H,Li, Na)

The monoclinic structure of tungsten trioxide WO₃ has been studied by combining a modified intermediate neglect of differential overlap (INDO) method and the supercell model. The fitted semiempirical parameters describe very well the features of the band structure and crystal structure. Calculations of H, Li, and Na impurities in a WO₃ crystal have been performed to study the absorption spectra and the equilibrium geometries of intercalated impurities. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 729–735, 1997     

Ab initio electronic structure of NiCoCrGa half-metallic quaternary Heusler compound

In this study, ab initio calculation results of electronic structure and elastic properties of NiCoCrGa quaternary Heusler compound are presented. Plane wave pseudopotential method is used with spin-polarized Generalized Gradient Approximation (σ-GGA) scheme of the Density Functional Theory (DFT). Static elastic constants of the cubic system satisfy mechanical stability criteria. The cubic phase of the system remains stable under tetragonal distortion. The spin-polarized electronic band structures and density of electronic states indicate a metallic band structure for majority spins, while minority spin structure has semiconducting character. This situation displays a slightly disturbed half-metallic behavior with high-spin polarization ratio (P = 0.961) at Fermi level E_F. Two electronic bands of minority spins resulting from d-states of cobalt atom cross Fermi level at Γ-point. This situation gives a finite but very low density of states at E_F. The material can be classified as a new half-metallic ferromagnet for spintronic applications.     

Exact-exchange Hartree–Fock calculations for periodic systems. II. Results for graphite and hexagonal boron nitride

The ab-initio LCAO -HF method that was presented in a previous work is applied here to the study of graphite and hexagonal boron nitride monolayers. The dependence of total energy, band structure and density matrix on the computational parameters that control truncations in infinite sums over the translation vectors g of the direct lattice is first considered. For these systems it comes out that very good results can be obtained by neglecting all but the first few terms in the sums. For instance, for exchange contributions it is sufficient to consider integrals associated with the first 13 g vectors, suitably grouped, to obtain an error in total energy below 0.0001 a.u. The calculations were performed using an STO -3G basis set; results concerning conformational minimum, bond energy, symmetric force constant, band structure, density of states, and population analysis are presented and discussed.     

Direct evaluation of one-electron properties in coupled cluster methods

Summary An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third orderT ₁ T ₂⁽⁰⁾ wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.     

The molecular structure of trifluoromethyl manganese pentacarbonyl. A study by gas-phase electron diffraction

The results of an SCF-MO calculation on the CH₂CCH radical are presented: population analysis indices and several one-electron properties are reported and the electronic structure of the radical is discussed. The spin density is almost equally associated with the terminal carbon atoms, and there is a large negative spin density associated with the central carbon atom.     

Direct calculation of lattice sums. A method to account for the crystal field effects

A method of direct calculation of lattice sums in three-dimensional crystals is reported. The method is based on annihilation of some lowest multipole moments of the unit cell by a redefinition of the unit cell content. As a result, properties of the infinite crystal can be calculated as usual by taking a finite cluster of unit cells, but surrounded by an additional surface layer of a charge density (e.g., a layer of point charges). This charge density distribution produces the electric field approximating that one of the rest of the infinite crystal. The method proposed is easily applicable in the SCFLCAO procedure as well as in any method using a cluster representation for an infinite crystal. The validity of the infinite crystal model for a finite crystal is also discussed.     

Elucidating linear and nonlinear optical properties of defect chalcopyrite compounds ZnX2Te4 (X=Al,Ga, In) from electronic transitions

We presented a theoretical study of electronic band structure of three compounds ZnAl₂Te₄, ZnGa₂Te₄ and ZnIn₂Te₄ using pseudo potential method within density functional theory. Calculated band structures show that all band gaps are direct with at Γ with values of 1.639eV for ZnAl₂Te₄, 1.026eV for ZnGa₂Te₄and 0.836eV ZnIn₂Te₄. The linear properties based on dielectric function and non-linear optical properties based on second harmonic generation (SHG) were computed. The origin of four critical points (peaks) determined from the second derivative of the imaginary part of the dielectric function is elucidated. The use of individual k-points and individual combination of valence and conduction bands dependent matrix of the dielectric function and the nonlinear optical susceptibility allowed to a precise determination of inter band optical transitions. Indeed, inter-band analysis shows the high intensity of non-linear effect compared to linear effect. Moreover, non-linear inter-band optical transitions involve lower valence bands and higher conduction bands.     

Potentials of an alternative scheme for ab initio polymer band structure calculations. Illustration on the chain of hydrogen atoms

An alternative scheme for ab initio polymer band structure calculations based on a Filon-type quadrature is proposed. This scheme avoids the explicit calculation and the storage of the “troublesome” Fourier transforms of the LCAO density matrix elements and is a first step towards a better control of the convergence of the different lattice sums appearing in the configuration space LCAO-SCF-CO method. The potential of the proposed technique is illustrated by a minimal basis set calculations on an infinite chain of H atoms.     

The Algebraic Structure of Physical Quantities

We present a general algebraic basis for arbitrary systems of units such as those used in physical sciences, engineering, and economics. Physical quantities are represented as q-numbers: an ordered pair u = {u,label_u}, that is, u q = X × W _B . The algebraic structure of the infinite sets of labels that represent the units has been established: such sets W _B are infinite Abelian multiplicative groups with a finite basis. W _B is solvable as it admits a tower of Abelian subgroups. Extensions to include the possibility of rational powers of labels have been included, as well as the addition of named labels. Named labels are an essential feature of all practical systems of units. Furthermore, q is an Abelian multiplicative group, and it is not a ring. q admits decomposition into one-dimensional normed vector spaces over the field X among members with equivalent labels. These properties lead naturally to the concept of well-posed relations, and to Buckinghams theorem of dimensional analysis. Finally, a connection is made with a Group Ring structure and an interpretation in terms of the observable properties of physico-chemical systems is given.     

Overlapping shells model applied to diamondlike crystals

The model based on the assumption of the existence of an interatomic distance-dependent, local, effective crystal field applied to the alkaline metals (Int. J. Quantum Chem. 52, 321–328 (1994)) is modified and applied to the diamondlike structure crystals (C, Si, Ge, Sn). In the referred to model, a part of the electron density was missed—not included in the calculation (the density in the spaces between the shells). Such an approach could be used for the alkaline metals, but for the covalent crystals, this is a bad approximation. To avoid that problem, we assumed that the atom shells can overlap in such a way that the entire electron density is taken into the calculation. In this case, the electron density is “moved” from the outside of the shells mostly into the interatomic bond region. We applied the modified model to the calculation of the binding energy and the bulk modulus for the diamondlike crystals. The results show that well-chosen parameters allows one to reproduce the proper values of the binding energy at the equilibrium position. The bulk moduli calculated for these crystals are in quite good agreement with ones calculated as (regular crystal structure) B = 1/3(C₁₁ + 2 C₁₂), where C₁₁ and C₁₂ are elastic constants. © 1997 John Wiley & Sons, Inc.     

Structural,electronic, and optical properties of Cd-halide-based inorganic LiCdX3 (X = F,Cl) perovskites for photovoltaic applications: A density functional theory study

Halide base perovskite LiCdX₃ (X = F, Cl) is tested by CASTEP (Cambridge Serial Total Energy Package) based on density function theory (DFT). The presented discussion is to explore the structural, electronic, and optical properties of LiCdX₃ (X = F, Cl). The calculated values of the lattice parameter are found to be 3.8 Å and 5.27 Å of LiCdF₃ and LiCdCl₃ respectively. The ideal structure of LiCdX₃ (X = F, Cl) is cubic and dynamically stable. Electronic properties show that materials are semiconductors. The results from band structure are further evaluated by the total and partial density of states. The partial and total density of states confirms the degree of localization of electrons. In optical properties, the highest absorption coefficient is observed in LiCdCl₃. The material is half metallic and has a narrow indirect band gap which may be used in photovoltaic applications.     

First principles study on the structural,electronic, and optical properties of Sc-doped AlN

Based on the density functional pseudo-potential method, the structural properties, the band structure, the density of states and the optical properties of the pure and Sc-doped AlN are calculated. The calculation results indicate that the defect of Sc(Al) exists steadily with a certain solubility in the doped system. Sc substitution of the Al site induces effective reduction of the band gap of AlN and the band gap being continuously reduced when increasing Sc concentrations. The existence of the strong hybridization between Sc 3d and N 2p indicates the transport of electrons from Sc atoms to N atoms. Besides, it is shown that the insertion of Sc atom leads to redshift of the optical absorption edge. The intensity of both the imaginary part of the dielectric function and the optical absorption of Al_{1 ? x} Sc _x N are found to decrease with increasing Sc concentrations in the low energy range.     

Density functional calculations of optical excitation energies by a transition-state method

Optical excitation energies of MnO⁻₄, CrO²⁻₄, and RuO₄ are calculated using the density functional methodology. A short outline of some important developments in this theory for the determination of excited-state properties is given. A practical working procedure for the calculation of transition energies including multiplet splitting is described. This method is based on a transition-state approach which is connected, as will be shown, to Slater's transition-state concept. Results obtained by this working procedure are compared to the energy differences between separately converged configurations of ground and excited states and the corresponding multiplet structure, denoted as the ΔSCF calculation in the following. © 1997 John Wiley & Sons, Inc.     

Energy band structure of (SN)x chain: Unrestricted Hartree–Fock and charge density wave solutions

The ab initio Hartree–Fock crystal orbital method is used for the calculation of the energy band structure of a one-dimensional model of (SN)_x. Two energy band structures are described corresponding to the self-consistent spin density wave (SDW ) and the self-consistent charge density wave (CDW ) solution, respectively.     

Chemical surface passivation of 3C‐SiC nanocrystals: A first‐principle study

The effect of the chemical surface passivation, with hydrogen atoms, on the energy band gap of porous cubic silicon carbide (PSiC) was investigated. The pores are modeled by means of the supercell technique, in which columns of Si and/or C atoms are removed along the [001] direction. Within this supercell model, morphology effects can be analyzed in detail. The electronic band structure is performed using the density functional theory based on the generalized gradient approximation. Two types of pores are studied: C‐rich and Si‐rich pores surface. The enlargement of energy band gap is greater in the C‐rich than Si‐rich pores surface. This supercell model emphasizes the interconnection between 3C‐SiC nanocrystals, delocalizing the electronic states. However, the results show a clear quantum confinement signature, which is contrasted with that of nanowire systems. The calculation shows a significant response to changes in surface passivation with hydrogen. The chemical tuning of the band gap opens the possibility plenty applications in nanotechnology. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2455–2461, 2010     

Ab initio studies on hydrogen-bonded chains. III. The linear,infinite chain of hydrogen cyanide molecules

Ab initio crystal-orbital calculations have been performed on the linear, infinite chain of HCN molecules applying basis sets from minimal to double-zeta-plus-polarization quality. From computed potential surfaces many properties of the electronic ground state of (HCN)_∞ could be deduced. Equilibrium structure, hydrogen-bond energy, dipole moment per molecule, dipole-moment derivatives, harmonic force constants, vibrational frequencies and electronic band structure are reported. Results on the polymer are compared with monomer, dimer and crystal data.     

Theoretical studies of thermal decomposition of anhydrous cadmium and silver oxalates

The results of first principles calculations of band structure, density of states and electron density topology of CdC₂O₄ and Ag₂C₂O₄ crystals are presented. The calculations have been performed with WIEN2k ab initio program, using highly precise full potential linearized augmented plane wave (FP LAPW) method within Density Functional Theory formalism. The obtained SCF electron density has been used in calculations of Bader’s AIM (atoms in molecules) topological properties of the electron density in crystal. The obtained results show important similarities in electronic structure and electron density topology of both compounds and allow supposing, that during the thermal decomposition process these compounds should behave similarly, which is in agreement with the experiment.     

First principles calculations of electronic and optical properties of Ag2S

A theoretical study of structural, electronic and optical properties of Ag₂S is presented using the full potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). In this approach, the modified Becke Johnson (MBJ) potential coupled with Local Density Approximation (LDA) was used for the exchange-correlation potential calculation. Ground state properties are determined for the bulk material in monoclinic phase. Band structure reveals that this compound is a direct energy band gap semiconductor. MBJLDA results for the band gap of this compound are much better than those obtained using LDA, Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) and Engel–Vosko's GGA (EV-GGA). A very good agreement is observed between MBJLDA band gap and corresponding experimental values as compared to other calculations. Optical constants including the dielectric function, refractive index, extinction coefficient, electron energy loss function, reflectivity and absorption coefficient are obtained and discussed.