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  • 1985-1989  (138)
  • 1985  (138)
  • Atomic, Molecular and Optical Physics  (138)
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 547-557 
    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 redundancy-free internal valence compliance constants of open-chain water dimer and formic acid cyclic dimer have been determined by the combined use of the CNDO/Force method and the compliance constant formalism. The final compliant fields of these dimers have been refined with the help of experimental frequency data.
    Additional Material: 2 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 559-565 
    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 double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree-Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rn of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.
    Additional Material: 1 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 585-594 
    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: Recent Xα calculations of bond energies and other related properties of first-row diatomic molecules show very encouraging agreement with experiment. In the worst cases, however, the Xα dissociation energies overestimate the experimental values by almost 2 eV. Therefore, we have examined several refinements of the Xα theory and their effects on molecular bond lengths, bond energies, and vibrational frequencies. Among them, gradient corrections to the Xα exchange energy and also some variations of the local spin-density correlation energy approximation are considered. We find that a local exchange-correlation functional with gradient corrections gives dissociation energies in significantly better agreement with experiment than the Xα approximation.
    Additional Material: 4 Tab.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 567-583 
    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: Here we present a detailed study of the theoretical approach to the tautomerization processes considering 2- and 4-oxo-pyrimidine and several of their derivatives. We look into molecular relaxation, suitability of semiempirical methods, and the effect of basis sets size in pseudopotential ab initio calculations. We found that no semiempirical method is suited for studying the relative stability of the tautomers, even ab initio calculations with minimal basis sets. On the other hand MNDO appears to be very useful for molecular relaxation and can be used, as well as Ab initio calculations, for reasonable estimates of relative tautomerization. We also considered the quality of prediction of other parameters, in particular the ionization potentials. We considered the correlation of experimental and theoretical values as a means to adjust the theoretical results to obtain more reliable predictions.
    Additional Material: 3 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 595-599 
    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 scaling property of the relativistic total energy E (Z, N) established by Marconi and the writer for heavy positive ions with N electrons and atomic number Z is demonstrated, by setting up the self-consistent relativistic Thomas-Fermi equation in d dimensions, to be a special case of the scaling property \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {E_d (Z,N,\alpha ) = Z^{{{(4 + 4d - d^2 )} \mathord{\left/ {\vphantom {{(4 + 4d - d^2 )} {d(4 - d)}}} \right. \kern-\nulldelimiterspace} {d(4 - d)}}} F_d ({N \mathord{\left/ {\vphantom {N {Z;\alpha ^2 Z^{{4 \mathord{\left/ {\vphantom {4 {d(4 - d)}}} \right. \kern-\nulldelimiterspace} {d(4 - d)}}} }}} \right. \kern-\nulldelimiterspace} {Z;\alpha ^2 Z^{{4 \mathord{\left/ {\vphantom {4 {d(4 - d)}}} \right. \kern-\nulldelimiterspace} {d(4 - d)}}} }});} {d \ne 4,} \\ \end{array} $$\end{document} α being the fine structure constant.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 601-612 
    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: Fully numerical two-dimensional Hartree-Fock-Slater calculations are reported for the diatomic molecules B2, C2, N2, CO, O2, F2, and BF. The model is identical to Becke's but the numerical method is different. Fully numerical ground-state total and orbital energies are reported for the first time. The basis-set truncation error in the LCAO calculations of Dunlap, Connolly, and Sabin influence the third and fourth decimals (in a.u.) of ET and εi respectively. Benchmarks of improved accuracy are provided for dissociation energies, bond lengths, and electronic multipole moments for future assessment of basis-set errors.
    Additional Material: 11 Tab.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 653-664 
    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 new computation procedure for direct calculation of the density matrix in the LCAO version of the restricted Hartree-Fock-Roothaan open-shell theory is analyzed. It is proved that the procedure is quadratically convergent and stable to the round-off errors independently of the Fock operator spectrum. The dependence of the limit matrix of the initial matrix is examined.
    Additional Material: 2 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 105-105 
    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
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985) 
    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
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 109-113 
    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 semianalytic scheme is proposed for the evaluation of Brillouin zone (BZ) double integrals such as are met in the evaluation of Compton profiles (CPS) and the angular distribution of annihilation photons (ADAPS) obtained in single-slit positron annihilation experiments. The difficulty that arises due to the jump discontinuities in the momentum density at the generalized Fermi surfaces (FS +HMC), pF = kF + g, where kF is the electron Fermi momentum vector and g is a reciprocal lattice vector, is addressed.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 115-133 
    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 electronic absorption spectra of some benzohydroxamic acids have been analyzed and interpreted using the results of molecular-orbital calculations. Charge density distributions, dipole moments, and the extent of delocalization of the MOS were used to interpret the observed solvent effects. Comparison between the spectra of benzohydroxamic acids and that of simple amides led to conclusions regarding the structural differences between the two classes of compounds.
    Additional Material: 12 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 135-144 
    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: PCILO computations have been carried out on the conformation of p-dimethylaminobenzylidene-p-nitroaniline [I(m)], p-nitrobenzylidene-p-dimethylaminoaniline [I(n)] and the corresponding stilbene [II(a)] and azobenzene [II(b)] derivatives. The aniline rings in Im and In are found to be twisted out of the plane containing the central atoms by 60° and 30°, respectively. The two phenyl rings in case of II(a) are twisted out of plane in opposite directions by 30° each. II(b) was found to be planar. The results have been compared with the earlier experimental findings and used as a possible explanation for the visible absorption spectra of the four molecules.
    Additional Material: 5 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 159-166 
    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: We modify the matricial form of the TDHF equations we suggested in an earlier article, and impose a further constraint, called unicity constraint, to the equations' solutions. Indeed, this further constraint, combined with the orthonormalization conditions already taken into account, allows the TDHF equations a form accepting only one spin-orbital set as a solution.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 167-171 
    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: Following a paper drawing up a matrix form of the time-dependent Hartree-Fock equations which allow the calculation of the nth harmonic generation, we establish the matrix form of the hyperpolarizability tensor. In case of linear polarization, we show that, if the ground-state orbitals are real, so are the perturbed ones. This involves an easy expression of the hyperpolarizability tensor.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 181-194 
    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: Ab initio SCF MO calculations at the STO-3G level have been carried out on CH2OHOPO3-H and CH2OHOPO32-, which have been considered as model systems for the Cl-phosphate moiety of sugars. The results predict higher anomeric energy for the phosphate moiety at Cl atom of pyranosides. Also a trans arrangement of the exocyclic O - P bond is preferred rather than a gauche arrangement, thus exhibiting a reverse exo-anomeric effect. A complete potential energy map has been constructed for CH3OPO3-H, a model system for C6-phosphate moiety. It is seen that the bond angle optimization brings down the relative energies of various conformations. The effect of the phosphate group on the preferred conformation of phosphate containing polysaccharides is also discussed.
    Additional Material: 5 Ill.
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  • 16
    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: In this paper we present numerical calculations of close-coupling equations to study vibrational predissociation of the T-shaped He…I2(B) van der Waals molecule. In the region of high vibrational excitation of the I2 subunit, the vibrational predissociation rates are related to the widths of the resulting resonances for the He-I2(B) collision. We apply a reasonable approximation to calculate the necessary background S matrix, i.e., the S matrix in absence of resonances. The rates of perpendicular vibrational predissociation, as a function of the initial I2 vibrational quantum number v1, show a maximum at v1 = 58 almost in agreement with the experimental data. However, an oscillatory and very interesting behavior of the rates in the region 60 ≤ v1 ≤ 65 is found.
    Additional Material: 2 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 203-218 
    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: Fick's law of diffusion has been generalized to include kinetic processes, the transport term of the Boltzmann equation, and nonlocal interaction processes. It is shown that the collision interaction term can be obtained by the introduction of a quantum stochastic potential equation. Some approximations of a nonlocal Boltzmann equation can be solved exactly. The solutions can be applied to problems of molecular pattern in biology.
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 233-234 
    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
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 231-232 
    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
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  • 20
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 219-229 
    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: Based on previous analyses of slowly convergent exchange lattice sums entering the configuration space restricted Hartree-Fock-Roothaan scheme for chain systems, an alternative computational strategy is developed. Within the present formalism, the traditionally used finite Fourier transform of k-dependent LCAO density matrices are by-passed and an advantageous computational organization is obtained.
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  • 21
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985) 
    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
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  • 22
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 235-244 
    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: Internal rotation energy levels for phenol, fluoracetaldehyde, and difluoracetaldehyde are estimated with two methods: first, by means of the reduced inertia moment formula introduced by Pitzer; second, with use of an internal axis system and by taking into account the influence of the overall rotation through the inertia factor. Two methods have been used to estimate potential barriers (CNDO/2 and PCILO). Results are related to the asymmetry of the tops. Theoretical far IR spectra for the three molecules are calculated. In the case of phenol, good agreement is found with experimental data.
    Additional Material: 7 Tab.
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  • 23
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 273-280 
    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: Hyperspherical coordinates and a generator coordinate representation are employed to find a simple form of the kinetic energy for a general three-particle problem. An expression is developed for the determination of adiabatic hyperangular states in a local potential using the finite element method.
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  • 24
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985) 
    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
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  • 25
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 375-379 
    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) energy of the hydrogen molecule is carried out by the Heitler-London method. The 2D integrals (which are more localized compared to 3D ones) are performed in the light of the 3D Slater integrals. A discussion of such 2D systems is briefly outlined for doped semiconductors.
    Additional Material: 2 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 381-391 
    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: We establish a theorem which gives a necessary and sufficient condition for a set of matrix irreps of a finite group to admit real coupling (Clebsch-Gordan) coefficients. The proof is based on the method used by Feit to prove that a full set of coupling coefficients for a finite group determines the group up to isomorphism. A consequence of the theorem is that a finite group with real coupling coefficients is necessarily quasiambivalent. The theorem is used to demonstrate that real coupling coefficients do not exist for the point-group hierarchies T ⊃ D2 and I ⊃ T or for the double-group hierarchies I* ⊃ D3*, I* ⊃ D5*, and O* ⊃ D3*.
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  • 27
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 323-374 
    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 importance of many-body interactions beyond the mean-field approximation of the Hartree-Fock (HF) self-consistent-field crystal orbital formalism is analyzed in one-dimensional (lD) transition-metal (3d) polymers with extended organic π ligands. The correlation energies are expressed in a quasiparticle picture. They are divided into long-range contributions that are coordinated with the basis of spatially uncorrelated Bloch orbitals and into short-range correlations derived for local rearrangement processes that are described in terms of a one-electron basis which breaks the translational symmetry of the lD system. Both contributions (long-range and short-range correlations) are fragmented into elements of physical significance (hole and electron self-energies for the former interactions; relaxation, pair-relaxation and pairremoval terms for the local virtual excitations). The magnitude of these elements is analyzed as a function of the characters of the one-electron states in the HF bands, the occupation patterns at the 3d centers, the available particle and hole channels in the elementary fluctuations and the energies and shapes of the various bands. The broad spectrum of possible amplifications and compensations leading to the quasiparticle shifts in metallomacrocycles is discussed. The different mechanisms to change the dispersions and to modify the width of the ∊(k) curves are studied. It is shown that electron correlation and relaxation in transition-metal polymers can lead even to a broadening of the energy bands. This behavior is in contrast to the influence of many-body effects in simpler homogeneous materials where electron correlation is in any case accompanied by a narrowing of the dispersions (i.e., detraction of the group velocities of particles and holes). Possible modifications in the shapes of the one-particle curves and the quasiparticle bands are also considered in the text [transition from a “normal ∊(k) dispersion” to an energy band with a negative slope as a result of electron correlation]. Simplified formulas are derived that allow for a rough assessment of the various correction terms even in structurally complicated transition-metal stacks with extended organic ligands. The approximate relations are used to correct the HF band structures of complex onedimensional metallomacrocycles as well as simpler crystalline materials by means of the quasiparticle approximation.
    Additional Material: 17 Ill.
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  • 28
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 393-406 
    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 local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.
    Additional Material: 4 Ill.
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  • 29
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 407-416 
    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 electronic energy band of the molecular crystal NMP-TCNQ is calculated by means of the EHMO/LCAO-MO-CO method. In the calculation, both NMP and TCNQ are treated as quasi-one-dimensional columns, respectively. The results demonstrate that (i) the positions of the electronic energy bands of a molecular crystal are determined by that of the corresponding molecular orbitals of the respective isolated molecules; (ii) the widths of energy bands are determined by the interaction between the molecular orbitals of adjacent molecules in the crystal. These facts support the conclusion which we have given in the previous articles. The relationship between the structure of energy bands of the crystal NMP-TCNQ and its electrical conductivity at room temperature is discussed and compared with the crystal TTF-TCNQ. The differences of electrical conductivities of both crystals can be explained by the formula given by Fröhlich and Sewell.
    Additional Material: 5 Ill.
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  • 30
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 417-425 
    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 density operator of an n level quantum system is known to be a positive semidefinite, hermitian operator of trace one. In a previous article we have established, through su(n) algebras, a formalism where density operators are built from coherence vectors in a n2 - 1 dimension, real, Euclidean space. The last two conditions are then automatically satisfied. Being positive semidefinite means a restriction to the domain of coherence vectors. In this article we clarify this domain and obtain several equivalent tests to know if a given vector is part of it.
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  • 31
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 427-437 
    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: Mulliken's atomic charges (MC) and potential derived (PD) point charges obtained from STO-3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogenbonded complexes. The results of the above-mentioned models are compared with the more accurate results of segmental multipole moment (SMM) expansion, and it is shown that the PD model is superior to the Mc model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6-31G and 6-31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6-31G** PD charges are compared with the 6-31G** SCF interaction energies available for the nine hydrogen-bonded dimers of ammonia, water, and hydrogen fluoride and a good con-elation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point-charge model. The electrostatic interaction energies obtained using STO-3G PD model are shown to be well correlated to the results of 6-31G and 6-31G** PD models.
    Additional Material: 6 Ill.
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  • 32
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 439-449 
    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 complete (nonreduced) αα probability density functions evaluated from the Hartree-Fock and simple Hartree product wavefunctions have been used to elucidate the angular features of spin correlation and the Fermi hole in the 23S state of helium and the ground state of beryllium. This approach shows that the local Fermi holes in these two cases are very similar and that the Fermi hole is essentially spherically symmetric when the reference electron is close to the nucleus. As the reference electron is removed to larger radial distances, appreciable polarization of the Fermi hole is observed. The polarization is greater in the direction of the nucleus than away from the nucleus, contrary to the situation in the Coulomb hole of the helium ground state where the polarization is greater away from the nucleus than toward the nucleus. Several other differences between the He 23S Fermi hole and the He 11S Coulomb hole are noted.
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  • 33
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    International Journal of Quantum Chemistry 27 (1985), S. 451-460 
    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 usefulness of the notion that a one-particle reduced local energy map can measure local errors in a trial wave function is investigated. Examination of the literature suggests that this notion rests on the assumption that a map of the relative error in the one-particle density behaves like the one-particle reduced local energy map. This is tested for several spinless one-dimensional one-particle systems. The assumption is discovered to be ill founded when applied to a certain contrived situation, and not to be quantitative when applied to familiar situations. The possibility remains, however, that the assumption may sometimes be useful for obtaining the correct ordering of trial wave functions with respect to the accuracy of certain types of expectation values.
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  • 34
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    International Journal of Quantum Chemistry 27 (1985), S. 501-525 
    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 new set of generators of the operator algebra over the electronic Fock space is introduced. It is shown that with this set of generators the “basis” Lie algebra can be associated and that the operator algebra of the Fock space is the homomorphic image of the corresponding universal enveloping algebra. The algebraic structure revealed is used for deriving the reduction formulas for the elements of the simplest spin tensor operators between the Gelfand states.
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  • 35
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    International Journal of Quantum Chemistry 27 (1985), S. 527-546 
    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 electron correlation theories for extended systems require an orthogonal and at the same time well-localized virtual orbital system. An iterative method is suggested, by which extremely nonorthogonal basis sets can be orthogonalized without destroying the localization, in contrast to other well-known procedures. With the help of a general formulation of the problem not only the localization but other properties can be achieved as well. The method is compared to Löwdin's orthogonalization. Calculations for model and real systems were carried out and the convergence properties and the stability of the fixed points of the iterative procedure were investigated.
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  • 36
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    International Journal of Quantum Chemistry 27 (1985), S. 613-623 
    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 new method of evaluation of energy matrix elements has been derived for bonded functions of Boys and a spinless Hamiltonian. In configuration-driven CI algorithm the new approach is two to four times faster than the original Reeves' one, the relative speed depending on the case. In integral-driven CI the new approach is about 10 to 12 times faster than the equivalent approach based on the Reeves' scheme.
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  • 37
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    International Journal of Quantum Chemistry 27 (1985), S. 637-637 
    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
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  • 38
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    International Journal of Quantum Chemistry 27 (1985), S. 625-635 
    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 comparison of Roothaan-Hartree-Fock methods (both restricted and unrestricted) with density functional ones (LCAO-Xα and cellular MS-Xαβ) is made using as test case the He22 + molecular ion. It is shown the analogy that exists between RHF and symmetry-adapted LCAO-Xα potential energy curves, as well as between UHF and symmetry-unconstrained LCAO-Xα ones. The influence of symmetry adaptation on the overall behavior of the potential energy curve is also discussed. Finally, the difference in the behavior of the LCAO-Xα and cellular MS-Xαβ calculations is explained as an artifact of the space partitioning in the latter technique. It is concluded that LCAO-Xα method is superior to cellular MS-Xαβ because it requires less effort to reach the same results and that the general behavior is similar to UHF, although the former affords a better equilibrium bond distance and a worse energy barrier than the latter.
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  • 39
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    International Journal of Quantum Chemistry 27 (1985) 
    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
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  • 40
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    International Journal of Quantum Chemistry 27 (1985), S. 641-651 
    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 calculations by means of the superposition of correlated configurations method (Hylleraas-CI), that is, the combination of configuration interaction with the Hylleraas-type correlation factors, needs the effective evaluation of some nontrivial integrals. This series of papers gives the formulas for all types of integrals needed for molecular calculations when Gaussian lobe functions are used as a basis set. The formulas for two-electron integrals are given in the present paper. The preliminary results for two-electron systems are presented.
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  • 41
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    International Journal of Quantum Chemistry 27 (1985), S. 665-675 
    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: Second-order Rayleigh-Schrödinger Hartree-Fock perturbation theory is applied to evaluate the correlation energy for the 4f14 shell of Yb. The partial-wave (PW) increments to the pair energies, and the total correlation energy are calculated using first-order radial pair functions obtained as the solution of two-dimensional differential equations. These equations are solved using the Chalmers University version of the finite difference method. The total second-order correlation energy amounts to 0.89573 hartree. The results for the pair energies, which are close to the all-external pair energies, are compared with related CI values. It turns out that the correlation effects within the 4f shell of rare-earth systems are dominated by the all-external effects. The ff and gg PWS are dominant in the description of the correlation effects in the 4f shell and provide 80% of the total correlation energy. Next in importance are the dd, hh, and dg PWS which provide 12% of the total correlation energy.
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  • 42
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    International Journal of Quantum Chemistry 27 (1985), S. 677-689 
    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 energies of the ground states of the mononuclear atomic systems, until now determined merely by approximate methods, turn out to exhibit some almost exact interdependencies. A simple statistical functional of the electronic structure (the “γ representation”) turns out to be decisive for the system energy. In this paper that interdependence is further traced for the N-electron systems in isoelectronic series (with constant N and varying Z). The resulting “combinatorial formula” reproduces the experimental data with the errors at least ten times smaller than those of the conventional Hartree-Fock approximation. The reason why there is such an exact formula for the ground-state energy remains to be clarified. The limiting behavior of our energy formula for large Z exhibits consistency with the Thomas-Fermi and the Z-1perturbation expansion models.
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  • 43
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    International Journal of Quantum Chemistry 27 (1985), S. 699-707 
    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: An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.
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  • 44
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    International Journal of Quantum Chemistry 27 (1985), S. 691-697 
    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 conventional partition functions of models with quadratically dependent energy spectra (e.g., translation in a box or free internal rotation), which are widely used in literature, exhibit an incorrect limit behavior in the region of low temperatures and/or small values of the characterizing molecular parameter. In particular, this leads to the absurd value  - ∞ for the contribution of these motions to the entropy term at these limit conditions. This incorrect behavior appears to be due to the replacement of rigorous summation by integration in conventional derivation of these partition functions. The derived improved practical formulas with the correct limit behavior indicate that it will be necessary to carry out quite substantial numerical corrections in the case of many reactivity characteristics reported in the literature. Particularly, the improved formulas should be applied with (small) molecular complexes at the typical temperatures of their observation, e.g., van der Waals molecules with free internal rotation. Simultaneously discussed is the possibility of application of the functional relation valid for a rigorous partition function of the considered type of energy spectrum. The reasoning in the case of the translational partition function indicates that, in principle, it can depend on the vessel shape. Possible consequences for thermodynamics of the ideal gas are analyzed.
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  • 45
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    International Journal of Quantum Chemistry 27 (1985), S. 709-730 
    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: N-representability conditions for a two-particle density operator implied by positive-semidefiniteness of the projection operator PN+1(φ1 Λ ΨN) are derived and discussed. The operator PN+1(φ1 Λ ΨN) projects onto an (N + 1)-particle antisymmetric function φ1 Λ ΨN, the Grassmann product of a one-particle factor φ1 and an N-particle factor ΨN. The polar subcone P2N(g, q) to the set of N-representable two-particle density operators P2N which corresponds to these conditions is found. It is shown that its extreme rays belong to two orbits for the action of the unitary group of transformations in one-particle Hilbert space. The facial structure of the convex set P2N exposed by elements of P2N(g, q) is analyzed. An example of the operator that changes the structure of its bottom eigenspace when the number of fermions N surpasses a certain value is noted. A new approach to the diagonal conditions for N-representability is found. It consists of the decomposition of the N-particle antisymmetric identity operator onto the mutually orthogonal projection operators.
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  • 46
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    International Journal of Quantum Chemistry 27 (1985), S. 731-741 
    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 constant-denominator perturbation formalism is developed employing a basis of circulant orbitals and a projected Møller-Plesset partitioning of the Hamiltonian operator. A formal justification for the classical Unsöld approximation is thereby provided. A calculation of correlation energy in the beryllium atom is carried out, and the results are compared with results obtained by the full configuration interaction method and conventional Møller-Plesset perturbation theory.
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  • 47
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    International Journal of Quantum Chemistry 27 (1985), S. 743-768 
    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 definition of a molecular property as a derivative of the electronic energy with respect to one or more applied perturbations is reviewed. The explicit enumeration of terms entering the derivative formulas is performed by considering in turn the various parameter spaces on which the energy and wave function depend. After deriving general expressions for first, second, and third derivatives for different types of perturbation, the parameter spaces involved in MCSCF and CI cases are identified and used to obtain expressions for the first and second derivatives. An example of an MCSCF third derivative is also given. In addition, the various equation systems defining the perturbed wave functions in each order are derived. Some attention is given to the efficient computer implementation of derivative calculations, and the present work is compared with that of other authors.
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  • 48
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    International Journal of Quantum Chemistry 27 (1985), S. 769-780 
    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 consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N-particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.
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  • 49
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    International Journal of Quantum Chemistry 27 (1985), S. 787-801 
    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
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  • 50
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    International Journal of Quantum Chemistry 27 (1985), S. 781-786 
    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: Systematic ab initio LCAO MO calculations with basis sets of increasing size have been performed to analyze the changes in relative stabilization energies of the two cyclic (D3h and C3h symmetry) and the noncyclic HF trimers. The results form the basis for a discussion of cyclic H-transfer reactions.
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  • 51
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    International Journal of Quantum Chemistry 28 (1985), S. 61-84 
    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: A propagator approximation scheme is presented in the context of an abstract*-algebra approach. The representation theory of such algebras is shown to play a crucial role in the definition of consistent approximations, i.e., approximate propagators based on model time evolutions and states. This procedure places superoperator methods of approximation on a sound Hilbert space footing. A generalization of the Fock vacuum property is introduced which leads to a simplification in the form of the model propagators. Finally a concrete example is considered that fulfills the conditions developed in this article showing that a consistent approximation to the electron propagator results in the Hartree-Fock-Boguliubov equations.
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  • 52
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    International Journal of Quantum Chemistry 28 (1985), S. 103-108 
    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: Wilson, Jankowski, and Paldus have recently applied nondegenerate many-body perturbation theory (MBPT) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H4). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low-order sum of the perturbation series is not very meaningful, depends strongly on details of the zero-order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.
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  • 53
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    International Journal of Quantum Chemistry 28 (1985), S. 181-202 
    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 well known one-to-one correspondence between the eigenstates of the total spin for a system of spin-½ particles and irreducible representations of the symmetric group with up to two rows in the Young shape is the basis of interesting formal developments in quantum chemistry and in the theory of magnetism. As an explicit manifestation of this correspondence the class operators of the symmetric group are demonstrated to be expressible in terms of the total spin operator. This correspondence does not hold for higher elementary spins. The extension to arbitrary spin is investigated using Schrödinger's generalization of the Dirac identity, which expresses the transpositions in terms of two-particle spin operators. It is shown that additional operators, which for σ = ½ reduce to the total spin operator, are needed for a complete classification. Some aspects of the formalism are developed in detail for σ = 1. In this case a classification identical with that provided by the irreducible representations of the symmetric group is obtained in terms of the eigenstates of two commuting operators, one of which is the total spin operator.
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  • 54
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    International Journal of Quantum Chemistry 28 (1985), S. 203-211 
    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: N molecular orbitals are transformed to K(≦N) molecular orbitals, which are appropriate for an orbital optimization by two-by-two orthogonal rotations among themselves. This transformation is determined by using the second-order structure of the variational energy surface. The optimum K/2 rotation angles are exactly determined. This helps to ensure the reliability of convergence. K/2 two-by-two rotations are repeated among these K transformed orbitals. Then, two-electron molecular integrals are calculated by transformations among only 16 elements and by a permutation among K4/8 elements. Calculational time is considerably reduced compared with that of more usual transformations. Test calculations have been carried out on the ground state of CO. It shows that this procedure brings the calculation to the local region rapidly and reliably.
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  • 55
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    International Journal of Quantum Chemistry 28 (1985), S. 213-232 
    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 formalism developed in the first two papers of this series is applied to the investigation of a new weak-field model. This crystal-field model lies on the use of a symmetry-adapted weak-field basis and an effective Hamiltonian involving in a symmetrical way both spin- and orbit-dependent contributions. Some general properties of this Hamiltonian are studied and complete calculation of its matrix elements is conducted in a symmetry-adapted weak-field basis in the case of an arbitrary configuration nlN in any symmetry. The case of a configuration ndN in octahedral symmetry is fully explored. In this case, the proposed weak-field model is restricted to a 12-parameter model which accounts for isotropic and anisotropic Coulomb interactions, isotropic and anisotropic spin-orbit interactions, and crystal-field interactions. A comparison between this 12-parameter weak-field model and the 14-parameter strong-field model is established. Equivalence between the latter two models requires two constraint relations to be satisfied for some strong-field parameters. These two relations are examined with various viewpoints.
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  • 56
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    International Journal of Quantum Chemistry 28 (1985), S. 233-237 
    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 electron density at the pyridine nitrogen atom and the π-electron density of the pyridine ring were calculated by the CNDO/2-MO method assuming standard bond lengths and angles. The indices were found to correlate with the pKa values of pyridine derivatives and with the electronic substituent constants of the Hammett type. The correlations were best for four-substituted pyridines, making the routine CNDO/2-MO calculations useful for studies of quantitative relations between structure and biological activity of the compounds.
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  • 57
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    International Journal of Quantum Chemistry 28 (1985), S. 239-244 
    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: Based on the literature values, the pK1 and pK2 for pyrazine and its six methyl derivatives, the correlation with electron density on the nitrogen atoms N1 and N4 was found. The effect of methyl group was proved to be additive. The total electron density, π-electron density, and dipole moments for compounds under study were determined by the CNDO/2-MO method.
    Additional Material: 2 Ill.
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  • 58
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    International Journal of Quantum Chemistry 28 (1985), S. 245-267 
    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 method which is well suited for calculating numerically the energies of the bent vibrating and rotating polyatomic molecule is given. By an analytical method using ladder operators the work of calculating the matrix elements of the Watson Hamiltonian is reduced to mere bookkeeping. This results in fast computation and good control of the errors introduced. To demonstrate the practical usefulness of the method, three test calculations on H2O and SO2 are reported and compared with results from the literature. It is intended to distribute the computer program developed to interested workers in the field.
    Additional Material: 7 Ill.
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  • 59
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    International Journal of Quantum Chemistry 28 (1985), S. 269-286 
    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
    Description / Table of Contents: We adapt the use of the Lie algebra su (n) we proposed in former papers to a system made up of two subsystems (respectively, nA and nB states). We show how reduced density operators, correlation problems, and overall and reduced evolution equations, may be made precise with this formalism.
    Notes: L'usage de l'algèbre de Lie su (n), proposé dans les articles précédents, est adapté a l'étude d'un système formé de deux sous-systèmes, respectivement à nA et nB états. On montre comment diverses notions (opérateurs-densités réduits, problèmes de corrélation, équations d'évolution globales et réduites) peuvent être précisées grâce au formalisme introduit.
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  • 60
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    International Journal of Quantum Chemistry 28 (1985), S. 287-295 
    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 potential energy of a homonuclear X4 molecule is an invariant of the atom permutation group S4 acting on the internal coordinates of X4. It is shown by means of invariant theory that six algebraically independent invariants and five additional invariants are required to express the general invariant function for this group. Explicit expressions for these 11 invariants are given.
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  • 61
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    International Journal of Quantum Chemistry 28 (1985), S. 297-309 
    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: An ab initio investigation of the potential energy hypersurfaces of the Na+/H2 system is presented. The calculations have been performed on SCF level and with the inclusion of correlation effects by means of the CEPA-PNO, IEPA-PNO, and PNO-CI methods. The basis set consists of gaussian lobes (12s, 8p, d) on Na and (8s, p) on H. The distance of the Na nucleus to the midpoint of H2 was varied between 0.0 and 10 bohrs, whereas the region of H—H distances considered was 0.5 to 10 bohrs. The angular dependence of the hypersurface was investigated as well. The system Na+/H2 has an absolute energy minimum for C2v geometry at R equal approximately 5.0 bohrs and rHH = 1.40 bohrs.
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  • 62
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    International Journal of Quantum Chemistry 28 (1985), S. 311-314 
    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 maximum entropy procedure (MEP) of Jaynes has been extended to the case involving constraints in complementary spaces. It has been rigorously shown that the sum of information entropies in position and momentum spaces is invariant to uniform scaling of the electron coordinates. A new MEP procedure requires that this sum of entropies must be maximized subject to the known constraints in both spaces. A specific application of this maximization procedure for synthesizing atomic-electron densities in coordinate and momentum spaces has been outlined.
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  • 63
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    International Journal of Quantum Chemistry 28 (1985) 
    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
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  • 64
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    International Journal of Quantum Chemistry 28 (1985), S. 335-348 
    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 unitary group reformulation of electron propagator theory is used to derive the second-order and 2p - h Tamm-Dancoff self-energy approximations for open-shell applications. A highest weight representation of the reference state is chosen in order to facilitate matrix element evaluation, but two special cases precluded by this choice are also discussed. Detailed numerical calculations are described for the lithium atom, oxygen molecule, and the amidogen radical.
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  • 65
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    International Journal of Quantum Chemistry 28 (1985), S. 315-334 
    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: We present molecular orbital (CNDO/2) calculations on the key fragments of different dihydrofolate reductase inhibitors. Distance geometry analysis, physicochemical parameter dependent QSAR, and molecular shape analysis raised some questions regarding the basicity of the ring nitrogen (N1) in these inhibitors and the effect of the various substituents on the basicity. We show that the ring nitrogen N1 of methotrexate has a considerably higher tendency to be protonated compared to that of folic acid. However, not all 2,4-diamino inhibitors are equally basic. Even 2-amino-4-hydroxyquinazoline is sufficiently basic to be protonated, but not the 2,4-diamino-5-sulfonyl derivatives. The pyrimidinium ion seems to be highly solvated, since in spite of its high protonation energy it is strongly basic. Triazines were found to be the most basic of all the classes studied.
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  • 66
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    International Journal of Quantum Chemistry 28 (1985), S. 349-373 
    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: General formulas have been derived for molecular integrals arising in the use of the identity derived by Harriman for describing the Fermi-contact interaction in a molecule. Computational aspects are discussed and numerical examples are shown for several sets of the usual Cartesian Gaussian-type orbitals.
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  • 67
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    International Journal of Quantum Chemistry 28 (1985), S. 375-386 
    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: We simplify a recently obtained approximate formula for the third-order interaction energy between two molecules expressed in terms of irreducible spherical polarizabilities and multipole moments of interacting systems. Similarly, we can simplify analogous higher-order expressions. Then we briefly examine the magnitudes of the various third-order contributions in comparison with the second-order categories of long-range interactions for some specific systems.
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  • 68
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    International Journal of Quantum Chemistry 28 (1985), S. 387-398 
    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 collection of families of equivalent reaction paths within the low lying regions of potential energy hypersurfaces can be characterized in terms of a group, the fundamental group of reaction mechanisms. This group is compared to the family of all general reaction mechanisms on a complete potential energy hypersurface (considering all nuclear configurations of a fixed set of nuclei). This latter family also has an algebraic structure (a groupoid) that contains a group for every reactant. This groupoid and its subgroups are defined in terms of sequences of open neighborhoods of critical points (representing chemical structures) on the hypersurface, and provide a complete algebraic description of all general reaction mechanisms. This approach simplifies the intractable problem of all possible reaction paths on a surface to a well defined algebraic problem of a discrete set of reaction mechanisms. The relevance of the approach to computer based quantum chemical synthesis planning is pointed out.
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  • 69
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    International Journal of Quantum Chemistry 28 (1985), S. 419-419 
    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
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  • 70
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    International Journal of Quantum Chemistry 28 (1985) 
    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
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  • 71
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    International Journal of Quantum Chemistry 28 (1985), S. 399-409 
    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: We studied the stability of guanine-cytosine and non-Watson-Crick pairs in the presence of H-bond interactions with various amino acid side chains, by using ab initio MO method. The external H-bond interactions stabilize or destabilize the base pairs, depending on the type of interacting residues and the site of the interaction. The pattern of the H-bond effect on the base-pair stability is quite different than in the case of adenine-uracil pair previously reported. From the present results, together with the previous results on adenine-uracil pair, we obtain a general rule for the effect of external H-bond interactions on the stability of base pairs. The site-specific effect of the H-bond interactions can be consistently explained by the cooperative interaction between external and base-pair H bonds. We discuss the application of the present results in the following biological processes: One is the protein-induced specific melting of double-stranded DNA, which is involved in transcription process. The present results suggest that H-bond interactions of protein residues at specific site of base pairs can weaken base-pair H bonding, which would assist the opening of double-stranded DNA. The other is the control of mutation in replication process. We suggest that proteins can discriminate non-Watson-Crick pairs against Watson-Crick pairs by H-bond interactions and can either induce or suppress mutation during DNA replication.
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  • 72
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    International Journal of Quantum Chemistry 28 (1985), S. 451-457 
    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: We have studied the effect of Hubbard interaction on solitonic excitations in the polymer trans-polyacetylene. These excitations are modeled using the Su, Schrieffer, and Heeger (SSH) Hamiltonian. Within this framework, we have calculated the full configuration interaction and restricted Hartree-Fock energies of solitonic excitations in trans-polyacetylene chains with 4-10 carbon atoms. These results are extrapolated to longer chains, and it is shown that the correlation energy for these chains approaches 3%. Thus, our calculations provide a justification, hitherto absent, of the accuracy of the Hartree-Fock calculations reported in the literature.
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  • 73
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    International Journal of Quantum Chemistry 28 (1985), S. 459-479 
    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 role of electron correlation effects on the bond-length alternation in linear metalliclike systems, as modeled by cyclic polyenes CNHN, N = 2n = 4v + 2, v = 1,2,…, is examined using the coupled cluster approach in the localized Wannier basis formalism. A recently developed approximate coupled pair approach which accounts for connected quadruply excited clusters is employed together with various truncation schemes for the localized doubly-excited cluster components. It is found that for the physical value of the coupling constant, the electron correlation has only a very slight effect on the potential energy curves, yielding almost the same values for both the magnitude of the bond-length alternation and for the stabilization energy relative to the symmetric equidistant structures as the restricted Hartree-Fock theory. This is in contrast to a strongly correlated region where the correlation effects stabilize the undistorted non-alternating structures. Different mechanisms of the bond-length alternation or Peierl's distortion as implied by a simple Hückel Hamiltonian and by the Pariser-Parr-Pople Hamiltonian models are also pointed out.
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  • 74
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    International Journal of Quantum Chemistry 28 (1985), S. 499-516 
    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 collisional exchange of energy between He atoms and a strongly polar diatomic, the LiH target, has been studied theoretically over a range of relative energies that had been previously sampled by experiments with molecular beams. The relative importance of the rotational and/or vibrational channels is examined by studying in detail the effect of the interaction via a model potential coupling parameter. The different behavior exhibited by differential cross sections (total and partial inelastic) is also analyzed in terms of the strength and shape of the interaction anisotropy.
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  • 75
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    International Journal of Quantum Chemistry 28 (1985), S. 481-498 
    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: General structures represented by graphs with unequal interactions (weighted edges) are considered and their characteristic polynomials (spectral polynomials) are obtained. It is shown that the procedure based on pruning terminal vertices previously developed by one of the present authors (K.B., Ref. 1) can be generalized to more common graphs in which nonuniform interactions (unequal couplings) occur. Special cases of the present approach are Möbius graphs, signed graphs, directed graphs, multigraphs, and pseudographs (i.e., graphs with multiple connections and graphs with loops, respectively). Weighted graphs (with general weights) are applicable to a variety of chemical problems such as problems of chemical kinetics, analysis of NMR spectra, the study of simple molecular orbitals, and molecular vibrations.
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  • 76
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    International Journal of Quantum Chemistry 28 (1985), S. 517-523 
    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: Model ring systems 2′-deoxy-2′-fluororibofuranose and deoxyribofuranose have been investigated using ab initio calculations with the 3-21G basis set. The energy barrier to pseudorotation between the N and S states has been evaluated for the three preferred orientations of the (3′)-OH group. Positions of the energy minima and the transition state have been optimized with respect to the (3′)-OH orientation. The barrier to pseudorotation of 2′-deoxy-2′-fluorofuranose is high and asymmetrical (ΔEN→S ≈ 20, ΔEN←S ≈ 8 kJ/mol), whereas the barrier of 2′-deoxyfuranose is lower and almost symmetrical (ΔE ≈ 11-12 kJ/mol). The results obtained show that the preferred configuration of the 2′-deoxy-2′-fluororibo-furanose (N state) is stabilized by an internal O(3′)-H…F interaction in accord with the crystallo-graphic data.
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  • 77
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    International Journal of Quantum Chemistry 28 (1985), S. 525-534 
    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: In reply to Kaldor's [Int. J. Quantum Chem. XX, XXX (1985)] criticism of our study of simple four-electron models, in which the degree of quasi-degeneracy can be continuously varied, by the finite-order nondegenerate many-body perturbation theory, we examine in more detail a simple two-state model that the used to substantiate his claim that “the low order sum of the perturbation series is not very meaningful” in view of its divergence. It is shown that in contrast to Kaldor's claim, the partitioning used increases the radius of convergence of the considered perturbation series and is in principle capable to make it convergent. It is also shown that the convergence of the series is not very essential and that even divergent series can provide useful estimate of the exact result, particularly when the resummation techniques, such as Padè approximants or continued fractions, are employed. Finally, the shortcomings of the existing multi-reference perturbation approaches, which Kaldor advocates, are pointed out.
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  • 78
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    International Journal of Quantum Chemistry 28 (1985) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 79
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    International Journal of Quantum Chemistry 28 (1985), S. 535-551 
    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 general method is presented to find in a least-squares sense a set of orthogonal eigenfunctions and their eigenvalues from local energy and numerical integration methods or by any other dissymmetric approach to solve the eigenvalue problem of a Hermitian operator. By this method a generalization of the minimum variance method to more than one eigenfunction is obtained, which is a variant of Scott's method. Also a new method is derived - called the minimum-overlap method - that is a least-squares numerical version of the standard Rayleigh-Ritz method. Test calculations on the atoms Be and Tm and the molecules H2 and CO have been performed with both numerical Hartree-Fock and Hartree-Fock-Slater methods. The least-squares solutions are an improvement over other methods in the case of accurate basis sets. Numerical Hartree-Fock calculations of moderate accuracy are found to be considerably faster than the analytic method.
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  • 80
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    International Journal of Quantum Chemistry 28 (1985), S. 553-564 
    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 large vibrational inelasticity observed in proton-O2 scattering at collision energies of ∼10.0 eV and for various angular distributions below the rainbow region is examined in terms of SCF adiabatic potential energy surfaces which exhibit strong O2+ “character” within a specific range of relative distances between colliding partners. The possibility for this O2 distortion during encounters with protons to be responsible for the unusually large inelasticity is discussed and the time factors that are likely to play an important role during the dynamics are also considered and analyzed.
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  • 81
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    International Journal of Quantum Chemistry 28 (1985), S. 565-571 
    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 INDO/2 version of the average hole potential (AHP) model is analyzed. The model is applied to study the geometric features, molecular inversion barriers, singlet-triplet splittings, etc., of a few small carbonyl molecules (H2CO, HFCO, F2CO) in the 1,3nπ* states with partial as well as complete optimization of all geometric parameters in the excited states. The results are compared with those obtained by a simple hole-potential (HP) model.
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  • 82
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    International Journal of Quantum Chemistry 28 (1985), S. 573-579 
    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 effects of four factors (different side chains, side-chain disorder, conformational change, and ions and water) on the energy band structures of proteins have been investigated with the aid of the CNDO/2 crystal orbital method. The results indicate that these factors are very important. The consequences of these effects on the semiconductive properties of proteins are discussed.
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  • 83
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    International Journal of Quantum Chemistry 28 (1985), S. 703-713 
    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 formalism was developed in the multiconfigurational variation of moments (MCM) framework, which yields physically meaningful orbital energies for occupied and virtual orbitals starting from self-consistent field (SCF) calculations. This is possible through a skillful distribution of the correlation energy on the orbital energies. The application of this method is demonstrated by SINDO1 calculations on the dissociation of H2 and the following symmetry-forbidden reactions: (1) torsion of ethylene; (2) ring opening of (a) cyclobutene, and (b) cyclopropyl cation; (3) cycloreversion of 1, 1-dicyano-2-methoxycyclobutane. The allowed reactions corresponding to 2a and 2b are investigated in the SCF scheme. The energy hypersurfaces are calculated for all reactions and the MO correlation diagrams are presented and discussed.
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  • 84
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    International Journal of Quantum Chemistry 28 (1985), S. 715-721 
    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 electronic structure of [TiCl4]n systems (n = 0, -1, -2, -3, and -4) has been investigated by the INDO method. Calculations show the stability of the tetrahedral structure over the square-planar one, for any value of n, in accord with experimental observation. The occupation of the 4p orbitals of the titanium atom was found to increase regularly as the dihedral angle decreases and reaches a maximum at the square-planar conformation. Energy partitioning analysis enabled much deeper understanding of bonding characteristics of the studied systems. It has been shown that the one-atom energy component may be a very sensitive measure of the stability of the central metal atom in its various oxidation states.
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  • 85
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    International Journal of Quantum Chemistry 28 (1985), S. 731-740 
    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: Molecular-orbital calculations, using the INDO procedures, were carried out on the tautomers of 1, 2, 4-triazole and its benzo-derivative as well as on 1, 2, 5-oxadiazole and its benzo-derivative. Calculations of the transition energy as well as the dipole moment helped to predict the predominant tautomer in an equilibrium mixture. The correspondence between the calculated and observed data is satisfactory. The results of calculations indicated some differences in the electronic structures of the tautomers of a compound.
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  • 86
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    International Journal of Quantum Chemistry 28 (1985), S. 741-756 
    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 comparative study of quasirelativistic equations used in atomic structure calculations has been performed. A uniform derivation of all the equations is presented, and some of their specific features are discussed in detail. Electron density distributions, orbital energies, and expectation values of rn obtained with different methods are compared with the ones resulting from the Schrödinger and Dirac equations. The most accurate are found to be the equations of Wood and Boring and of Barthelat, Pelissier, and Durand. (They reproduce almost exactly the Dirac electron densities and expectation values.) The simplest, though least accurate, equation is proposed by us. It gives the relativistic energy corrections with about 6% accuracy and retains exactly the form of the nonrelativistic Schródinger equation. Consequently, its application in analytical SCF-CI calculations does not require any additional integral calculation.
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  • 87
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    International Journal of Quantum Chemistry 27 (1985) 
    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
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  • 88
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    International Journal of Quantum Chemistry 27 (1985), S. 45-58 
    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 relations between isoscalar factors for corepresentations of antiunitary magnetic point groups are discussed in the case of associated corepresentations. The tables of the isoscalar factors for the single- and double-valued corepresentations of all tetragonal, orthorhombic, monoclinic, and triclinic Shubnikov point groups are given. Some peculiarities of the calculation method of the isoscalar factors for corepresentations are considered.
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  • 89
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    International Journal of Quantum Chemistry 27 (1985), S. 59-70 
    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 representation matrices of the unitary group generators Ek1 are equivalent to the representation matrices of cyclic permutations (k, k ± l, …, l ∓ 1, l). A method is presented for simultaneous computation of matrices corresponding to all different generators at a cost of less than one multiplication per nonzero element. The number of operations necessary for calculation of individual matrices for single generators or for products of two generators is at most proportional to the number of matrix elements of the final matrix. This approach eliminates the need to store the representation matrices in CI calculations.
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  • 90
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    International Journal of Quantum Chemistry 27 (1985), S. 1-10 
    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: Ab initio molecular orbital calculations using a 3-21G basis set have been used to optimize geometries for pyrrole, CH3(X)CCH2, CH3(H)CCHX (both cis and trans), c-C3H5X, and CH2CHCH2X, where X is CN and NC. In all the alkenyl derivatives methyl groups are found to adopt the conformation in which the methyl hydrogen eclipses the double bond. 6-31G*∥3-21G level calculations show the alkenyl cyanides to be of similar energy to pyrrole, but the isocyanides are ∼20 kcal mol-1 higher in energy. For both substituents the cyclopropyl derivatives are higher in energy by ∼10 kcal mol-1. At the 6-31G* level ring strain is 27.7 kcal mol-1 for the cyanide and 30.6 kcal mol-1 for the isocyanide. Data on the relative energies of RCN and RNC are compared when R is (i) a saturated hydrocarbon, (ii) an unsaturated hydrocarbon, (iii) an α-carbenium ion, (iv) an allyl cation, and (v) an α-carbanion.
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  • 91
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    International Journal of Quantum Chemistry 27 (1985), S. 11-44 
    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 new quantal approach to the problem of chemical reactions, of the type A + BC → AC + B, is proposed. The general formalism is based on a change of representation for the Hamiltonian system, such that in the new (ideal space) representation the transformed Hamiltonian may present, simultaneously, information on both the “reactants” and the “products” of the dynamical process. The change of representation is carried out by means of a unitary transformation that physically corresponds to creating bound BC and AC molecules, respectively, starting from free atoms. The transformation is explicitly realized by using models available in the literature, and the ideal space Hamiltonian is fully obtained, showing that it contains, in its structure, all the channels (inelastic, reactive, dissociative, etc.) available to the system. A discussion of the dynamics, at the light of the new Hamiltonian, seems to indicate that the theory will be particularly suited for numerical applications to the problem of chemical reactions and, more generally, that it may lead to a “unified” approach for both the subreactive and rearrangement regimes, in atom-diatom encounters.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 92
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 103-103 
    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
    Type of Medium: Electronic Resource
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  • 93
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 97-101 
    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: We provide an alternative to the biquadratic analytic scheme BIQ published earlier. This form, AMPLIN, is similar to the older linear analytic scheme, LIN. This scheme is much faster than BIQ.
    Type of Medium: Electronic Resource
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  • 94
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 89-96 
    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 method of Dupuis and King for generating matrix elements of a totally symmetric one-electron operator in terms of symmetry-distinct integrals only is generalized to the case of nontotally symmetric operators. For operators constructed from two-electron integrals, explicit reduction of integral processing to permutationally inequivalent symmetry-distinct integrals only is described, while for one-electron operators further reductions are derived using double coset decompositions. Finally, some computational consequences of this approach are briefly discussed.
    Type of Medium: Electronic Resource
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  • 95
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 71-87 
    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 ground and excited singlet and triplet states of 9,10-anthraquinone and its 1,4-dihydroxy and 1,4-diamino derivatives are investigated by ab initio configuration interaction calculations, using a floating Gaussian basis. For anthraquinone the calculated electronic absorption spectrum is consistent with previous experimental and theoretical results. The possible mechanisms of intersystem crossing and intensity borrowing in phosphorescence are discussed in terms of first- and second-order spin-orbit and vibronic perturbations of the computed singlet and triplet states. The calculated spectra of the 1,4-disubstituted derivatives are more complex than previously suggested from low-resolution polarized absorption studies. The principal effect of 1,4-substitution by electron donating groups is shown to be a powerful conjugative effect which significantly modifies selected molecular orbitals of anthraquinone; the resultant effect on the absorption spectra is the creation of two new substituent-induced π → π* transitions, one of which corresponds to the intense visible absorption band of these systems.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 96
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 145-157 
    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 orthogonalized direct diagonalization (ODD) method is used to predict the valence-shell ionization spectra for the series of hydrocarbons ethane (C2H6), ethylene (C2H4), and acetylene (C2H2) within an EOM/propagator formalism. Both (a) third-order and (b) higher-order (with h5 terms in the excitation operator manifold) calculations are presented in order to illustrate the effect of the extended operator manifold on the predicted valence-shell spectra. It is shown that the major effect of the h5 manifold is concentrated in its “occupied” part. Along with a general shifting of the main lines for outer valence ionizations to lower values (together with a slight reduction in pole strength), it is found that the effect of the h5 manifold in the inner valence region is dependent on the system being studied.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 195-202 
    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: Consideration of R(4) as the degeneracy group for the singly excited states of helium allows the assignment of R(4) irreducible representations (irreps) to these states. Induction of these irreps onto the irreps of SU(4) and U(4) provides a sufficient number of invariants to define the energy levels. Empirical equations allow all of the singlet states to be related to the first ionization energy and the Rydberg constant, to a good approximation. Empirical equations can also be derived for the triplet states, but their relation to the ionization energy and/or the Rydberg constant is not obvious.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 28 (1985) 
    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
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 803-804 
    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
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 28 (1985), S. 17-26 
    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: An expression for electron transfer rate has been obtained through the solution of a time wave equation by the variational method by defining the wave function as a linear combination of functions corresponding to electron localization on the donor and on the acceptor. A dependence of electron transfer on temperature, on the electronic and vibrational characteristics of the system has been derived. An activation energy temperature-variation effect has been obtained. It has been proved that many-electron transfers are impossible.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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