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  • Electronic Resource  (2,955)
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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 61-72 
    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 contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23-50% depending on how H0 was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.
    Additional Material: 6 Tab.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 83-89 
    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 shown that the turn-over rule which is used to simplify matrix elements between spin-projected Slater determinants may also be used to simplify formation of matrix elements between any orthonormal set of spin-coupled Slater determinants. The coefficients for the spin-coupling may then be chosen freely to reduce the number of important configurations in the secular equation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 435-450 
    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: The concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium.The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree-Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li2, Na2, and K2 show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.
    Additional Material: 3 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 539-546 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: SCF equations for any pure spin state are given for a spin-free system with many-particle interactions. The equations are very simple and explicit. Due to the use of different antisymmetric requirement our equations are different from some of the other methods. In our method, the abstract group theory formalism is converted into some explicit and straightforward equations which makes the many-particle interaction problem easier to handle.
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  • 5
    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 shown that any expectation value of any observable associated with a molecule is the sum of loge contributions and of loge pair contributions. This result provides a rigorous theoretical basis for the study of additive properties of molecules.It is demonstrated that molecular wave functions (exact or approximate) can be expressed as a sum of functions corresponding to the various electronic events. Furthermore any of these event functions can be expressed in terms of correlated loge functions. This expression suggests many kinds of variational procedures of calculating wave functions (known methods and new ones).The case in which noncorrelated completely localized loge functions are used is discussed. If continuous functions are used the variational equation reduces to a sum of independent variational equations, each one corresponding to a particular electronic event. This is not so when discontinuous functions are used or when a delocalized function is added to replace the correlation interloge function.The noncorrelated completely localized loge model is analyzed in more detail. It is seen that local spin operators can be introduced and that each event density operator is the product of the loge density operators. Therefore that model is an independent loge model. The corresponding generalized self-consistent field equations are derived. This treatment helps us to understand how a localized state of a molecule can produce an ion containing a delocalized region, a phenomenon which is sometimes at the origin of some misunderstanding in photoelectron spectroscopy. Finally it is seen how virtual loge functions can be introduced to describe excited states.
    Additional Material: 2 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 605-617 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is proposed for the calculation of matrix elements among various states of atoms. A set of tensor operators is the only entity in the formalism, and all formulas involve merely the vacuum expectation values of these tensor operators and the recoupling transformation coefficients. Some numerical examples are given for the Coulomb interaction matrix elements.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 423-426 
    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 formalism in order to deal with SCF eigenspace manipulation is developed. It can be shown that the initial generalized secular equation splits into a set of secular equations, each of which in turn can modify independently any predetermined subset of the SCF manifold.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 789-797 
    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 calculated the Verdet constant of the hydrogen molecule. We found that the angle of rotation may be represented by φ0 = A0Hv2/(v02 - v2)2 where A0 is 3.23 × 10-33 microminutes sec2 per oersted-cm-atmosphere. This is in agreement with the experimental observations where φ0 is given by the same frequency dependence with the constant A0 × 2.72 = 10-33 in terms of the same units.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 893-899 
    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 spin-projected extended Hartree-Fock equations discussed in Part I for an even number of electrons are given here for the odd-electron case.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 925-940 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Model Hamiltonians for all valence electron calculations are examined with regard to the possibility of obtaining consistent sets of matrix elements for the description of electromagnetic processes such as photon absorption, optical activity, and magneto-optical activity. Linear and angular momentum and position operator matrix elements are related to Hamiltonian matrix elements through symmetry relations and equations of motions. The possibility of elimination of empirical interatomic matrix elements is studied.
    Additional Material: 1 Tab.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 951-970 
    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: Simple rules for an estimate of the correlation effects in the low-lying states of alternant hydrocarbons, as described by the Pariser-Parr-Pople Hamiltonian, are formulated. These rules are based on the alternancy and spin symmetry classification of states in both strongly and weakly correlated limits and on the valence bond characteristics of those states in the fully correlated limit. It is shown that the largest effect of the electron correlation will be found for the singlet “minus” states (using Pariser's classification of the alternancy symmetry species), a smaller effect for the triplet “plus” states, and a much smaller effect for the remaining states. These rules are exemplified by limited CI calculations including all monoexcited and all mono- and bi-excited configurations, respectively, for a number of π-electronic systems. In view of these rules the success of the PPP model in the monoexcited CI approximation may be understood.
    Additional Material: 7 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 335-345 
    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 a previous publication [1] we analyzed the stability of rare gas halides on the basis of exchange perturbation theory of the Rayleigh-Schrödinger type, using a three-center, four-electron model. In this paper, the analysis is extended to a (n + 1)-center, (n + 2)-electron model for rare gas halides of composition RXn, where R is the rare gas atom and X the halogen atom, in order to investigate the validity of the three-center, four-electron model. The compounds analyzed are XeFn, XeCln, KrFn and KrCln with n = 3 and 4, in different geometric configurations and for different states of total spin S. As before, we use exchange perturbation theory in first and second orders. The results are in good agreement with those obtained in the previous analysis and with experiments. Specifically, it is found that chlorides of rare gas atoms are not stable, that XeF4 has the square-planar configuration and that trifluorides cannot exist. The possible existence of KrF4 is discussed.
    Additional Material: 2 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 373-394 
    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 generalized form of the coupling operator technique in SCF theory has been developed. In the formalism presented here, the monoconfigurational problem may be treated as a particular case of the multiconfigurational framework. The matrix form of the operators has been analyzed; in the LCAO context a structure has been found which is very adequate for computational purposes.Some examples are also presented which show the usefulness of the theory, emphasising the CNDO and INDO approximations. Within the application of the method to ab initio calculations, some He and second row atoms states have been studied. The He first excited singlet is also studied, the result of the analysis of such a problem being that the nonorthogonality between the singlet functions of the fundamental and of the first excited states play a primordial role in the efficiency of the method.In no case have the calculation problems, appearing in the application of the theory, been of a more difficult nature than those normally found in the application of the formalism for closed shells.
    Additional Material: 3 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 467-489 
    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 variational calculation of the interaction between two H2 molecules using minimal basis set of 1s functions is performed to check the efficiency of various versions of the perturbation theory for intermolecular interactions. The matrix procedure starting with the zero-order Hamiltonian which is symmetric with respect to intermolecular electron permutations shows better convergence than the procedures using nonsymmetric zero approximations. This conclusion follows from the calculations of ground state and four lowest excited states for three geometric configurations of the H4 system. The behaviour of the potential curves is interpreted in terms of symmetric perturbation theory. The various contributions to the interaction energy are considered in detail. The importance of charge transfer states for the description of the intermediate range of intermolecular separations is specially emphasized.
    Additional Material: 9 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 559-564 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Transitions from symmetry-adapted to symmetry-broken solutions of variational problems are classified according to the nature of the discontinuity involved. Two systems in which a second-order transition occurs are studied.
    Additional Material: 3 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 585-604 
    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: Occupation number representation of the two-dimensional harmonic oscillator and some operator formulae are used in a simple algebraic derivation of complicated integrals. The calculation of full oscillator- and radial integrals of r̂w and exp (\documentclass{article}\pagestyle{empty}\begin{document}$ (iw\hat{\varphi})$\end{document}), where w is an arbitrary positive or negative integer, are performed by an integral transform, leading to a generalized Gauss matrix element. Thus it is possible, because of the back transformation, to derive from one generalized Gauss matrix element all matrix elements which are permitted by the selection rules. Some integrals of r̂w and exp (\documentclass{article}\pagestyle{empty}\begin{document}$ (iw\hat{\varphi})$\end{document}), Laguerre polynomials, and Bessel functions are completely new. For the already known integrals, the mathematical labour is considerably reduced. The relation between the two-dimensional oscillator and the hydrogen atom and their angular momentum properties are discussed. A survey on the various methods applied to the oscillator problem, from complex integration to noncompact Lie groups, and a comprehensive bibliography on this important spectroscopic field are given.
    Additional Material: 604 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 693-706 
    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 radial one-electron Schrödinger equation can be written as a nonlinear first-order differential equation by making a suitable logarithmic transformation. The resulting Riccati equation has the equivalent Hammerstein integral representation [1], \documentclass{article}\pagestyle{empty}\begin{document}$$ \beta (r) = \int_{r' = 0}^\infty P(r') N(r,r')dr' \quad 0\buildrel{〈}\over{=} r 〈 \infty $$\end{document} where the kernel, N(r, r′) is \documentclass{article}\pagestyle{empty}\begin{document}$$ N\left( {r,\,r\prime} \right) = H\left( {r,\,r\prime} \right)\exp \left\{ {\int_{\xi = r\prime}^r {R\left( \xi \right)\beta \left( \xi \right)d\xi } } \right\} $$\end{document} and H(r, r′) is the Heaviside unit step function. This kernel is a more general one than that developed in ref. [1]. Both kernels apply in cases where the Riccati equation corresponds to a Sturm-Liouville problem.It is shown that this integral equation can be integrated by parts so that, for any local potential, the integrand decreases as the cyclic folding procedure is applied. During this cyclic folding, the kernel generates an equation that contains only coefficients of β(r)0 and β(r)1. Consequently, after truncating at the end of the nth cycle, it is possible to write down a Padé-type approximation to the logarithmic derivative as a known function of the independent variable. All coefficients in this approximation can be evaluated as simple algebraic formulations of P(r), R(r), and integrals over P(r).
    Additional Material: 1 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 755-764 
    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 difference in the electron correlation between H- and other two-electron atoms is clarified by the introduction of the r12 term in the wave function. By using the expansion of r12, a certain modification of the usual electron correlation factor 1 + Cr12 is introduced and its effectiveness is examined. Calculations are carried out for the ground state and the three lowest excited states (23S, 23P and 21P). The peculiar electron correlation in the ground state of H- is shown by looking at the Coulomb hole for closed- and open-shelf models in comparison with those for other two-electron atoms.
    Additional Material: 2 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 777-782 
    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 virtual orbital transformation is proposed involving pairing of localized occupied orbitals with virtual orbitals. The virtual orbitals are transformed so that each virtual orbital is as “close” as possible to its occupied counterpart, where closeness is the inverse of the particular definition of localization. The appropriate transformation is derived for the special case of Foster-Boys localization, and an illustrative CNDO/2 calculation on HNO is presented. INDO CI results on the series N2, CO, BF indicate that use of this transformation may reduce the number of energetically significant configurations.
    Additional Material: 1 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 817-821 
    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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  • 23
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974) 
    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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  • 24
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 857-892 
    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: Multiconfiguration wave functions constructed from contracted Gaussian-lobe functions have been found for the ground and valence-excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the 1A1(π → π*) state. The 1A1(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three-configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.
    Additional Material: 25 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 941-950 
    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: Standard sets of Gaussian atomic orbitals (STO-3G, STO-4.31G) are used to evaluate spin-orbit coupling constants in linear molecules (CO2+, NNN) and spin-orbit effects on singlet-triplet transition intensities in formaldehyde. All spin-other orbit effects have been included. In all cases spin-other orbit interactions form a large fraction of the matrix elements. Simple formulae to evaluate spin-orbit one- and two-electron integrals over atomic orbitals are presented. Standard molecular integral programs can be used for the computation of spin-orbit integrals.
    Additional Material: 1 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 363-372 
    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 spin projected extended Hartree-Fock equations for successive optimization of the orbitals are derived for the four-electron case and applied to butadiene in the PPP approximation. The method shows an excellent convergence and gives 91.4% of the correlation energy for the given model-Hamiltonian.
    Additional Material: 2 Ill.
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  • 27
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 427-433 
    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 simple equation for the evaluation of resonance integrals from overlap integrals and ionization potentials of the molecular fragments is suggested for molecules-in-molecules π electron calculations. The singlet π → π* transition energies of some benzene derivatives containing donor substituents were calculated. The best results were obtained if in the expression of the resonance integral the first experimental ionization potential of the methyl derivative of the donor groups is used.
    Additional Material: 4 Tab.
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  • 28
    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 modified INDO procedure has been used to calculate the proton hyperfine splittings in benzyl and the isoelectronic anilino, phenoxy and 2-azabenzyl as well as 2- and 3-thenyl radicals. The present procedure differentiates between s-, p- and d-orbitals on an atom in estimating various integrals involving them, satisfies the rotational invariance requirements and employs an orthogonalized basis set of atomic orbitals for obtaining core-Hamiltonian matrix elements. The calculations based on using the exponents which depend only on the type of orbital and the nature of atom fail to provide correct relative order of ortho and para proton splittings in benzyl as well as anilino, phenoxy and 2-azabenzyl radicals. On the other hand, use of the exponents which are modified according to the charge densities in various orbitals leads to a high absolute value for para proton splitting compared to that for ortho proton splitting which in case of all these radicals is in agreement with experiment. A spin density calculation on benzyl, anilino and phenoxy radicals considering the variation of one-center one-electron and one-center two-electron integrals for different protons with their charges is found to yield further improvement in the relative order of ortho and para proton splittings in all these radicals. In 2- and 3-thenyl radicals the role of 3d-orbitals on sulfur has also been examined. To our knowledge, no unrestricted INDO calculations including 3d-orbitals on sulfur have been reported in the literature so far.
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  • 29
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 137-150 
    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 order to make a better assessment of the distinguishable electron method developed by Kirtman and co-workers, we have applied the method to some two-electron atoms and to H2 and LiH. Our results lend support to the contention held by Kirtman and co-workers that the distinguishable electron method is a practical way of calculating reasonably accurate physical properties.
    Additional Material: 10 Tab.
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  • 30
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 179-191 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is given for obtaining the common molecular integrals over generalized gaussian functions: \documentclass{article}\pagestyle{empty}\begin{document}$$ \chi_i = x^{\lambda_i}_i \exp \big\{ - \big(\alpha_i x^2_i + \alpha^{\prime}_i x^{\prime 2}_i + \alpha^{\prime\prime}_i x^{\prime\prime 2}_i\big)\big\} $$\end{document}The present algorithms are expected to be more efficient than those given in earlier work by the same author.
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  • 31
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 201-208 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper, we point out how the precision of the LCAO density matrix elements of polymers may affect the computed properties. We propose to use a more adapted approach in order to evaluate these quantities.
    Additional Material: 2 Ill.
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  • 32
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    International Journal of Quantum Chemistry 8 (1974), S. 255-261 
    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 pair distribution functions evaluated for the 23S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree-Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree-Fock solution between He and Li+, the Coulomb hole has a different shape for He than for Li+ and the other isoelectronic ions.
    Additional Material: 3 Ill.
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  • 33
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    International Journal of Quantum Chemistry 8 (1974), 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: Starting from a knowledge of approximate wave functions of the isolated molecules (or atoms) A and B, a method is proposed to build up a zeroth-order ground state and excited configurations for the complex AB in which the molecular orbitals keep their local significance. The standard Rayleigh-Schrödinger perturbation in this basis provides a decomposition of the zeroth-order interaction energy as a sum of the electrostatic and repulsion energy. In the second order, it is possible to identify the classical dispersion and polarization forces (modified by a term of order S2) and two additional contributions which are linked to the exchange possibility. The intramolecular correlation component is taken into account and compared with the correlation on the isolated molecules. It is moreover suggested that since we work in a rather limited basis set, the perturbed energy of AB must be compared with the unperturbed energies of A and B calculated in a basis including the vacant orbitals on their respective partner. Finally a possibility for going beyond the second order is described.
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  • 34
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    International Journal of Quantum Chemistry 8 (1974), S. 45-60 
    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: Spin-projected one-particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki-Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two-particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin-extended equations are formulated.
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  • 35
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    International Journal of Quantum Chemistry 8 (1974), S. 91-95 
    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 variation of the polarizability of H2+ and H2 with internuclear separation R = 1.6 - R = 2.4 a.u. for H2+ and R = 1.0 - R = 2.0 a.u. for H2 is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H2+ and 6.52% for H2.
    Additional Material: 4 Tab.
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  • 36
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    International Journal of Quantum Chemistry 8 (1974), S. 119-136 
    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: Various floating one-center perturbation schemes are developed for H2+-like molecules. Previous work for the ‘1s’ hydrogen atom approach is extended through third order in the energy. In the molecular puff approach an exact ‘closed form’ solution is obtained for the zeroth-order problem, which corresponds to a double layer molecular puff. Semianalytical results for the first-order correction to the floating molecular puff wave function and for the energy through third order are developed which offer a convenient alternative to previous approaches. Explicit calculations for ground state H2+ show that for R 〉 3aO the ‘1s’ and the more complicated ‘puff’ treatments are equivalent and that neither the ‘1s’nor the molecular puff function is an adequate zeroth-order wave function for the important intermediate values of R. The usefulness of some of these methods in a variety of problems, where one-center zeroth-order wave functions do appear to be adequate, is discussed briefly.
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  • 37
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    International Journal of Quantum Chemistry 8 (1974), S. 171-177 
    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 the framework of the Heitler-London method, a method for determining the allowed molecular multiplets is proposed. The method is based on the connection of the total molecular spin with the permutation symmetry of the coordinate wave function and on the isomorphism of the molecular point group with a certain subgroup of the electron permutation group. The method does not depend on the approximation in which the molecular ions are considered.
    Additional Material: 2 Tab.
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  • 38
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    International Journal of Quantum Chemistry 8 (1974), S. 223-233 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An information-theoretic degree of symmetry adaptation of a ket with respect to a given group is introduced. Then the general equivalence between spin-free electronic kets and antisymmetrized space-spin kets is obtained so long as our attention is restricted to spin-independent observables. It is noted that there are spin-free kets for which there exists no single antisymmetrized space-spin ket giving all the same expectation values; the converse is also noted.
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  • 39
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    International Journal of Quantum Chemistry 8 (1974), S. 971-980 
    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: Wave functions which are a linear combination of H2+-type elliptical orbitals are optimized to provide either an upper bound or a lower bound to the H2+ ground state. For the latter, Temple's formula is used. Three criteria are considered to determine the relative accuracy of these wave functions: (i) energy (calculated versus exact eigenvalue); (ii) average error; and (iii) local energy. Although the lower-bound optimized wave functions obtained are the most accurate available for H2+ from approximate wave functions, they are still inferior to the corresponding upper-bound wave functions by criteria (i) and (ii). In particular, using criterion (ii), it is shown numerically that the upper-bound functions are “correct to second order,” while the lower-bound functions are almost, but not quite, “correct to second order.” Despite this, the local energy analysis, criterion (iii), reveals that the lower-bound wave functions can be more accurate than the upper-bound functions in some regions of space, and hence give more accurate values for physical properties sensitive to these regions. Examples considered are the dipole-dipole and Fermi contact interactions.
    Additional Material: 1 Ill.
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  • 40
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    International Journal of Quantum Chemistry 8 (1974), S. 643-676 
    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 brief survey of the maximum overlap method is presented and some computational aspects of the approach are discussed. The hybrid compositions and bond overlaps are reported for some thirty small ring compounds and a list of characteristic hybrids for various structural environments is given. The table of characteristic hybrids is extended to acyclic hydrocarbons and the transferability of the maximum overlap hybrids is demonstrated. Those aspects of the method which depend on geometrical properties of molecules have been considered in some details and the discussion is extended to some structural features of cyclic systems. In particular the asymmetry of bonds of spiro carbon atom is examined and rationalization of puckering of large macrocyclic systems is presented. In the summary it is pointed to the method and its potential to discuss structural aspects of molecules at the particular level of accuracy expected to be of great use in organic and physical organic chemistry. Further development and improvement of the method is mentioned, but already in the present form it can produce hybrids which may constitute a useful basis for other more ambitious semiempirical calculations.
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  • 41
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    International Journal of Quantum Chemistry 8 (1974), S. 715-732 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is presented that leads to a simple derivation of the explicit relation between pair-correlated DODS schemes (e.g., the alternant molecular orbital method and the extended valence bond method) and configuration interaction.This result is based on a reduction formula for the representations of the general linear group, GL(m), carried by the N-electron function space. Generally, this paper deals with the effect of “partitioned” orbital transformations on states with “local” permutation symmetry.
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  • 42
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    International Journal of Quantum Chemistry 8 (1974), S. 765-775 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of orthonormality-constrained variation is extended using a dual-basis set instead of a single orthonormal basis. The complete and the partial variation methods are discussed and applied to electronic systems. It is found that the present formulation leads to the most general equation in the coupling operator method.
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  • 43
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    International Journal of Quantum Chemistry 8 (1974), S. 799-816 
    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 the spirit of Löwdin's extended HF scheme, an SCF method for the description of the molecular ground state, based on complex molecular orbitals, is developed. As a special case the method of parity mixing in orbitals is formulated. A calculational procedure for solving derived secular equations is described and numerical results, obtained in the minimal basis set, are reported for the N2 and CO molecule. Resulting ground state energies are close to the energies of the CI calculations with the same set of orbitals.
    Additional Material: 4 Tab.
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  • 44
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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: An antisymmetric pair function can be built upon two kinds of monoelectronic functions, the former ones being correlated local functions and the second ones nonlocal functions taking external effects into account. This function, brought into the generalised product function procedure by means of the density matrix formulation, makes possible the study of correlation within N-electronic systems. The results of a first application of this method to the fundamental and to 1P and 3P excited states of two-electron systems are given.
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  • 45
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    International Journal of Quantum Chemistry 8 (1974), S. 915-924 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio SCF calculations are reported for the porphin molecule. The positions of the central protons have been optimized, and the equilibrium geometry is found to be a linear NH ⃛ HN arrangement. The NH vibrational frequencies have been computed and are compared to experimentally measured quantities. Several low ionized states have also been studied in separate spin-restricted SCF calculations. The lowest state is found to have B1u symmetry with an ionization potential of 8.0 eV.
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  • 46
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    International Journal of Quantum Chemistry 8 (1974), S. 981-993 
    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 the use of three bases containing 3p STO's possessing different diffuseness, the electronic structure of several excited states (valence- and Rydberg-type) of planar formaldehyde is investigated by limited CI calculations. The spatial extension of the valence-type state is independent of the bases, whereas a diffuse orbital is important in describing the Rydberg-type state. The natural orbital analysis shows that the Rydberg-type states can be described as an outer electron plus an electronic cloud representing the ionized state to which the Rydberg states converge.
    Additional Material: 2 Ill.
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  • 47
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    International Journal of Quantum Chemistry 8 (1974) 
    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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  • 48
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    International Journal of Quantum Chemistry 8 (1974), S. 29-43 
    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 interaction energy between two water molecules A and B is calculated by the method described in Paper I [1], previously applied for the interaction between two helium atoms (Paper II) [2]. This interaction energy is obtained as the difference between the energies of the complex (A + B) and the monomers (A) and (B), obtained by a perturbation method. The results obtained with the perturbation developed up to the second order in a minimal atomic basis set are decomposed into classical contributions and contributions linked to the exchange possibility. Charge transfer contributions are important and the localized character of the hydrogen bond is examined. It is pointed out that the definition of the set of excited configurations for the calculation of the energies of the isolated monomers is important, especially when one tries to use a small atomic basis set. A similar effect in SCF-type calculations is evaluated. The contribution of higher orders is evaluated by the CIPSI method.
    Additional Material: 5 Ill.
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  • 49
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    International Journal of Quantum Chemistry 8 (1974), S. 73-78 
    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 analytical expansion self-consistent field method was employed to perform ab initio calculations for the ground states of the rare-earth ions, Tm2+, 4f13, 2F, and Tm3+, 4f12, 3H, (Z = 69). In each case the total number of basis functions used in the analytical expansions was 29, distributed as follows: 10, 8, 5, and 6, for the symmetries s, p, d, and f, respectively. All of the orbital exponents of the basis functions were optimized repeatedly, to the extent of the single-precision computer representation. Values of 〈rn〉 for the 4f orbital of both ions are also presented, for the convenience of experimentalists.
    Additional Material: 4 Tab.
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  • 50
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    International Journal of Quantum Chemistry 8 (1974), S. 97-105 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Static dipole polarizabilities and shielding factors for the 2p open shell atomic systems are presented using coupled Hartree Fock theory in the framework of the Roothaan formalism. Calculations have been performed for the ground as well as for some valence excited states. A variational approach has been adopted for the determination of the first-order perturbed functions. The results are compared with those obtained from the correlated calculations and other techniques. The shielding factor values are in excellent agreement with the theoretical N/Z ratio.
    Additional Material: 1 Tab.
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  • 51
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    International Journal of Quantum Chemistry 8 (1974), S. 153-161 
    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: Some sets of icosahedral irreducible tensors can only be defined with respect to one of two seemingly equivalent choices of axes. The problem is explained and the cases when such an alternative choice may cause mixing of sets belonging to different irreducible representations are determined. It is found that the amount of mixing is a property of the spherical basis sets and is independent of the rank and of the permutation symmetry of the tensorial sets. It is further found that certain operators which change the handedness of the coordinate axes can similarly affect these sets, notwithstanding the centrosymmetry of the icosahedron.
    Additional Material: 2 Tab.
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  • 52
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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 structure of the ion FH2+ is investigated on the basis of semiempirical (INDO) and nonempirical (extended gaussian basis set) calculations. In agreement with experiment, both methods predict that, when going from FH to FH2+, there is a lengthening of the F—H bond; also in agreement with infrared analysis, the calculations indicate a bent structure for the fluoronium ion (valence angle at about 120°). The analysis of the FH protonation path reveals the existence of a potential barrier which is exclusively produced by solvation effects; the dependence of the proton affinity of FH on the dielectric constant of the reaction medium is also discussed.
    Additional Material: 4 Ill.
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  • 53
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    International Journal of Quantum Chemistry 8 (1974), S. 235-245 
    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: Various instances in which weakly or nonsymmetry-adapted kets may arise in the description of electronic systems are discussed. These cases include some types of selfconsistent field kets, exchange perturbation kets, and multistate kets.
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  • 54
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    International Journal of Quantum Chemistry 8 (1974), S. 267-291 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new method is used to arrive at Kotani's formula (vide infra) for the character of the representation of the group of spatial symmetry provided by functions which are eigenfunctions of the total spin operator. An alternative form involving determinants of the symmetric functions is also given. The results are applied to some cases which were untreated before and have particular interest in valence-bond calculations. The problem of the construction of bases functions of the given symmetry is also discussed, and a solution with a wide range of applicability is given.
    Additional Material: 5 Tab.
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  • 55
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    International Journal of Quantum Chemistry 8 (1974), S. 319-333 
    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 calculated the second-order perturbed energy and the first-order perturbed wave function of the hydrogen molecular ion by the Green function method based on a united atom with effective nuclear charge, Z. Since the perturbation is given by (Z/r)  -  (1/rA)  -  (1/rB), its magnitude depends on the parameter Z. We obtain an analytical expression for the second-order perturbed energy as a function of Z and the internuclear distance R. We discuss a variety of methods to determine the best values for Z and to derive the potential energy curve and the force constant for H2+; these methods vary in the accuracy of their results.
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  • 56
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    International Journal of Quantum Chemistry 8 (1974), S. 395-422 
    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 review of the nonrelativistic self-consistent symmertrized orthogonalized-plane-wave (SCSOPW) method used for determining electronic energy bands in periodic solids is given. Working equations based on the full use of group theory at all stages are presented for elemental crystals. As an example the method is applied to the trigonal selenium crystal.
    Additional Material: 5 Ill.
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  • 57
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    International Journal of Quantum Chemistry 8 (1974) 
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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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  • 58
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    International Journal of Quantum Chemistry 8 (1974), S. 633-633 
    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 8 (1974), S. 627-632 
    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: 1 Tab.
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  • 60
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    International Journal of Quantum Chemistry 8 (1974), S. 677-692 
    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 transformation exists which allows the general Riccati equation \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c}{{dy\left( r \right)} \mathord{\left/ {\vphantom {{dy\left( r \right)} {dr = A\left( r \right) + }}} \right. \kern-\nulldelimiterspace} {dr = A\left( r \right) + }}B\left( r \right)y\left( r \right) + C\left( r \right)y\left( r \right)^2 \hfill & 0\leqq r 〈 b \end{array}$$\end{document} to be written in a simpler form: \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ d\beta (r)/dr\, = \,P(r)\, + \,R(r)\beta (r)^2 \quad 0\buildrel{〈}\over{=} r 〈 b $$\end{document} The transformed equation has the equivalent nonlinear Hammerstein integral equation \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c}\beta (r) = K\int_{r^{\prime} = 0}^b P(r^{\prime}) N(r, r^{\prime})dr^{\prime} \quad 0\buildrel{〈}\over{=} r 〈 b \end{array}$$\end{document} if the kernel N(r, r′) satisfies three conditions: \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {({\rm i})} & {\{ d/dr - R(r)\beta (r)\} N(r,r)} \\ \end{array}\, = \,\delta (r,r)/K $$\end{document} and \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {({\rm ii})} & {\{ d/dr'\, + \,R(r')\beta (r')\} N(r,r')} \\ \end{array}\, = \, - \delta (r,r')/K $$\end{document} and \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {({\rm iii})} & {{\rm [}\beta (r')N(r,r'){\rm ]}_{r' = 0}^b } \\ \end{array} = 0 $$\end{document}A solution of the nonlinear integral equation is devised by repeatedly integrating the Hammerstein equation. During this procedure the kernel generates an equation that contains only coefficients of β(r)0 and β(r)1. As a result, after truncating at the end of the nth cycle, it is a simple matter to write down a Padé-type approximation: all coefficients in this approximation are capable of being evaluated in terms of simple algebraic formulations of P(r), R(r), and integrals over P(r).The zeroes of the denominator of the Padé-type approximation define the points where singularities occur in β(r).
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  • 61
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    International Journal of Quantum Chemistry 8 (1974), S. 783-788 
    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 ab initio multiconfiguration self-consistent-field (MC SCF) techniques and computer programs of Basch [1, 2] and the ab initio configuration interaction (CI) techniques and programs of Whitten and Hackmeyer [3] have been combined and generalized to form a general technique and program to yield optimized ab initio MC SCF wavefunctions for any set of Slater determinants. The Slater determinants are read in as input data to the program along with the spin parity that is being considered (optional) and the program successively does the CI calculation and one iteration of the SCF calculation, constructing the proper Fock-Hamiltonians by examining the set of Slater determinants and their CI coefficients. The Fock-Hamiltonian matrices are calculated and diagonalized in succession, a single two-dimensional array being used to store these matrices. The basis function integrals are read from a tape only once during each MC SCF iteration (one MC SCF iteration = a CI calculation followed by one iteration of the SCF calculation).
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  • 62
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    International Journal of Quantum Chemistry 8 (1974), S. 839-855 
    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 general methods of deriving the extended Hartree-Fock equations are described. The rules for going over from the energy expression in the ordinary method of calculation to that in an extended one are reformulated and illustrated. The extended Hartree - Fock equations for berylliumlike atomic systems based on the use of nonorthogonal radial orbitals are given and solved. The numerical values of overlap integrals and total energies are given and discussed.
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  • 63
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    International Journal of Quantum Chemistry 8 (1974), S. 901-913 
    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 random phase approximation (RPA) or time-dependent Hartree-Fock approximation (TDHF) is reconsidered for the calculation of the dynamic polarizability for atoms. An integral equation which admits a simple numerical treatment is established. The asymptotic approximation for the electron propagator is tested for its applicability by means of comparisons with earlier results.
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  • 64
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    International Journal of Quantum Chemistry 8 (1974), S. 995-995 
    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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  • 65
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    International Journal of Quantum Chemistry 8 (1974), S. 315-316 
    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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  • 66
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    International Journal of Quantum Chemistry 8 (1974), S. 347-362 
    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 intermediate-field coupling case. The Wigner-Eckart theorem is formulated for a simple irreducible tensor operator as well as for the Kronecker and scalar products of these operators. The expressions required for the calculation of Coulomb repulsion, crystal field splitting, spin-orbit interaction, and Zeeman effect are given in detail. Recent applications to various problems in spectroscopy and magnetism of transition metal compounds are referred to.
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  • 67
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    International Journal of Quantum Chemistry 8 (1974), S. 523-537 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we show that with the equivalent transformation Pr = (-1)P(Pσ)-1 the spin function dependent methods such as Slater's method without group theory or Goddard's method with group theory differ only in different antisymmetric requirements from the present Waller-Hartree spin function free method. There exists a one-to-one correspondence between Slater's determinantal wave function and the Waller-Hartree double determinantal wave function. Explicit expressions for the S2 operator, Löwdin's spin projector, matric basis and several different forms of spin-projected functions are given for the Waller-Hartree formalism. The results are compared with other methods including those of Slater, Matsen, Gallup, Goddard and Segal. The differences are quite significant. New spin operators are worked out using creation-destruction operators. A knowledge of group theory is not required in this Waller-Hartree method. We have also shown that the Waller-Hartree method is more convenient than Slater's method with spin functions especially in the evaluation of the functional HΨ/Ψ. The advantages and disadvantages in the use of a linear combination of N! Hartree products and linear combinations of all possible double determinants are discussed. In addition, a formula for the calculation of the Sanibel coefficients C(S, M, i) is obtained.
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  • 68
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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 method for quantitative comparison of various conformers of cyclic macromolecules in terms of nonbonded interaction energy terms is proposed. The first step in the procedure is an analytical evaluation of a set of Cartesian atomic coordinates consistent with the ring closure condition and prescribed values for internal parameters. A variant of the same technique enables different conformations of the macromolecule to be generated. Nonbonded interactions of the electrostatic, polarization and dispersion type and van der Waals repulsion are calculated using the generated coordinates, empirical bond polarizability data and results of simple molecular orbital calculations. An application of the proposed techniques to the closed symmetric conformation of valinomycin indicates that the macromolecule by itself is somewhat constrained in this state but that its affinity for a potassium ion is very strong - much stronger than the hydration energy of the latter.
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  • 69
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    International Journal of Quantum Chemistry 8 (1974), S. 623-625 
    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
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  • 70
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    International Journal of Quantum Chemistry 8 (1974), S. 635-642 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: General formulas are obtained for evaluating a basic type of one-center two-electron integral which arises in the computation of expectation values of spin-spin and spin-orbit operators over explicitly correlated wave functions. The correlation terms are assumed to be in the form of products of Slater functions and powers (not necessarily integer) of the interelectronic coordinate rij.
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  • 71
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    International Journal of Quantum Chemistry 8 (1974), S. 745-754 
    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 chemical shift and the diamagnetic susceptibility of the hydrogenic atom with magnetic dipole and origin of the external magnetic field vector potential noncoincident with the hydrogenic nucleus have been calculated from perturbation theory using a set of expansion functions whose radial parts are single exponent associated Laguerre functions. In contrast to hydrogenic expansion functions these functions give rapid convergence to the exact values of the second-order energy summations when centred at the hydrogenic nucleus. The rate of convergence is fairly insensitive to the choice of expansion function exponent.
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  • 72
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    International Journal of Quantum Chemistry 8 (1974), S. 17-28 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ground state energy of the He2 system is calculated according to the techniques described in Paper I around the van der Waals equilibrium, without assuming the constancy of the intraatomic correlation energies. The second-order results do not present an attractive region; the S2 decrease of the intraatomic correlation correlation corrections is larger than the attractive interatomic correlation corrections. The further orders reverse progressively the situation and finally give a qualitatively correct potential curve after the fifth order. Reaching almost exact solutions in the considered basis, one can demonstrate that the intermolecular calculation of the system A + B in the union of the basis for A and B involves an energy decrease which simply represents the effect of the extension of the basis set; and that a proper intermolecular calculation must compare the A + B energy with the A and B energies calculated in conveniently extended basis sets including the vacant MO's of the partner.
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  • 73
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    International Journal of Quantum Chemistry 8 (1974), S. 79-82 
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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: Molecular orbitals of some of the 3d-transition metal phthalocyanines have been calculated. π-Electron charge densities over the atomic sites and the optical properties of the metal phthalocyanines have been calculated. The effect of the introduction of different metal atoms in the centre of the organic ring on the physical properties of the metal phthalocyanines has been discussed.
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  • 74
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    International Journal of Quantum Chemistry 8 (1974), S. 107-117 
    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: Some problems connected with the convergence of iterative solutions of the Hartree-Fock equations for the open shell systems are discussed. The nonuniqueness of the Hartree-Fock operator form is used.The method of iterating by the operator's power is developed for obtaining solutions of the Hartree-Fock equations. Some particular results for the molecules Li2+, Li2- are presented.
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  • 75
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    International Journal of Quantum Chemistry 8 (1974) 
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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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  • 76
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    International Journal of Quantum Chemistry 8 (1974), S. 163-169 
    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 connection between the electron coordinates permutation group and the molecular point group is exhibited in the framework of the Heitler-London method. It is shown that the initial wave function of a molecule in the Heitler-London method can be written in such a form, that the effect of the point group operations upon this function corresponds to the permutation of the sets of electron coordinates of the ions and the subsequent multiplication of this function by some constants.
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  • 77
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    International Journal of Quantum Chemistry 8 (1974), S. 209-221 
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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: General forms for asymptotic wave functions are derived from properties of the relevant Green's function. The use of separable potentials constructed from the asymptotic functions is described and the relation with integral transform functions is discussed.
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  • 78
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    International Journal of Quantum Chemistry 8 (1974), S. 247-253 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energies of the single-configuration lowest π - π* singlet and triplet states of some conjugated hydrocarbons have been calculated by the MC-SCF method using the conjugate-gradient technique of minimisation. The results are compared with those calculated by other methods currently in use, like (a) single-configuration calculation with VN-1 potential for virtual orbitals; (b) CI calculation involving singly excited states; and (c) TDHF method. It has been concluded that the results for the MC-SCF method are very good, considering that only a single open-shell configuration is involved.
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  • 79
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    International Journal of Quantum Chemistry 8 (1974), S. 263-266 
    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-center core-electron attraction integral VAB in zero-differential overlap semiempirical MO methods is examined. It is concluded that core-valence orthogonality and valence symmetrical orthogonalization effects must be considered, and that these effects provide justification for the CNDO/2 approximation VAB = ZBγAB.
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  • 80
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    International Journal of Quantum Chemistry 8 (1974), S. 293-314 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The problem of the evaluation of first- and second-order energies by the use of arbitrary variational wave functions is examined in detail for time-independent perturbations as well as for time-dependent perturbations. By using a compact formalism the general formulae to be used for the case of a fully optimized set of variational parameters are readily obtained and the most prominent features are examined. The generality of the approach is tested by showing how some widely used methods are obtained by using particular types of variational wave functions. The case of incompletely optimized sets of variational parameters is examined examined extensively and several approaches at different levels of approximation are proposed. Emphasis is put upon the importance of considering, in the calculation of higher-order energies, the variational parameters which may be of negligible importance, and thus often neglected, in the absence of perturbations.
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  • 81
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    International Journal of Quantum Chemistry 8 (1974), S. 491-498 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A Brillouin-Wigner perturbation expansion is derived for the generalized eigenvalue equation (F0 + F1)Ψ = μAΨ. The theory is applied through second order to calculate the ground-state energies of the helium atom and the hydrogen molecular ion. The results are compared with the corresponding Rayleigh-Schrödinger expansion. For the examples we consider, the Brillouin-Wigner results through second order are generally superior to the Rayleigh-Schrödinger ones.
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  • 82
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    International Journal of Quantum Chemistry 8 (1974), S. 547-557 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A technique for Slater orbital exponent optimization in an HF—SCF—LCAO—MO calculation is proposed in which orbital exponent variation is incorporated into the SCF scheme. This is accomplished by rewriting Slater's rules so that the shielding terms depend on the molecular charge distribution through the elements of the population matrix. The SCF scheme then includes a calculation of a new set of orbital exponents from the coefficients of self-consistent molecular orbitals obtained from the previous set of exponents. The process is iterated until the energy attains its lowest value.The technique is illustrated by minimal basis calculations on LiH, BH, and HF. Near optimization is obtained with considerably less effort than is necessary for other reported techniques. Aside from interesting properties, the technique can be important for extended basis calculations where exponent optimization is a difficult task.
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  • 83
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    International Journal of Quantum Chemistry 8 (1974), S. 619-621 
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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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  • 84
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    International Journal of Quantum Chemistry 8 (1974), S. 707-714 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is presented for generating open-shell equivalence-restricted SCF orbitals in high-symmetry situations using Roothaan-Hartree-Fock programs which are adapted for lower symmetry.
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  • 85
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    International Journal of Quantum Chemistry 8 (1974), S. 733-743 
    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 half-projected Hartree-Fock function (HPHF) for singlet states is defined as a linear combination of two Slater determinants which contains only spin eigenstates with even spin quantum numbers. The possible uses of such an approach for determining molecular properties are investigated computing the potential energy curve, binding energy, force constant, and dipole moment variation corresponding to the lithium hydride ground state. Full projected and restricted Hartree-Fock calculations (PHF and RHF) are performed simultaneously for comparison purposes. It is found that the HPHF model yields very satisfactory results, very close to those of the PHF scheme. Both models predict properly the molecular behavior as a function of nuclear separation, whereas the RHF one fails. A discussion is given in terms of configuration equivalents. It is concluded that the HPHF scheme seems to be useful for determining molecular properties specially in the case of large systems in which the more sophisticated methods are unmanageable.
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  • 86
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1163-1175 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Highly polished surfaces of nylon 6, nylon 66, polychlorotrifluoroethylene and polypropylene were etched by aromatic and chlorinated hydrocarbons at temperatures between 25 and 75°C to reveal surface morphology. Comparison with micrographs obtained with microtomed sections shows the absence of etching artifacts which are known to accompany the use of oxidizing etching agents.
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  • 87
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1207-1209 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 88
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1371-1381 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Small-angle polarized light scattering from a deformed three-dimensional spherulite is formulated on the basis of the deformation model proposed in Part II of this series. The intensity distribution of scattered light is discussed chiefly for the cross-polarization condition, the so-called Hv polarization, as a function of elongation of the spherulite. In the undeformed state, the scattered intensity distribution forms the typical fourleaf clover pattern, and the intensity decreases with increasing fraction of crystals oriented randomly (type R crystals) within the crystal lamellae of the spherulites. In a system composed of type R crystals and folded-chain crystals (type B crystals) within the lamellae, the four-leaf pattern moves to the horizontal zone near the equator with increasing elongation of the spherulite, and, simultaneously, extends to some extent to the vertical zone near the meridional direction as a parameter measuring the ease of lamellar untwisting increases. In a system composed, in addition to type R and type B crystals, of crystals transformed from type B to type Ca and type Cr due to tilting and unfolding of polymer chains, respectively, within the crystal lamellae an eight-leaf pattern appears, even at small elongation up to about 30%. Each lobe of the eight-leaf pattern undergoes a characteristic change with increasing elongation. In both systems, the scattered intensity increases with sharpening of orientation distribution of crystals within the crystal lamellae.
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  • 89
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1441-1456 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The theory of Franklin et al. is employed for the calculation of the maximum form birefringence of a polymer having lamellar morphology. The results confirm the experimental conclusion that for low-density polyethylene, the form birefringence approaches 3% of the total birefringence. The theory also predicts the parabolic dependence of the form birefringence on the refractive index of the amorphous phase. It may be applied to estimate the dynamic form birefringence and leads to a value of the dynamic strain-optical coefficient which is of the order of 2-15% of the total.
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  • 90
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1477-1483 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effect of drawing on the glass-transition temperature of amorphous poly(ethylene terephthalate) has been studied. The Tg decreases to a minimum at a draw ratio of 1.5, then increases to a maximum at a draw ratio of about 2.0, and again decreases with increasing draw ratio. The relationship between the change of structure and Tg is discussed in terms of the configurational entropy and the rate of molecular motion in local-mode relaxation. On the basis of configurational entropy, the decrease of Tg at the beginning of drawing depends on the increase of configurational entropy, while at draw ratios above 2.0 it depends on the increase of entropy associated with intermolecular interaction. From the point of view of molecular motion, it is concluded that the change of Tg is determined by local oscillations in the amorphous region.
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  • 91
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1537-1546 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Free electrophoresis, differential spectral UV analysis, and the determination of the coefficients of selective sorption were used to investigate, in aqueous solutions of halides, the behavior of two polycations, poly[1(2-hydroxyethyl)pyridinium methacrylate] and poly[1(2-hydroxyethyl)trimethylammonium methacrylate]: i.e., one species with and the other without a pyridine ring in the side chain. Electrophoretic data were used to estimate the length of the electrophoretic segment and the approximate charge of the polyion in solutions of the individual salts. A comparison of the data showed that the interaction is not due to the presence of the pyridine ring in the side chain and that the order of activity of the halide anions is the same for both types of polymers.
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  • 92
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1565-1574 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: When isotactic polystyrene (i-PS) is crystallized from the melt or from the glassy state at rather large supercooling an additional melting peak appears on the curve during scanning in a differential calorimeter. The overall rate of crystallization deduced from the total peak areas as a function of crystallization time did not fit the Avrami equation well. When we omit the area of the additional melting peak in the kinetic analysis a much better fit is obtained. We also observed that no lamellar thickening occurs during isothermal crystallization. In view of the low degree of crystallinity of i-PS these results lead to the idea that a secondary crystallization process takes place within the amorphous parts of the spherulites resulting in this additional melting peak on the DSC curve. The large supercooling needed and the increase in peak area with increasing molecular weight make us suppose that intercrystalline links are probably responsible for the additional melting peak of bulk-crystallized i-PS. Electron microscopic studies of surface replicas of i-PS support this view.
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  • 93
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    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1639-1648 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The theory of the preceding paper is compared with previously unpublished experimental results on the viscoelastic properties of two polystyrene fractions of molecular weight 1.9 × 106 and 1.2 × 106 in nitropropane, which is very nearly a theta solvent, and in toluene, a good solvent. At the concentrations used, around 1%, the theory predicts extensive departures from non-draining toward free-draining behavior; these effects are observed. The theory similarly fits experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in decalin and dioctyl phthalate in the same concentration range.
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  • 94
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1849-1856 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Main-chain scission was the predominant effect when dilute solutions of three linear polystyrenes in 1-methylnaphthalene and polybenzyl oligomer received up to 2000 megaroentgen of 1.5-MeV electrons. Values of energy per scission were independent of dose and of the same magnitude as literature values in dioxane and benzene solutions when compared at the same dose rate. In all cases as irradiation progressed, Mw/Mn approached a value of 2 and Mz/Mw approached a value of 1.5 characteristic of a random distribution. Starting from one initial distribution, random numbers were used to simulate random chain scission. A 500 MR (megaroentgen) distribution calculated in this manner matched the experimental distribution after a 500 MR irradiation.
    Additional Material: 4 Ill.
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  • 95
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1865-1874 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relationship between the critical point and the precipitation threshold is examined in the Flory - Huggins approximation with concentration-independent interaction parameter χ. Approximate explicit expressions for the difference between the critical point and the threshold can be derived by series expansion of threshold conditions. In the first-order approximation, the concentration difference depends only on the chainlength averages xw, xz, and xz+1, in the second-order approximation it depends on xw, xz, xz+1, and xz+2, etc. For polymers of low polydispersity, the second-order approximation gives a good estimate of the concentration difference; for instance, for polymers with exponential distribution and xw/xn 〈 1.25, the error is lower than ca. 1%. The approximation is not suitable for polymers with xz+1 ≫ xz (including polymers whose cloud-point curve exhibits a triple point). Irrespective of the polydispersity of the polymer, the threshold as well as the whole cloud-point curve depend only on the weight-average and higher averages, xw, xz, xz+1, …, xz+k, where k → ∞; they are, however, independent of the number average xn.
    Additional Material: 1 Ill.
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  • 96
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 1925-1937 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The glass-transition region of crosslinked polymers prepared from poly(1,2-propylene phthalate fumarate) and styrene was studied using a torsion pendulum. The glass-transition temperature and the modulus in the rubbery region of these polymers were analyzed in terms of the crosslink density. The styrene concentration at which the maximum crosslink density occurs, as estimated from the viscoelastic data, is found to be in agreement with estimates made by other workers using chemical methods.
    Additional Material: 8 Ill.
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  • 97
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 2209-2251 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Stress crazing is studied in three forms of crystalline, isotactic polypropylene (PP): (1) smectic/nonspherulitic, (2) monoclinic/nonspherulitic, and (3) monoclinic/spherulitic PP. Optical and scanning electron microscopy as well as stress - strain measurements are used to characterize crazing behavior in these three forms as a function of temperature (-210 to 60°C) and of the gaseous environment (vacuum, He, N2, Ar, O2, and CO2). Forms 1 and 2 are found to craze much like an amorphous, glassy polymer in the temperature range between -210 and -20°C, irrespective of environment. The plastic crazing strain is large close to the glass-transition range (ca. -20°C) of amorphous PP and in the neighborhood of the condensation temperature of the environmental gas. Near condensation, the gas acts as a crazing agent inasmuch as the stress necessary to promote crazing is lower in its presence than in vacuum. A gas is the more efficient as a crazing agent, the greater is its thermodynamic activity.Spherulitic PP (form 3) crazes in an entirely different manner from an amorphous, glassy polymer, showing that the presence of spherulites influences crazing behavior much more profoundly than the mere presence of a smectic or monoclinic crystal lattice. Below room temperature, crazes are generally restricted in length to a single spherulite, emanating from the center and going along radii perpendicular, within about 15°, to the direction of stress. They never go along spherulite boundaries. Gases near their condensation temperature act as crazing agents much as in nonspherulitic PP. Above room temperature the crazes are no longer related to the spherulite structure, being extremely long and perfectly perpendicular to the stress direction. Apparently the crystals are softened enough by thermally activated segmental motion to permit easy propagation of the craze. The morphology of the fracture surfaces and its dependence on temperature and environment is described and discussed. Concerning the action of gases as crazing agents it is argued that the gas is strongly absorbed at the craze tip, where stress concentration increases both the equilibrium gas solubility and the diffusion constant. Hence, a plasticized zone is formed having a decreased yield stress for plastic flow. This is considered to be the main mechanism by which the gas acts as a crazing agent. In addition, reduction of the surface energy of the polymer by the adsorbed gas eases the hole formation involved in crazing.
    Additional Material: 25 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 2267-2280 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effects of swelling and annealing treatments on viscoelastic behavior were studied in melt-crystallized and solution-crystallized samples of isotactic polypropylene (iso-PP) over the temperature range -150 to 150°C. The log E″ versus T curves exhibited α, β, and γ peaks in order of decreasing temperature. The β peak of the melt-crystallized sample shifted to higher temperatures after annealing, but was not affected by swelling. The α peak of melt-crystallized polymer was affected by swelling treatments. It increased in height and shifted to lower temperatures almost linearly with the volume fraction of absorbed solvent. The magnitude of the shift was independent of the solvent species - toluene, p-xylene, tetralin, carbon tetrachloride - however, it depended significantly on the temperature at which the sample had been heat treated. For solution-crystallized polymer, no peaks in log E″ were observed in the temperature range of the β peak of melt-crystallized material, but the α peak appeared larger and broader, and at higher temperature than the corresponding peak in the melt-crystallized polymer. After swelling or annealing, the low-temperature component of the α peak of the solution-crystallized sample decreased in height and at the same time a new loss peak appeared at -55 and 0°C, respectively, is swollen and annealed samples. In particular, in the case of annealing treatments, the high-temperature component of the α peak shifted to still higher temperatures. From these results on the solution-crystallized sample it can be deduced that the segmental motions in the amorphous phase are very strongly constrained by surrounding crystalline phases as compared with those in the amorphous phase of the melt-crystallized sample, and the constraints imposed on the segmental motions are released to a great extent by both treatments. Finally, swelling effects on the γ peak were examined. The γ peak of the melt-crystallized sample decreased in height after swelling. On the other hand, the γ peak of the solution-crystallized sample separated into two peaks, which might be attributed to the mechanical relaxations in the crystalline and amorphous phases.
    Additional Material: 9 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 12 (1974), S. 2347-2360 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Viscosity and normal stress behavior were measured for poly(methyl methacrylate) samples of various average molecular weights in diethyl phthalate solution at 30 and 60°C. All samples conformed approximately to the most probable distriution (M̄w/M̄n = 2). Concentrations ranged from 0.113 to 0.38 g/ml, and M̄w from 53,800 to 1,620,000. Despite considerable evidence in the literature of unusual linear viscoelastic behavior for this polymer, its nonlinear properties appear to be rather conventional. The viscosity-shear rate master curve was similar to that found earlier for concentrated solutions of polystyrene and poly(vinyl acetate) of comparable molecular-weight distribution. The viscosity time constant τo parallels τR, the characteristic time of the Rouse model, although the residual dependence of τo/τR on concentration and molecular weight appears to be slightly different from that for polystyrene and poly(vinyl acetate). Similar conclusions apply to the recoverable compliance Je,o estimated from the normal stress behavior of each solution, and its relationship to the Rouse model compliance JR.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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