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  • 1975-1979  (192)
  • 1977  (192)
  • Computational Chemistry and Molecular Modeling  (192)
  • 1
    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
    Additional Material: 2 Ill.
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  • 2
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 185-185 
    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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  • 3
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 187-187 
    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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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977) 
    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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  • 5
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 189-211 
    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: The theory of pth-order singular differential equations is adaptable to the study of the system of recurrence relations occurring in the problem of a one-dimensional chain with pth-neighbor interactions. By using Green's formula, a mapping is defined between the space Vn of eigenvectors to the dynamical matrix and the symplectic space V2p of boundary conditions for the recurrence equations. The properties of the resolvent are obtained from an analysis of the solutions of a system of inhomogeneous equations and Green's matrix is constructed for the case of standard Sturm-Liouvilletype boundary conditions. The Weyl surface is discussed and its properties used for the construction of square summable sequences which in turn can be employed in expansion formulas. The generalization of Weyl's m-function in the second-order case (p = 1) becomes for p ≥ 2 a p × p matrix M(λ), where λ is a complex parameter. The imaginary part Im {M(λ)} is related to the spectral properties and serves as basis for the discussion of different concepts of spectral density for the normal modes of lattice dynamical problems. An important practical result is the equation M = -Ψa-1Φa valid in the limit point case, generalizing the corresponding second-order formula.
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  • 6
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 233-245 
    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 perturbation theory based on the paired excitation multiconfiguration self-consistent field approach of Clementi and Veillard is considered. The coupled first-order perturbed orbital equations are analysed and an appropriate computational scheme for their solution is discussed. The proposed computational scheme is analogous to the technique employed for the solution of the coupled Hartree-Fock equations in the one-configuration approximation. However, because of the presence ofnondiagonal Lagrangian multipliers and the use of different one-electron operators for different orbitals, the present scheme raises some new computational problems. In this context a new technique for the solution of the unperturbed multiconfiguration self-consistent field equations is proposed. A simple illustration of the superiority of the multiconfiguration perturbation approach with respect to the ordinary coupled Hartree-Fock scheme is given. Also the validity of the variation formulation of the presented scheme and its relation to the finite-field approach are discussed.
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  • 7
    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 computational procedure which introduces some electron correlation into quantum mechanical calculations is described. Diverse applications are given. Among these, the method gives values of 65.6 kcal/mole for the dissociation energy of LiH, 62.0 kcal/mole for the ring-opening energy of cyclopropane, and 9.123 × 155 dynes/cm for the O-H stretching force constant of H2O. These results, and others given, suggest that our procedure has great potential and provides a very economical method for introducing electron correlation into a wave-function.
    Additional Material: 4 Ill.
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  • 8
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 247-257 
    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 Rayleigh-Schrödinger polarization and the Hirschfelder-Silbey (HS) perturbation theories are applied, through the 38th order, to the interaction of a ground-state hydrogen atom with a proton. The calculations were made with high precision using a large basis set of orbitals expressed in the confocal elliptic coordinates. The results obtained show that for small internuclear separations R the polarization series converges slowly in an oscillatory way to the energy of the ground 1sσg state of the H2+ molecule. At large R, however, the polarization expansion reproduces only the Coulomb part of the interaction energy effectively. When the value of the Coulomb energy is reached, the rate of convergence deteriorates drastically so that the exchange energy is not reproduced practically. The HS method converges fast when applied to both the 1sσg and the 2pσu states, the rate of convergence being roughly independent of the internuclear distance. If the finite basis set employed to solve the perturbation equations is stable under the symmetry operations, the HS expansion is shown to converge to the energy obtained by minimizing the Rayleigh-Ritz functional within the space spanned by the functions used in the perturbation theory calculations.
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  • 9
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    International Journal of Quantum Chemistry 11 (1977), S. 435-440 
    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 FSGO model has been used to make ab initio calculations of the geometry of B2H5+ ion. The results indicate that the acetylenic structure has the lowest energy (-43.881 a.u.) and the planar structure has the highest energy (-43.838 a.u.). The energy of the non-symmetric structure is only slightly higher (-43.879 a.u.) than that of the acetylenic one. Results of CNDO/2 calculations reported here also predict the acetylenic structure to be the most stable one.
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  • 10
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    International Journal of Quantum Chemistry 11 (1977), S. 441-450 
    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 series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron isoelectronic series of sulfur hydrides. Conclusions from these results suggest that meaningful proton affinities cannot be calculated without the inclusion of a d function on the heavy atom and a p function on the hydrogen atoms.
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  • 11
    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 formulated a pharmacological-physiological systems analysis and control theory based on interactive neuronal feedback loops (the effects of endogenous neurochemical diseases and exogenous psychotropic and other CNS drugs on neurotransmitter synthesis and release, reuptake, and metabolism) for normal, abnormal, and catastrophic situations.We were concerned primarily with the problems of stability or instability which might lead the system to exhibit catastrophic behavior. We set up the systems diagrams for the neurotransmitter systems and in that single framework were able to describe endogenous neurochemical disorders, the effect their drug treatment modalities had on the dynamic neurochemical balance, the effect psychotropic or other CNS drugs such as narcotics and narcotic antagonists had on neurotransmitter balance, and the interactive effect that multiple drug administration would have on neurotransmitter balance. Endogenous neurochemical disorders such as schizophrenia, Parkinsonism, depression, and mania should show up mathematically either as overly damped solutions if there is too little normal neurotransmitter or as catastrophically divergent instabilities if there is too much normal neurotransmitter. Improper mixed drug therapies, as well as the devastating effect of eating foods such as cheese (which contains sympathomimetic amines which potentiate the release of catecholamines from the presynaptic nerve endings) while on MAOI therapy also show up as mathematical, usually catastrophic, instabilities. We also indicated how this systems analysis and control theory could be put on small interactive computer terminals for use in clinical management and proper drug therapy of patients with neurochemical disorders.
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  • 12
    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 relation between the completeness condition for an appropriate one-particle basis set and the occupation number representation (second quantization) is shown for the time-independent case. The explicit expressions for the basic symmetric operators are derived in the Dirac bra-ket notation. The physical meaning of these operators, the algebra as well as the connections with the one-electron density matrix and with the projector on the Fermi sea in the one-electron approximation, follow directly from these expressions. The generalization for a nonorthogonal basis and the algebra for corresponding basic operators are formulated. The connection with the notion of the molecular diagrams of different kinds for the nonorthogonal atomic orbitals is shown. The Mulliken populations and the Chirgwin-Coulson bond orders are equal to the diagonal and offdiagonal elements of the molecular diagram 1, respectively. The matrix elements of the projector on the Fermi sea in the one-electron approximation in the representation of nonorthogonal atomic orbitals are elements of the molecular diagram 2.
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  • 13
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    International Journal of Quantum Chemistry 11 (1977), S. 525-542 
    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: Exact solutions to the quantum mechanical problem of an anisotropic oscillator in a one-dimensional magnetic field are obtained. These solutions (eigenenergies and wave functions) are then applied to the problem of calculating the magneto-optical properties of a charged spinless particle constrained to move in a harmonic potential field. General expressions for the dipole strengths and rotational strengths associated with radiation induced transitions between the eigenstates of this model system are developed, and these quantities are further related to observables of magneto-optical absorption spectroscopy and Faraday effect studies.
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  • 14
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    International Journal of Quantum Chemistry 11 (1977), S. 561-576 
    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: It is known that the 2l+1 spherical harmonics Ylm can be transformed into cyclically equivalent orbitals, of which only a few examples have so far been given explicitly. In this article the totality of such cyclic sets is derived.It is demonstrated that other kinds of equivalent spherical harmonics do not exist.Finally a set of five equivalent d orbitals related to icosahedral symmetry is introduced.
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  • 15
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    International Journal of Quantum Chemistry 11 (1977), S. 543-559 
    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: Quasi-relativistic (QR) versions of the CNDO and Mulliken-Wolfsberg-Helmholz (MWH) semiempirical methods based on the SCF-QR-MO-LCAO method given earlier are worked out. For the CNDO method only the basic formulas and matrix element expressions are given, while for the MWH one, the parametrization as well as the basis functions and group spinor overlap integral calculation were discussed. (PtCl6)2- complex was chosen for a test calculation. The energy level values and LCAO coefficients were obtained and compared with the nonrelativistic calculations. One of the results was the occurrence of a very strong reduction of the spin-orbit interaction due to covalency. The calculation proves the semi-empirical versions of the QR-MO-LCAO method to be quite realizable in practice.
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  • 16
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    International Journal of Quantum Chemistry 11 (1977), S. 577-589 
    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 problems of permutational symmetry of the density matrices in reduction are studied. Some necessary and sufficient conditions for N, [λ1], [λ2]-derivability problem are given.
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  • 17
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    International Journal of Quantum Chemistry 11 (1977), S. 591-604 
    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: This paper is concerned with a new application of projected-unrestricted Hartree-Fock theory, namely, the calculation of electronic spectra for symmetric molecules. The excited electronic state is represented by a single determinant whose unrestricted nature allows for orbital rearrangement relative to the self-consistent ground state. The self-consistent calculation must be followed by spin projection to obtain appropriate spin eigenstates. It was necessary to develop modified procedures for portions of the spin projection calculation because our method of constructing the wave functions produces degeneracies among the natural orbitals. Illustrative calculations using the all-valence-electron INDO approximations produced results which compared favorably with configuration-interaction treatments. The method described here should be most useful, however, in conjunction with ab initio calculations using flexible basis sets.
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  • 18
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    International Journal of Quantum Chemistry 11 (1977), S. 605-611 
    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 parameter optimization method of Part I is applied to the exponents of real STOS of first row atoms. In addition to minimum basis ground states, some independently optimized excited states are discussed in the case of Be. Local minima on the energy versus parameter surface are found in 4-configuration functions for the ground state of N. They are not present in either the simpler minimum basis function or in a more complete 8-configuration function.
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  • 19
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    International Journal of Quantum Chemistry 11 (1977), S. 613-625 
    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: For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two-electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre-Elder procedure. We compare SCF calculations on the phosphorus molecule using Td symmetry with those using various subgroups of Td. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry-related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.
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  • 20
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    International Journal of Quantum Chemistry 11 (1977), S. 759-766 
    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 two-parameter ω-technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest-neighbour electronic repulsion integrals into the conventional ω-technique.
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  • 21
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    International Journal of Quantum Chemistry 11 (1977), S. 767-773 
    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: Gaussian orbital LCAO MO calculations are reported for pyrazine in its ground and first excited triplet state, together with calculations on its anion and cation. Energies, population analysis indices, and one-electron properties are compared across the series in order to investigate the differences in electron distribution.
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  • 22
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    International Journal of Quantum Chemistry 11 (1977), S. 907-916 
    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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  • 23
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    International Journal of Quantum Chemistry 11 (1977), S. 917-929 
    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: Löwdin has presented his angular momentum projection operators in two forms, the sum form deduced from the product form. A direct proof of the sum form is presented here, together with a brief account of application of the technique to the pd configuration.
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  • 24
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    International Journal of Quantum Chemistry 12 (1977), S. 61-81 
    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: New, more accurate, Hartree-Fock limit energies (EHF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with EHF values for other small closed shell molecules, are employed to calculate correlation energy (Ec) contributions to reaction heats. Cancellation to within 98% of the total Ec involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to Ec from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, Ec for the valence shell is evaluated in terms of Ec per lone pair, Ec per X—H bond, and Ec per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.
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  • 25
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    International Journal of Quantum Chemistry 12 (1977), S. 83-92 
    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 Hartree-Fock and first natural spin determinants were compared as reference determinants for calculating various one-electron properties such as ρ(0), 〈½∇〉, 〈r-2〉,…, 〈r3〉, and r-112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree-Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one-particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one-electron expectation values accurately.
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  • 26
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    International Journal of Quantum Chemistry 12 (1977), S. 93-103 
    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
    Notes: Coupled Hartree-Fock perturbation theory has been applied to compute the nuclear magnetic shielding tensors for 17O, 14N, and 13C in the molecules of water, ammonia, and methane with four wave functions of increasing accuracy, expanded over basis sets of Gaussian functions. The agreement with the experimental data available for ammonia and methane is very good. Quantities necessary to evaluate the shilding for an arbitrary gauge are also given. The degree of gauge-invariance of the calculated properties is nt satisfactory in the ammonia, while better results are found for water.
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  • 27
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    International Journal of Quantum Chemistry 12 (1977), S. 105-113 
    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: Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H2. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.
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  • 28
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    International Journal of Quantum Chemistry 12 (1977), S. 133-143 
    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 number of molecular one-electron progperties have been analyzed by partitioning their electronic components over energy localized molecular orbitals (LMO). The ammonia and ethane molecules, calculated in an Approximately double zeta qualtiy basis set, were considered. The partitioning of the electronic components of certain one-electron properteies over LMO allows a quantitative rationalization of the sensitivity of certain properties to basis set effects due to the differeing degree of difficulty of accurately determining different LMO as measures of the molecular electron density.
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  • 29
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    International Journal of Quantum Chemistry 12 (1977), S. 115-131 
    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: Three simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σg+(1A1*)) and to the two lowest of CH2+(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian-lobe basis sets by least-square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms-in-molecule approach.The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σg+(1A1*)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.
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  • 30
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    International Journal of Quantum Chemistry 12 (1977), S. 193-205 
    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 focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the 3P → 1D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.
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  • 31
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    International Journal of Quantum Chemistry 12 (1977), S. 225-226 
    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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  • 32
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    International Journal of Quantum Chemistry 12 (1977), S. 215-223 
    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 invariance question int he CNDO and INDO levels of approximation is discussed with particular reference to one-center and two-center two-electron integrals and rotation of molecule-fixed coordinate axes. It is shown that asufficient condition for rotational invariance for the cone-center two-electron integrals is Jμμ = Jμμ, +2Kμμ, where J and K are the Coulomb and exchange integrals over orbitals μ μ′ with the same azimuthal quantum number. CNDO and INDO procedures, which explicitly employ Löwdin's orthogonalized basis set of atomic ortbitals (OAO) and differentiate between s-, p-, and d-orbitals on an atom in calculating various integrals, have also been examined in relation to the rotational invariance requirement. An expression which satisfies rotational invariance for two-electron Coulomb repulsion integrals over OAOS is also given.
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  • 33
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    International Journal of Quantum Chemistry 12 (1977), S. 227-229 
    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
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  • 34
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    International Journal of Quantum Chemistry 12 (1977) 
    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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  • 35
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    International Journal of Quantum Chemistry 12 (1977), S. 231-231 
    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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  • 36
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    International Journal of Quantum Chemistry 12 (1977), S. 273-289 
    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 localized-site cluster expansion technique is applied to the infinite linear Heisenberg model with both nearest-neighbor and next nearest-neighbor interactions. These cluster ansätze are systematically studied and improved, up to the so-called 5-site approximation. Generally we find the present cluster ansätze yield the most accurate variational results yet available.
    Additional Material: 20 Ill.
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  • 37
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    International Journal of Quantum Chemistry 12 (1977), S. 255-271 
    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 and systematic localized-site cluster expansion is described. It provides simple physically appealing and computationally feasible wave function ansätze, as well as, via extension of the cluster expansion, a unique expression for general, possibly exact, wave functions. We show that a variety of matrix element evaluation techniques are available and that they are sometimes exact though relatively simple. These techniques often proceed in terms of computational time proportional to the number of different types of sites, rather than their total number. Thus it seems we have a new and viable many-body theory, which is expected to be most accurate and most readily implementable when a physical picture with slightly perturbed localized sites is relevant.
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  • 38
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    International Journal of Quantum Chemistry 12 (1977), S. 291-303 
    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 investigate the total spin structure of an approximate localized-site wave function for a collection of paramagnetic sites interacting so as to favor a singlet ground state. As the number of sites becomes infinite we obtain the distribution of weights of the different symmetry components of the localized site wave function; further, although only a very small fraction of such nonsymmetric wave functions is actually singlet, we find that it generally yields the same bulk property expectation values as its singlet-projected component.
    Additional Material: 6 Ill.
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  • 39
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    International Journal of Quantum Chemistry 12 (1977), S. 327-334 
    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: For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher-Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.
    Additional Material: 1 Ill.
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  • 40
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    International Journal of Quantum Chemistry 12 (1977), S. 305-315 
    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 recently proposed scheme based on the variation-iteration method is applied to the solution of the Hartree-Fock equations for atomic systems. The procedure depends on the repeated application of a Green's integral operator which involves a single numerical quadrature at each stage. The integrations are performed by means of a prescription described in a recent paper by the present authors and it is shown that the parallel philosophies of the self-consistent field and the variation-iteration approaches combine quite naturally. Representative calculations are carried out on three-and four-electron systems and the flexibility of the proposed scheme is demonstrated by considering solutions of various forms of the SCF equations.
    Additional Material: 4 Tab.
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  • 41
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    International Journal of Quantum Chemistry 12 (1977), S. 317-326 
    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: By use of the pseudo-inverse matrix technique the generalization of the Löwdin orthogonalization, given by Kashiwagi and Sasaki, is shown to be valid in a case of singular metric matrices for two basis sets of functions. The application of the same idea to the inverse vibrational problem brings about new procedures for solving this problem in an iterative way.
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  • 42
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    International Journal of Quantum Chemistry 12 (1977), S. 515-525 
    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: Ab initio valence bond calculations for the ground and excited states of HF and HF+ are presented. Total energies, equilibrium geometries, dissociation energies, dipole moments, and spectroscopic constants for HF and HF+ have been calculated. The photoelectron spectrum of HF has been examined and interpreted by means of the valence bond formalism. The ground state of the protonated species H2F+ has been investigated.
    Additional Material: 1 Ill.
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  • 43
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    International Journal of Quantum Chemistry 12 (1977), S. 545-547 
    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-parameter function, ϕ = (C1 + C2rn-1) exp (-ζr), (n = 2-5), has been used as a basis function to determine the independent particle model energy of two-electron atomic systems in their ground state. The best energy is found for n = 3 (He - B3+) and for n = 4 (H-). Our energy values are significantly close to Hartree-Fock results.
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  • 44
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    International Journal of Quantum Chemistry 12 (1977), S. 549-559 
    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: Energy-shifted perturbation theory is studied in connection with corrections to Koopmans' theorem. The first three vertical Ionization potentials of N2, C2H2, and HCN are computed with basis sets of double-zeta Gaussian-type orbitals and double-zeta GTO plus polarization functions. The average absolute deviation of calculation ionization potentials from the observed values is found to be 0.4 eV, whether one uses Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory.
    Additional Material: 6 Tab.
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  • 45
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    International Journal of Quantum Chemistry 12 (1977), S. 561-568 
    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 first order Hartree-Fock equations of the 1s2p3s 4P0 state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree-Fock energy up to third order with high accuracy. The third order Hartree-Fock energies for Li to Ne7+ are compared with those derived from experiment and other theoretical calculations.
    Additional Material: 2 Tab.
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  • 46
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    International Journal of Quantum Chemistry 12 (1977), S. 591-591 
    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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  • 47
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    International Journal of Quantum Chemistry 12 (1977), S. 569-578 
    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: Advantages and difficulties of numerical integration in relation to a transcorrelated solution of the molecular Schrödinger equation are discussed. Because singularities in the two-electron integrals can be completely removed in a transcorrelated calculation, the major difficulty remaining to be resolved is that of singularities in the one-electron integrals. A general method of treating this problem is given which involves the derivation of some new polycentric expansion functions which are everywhere finite under the one-electron part of the Hailtonian. The important improvements obtained are illustrated by some calculations on LiH.
    Additional Material: 4 Ill.
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  • 48
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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
    Notes: A condition for the equivalence of the Löwdin orthogonalization method and various localization methods is derived, taking the matrix elements of the localizing operator into consideration. In the example of the π atomic orbitals of benzene, it is shown that the “ultralocalized” functions defined in the Anderson fashion with help of the Boys minimum-fluctuation criterion do not fulfill this condition, in contrast with a Ruedenberg-type localization.
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  • 49
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    International Journal of Quantum Chemistry 12 (1977) 
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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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  • 50
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    International Journal of Quantum Chemistry 12 (1977), S. 623-637 
    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
    Notes: Functions of several variables, such as the electron density and the nuclear Born-Oppenheimer potential, may be analysed very effectively using orthogonal trajectories. In particular the behaviour of these trajectories at critical points of the functions is investigated in detail. The use of orthogonal trajectories in the virial partitioning of Bader and in the definition of reaction coordinates is extended. A chemical interpretation of the critical points is suggested. The relevance of catastrophe theory is illustrated.
    Additional Material: 7 Ill.
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  • 51
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    International Journal of Quantum Chemistry 12 (1977), S. 609-622 
    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: Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X1 σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: re = 1.125 Å (1.128 Å), Be = 1.943 cm-1 (1.9312 cm-1), aBe = 0.0156 cm-1 (0.0175 cm-1), We = 2247 cm-1 (2170 cm-1), WeXe = 12.16 cm-1 (13.29 cm-1), where the experimental values are given in parenthesis.
    Additional Material: 3 Ill.
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  • 52
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    International Journal of Quantum Chemistry 12 (1977), S. 915-923 
    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: MO calculations of electronic structure and optical transitions for [VOn]5 -; 2n (n = 4, 5, 6) clusters in V2O5 monocrystals have been carried out by means of the semiempirical CNDO CI method. Using the calculated results, a complete analysis of V2O5 optical data as available in the literature and as obtained in the electroreflectivity experiments presented in this paper is performed. An identification of optical transitions in a wide energy range is presented. The optical properties of vanadium pentoxide are shown to be due to the localized charge transfer electronic transitions in the clusters. The fine structure of optical spectra is connected with the covalent splittings of the vanadium 3d and oxygen 2p atomic levels.
    Additional Material: 4 Ill.
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  • 53
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    International Journal of Quantum Chemistry 12 (1977), S. 971-983 
    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: This paper formulates a number of problems of the two-photon spectral theory and characterizes the analytical methods of solving them as worked out by the authors. The efficiency and wide application of the Laplace transform method is demonstrated by the most typical examples of the cross section analytical calculations of two-photon processes, dynamical polarizability, and bremsstrahlung at the scattering.
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  • 54
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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
    Notes: Particle-hole and pairing relationships are obtained within the framework of the unitary group formulation of the many-electron problem using the concept of particle-hole conjugation. Besides the familiar relationships for alternant hydrocarbons, relationships among various pericyclic reaction paths are obtained.
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  • 55
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    International Journal of Quantum Chemistry 12 (1977), S. 1001-1015 
    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 assignment of the alternancy quantum number to the N-electron states of neutral alternant hydrocarbons is discussed within the spin-free unitary group formulation. Alternancy is defined with respect to both molecular graphs and molecular orbital eigenvalues. The properties of the molecular orbitals of alternant hydrocarbons result from requiring the assignments in terms of atomic orbital and molecular orbital Gel'fand states to be consistent. State correlation arguments are used to remove the arbitrary phase factor present in previous treatments.
    Additional Material: 1 Ill.
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  • 56
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    International Journal of Quantum Chemistry 12 (1977), S. 1017-1031 
    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 algebra of irreducible tensor operators is developed in the strong-field coupling case. The method is of general applicability to any symmetry group G including nonsimply reducible groups and mixed configurations. The Wigner-Eckart theorem is given for irreducible tensor operators as well as for their Kronecker and scalar products. The expressions required for the calculation of ligand field splitting, Coulomb repulsion, spin-orbit interaction, and Zeeman effect are given in detail. Applications to problems in the spectroscopy and magnetism of transition metal compounds are referred to.
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  • 57
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    International Journal of Quantum Chemistry 12 (1977), S. 1033-1038 
    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 relationship between well known necessary conditions for N-representability of the reduced two-density matrix is investigated. It is shown that the G-condition implies two conditions of the operator endomorphism type: the C- and the B-condition.
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  • 58
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    International Journal of Quantum Chemistry 11 (1977) 
    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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  • 59
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    International Journal of Quantum Chemistry 11 (1977), S. 1-15 
    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 influence of errors in molecular integrals on the calculated RHF energy values is considered for two models which correspond to round-off and shift errors. The energy variations induced by errors in elements of one- and two-electron matrices and the overlap matrix are represented in a quadratic approximation and the same degree of accuracy is maintained for mean values and standard deviations. The formulas given point out that mean values are less than zero when some of the errors are non-shifted. Special care is required when Gaussian lobe functions are used.
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  • 60
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    International Journal of Quantum Chemistry 11 (1977), S. 17-20 
    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 derivation of most general existence conditions for surface states of a semi-infinite Kronig-Penney crystal is reported. They reduce to Steslicka's conditions under a subsidiary restriction and also indicate that the surface-state energies may lie in the allowed bulk bands. Numerical computations supporting the qualitative conclusions are provided.
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  • 61
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    International Journal of Quantum Chemistry 11 (1977), S. 49-57 
    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 helix-coil phase transition of DNA is studied through a model equivalent to the one used in the theory of superconductivity. A distribution function for the excitations analogous to the usual Fermi function is obtained which depends on the parameter T0, the maximum temperature at which all pairs of bases are bonded. The expression for the number of unbonded pairs of bases depends only on the two parameters, T0 and Tc (critical temperature).
    Additional Material: 4 Ill.
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  • 62
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    International Journal of Quantum Chemistry 11 (1977), S. 59-71 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The goodness of the local fit of an approximate wave-function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ0, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave-functions for H2 are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z2, r2, x2 + y2, 3z2 -; r2, ξ, rA-1, r12-1, and EL (the reduced local energy). The success rate is high (〉90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave-function.
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  • 63
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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
    Notes: The potential energy curves of the bending mode of PH2 in the ground 2B1 and the excited 2A1 states have been calculated using ab initio SCF-MO wave-functions. The radical is found, in agreement with experiment, to be bent in the two states. The calculated results clarify the interpretations of the anomalous behaviour of observed vibrational intervals, and offer an explanation of the ‘quasilinearity’; of the radical in the 2A1 state.
    Additional Material: 1 Ill.
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  • 64
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    International Journal of Quantum Chemistry 11 (1977), S. 103-127 
    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: Quantum mechanical tunneling theory is applied to the problem of synaptic vesicle release and to the problem of electric transmission at the ephaptic junction. In the synapse the tunneling produces conformational changes in macromolecules to open and close vesicle macrogates. Quantum mechanical tunneling as a basis for charge transfer and physical release of vesicles at junction membranes provides a unified concept of ephaptic and synaptic transmission. Details of this model are in agreement with experimental data for miniature endplate potential frequency and delay effects as a function of polarization, osmotic pressure, and temperature. The theory accounts for anatomical specializations at the synaptic cleft and the narrow junction observed for the ephapse.
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  • 65
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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
    Notes: Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh-Ritz method in the replacement of the usual kinetic energy operators T̂(μ) with operators T̂′(μ) = T̂(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ∇Ψ · ∇Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ∇Ψ and the change of ∇Ψ across surfaces of discontinuity.
    Additional Material: 5 Ill.
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  • 66
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    International Journal of Quantum Chemistry 11 (1977), S. 129-135 
    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 investigate whether or not a previously proposed variation-perturbation method for calculating static polarizabilities can be used also to calculate dynamic polarizabilities. We find that the method can be used for frequencies below the first excitation frequency of the system. By amending and supplementing the procedures for solving the second-order equations we can obtain the same accuracy for dynamic polarizabilities as in the previous procedure for static polarizabilities.
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  • 67
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    International Journal of Quantum Chemistry 11 (1977), S. 325-339 
    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 recursive numerical integration scheme based on the method of Clenshaw and Curtis is proposed for the efficient implementation of the variation-iteration procedure for the computation of approximate energies and wave functions for atomic systems. Extensive numerical tests are carried out to assess the accuracy and efficiency of the method and inaccuracies in some earlier calculations are pointed out.
    Additional Material: 5 Tab.
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  • 68
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    International Journal of Quantum Chemistry 11 (1977), S. 341-348 
    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: With the basic equivalent transformation Pσ = ∊(P)(Pr)-1 the dual bases of symmetric groups can be constructed. The importance of the double antisymmetrization is shown. The advantages of the use of the m basis as compared to the Wigner (matric) basis are discussed.
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  • 69
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    International Journal of Quantum Chemistry 11 (1977), S. 349-358 
    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 algorithm for the computation of the density of states distributions of stereoregular polymers is presented. It is related to the Gilat-Raubenheimer technique for three dimensional systems. Its application to polyethylene is briefly described.
    Additional Material: 3 Ill.
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  • 70
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    International Journal of Quantum Chemistry 11 (1977), S. 380-380 
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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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  • 71
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    International Journal of Quantum Chemistry 11 (1977), S. 359-379 
    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 formalism described in the first paper of this series is applied to the chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2, the covering of SO(3) ⊃ D∞ ⊃ D4 ⊃ D2. The state vectors (|αJaΓγ) adapted to each link of the chain under consideration and the corresponding coupling coefficients \documentclass{article}\pagestyle{empty}\begin{document}$ f\left( {\begin{array}{*{20}c} {J_1 } & {J_2 } & J \\ {a_1 \Gamma _1 \gamma _1 } & {a_2 \Gamma _2 \gamma _2 } & {a\Gamma \gamma } \\ \end{array}} \right) $\end{document} are given in analytical form. The material reported here is very convenient for a quantum-mechanical description of molecular and nuclear systems with linear, tetragonal, or orthorhombic symmetry. In this respect, we present an outline for its applications to the electronic and vibrational-rotational spectroscopy of molecular aggregates and to the rotational spectroscopy of molecules or nuclei. In addition, we briefly show how the material may simplify the second-order non-Lie subgroup type approach to the representation theory of SU(2).
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  • 72
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    International Journal of Quantum Chemistry 11 (1977) 
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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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  • 73
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    International Journal of Quantum Chemistry 11 (1977), S. 393-398 
    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 relations between the Waller-Hartree spin-free method and the symmetric group theory are given. It is shown that the Gallup method is a special case of ours with S = M. Furthermore, all the irreducible representation matrices and other matrices needed are written explicitly in terms of Sanibel coefficients which makes the method more useful. However, it was shown that the cases with S ≠ M for the spin-free pure spin states might be beyond the power of the symmetric group theory.
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  • 74
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    International Journal of Quantum Chemistry 11 (1977), 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: A quantum calculation of the optical activity and gyrotropic birefringence is used in a molecular crystal to deduce symmetry properties. A study of the variation of the components of these tensors, when a change of origin occurs, is used to account for the formula for the electric excitation proposed by Landau and Lifchitz. It is shown that the results obtained are valid in the case of crystals with nonlocalized electrons.
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  • 75
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    International Journal of Quantum Chemistry 11 (1977), S. 451-472 
    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: Within the Schrödinger-Infeld-Hull factorization framework it is shown that, by introducing a parameter ε in the quantization condition, that is, ε(j-|m|)=integer ≥ 0, and, thus, considering “symmetrized” ladder operators, one can use the same formulas to handle both class I (ε = +1) and class II (ε = -1) problems. Starting from this unified point of view, after building up the associated angular momentum operators and their ε-dependent eigenfunctions, one unique closed-form expression of the coupling coefficients is obtained. This expression embodies many sparse and known previous results, without being more intricate than any of them. The basic material, allowing the application of a Wignera-Eckart theorem to matrix elements of an operator on the basis of eigenfunctions of factorizable equations, and a quick determination of the associated selection rules are given. Some examples are treated as an illustration.
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  • 76
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    International Journal of Quantum Chemistry 11 (1977), S. 473-484 
    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 an application of a reaction field theory of solvent effects has been made to study proton transfer mechanisms in hydrogen bonded systems coupled to an environment. The latter is simulated with reaction fields having variable strength and direction (defined with respect to the supermolecule's total dipole moment direction), together with superposed uniform external electric fields. Changes in proton potential curves and some other properties of a model water dimer and a water trimer are reported. The results are discussed in relation to relevant phenomena in biology and biochemistry, namely proton relay systems in enzymatic catalysis.
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  • 77
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    International Journal of Quantum Chemistry 11 (1977), S. 524-524 
    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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  • 78
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    International Journal of Quantum Chemistry 11 (1977), S. 705-713 
    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: It is proved that in general the INDO approximation to the full Roothaan theory does not lead to expressions which are invariant under a rotation of local atomic axes. However, when only s- and p-functions are used in the atomic basis set, the equations obtained are invariant due to the special properties of the p-functions. When d-orbitals are included into the basis set, rotational invariance is lost but can be restored if a supplementary approximation is introduced.
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  • 79
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    International Journal of Quantum Chemistry 11 (1977), S. 733-741 
    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: We use a variation-perturbation method to calculate the electric polarizabilities and the electric dipole moment of the LiH molecule. We obtain 4.455 for the perpendicular polarizability and 4.001 (×10-24 cm3) for the parallel polarizability. Our result for the electric dipole moment at equilibrium nuclear distance is 5.866, which is in excellent agreement with the experimental value 5.828 debye units.
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  • 80
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    International Journal of Quantum Chemistry 11 (1977), S. 725-732 
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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
    Notes: The potential energy curves for the NiH and linear HNiH molecules resulting from the 3d84s2 and 3d94s configuration of nickel are calculated using the unrestricted Hartree-Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d84s2 configuration is by means of an sp hybrid orbital which comes from the 4s2 shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d94s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.
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  • 81
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    International Journal of Quantum Chemistry 11 (1977), S. 715-723 
    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 report in this work SCF atomic calculations for Li, Be, B, C, and Ne using a basis set of completely loge-localized functions. For these second row atoms the total volume R3 was partitioned into a spherical loge of radius R and its volume complement. The loge-localized basis functions were constructed as a product of Slater-type orbitals and a cut-off factor. The energy values obtained differ significantly from the Hartree-Fock ones indicating that the delocalization effects - not included in these calculations - are important.
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  • 82
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    International Journal of Quantum Chemistry 11 (1977), S. 743-752 
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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
    Notes: A series of five different Iterative Natural Orbital (INO) procedures are tested for the ground state of water and are compared on the basis of their respective convergence properties. The choice of configuration space employed in these methods is shown to be a key factor in determining the results of such calculations. If the CI space is generated by taking all single excitations with respect to a series of dominant or reference configurations, it is concluded that the practice of varying such generating species at each iteration is highly desirable. In general the choice of the configuration space is found to be much more important than the attainment of strict NO convergence, whereby experience indicates that inclusion of all singly and doubly excited configurations (or at least a select subset thereof) relative to a series of dominant configurations provides the most efficient means of approximating the true NOS of a given system within the general INO framework.
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  • 83
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    International Journal of Quantum Chemistry 11 (1977), S. 753-758 
    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 additivity model as suggested by Moss et al. has been used for predicting spin densities in methyl-substituted radical anions. Linderberg's relation has been employed for evaluating the core-resonance integrals (βrs) and a heteroatom model for the methyl group has been used.
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  • 84
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    International Journal of Quantum Chemistry 11 (1977), S. 775-812 
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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
    Notes: When electron pair correlations are incorporated into generalized valence bond wave functions, the necessary and sufficient wave functions for the quantitative description of chemical reactions are achieved. The resulting electron pair correlation functions are shown to be invariant; hence the generalized valence bond orbitals contain all the information in the correlated wave functions. In the case of pair correlation energies, this information is expressed through a simple function of the orbital overlaps. The resulting overlap approximation is applied to ground states, excited states, and transition states for chemical reactions. In all cases the exact energy is reproduced to within 0.5 kcal/mol (0.001 hartree). The pairwise correlated generalized valence bond method provides an opportunity to accurately predict reaction pathways for system of chemical interest.
    Additional Material: 11 Ill.
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  • 85
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    International Journal of Quantum Chemistry 11 (1977), S. 869-880 
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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
    Notes: Green's functions and the symbol manipulative computer language LISP have been used to obtain exact, closed form, first-order functions and second-order energies for the first fourteen states of the hydrogen atom in electric and magnetic fields.
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  • 86
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    International Journal of Quantum Chemistry 11 (1977), S. 813-848 
    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 time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman-like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one- and two-particle operators between spin symmetry adapted ground, mono- and bi-excited configurations of a closed shell system. Two coupling schemes are considered for bi-excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.
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  • 87
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    International Journal of Quantum Chemistry 11 (1977), S. 849-867 
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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
    Notes: A time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono- and bi-excited configurations.
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  • 88
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    International Journal of Quantum Chemistry 11 (1977), S. 881-884 
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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
    Notes: Some of Moccia's formulas (Int. J. Quant. Chem. 8, 293 (1974)) for corrections to “not completely optimized variational parameters” are compared with those resulting from a perturbation theory analysis. It is not possible to choose the zero-order Hamiltonian (at least not in any simple way) so as to get exact agreement, but one choice does come close.
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  • 89
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    International Journal of Quantum Chemistry 11 (1977) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 90
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    International Journal of Quantum Chemistry 11 (1977), S. 895-895 
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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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  • 91
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    International Journal of Quantum Chemistry 11 (1977), S. 885-894 
    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: Gaussian orbitals are used to calculate Temple lower bounds for H2+, HeH++, and H3++. Molecular orbitals are constructed from individual Gaussian-type orbitals (GTO) and from GTO contractions adapted for either upper or lower bounds of the hydrogen atoms. The MOS are optimized by minimizing either the upper bound, 〈H〉, or the variance, 〈(H - E)2〉. The best Temple lower bounds achieved by these methods are -0.60336 a.u. for 2+, - 1.06224 a.u. for HeH++, and -0.13003 a.u. for H3++. Comparison is made with other types of molecular orbitals and with the exact wave functions for 2+, HeH++. Analysis of the nuclear cusps is given. A prescription for constructing lower bound molecular orbitals is offered.
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  • 92
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    International Journal of Quantum Chemistry 11 (1977), S. 897-905 
    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
    Additional Material: 2 Ill.
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  • 93
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    International Journal of Quantum Chemistry 11 (1977), S. 931-941 
    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: One of the variants of Löwdin's partitioning technique that makes use of a Brillouin-type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin-Löwdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l - m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin-Löwdin method.
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  • 94
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    International Journal of Quantum Chemistry 11 (1977), S. 943-957 
    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: Infinite sets of functions in Hilbert space are characterized by their completeness properties and the extent of linear independence. Different measures of linear independence such as orthonormality, Gram's determinant, the special measure of linear independence, and the asymptotic dimension are related to each other and with the degrees of completeness such as overcompleteness, exact completeness, and incompleteness as far as possible.
    Additional Material: 2 Ill.
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  • 95
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    International Journal of Quantum Chemistry 11 (1977), S. 959-970 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Presenting a relatively simple ab initio method to calculate full van der Waals interaction potentials between molecules, we give rules for the optimization of basis functions which permit the reliable evaluation of second order long range interactions. Closed expressions for the long range interaction energy are derived in which the orientational dependence is simplified to the utmost. Calculations show that even for molecules which have no dipole moment, such as ethylene, the strongly anisotropic electrostatic interactions are of the same magnitude as the dispersion interactions, but also that the anisotropic (“cross”) terms in the dispersion energy are about equal in size to the corresponding “quadratic” terms. Even though these anisotropic forces cancel to a large extent in the cohesion energy of the ethylene crystal, they can have important effects on some of the other crystal properties.
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  • 96
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    International Journal of Quantum Chemistry 11 (1977), S. 971-978 
    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 quantum chemical methods employed by us to investigate the stabilities, charge densities, and bonding characteristics of atomic and molecular anions are briefly reviewed. The results of our work on chemically interesting species are surveyed, as are our initial results on the treatment of solvation effects in anionic systems. Finally, a simple-minded approach to the problem of finding shape resonances for electron-atom scattering processes is outlined.
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  • 97
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    International Journal of Quantum Chemistry 11 (1977), S. 979-989 
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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
    Notes: The linear response theory is used to study the line shape of two coupled oscillators, decaying in two different baths, when one of the oscillators is coupled to the radiation field. The baths are considered to be thermally excited. The analysis is based on the computation of the correlation functions 〈ai+ (t)ai (0)〉 and 〈ai (t)ai+(0)〉 of each oscillator, taking the coefficients associated with the operators ai+ and ai in the Heisenbemg representation as the starting point of the calculation. The line shape in different cases is also discussed.
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  • 98
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    International Journal of Quantum Chemistry 11 (1977), S. 1001-1004 
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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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  • 99
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    International Journal of Quantum Chemistry 11 (1977), S. 991-1000 
    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 solution of the quantum-mechanical one-particle problem involving a Coulomb potential with a cut-off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
    Additional Material: 1 Ill.
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  • 100
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    International Journal of Quantum Chemistry 11 (1977), S. 1017-1020 
    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 tunneling transfer probability has been considered within the framework of the time dependent perturbation theory. It has been found that the probability of proton transfer may be enhanced by several orders when a dynamic potential barrier is assumed.
    Additional Material: 1 Ill.
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