An improved LCAO interpolation scheme for energy band structures. Application to four compounds (ScN,ScP, TiN,ZrN) crystallizing in the sodium chloride structure

An improved version of the LCAO interpolation scheme using metal s-, p-, d-, and non metal s-, and p-basis functions is presented for transition metal compounds with sodium chloride structure. This method enables us to interpolate with reasonable accuracy occupied bands as well as unoccupied energy bands up to 0.9 Rydberg above the Fermi level for the compounds ScN, ScP, TiN and ZrN. Due to the limited basis, problems arise however with bands of predominantly transition metal f or non metal d character lying in this energy range - as is the case for ScP.Optimized parameter sets are presented for the compounds ScN, ScP, TiN and ZrN. They were used for the calculation of the imaginary part of the complex dielectric function, ₂(), as will be shown in two forthcoming papers.     

Thorium equilibria with the sodium form of clinoptilolite and mordenite

A study has been performed in order to examine the iron exchange behavior of tetravalent thorium ions using natural sodium clinoptilolite and mordenite. The free energy values, G ⁰, were calculated and found to be 3.33 kJ/g eq for the Th/Na-CLI system, and for Th/Na-MOR 3.94 kJ/g eq. Despite the fact that the overall preference of the zeolites is for the sodium ions, thorium uptake was quite significant for mordenite, covering 30% of its theoretical exchange capacity at the equilibrium point, while for clinoptilolite only 10% was occupied.     

Changes in peak width and concentration at the inlet and outlet of a chromatographic column

The original plate model of chromatography is extended to the sorption process occurring at the column inlet and the desorption process at the column exit. At the column inlet it is shown that sufficiently wide feed bands undergo no change in concentration but a fall in band width, i.e., the volume of mobile phase occupied by the solute band is reduced. The reduction factor is (1 + k) where k is the mass distribution ratio (capacity factor). Narrower bands suffer partial reduction in both band width and concentration. On desorption at the outlet, however, the change is always in band width and not concentration. A perfect detector registers the true concentration-time profile of the band in the column if the solute mass fraction in the stationary phase is below 10^?3 at the column outlet. The risks of stripping the stationary phase at high solute concentrations in analytical and preparative or production gas chromatography are compared.     

Consequences of Substitution in the Photoelectron Spectra of [2, 2]Paracyclophanes: Separation of ‘through-space’ and ‘through-bond’ interactions as a consequence of fluorosubstitution

The PE. spectra of [2, 2]paracyclophane ( 1 ), 4-amino[2, 2]paracyclophane ( 2 ) and 1, 1, 2, 2, 9, 9, 10, 10-octafluoro[2, 2]paracyclophane ( 3 ) are presented. The bands corresponding to ejection of the photoelectron from the five highest occupied π-orbitals have been assigned. The ‘observed’ orbital energies (i.e. the negative ionization potentials) are discussed in terms of ‘through space’ and ‘through-bond’ interactions between the semi-localized π-orbitals ( e_1g ) of the benzene moieties and the C, C-σ-orbitals of the ethylene bridges. The PE. spectrum of 3 shows that the fluorine-induced lowering of the C, C-σ-orbital energy effectively ‘turns-off’ the ‘through-bond’ interaction. The resulting pattern of the first four bands confirms the assignment given for 1 . Finally the band shifts induced by an amino group in position 4 are again in agreement with this assignment. Attention is drawn to the phenomenon of ‘orbital switching’ as a consequence of substitution in loosely coupled systems such as 1 .     

Simplified accurate approximation for the Kohn-Sham potential using the KLI method

The method of Krieger, Li, and Iafrate (KLI) [Phys. Rev. A46, 5453 (1992) and A47, 165 (1993)] is employed to calculate the Kohn-Sham (KS) potential, V_κσ, for the exchange-only case in which the electron-electron interaction between “core” electrons in the Hartree-Fock exchange energy functional is treated in the local-spin-density (LSD) approximation with and without self-interaction-correction (SIC). The resulting V_κσ(r) maintains the important analytic properties exhibited by the exact KS potential. When the core is taken to include all occupied states except those in the last two occupied subshells of the atom, we find that properties strongly dependent on the valence electron states continue to be accurately approximated. In particular, when the LSDSIC approximation is employed, we find the results of self-consistent calculations of the ionization potential and electron affinity are within 0.3 mRy of the exact KS results and that the energy eigenvalue corresponding to the highest energy occupied orbital and <r²> have an average error of a few tenths of 1% for both atoms and negative ions for Z ≤ 20. Similarly, slightly less accurate results are obtained when the LSD approximation is employed. These results suggest that the KLI method may be accurately and more easily applied to multiatom systems when this additional approximation is made. © 1997 John Wiley & Sons, Inc.     

Electron densities and chemical bonding in TiC,TiN, and TiO derived from energy band calculations

The chemical bonding in the interesting class of refractory transition metal compounds is illustrated for TiC, TiN, and TiO. Self-consistent augmented plane wave (APW ) calculations are already available for these compounds. Using the respective potentials we have repeated the band calculations on a finer k grid with the linearized APW method to obtain accurate densities of states (DOS ). These DOS can be divided into local partial contributions to characterize the bonding. Further information can be obtained from a decomposition of the metal d DOS into t_2g and e_g symmetry components. These partial local DOS are compared with the LCAO counterpart and give a first picture of the chemical bonding in these compounds. The electron densities corresponding to the occupied valence states are obtained from the LAPW calculations. They provide further insight into characteristic trends in the series from TiC to TiO: around the nonmetal site the density shows increasing localization; around the metal site the deviation from spherical symmetry changes from e_g to t_2g. These effects can be traced back to the three types of valence bands. Electron density plots of characteristic band states (all energies of a selected k point in the Brillouin zone) will be shown. These plots can describe the different types of bonding occurring in these systems.     

meso-tetrakis[2.2]paracyclophanylporphyrin: Electronic structure and electrochemical behavior

Replacement of all phenyl groups in meso-tetraphenylporphyrin, TPP, by [2.2]paracyclophane, PCP, enhances the increase of energy of the HOMO and HOMO-1 of porphine, P, already noticed for the mono-[2.2]paracyclophanyl-substituted TPP, and fills the energy gap by the occupied MOs of the PCP units. The first oxidation half-wave potential is respectively decreased to 0.52 V. The CNDO/S-CIS calculations agree with the experimental bathochromic shifts of all bands in the electronic spectra of the considered atropoisomers of the title compound, TPCPP, as compared to TPP. In the excited B states the interactions between the PCP and porphine units are represented mainly by the charge transfer of 0.44 e from PCP to P, according to transition density matrix calculations. While electroreduction of the title compound results in a successive formation of the anion radical and dianion, oxidation represents a four-step process involving one electron transfer per step, and resulting in the oxidation of two PCP units. Formation of the conductive polymeric film on the electrode seems to be connected with the transient formation of a quinoid system of bonds.     

The study of benzimidazoles

The nature of the first two long-wave bands in the UV spectra of 2-substituted benzimidazoles has been analyzed on the basis of photoelectron spectra (PES). Three basic types of spectroscopic situations are typical of these compounds: 1) a change in the sequence of the occupied MO of the ground state does not influence the order of the excited energy levels; 2) when the π-levels are in the same order, inversion of the excited states occurs; 3) reversal of the occupied π-MO of the ground state causes the inversion of the excited states. For communication 7 see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1761–1766, October, 1993.     

Holo‐ and Hemidirected Coordination Spheres in a Novel Three‐Dimensional Polymeric KIPbII Heteropolynuclear Complex: X‐Ray Crystal Structure of [KPb(AcO)2(SCN)]n

A novel three‐dimensional polymeric K^IPb^II heteropolynuclear complex, [KPb(AcO)₂(SCN)]_n, with mixed acetate and thiocyanate ligands, has been synthesized and characterized. Its single‐crystal X‐ray structure (Fig. 1) shows three types of K⁺ ions with coordination numbers of seven, and three types of Pb²⁺ ions with coordination numbers of eight, eight, and nine, respectively. The Pb centers (Pb(1) and Pb(3); Fig. 1) with coordination numbers of nine and eight, respectively, possess stereochemically ‘inactive’ electron lone pairs, and the coordination sphere is holodirected. However, the arrangement of O‐, N‐, and S‐atoms for the eight‐coordinated Pb(2) suggests a gap or hole in the coordination geometry around this atom. This ‘hole’ is possibly occupied by a stereochemically ‘active’ electron lone pair of Pb(2), and its coordination sphere is, thus, hemidirected.     

Synthesis and Structure of Os5(μ-Cl)2(CO)16(CNBut)2: A Cluster with a “Hook” Arrangement of Metal Atoms

Os₅(-X)₂(CO)₁₆(L)₂ (X=Cl, 1, Br; L=CNBu ^t ) clusters have been prepared by the reaction of Os₃(-X)₂(CO)₁₀ with Os(CO)₄(L) at a 1:2 molar ratio in solution at 60°C. The crystal structure of the chloro compound reveals that the Os₃(-Cl)₂ fragment present in the precursory cluster is maintained in 1 with a coordination site cis to the Cl ligands occupied by the unusual Os(CO)₄Os(CO)₃(L)₂ unit. The resulting hook arrangement of the Os₅ skeleton has not been observed previously. The OsOs lengths are in the range 2.8384(6)–2.8999(6)Å. The OsOs bonds associated with the pendant fragment are both considered dative bonds.     

Simulation of the structure of some silicon carbide clusters by the MNDO method

Simulations of the geometric and electronic structure of C₄₄, C₄₅, Si₄₅, C₄₀Si₅, and C₄₄Si clusters were performed by the MNDO method. The geometries of the filled clusters, calculated by the MM2 method, were used as initial approximations. It was found that the filled clusters C₄₅ and C₄₄Si are transformed into endohedral clusters X@C₄₄ (X-C or Si, respectively) after energy optimization. The highest occupied energy level of the HOMO of the filled tetrahedral cluster Si₄₅ ofT symmetry is triply degenerate and is only occupied by four electrons. The structure of Si₄₅ ²⁻ dianion ofT symmetry was calculated. Two filled structures for the C₄₀Si₅ cluster were found. The coordination numbers of the central Si atom in these structures are 4 and 3, respectively. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 54–56, January, 1997.     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Structural and electronic properties of infinite cis and trans polyenes: Perturbation theory of electron correlation effects

The geometrical structure of five infinite polyene models (equidistant and alternating trans, equidistant cis, cis-transoid, and trans-cisoid) have been optimized using three different atomic basis sets at the Hartree–Fock level and by including electron correlation effects within the second order of Møller–Plesset perturbation theory. The single-particle energy bands have also been corrected for correlation effects applying the electron polaron method. Bond alternation has always reduced the energy (both for trans and cis) polyenes but this stabilization energy has decreased with an increasing basis set and has saturated about 3 mH for trans and trans-cisoid and about 7.5 mH for the cis-transoid model. On the absolute energy scale, however, the alternating trans structure has always turned out to be more stable than either the cis-transoid or the trans-cisoid one. The energetic order is in all cases trans < cis-transoid < trans-cisoid. Using the largest basis set with correlation, the corresponding energy differences are ΔE(trans → cis-transoid) = 1.69 mH and ΔE(trans → trans-cisoid) = 6.12 mH, respectively. The HF values of the valence-band widths vary in the region of 4–6 eV for the cis models and about 7 eV for the trans one. Correlation reduced them by about 20%, and the centers of the bands were shifted upward by about 2 eV due to self-energy renormalization. The best values for the electron polaron valence bandwidths are 6.4, 4.2, 3.3, and 5.2 eV for the alternating trans, trans-cisoid, cis-transoid, and equidistant cis models, respectively. The vertical ionization potentials of the above four structures are 4.80, 5.47, 5.71, and 4.18 eV, respectively. The conduction bands have a width of 6–8 eV at the HF level (except equidistant cis with 4.6 eV for the larger basis sets) that will be reduced by about 15–20% due to polaron formation. The bands are shifted in this case uniformly downward by about 2–3 eV due to correlation. The best values obtained for the conduction bandwidths are 4.7, 6.4, 5.6, and 3.7 eV, respectively. These band shifts reduce the HF value of the fundamental gap by several eV's for all models. For the largest basis set, the ΔE_gap values change from 6.6, 6.9, 7.7, and 5.3 eV (HF results for the alternating trans, trans-cisoid, cis-transoid, and equidistant cis models, respectively) to 2.7, 3.2, 4.5, and 2 eV, respectively, at the correlated level.     

Moments and characteristic polynomials of bipartite Hückel graphs

Moments (u _k ) and coefficients of characteristic polynomials (a _k ) have been evaluated in terms of molecular fragments up tok = 12 for bipartite Hückel graphs. Based on combinatorial analysis, each coefficient can be derived as a combination of binomial factors mapping to the corresponding multi-component graphs. The general formula becomes lengthy as k increases, but can be considerably simplified for a homologous series. This has been illustrated by dealing with the cata-condensed benzenoid hydrocarbons as a corollary where a rather compact set ofa _k has been deduced. On combining the present result with Coulson's formula, one gains insight into the relative stability of isomers in relationship to the energy contribution of fragments classified as stabilized and destabilized species.received by the Publisher 20 September 1989     

The fermi surface of beryllium

The Fermi surface (FS ) of beryllium has been calculated using the augmented plane wave energy bands for the material. The extremum area and the FS caliper distances are in excellent agreement with the de Haas–van Alphen measurements, and are better than existing ab initio calculations.     

Synthesis and optical properties of quasi-2D CdS x Se1 − x nanoparticles

Colloidal 2D CdS _x Se_{1 ? x} nanoparticles have been synthesized by a solution method in octadecene using oleic acid as a stabilizer. Growth of quasi-2D nanoparticles has been promoted by the presence of cadmium acetate in the reaction mixture. The resulting nanoparticles are platelets with lateral sizes 20–30 nm. The absorption and luminescence spectra of these nanoparticles show narrow bands of lh-e and hh-e exciton transitions corresponding to 2D systems. The spectral position of the lowest energy hh-e transition monotonically changes within 382–461 nm with a change in the composition of nanoparticles. The observed absorption bands are broader than those for the individual CdSe and CdS nanoparticles. The suggested method makes it possible to vary the exciton band position for quasi-2D nanoparticles by changing their composition.     

Interaction between polymers: Dispersion energy of two infinite linear chains

Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree–Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.     

Theoretical studies on the conformation of saccharides

The stereochemistry of d-glucopyranose has been studied theoretically in 11 solvents. The stability of the individual conformers in solution has been compared using a method in which the total energy is divided into the energy of an isolated molecule and the solvation energy. The structure and the energy of the isolated molecule have been estimated by geometry optimization using the PCILO quantum chemical method. The solvation energy consists of electrostatic, dispersion, and cavity terms which have been determined from calculated properties of the solute and physiochemical properties of the solvents. The influence of the solvent on rotation of the individual pendant groups and the stability of anomers have been investigated. The calculated composition of the anomeric mixture of d-glucopyranose in various solvents at 25°C (e.g., in pyridine 49% is -anomer, in dimethyl sulfoxide 46%, and in water 32%) is in good agreement with the available experimental data and clearly demonstrates that the solvation properties of - and -d-glucopyranose differ. Based on the calculated abundances of anomers the magnitude of the anomeric effect has been estimated and compared with the results of corresponding calculations on other compounds.     

Evaluation of moments and their application in Hückel molecular orbital theory

Moments of acyclic carbon chains are treated in a systematic way. Explicit formulas in terms of connectivities are tabulated up to ₁₄. This facilitates the evaluation of moments by simply counting the numbers of various fragments involved. The total electron energy is analyzed by means of moments and the meaning of additivity is interpreted. An approximate formula for E is parametrized by truncation, preserving only five bond parameters. Based on these, we attempt to better rationalize and reformulte the concept of aromaticity.Formerly used names: Kiang, Yuan-sun; Tang, Au-chin     

Vibrational energy transfer in near resonance due to dipole–dipole interactions

The contribution of long-range forces to the observed rates of V → V energy transfer processes has been studied. The theoretical model uses the first order perturbation approximation to generate a probability function, with the dipole–dipole perturbing potential as given by Margenau: V_if = [(1/6)^1/2_{μ1 · μ2}]R^?3. The probability function derived is shown to be a strong function of the energy mismatch between the IR bands of the colliding molecules. The calculation emphasizes the importance of rotational state population effects, the most important J states being those which minimize the energy mismatch. A complete analysis of energy transfer between CO(v) and COS(000) where v = 1,2, ? 13 is presented. The calculation reveals the importance of combination bands in the energy transfer mechanism of polyatomics. The temperature dependence for near-resonant processes is also studied and the importance of the V → R energy transfer leads to the classification of ω₀ (band-center energy mismatch) into three categories small, medium, and large, according to the temperature dependence that the corresponding processes exhibit. The predictions of the theoretical model are compared to experimental data for the same system.