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  • Atomic, Molecular and Optical Physics  (246)
  • Engineering  (32)
  • AERODYNAMICS
  • Wiley-Blackwell  (278)
  • 1965-1969  (278)
  • 1925-1929
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  • Wiley-Blackwell  (278)
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  • 1
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 2
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 3-28 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
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  • 3
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 1-2 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 4
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 47-66 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three methods for finding natural frequencies and modes of complex structures composed of beam elements are described and compared. The analysis is extended to include hysteretic damping for the determination of response and transmissibility without a modal analysis. Experimental comparison is given for the response of a simple engineering structure.
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  • 5
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 101-122 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.
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  • 6
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 67-73 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite difference treatment of two-dimensional problems in elastostatics is usually based on the differential equations for the displacement vector or the Airy stress function, depending on whether boundary conditions are on displacement or stress. In either case, determination of stresses requires numerical differentiation and therefore use of a rather fine grid. Moreover, neither method is suited to the treatment of mixed boundary conditions. The alternative method developed in this paper uses the first derivatives of the displacement components at the grid points as basic variables and hence does not require numerical differentiation in the evaluation of stresses. Appropriate finite difference equations are established, and their use is discussed in connection with a specific example with known explicit solution.
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  • 7
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 29-45 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory, function generator routine and testing procedures are given for a six-node 18 degree of freedom triangular element. At corner nodes the variables are the displacement and the two slopes. At midside nodes the variables are the displacement, the slope normal to the side, and the rate of change of this along the side - i.e., the rate of torsion. Of two options, one divides the triangle into three and takes different quartic displacements in the three regions, and the other uses displacement functions with singularities at the vertices. According to a test which compares the energies of the two formulations by eigenvalues, the second is the better if the integration is accurate. The same test, together with others based on finite differences and on nodal values, etc. checks the correctness of the routine decisively.
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  • 8
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 123-133 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The large deflection problem of a rectangular plate is analysed by using the finite element method and employing the iteration technique. In the present study, the stiffness matrix of a rectangular plate element for bending proposed by Greene is employed, and results of numerical examples duly justifies applicability of the present method.
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  • 9
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 75-100 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents first a general formulation of the elasto-plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.
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  • 10
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 11
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 151-162 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.
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  • 12
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 135-149 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The assumed stress distribution approach is used to derive the stiffness matrix of a plate-bending element of general polygonal shape having any number of nodes. The effect of assuming various numbers of unknown coefficients in the stress distributions is examined and the convergence properties of the resulting elements compared with others derived form assumed displacements.
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  • 13
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 169-175 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for obtaining the Green's functions for Laplace's, Poisson's, and the transient heat diffusion equations is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equations by matrix multiplication, with subsequent considerable savings in machine time.
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  • 14
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 177-180 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the large numbers of non-linear algebraic equations occurring in analyses of non-linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations.Examples presented show that in the finite element analysis of moderately non-linear structural systems the technique provides sufficiently accurate solutions. For more non-linear systems the technique provides excellent starting values for the Newton-Raphson method.
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  • 15
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 163-167 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Deformation functions which, in addition to satisfying the continuity conditions at nodes. Also satisfy. Approximately, the governing differential equation within the element allow system eigenvalues to be found more accurately, with a given number of elements, than is possible with previously published deformation functions. This is illustrated for the case of beams.
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  • 16
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 201-203 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 17
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 205-221 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher-dimensional spaces, independent of specific co-ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non-Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
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  • 18
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 224-224 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 19
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 20
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 225-245 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented based on matrix algebra for the dynamic analysis of a mixed rotating and non-rotating vibration system. Such systems occur in practice when turbo-alternator sets are mounted on flexible steel foundations.The mathematical model considered consists of a rotating non-uniform, bi-symmetric shaft connected via three or more flexible-film bearings to a flexible structure throughout which mass is distributed. The shaft, which is assumed to rotate at constant speed, is heavy, flexible and carries several rigid axi-symmetric discs. Viscous damping is assumed to act in all parts of the system and gravitational effects are ignored.
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  • 21
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 181-200 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Surface displacements at the end of a semi-infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter-part half-space solution.The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half-space is found by using the Boussinesq solution. Then, the excess tractions on the half-space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid-section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed.With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half-space; 2. a rigid punch in contact with an elastic cylinder.
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  • 22
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 247-259 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of the this paper, topological properties of finite element models of functions defined on spaces of finite dimension were examined. In this part, a number of applications of the general theory are presented. These include the generation of finite element models in the time domain and certain problems in wave propagation, kinetic theory of gases, non-linear partial differential equations, non-linear continuum mechanics, and fluid dynamics.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 275-277 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 24
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 261-274 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A presentation is made of a rectangular plate bending element, the use of which corresponds to the finite difference method. The element stiffness matrix is arrived at by approximation of the strain energy of the element by suitably selected finite difference expressions which contain not only values in respect of the deflection, but also values of its first derivatives. On the basis of the connection found between the two methods, some changes are suggested in the finite difference method, which involve a more realistic way of considering the detailed distribution of the loading. The effect of these modifications is illustrated in two applications.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 279-299 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When calculating complex interconnected systems (electrical, power, water supply, gas systems, etc.) by digital computer, a number of common problems arise, connected both with the mathematically correct formulation of the problem under investigation, and with the algorithms of the solution, the programming of which makes it possible to reduce the computing time, the store capacity and the volume of input data required. The present article is devoted to the solution of these problems. The procedure is illustrated by formulating and manipulating the equations relating to complex interconnected mine ventilation networks.
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  • 26
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 301-310 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Solution of plane elastic problems by piecewise linear approximation is outlined. This method is based upon Galerkin error distribution technique, which leads to simultaneous algebraic equations identical to those associated with the Finite Element Method. In addition, this method permits definition of the discretization error, which can be computed once the displacement components are known. Properties of the interpolation functions are discussed, and a sequence of internally compatible plane elastic elements is defined.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 311-331 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress-ratio, linear programming-cutting plane and usable-feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non-convex stress constraints and numerous relative optima. Instances are given of non-fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 333-349 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re-entry to the structural analysis program for the purpose of computing dynamic stresses.A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 351-378 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of non-linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non-convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in-plane loads may be performed efficiently by means of non-linear programming.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 379-394 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo-viscoelastic observations.
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 395-395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    International Journal of Quantum Chemistry 2 (1968) 
    ISSN: 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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    International Journal of Quantum Chemistry 2 (1968), S. 413-430 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Une théorie de perturbation est décrite qui est basée sur l'équation de Schrödinger dependant du temps; l'interaction électrostatique des électrons est considerée, l'interaction, des spins est negligée. En prenant des fonctions d'onde, données par la méthode de la densité projetée des électrons decrite en Part I, les énergies des états électroniques excités sont calculées. Les spectres électroaiques de quclqucs porphyrines sont calculés et sont trouvés en bon accord avec l'expérience.
    Abstract: Es wird eine Störungstheorie dargostellt, die auf der zeitabhängigen Schrödinger-gleichung beruht; Coulombwechselwirkungen werden berücksichtigt, Spineigenschaften vernachlässigt. Wellenfunktionen, die nach der in Teil I beschriebenen Methode der projizierten Elektronendichte erhalten wurden, werden als Basissatz verwendet, und die Energien von angeregten π-Elektronenzuständen werden berechnet. Für eine Reihe von Porphyrinen werden die Elektronenspektren berechnet, und es wird eine gute Über-einstimmung mit dem Experiment festgestellt.
    Notes: A perturbation theory based on the time-dependent Schrödinger equation is presented; Coulombic interactions are taken into account and spin properties are neglected. Using wave functions given by the projected electron density method described in Part I as a basis set the energies of excited π-electron states are calculated. For a series of porphyrin compounds the electronic spectra are calculated and are found to be in good agreement with experiment.
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    International Journal of Quantum Chemistry 2 (1968), S. 463-470 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Les méthodes Hückel MO et SCF-ASMO-CI (sémi-empirique) ont été employées pour calculer des énergies de transition de sept tautoméres possibles de la flavine et de deux imino-flavines (bases de Schiff). Les énergies de transition calculées indiquent que la tautomérie et la formation de bases de Schiff sont accompagnées d'un déplacement bathochrome par rapport au spectre d'absorption de la riboflavine. Ce déplacement est particuliérement prononcé dans le cas des formes énoliques de la molécule d'isoalloxazine. Les tautomères énoliques ont aussi ses niveaux triplets les plus bas bien au-dessous des triplets des autres tautomères. On discute la signification de ces résultats.
    Abstract: Die Hückelsche MO-Methode und die halb-empirische SCF-ASMO-CI-Methode wurden für die Berechnung der Übergangsenergien sieben möglicher Flavintautomeren und zwei Iminoflavinen (Schiffscher Basen) benützt. Die berechneten Übergangsenergien zeigen dass die Tautomerie und die Bildung Schiffscher Basen mit einer bathochromischen Verschiebung hinsichtlich des Absorptionsspektrums des Riboflavins verbunden ist. Diese Verschiebung ist im Falle der 4-Enolformen des Isoalloxazinmoleküls besonders ausgeprägt. Die 4-Enoltautomere haben auch tiefste Triplettniveaus wohl unter den Tripletten anderer Tautomeren. Die Bedeutung dieser Resultate wird diskutiert.
    Notes: The Hückel MO and semiempirical SCF-ASMO-CI methods have been employed to calculate transition energies of seven possible flavin tautomers and two imino flavins (Schiff bases). The calculated spectral transition energies indicate that the tautomerism and Schiff base formation are accompanied by a bathochromic shift with reference to the absorption spectrum of riboflavin. This shift is especially pronounced in the case of the 4-enol forms of the isoalloxazine molecule. The 4-enolic tautomers also have lowest triplet levels well below the triplets of other tautomers. The significance of the results has been discussed.
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  • 36
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 2 (1968), S. 521-530 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On a observé que certains substituants introduits sur un système acénique peuvent changer le lieu de la fixation de l'oxygène au cours de la photooxydation. Ce fait ne peut ětre interprété en calculant les énergies de paralocalisation. L'hypothèse d'un complexe intermédiaire correspondant à une extension du systeme délocalisé permet au contraire de rendre trés bien compte des résultats expérimentaux.
    Abstract: Es wurde bemerkt, dass gewisse Substituenten, die in Acenderivaten eingeführt sind, den Anheftungsplatz des Sauerstoffs während der Photooxydation verändern können. Dieses Phänomen kann nicht mit einer Berechnung der Paralokalisierungsenergien erklärt werden. Wenn aber ein intermediürer Komplex eingeführt wird, was einer Erweiterung der delokalisierten Bindung entspricht, ist es möglich eine befriedigende Erklärung der experimentellen Tatsachen zu geben.
    Notes: It has been observed that some substituents introduced in acenic derivatives are able to change the site of the fixation of oxygen during photooxidation. It is not possible to interpret this phenomenon by calculating the paralocalization energies. However, if an intermediate complex is introduced, which corresponds to an extension of the delocalized bond, a satisfactory explanation of the experimental results is possible.
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  • 37
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: La méthode des orbitales moléculaires alternantes (AMO) est plus efficace quand les orbitales moléculaires sont choisies d'une maniére optimale. Une méthode est présentée pour la détermination de la combinaison la plus efficace et pour le choix des orbitales moléculaires. Application aux systémes non-alternants (le fulvéne et l'azuléne) montre qu'on peut obtenir une amélioration substantielle dans la valeur de l'énergie par la détermination optimale des MO.
    Abstract: Die Methode der Alternierenden MO(AMO) ist wirksamer, wenn die MO auf optimale Weise gewählt werden. Es wird ein Verfahren für das beste Paarungs-Schema und die Wahl der MO gegeben. Anwendung an nicht-alternierenden Molekülen (Fulven und Azulen) zeigt, dass man eine wesentliche Verbesserung in der Energie erreichen kann, wenn die optimalen MO angewandt werden.
    Notes: The alternant molecular orbital method (AMO) is more efficient if the molecular orbitals are chosen in an optimal way. A method is given of how to determine the most effective pairing scheme and how to choose the starting molecular orbitals. Applications to non-alternant systems (fulvene and azulene) show that one can achieve substantial improvement in the energy by determining the best MO's.
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  • 38
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On analyse quelques travaux récents sur des molécules à un et deux électrons. On discute des résultats obtenus de calculs variationnels et des théories de perturbation pour l'état fondamental et pour des états excités. On s'intéresse surtout aux résultats qui sont suffisamment exacts pour permettre des conclusions définies en ce qui concerne ou le systéme ou la méthode.
    Abstract: Neue theoretische Arbeiten über Ein- und Zweielektronenmoleküle werden besprochen. Resultate, die mit der Variationsmethode und der Störungstheorie erhalten worden sind, werden für den Grundzustand und für angeregte Zustände diskutiert. Die Betonung wurde auf solche Resultate gelegt, die genügend genau sind, um bestimmte Schlüsse mit Rücksicht auf entweder das System order die Methode zuzulassen.
    Notes: Recent theoretical work dealing with one- and two-electron molecules is reviewed. Results obtained using both the variational method and the perturbation theory are discussed for the ground states as well as for excited states of the molecules. Emphasis is placed on those results which are sufficiently accurate to yield definite conclusions with regard to either the system or the method.
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  • 39
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 1 (1967), S. 379-401 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: By means of the HMO method a postulate by Clar is justified. According to this postulate certain localized benzene-like regions exist in condensed aromatic hydrocarbons. A measure of the benzene character, butene character, etc., of certain parts of these molecules is derived and a simple method to calculate it is described. The importance of these measurements for discussions of chemical reactivity is pointed out.
    Abstract: Mit Hilfe der HMO Methode wird gezeigt, dass das Postulat von E. Clar, gewisse Sechsring-Einheiten in kondensierten Aromaten stellen lokale benzoide Gebiete dar, berechtigt ist. Eine Masszahl (Character order) für den benzoiden, butenoiden usw. Charakter bestimmter Teile kondensierter Aromaten wird abgeleitet und ein einfaches Rechenverfahren zu ihrer Ermittlung angegeben. An Hand der Charakterogramme von 41 kondensierten Aromaten wird die Bedeutung dieser Zahlen für die Diskussion der chemischen Reaktivität aufgezeigt.
    Notes: Partant de la méthode HMO on vérifie qu'un postulate de Clar est justifié. D'après ce postulat il existe dans les hydrocarbures aromatiques condensés certaines régions localisées de caractère benzènoide. On propose un indice pour le caractère benzèneoide, butènoide, etc., de certaines parties de ces molécules, et on présente une méthode simple pour calculer ces indices. On discute l'importance de ces indices pour la réactivité chimique.
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  • 40
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    International Journal of Quantum Chemistry 1 (1967), S. 421-425 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On a calculé, pour un déterminant de Slater projeté sur un sous-espace de spin défini, les fonctions de densité pour deux électrons, définies par McWeeny.
    Abstract: Die Zweielektronenfunktionen von McWeeny, sind für eine Spin-projizierte Slaterdeterminante berechnet worden.
    Notes: The two-particle density functions introduced by McWeeny are calculated for a spin-projected Slater determinant.
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  • 41
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    International Journal of Quantum Chemistry 1 (1967), S. 403-419 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: La fonction d'onde d'un système à n électrons dans la méthode Hartree-Fock généralisée (EHF) est définie (Löwdin, Phys. Rev. 97, 1509 (1955)) comme le meilleur déterminant de Slater construit de spin-orbitales d'une flexibilité complète et projeté sur un sous-espace de symmétrie correcte. On compare cette fonction à l'interaction de configurations équivalente pour l'état 1S d'un atome à deux électrons. On démontre qu'il existe dans ce cas-ci un nombre infini de solutions du problème variationnel avec des énergies inférieures à celles de la fonction Hartree-Fock ordinaire, et avec des spin-orbitales satisfaisant à toutes les conditions de l'extrémum. On présente deux méthodes pour obtenir les spin-orbitales EHF. Une application à l'état fondamental de l'hélium avec une base contenant 4(s), 3(p0, 2(d0)) et 1(f0) orbitales de Slater donne 90% de l'énergie de corrélation.
    Abstract: Die verallgemeinerte Hartree-Fock Funktion eines Systems mit n Elektronen ist als die beste projizierte Slaterdeterminante, die aus vollständig allgemeinen Einelektronfunktionen gebaut ist (Löwdin, Phys. Rev. 97, 1509 (1955)). Die Konfigurationswechselwirkungsfunktion, die zu einer verallgemeinerten Hartree-Fock Funktion äquivalent ist, wird für den 1S Zustand eines Zweielektronenatoms diskutiert. Es wird gezeigt, dass in diesem Falle unendlich viele Lösungen des Variationsproblems existieren, die tiefere Energien als die gewöhnliche Hartree-Fock Funktion haben. Zwei Lösungsmethoden werden beschriebn. Mit einer Basis von 4(s), 3(p0), 2(d0) und 1(f0) Slaterorbitalen wird 90% der Korrelationsenergie des Heliumatoms im Grundzustand erhalten.
    Notes: The extended Hartree-Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97, 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the 1S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree-Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p0), 2(d0) and 1 (f0) Slater orbitals has produced 90% of the correlation energy.
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  • 42
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    International Journal of Quantum Chemistry 1 (1967), S. 451-461 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: The formalism of the LCAO—SCF—CO method is described. This method enables the theoretical study of conjugated periodic systems. In these systems some integrals of the SCF operator matrix elements are evaluated by a semi-empirical procedure.
    Abstract: Die LCAO—SCF—CO Methode für periodische, konjugierte Systeme wird beschrieben. Eine semi-empirische Methode für Berechnung der Integrale, die die Matrixelemente des SCF-Operators bilden, wird angegeben.
    Notes: On décrit le formalisme de la méthode LCAO—SCF—CO permettant d'étudier les propriétés des systèmes périodiques conjugés et un procédé semi-empirique pour évaluer les intégrales intervenant dans les éléments de matrice de l'operateur du champ autocohérent de ces systèmes.
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  • 43
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    International Journal of Quantum Chemistry 1 (1967), S. 427-450 
    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
    Description / Table of Contents: The LCAO—HCO method is described. Starting from classical procedures of quantum chemistry, this method enables the theoretical study of periodic systems. The explicit form of some properties is deduced in the Hückel approximation. This method is compared with the tight-binding approximation and applied to the study of polyenes, polyacenes, and graphite. Finally, the general validity of the process is discussed.
    Abstract: Die LCAO—HCO Methode wird beschreibt. Diese Methode ist von der gewöhnlichen Quantenchemischen Methoden inspiriert, und für das Studium periodischer Systeme konstruiert. Gewisse charakteristische Grössen werden in der Hückel-approximation in expliziter Weise abgeleitet. Die Methode wird an die “tight-binding approximation” verglichen und an Polyenen, Polyacenen, und Graphit angewendet. Die Gültigkeit der Methode wird diskutiert.
    Notes: On décrit la méthode des orbitales cristallines, combinaisons linéaires d'orbitales atomiques (LCAO—HCO), inspirée des procédés classiques de la chimie quantique et permettant d'étudier théoriquement les systèmes périodiques. On déduit la forme explicite de quelques grandeurs caractéristiques dans l'approximation de Hückel. La méthode est comparée à l'approximation dite des électrons “quasi-atomiques” et appliquée aux polyènes, aux polyacènes, et au graphite. La validité générale du procédé est discutée dans la conclusion.
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  • 44
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    International Journal of Quantum Chemistry 1 (1967) 
    ISSN: 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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  • 45
    ISSN: 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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  • 46
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On décrit la méthode de perturbation du premier ordre en 1/Z, de l'approximation Hartree-Fock généralisée pour les atomes à deux électrons. Plusieurs résultats imprévus en découlent: (a) on prouve qu'il faut développer les orbitales en puissances de Z-1/2 plutǒt qu'en puissances de Z-1; (b) on montre qu'on peut au premier ordre découpler la partie associée à l'approximation Hartree-Fock restreinte; les énergies du second ordre sont donc additives; (c) l'équation qui décrit “l'orbitale de corrélation” au premier ordre admet en générale d'une infinité de solutions de toutes symmétries angulaires; (d) “l'équation de corrélation” au premier ordre est une équation aux valeurs propres linéaire et homogène avec un potentiel non local. Elle contient un paramètre μ et une valeur propre ω(μ), qui peut être interprétée comme l'amplitude de probabilité et l'énergie d'un état virtuel de corrélation. L'énergie de corrélation au second ordre est 2μ2ω.On présente des solutions numériques des “orbitales de corrélations” premier ordre. L'énergie de corrélation approximative au second ordre est presque 90% de la valeur exacte.On décrit la méthode de perturbation du premier ordre en 1/Z pour le développement naturel et von obtient les équations intégro-différentielles couplées du premier ordre. On discute la relation étroite entre les “orbitales de corrélation” du premier ordre de la méthode Hartree-Fock généralisée et les “orbitales de corrélation” naturelles du premier ordre. Une comparaison des résultats numériques aux ceux de Kutzelnigg en confirme la ressemblance.
    Abstract: Die Störungstheorie erster Ordnung in 1/Z der verallgemeinerten Hartree-Fock Approximation für Zweielektronatome wird beschreibt. Mehrere unerwartete Resultate ergeben sich: (a) es wird gezeigt, dass die Orbitale in Potenzen von Z-1/2 eher als in Potenzen von Z-1 entwickelt müssen; (b) es wird gezeigt, dass der Korrelationsteil der Orbitale von dem Teil, der mit der beschränkten Hartree-Fock Approximation beigeordnet ist, losgekoppelt werden kann, so dass die Energien zweiter Ordnung additiv sind; (c) die Gleichung der “Korrelationsorbital” erster Ordnung hat unendlich viele Lösungen aller Winkelsymmertrien; (d) die Korrelationsgleichung erster Ordnung ist eine lineare, homogene Eigenwertgleichung mit einem non-lokalen Potential. Sie enthält ein Parameter μ und einen Eigenwert ω(μ), die als Wahrscheinlichkeitsamplitude und Energie eines virtuellen Korrelationszustands erklärt werden können. Korrelationsenergie zweiter Ordnung ist 2μ2ω.Numerische Lösungen für die Korrelationsorbitale erster Ordnung werden gegeben. Die approximative Korrelationsenergie zweiter Ordnung beträgt fast 90% des exakten Wertes.Die Störungstheorie erster Ordnung in 1/Z der natürlichen Entwicklung wird beschreibt und die gekoppelten Integro-Differentialgleichungen werden abgeleitet. Die nahe Benziehung zwischen den “Korrelationsorbitalen” erster Ordnung der verallgemeinerten Hartree-Fock-gleichungen und den “natürlichen Korrelationsorbitalen” erster Ordnung wird diskutiert. Die Ähnlichkeit wird durch Vergleichung der numerischen resultate mit den numerischen Resultaten Kutzelniggs bekräftigt.
    Notes: The first-order 1/Z perturbation theory of the extended Hartree-Fock approximation for two-electron atoms is described. A number of unexpected features emerge: (a) it is proved that the orbitals must be expanded in powers of Z-1/2, rather than in Z-1 as expected; (b) it is shown that the restricted Hartree-Fock and correlation parts of the orbitals can be uncoupled to first order, so that second-order energies are additive; (c) the equation describing the first-order correlation orbital has an infinite number of solutions of all angular symmetries in general, rather than only one of a single symmetry as expected; (d) the first-order correlation equation is a homogeneous linear eigenvalue-type equation with a non-local potential. It involves a parameter μ and an eigenvalue ω(μ) which may be interpreted as the probability amplitude and energy of a virtual correlation state. The second-order correlation energy is 2μ2ω.Numerical solutions for the first-order correlation orbitals, obtained variationally, are presented. The approximate second-order correlation energy is nearly 90% of the exact value.The first-order 1/Z perturbation theory of the natural-orbital expansion is described, and the coupled first-order integro-differential perturbation equations are obtained. The close relationship between the first-order extended Hartree-Fock correlation orbitals and the first-order natural correlation orbitals is discussed. A comparison of the numerical results with those of Kutzelnigg confirms the similarity.
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  • 47
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    International Journal of Quantum Chemistry 1 (1967), S. 493-519 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Le problème moléculaire de N électrons est reformulé à l'aide de la densité de particules et de son champ canonique conjugué. On emploie la représentation de Weyl des relations de commutation canoniques, et on introduit une fonctionnelle caractéristique du système moléculaire comme un valeur moyenne de la fonctionnelle de Weyl. On déduit l'équation Hamiltonienne de mouvement de la fonctionnelle caractéristique et on en discute l'approximation à cumulants. Dans cet article-ci on présente une discussion générale, indépendante du choix spécial de l'Hamiltonien.La représentation de la fonctionnelle de densité peut ětre considérée comme un pas vers une formulation d'une chimie quantique renormalisée. Les cumulants d'ordre inférieur de la fonctionnelle caractéristique sont accessibles aux mesures de précision effectives; d'autre part la plupart des résultats expérimentaux sont représentés correctement par une fonctionnelle caractéristique de type Gaussien. La signification des corrélations d'ordre supérieur n'est pas encore connue. On discute leur importance possible pour les systèmes biologiques et on pose la question à quel point la mécanique quantique est vérifiée expérimentalement pour les systèmes extrěmement complexes.
    Abstract: Das molekulare N-Elektronenproblem wird mit Hilfe des Teilchendichteoperators und seinem kanonisch konjugierten Feldoperator reformuliert. Die Weylsche Darstellung der kanonischen Vertauschungsrelationen wird benützt und ein charakteristisches Funktional des molekularen Systems wird definiert als Erwartungswert des Weylschen Funktionals. Die Hamiltonschen Bewegungsgleichungen für das charakteristische Funktional werden abgeleitet und ihre Kummulantennäherung wird diskutiert. Dieser erste Teil beschränkt sich auf eine allgemeine Diskussion, unabhängig von einer speziellen Wahl des Hamilton-operators.Diese Darstellung kann als erster Schritt zur Formulierung einer renormierten Quantenchemie betrachtet werden. Die Kumulanten tiefster Ordnung des charakteristischen Funktionals sind Präzisionsmessungen zugänglich und umgekehrt sind die meistem Experimente durch ein charakteristisches Funktional vom Gausschen Typus korrekt dargestellt. Die Bedeutung der Korrelationen höherer Ordnung ist weder theoretisch noch experimentell bekannt, ihre mögliche Bedeutung für biologische Systeme wird erwähnt. Die Frage der empirischen Verifikation der Quantenmechanik für äusserst komplizierte Systeme wird aufgeworfen.
    Notes: The molecular N-electron problem is formulated in terms of the particle density Q(r) = ∑σ(r - qn) and its canonically conjugated field. Weyl's representation of the canonical commutation relations is used and a characteristic functional of the molecular system is introduced as the expectation value of Weyl's functional exp {i(α, Q) + i(β, P)}. The Hamiltonian equation of motion for the characteristic functional is derived and its cumulant approximation is discussed. The first paper is restricted to a general discussion, independent of a special choice of the Hamiltonian.The density functional representation may be considered as a step towards a formulation of a renormalized quantum chemistry. The lowest order cumulants of the characteristic functional are accessible to actual precision measurements; on the other hand, most experiments are correctly represented by a characteristic functional of the Gaussian type. The significance of the higher order correlations is neither theoretically nor experimentally disclosed yet, their possible importance for biological systems is mentioned, and the question is raised of how far quantum mechanics is empirically confirmed for extremely complex systems.
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  • 48
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    International Journal of Quantum Chemistry 1 (1967), S. 535-559 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On définie la notion d'Hamiltonien localement dégénéré. On démontre qu'un tel Hamiltonien est, par rapport à un nombre quantique particulier, dégénéré dans un seul niveau. On étudie quelques exemples de systèmes d'une seule particule et on les compare au problème de Kepler. On trouve dans ces exemples que le niveau dégénéré se trouve à la valeur limite à grandes distances de l'énergie potentielle. On déduit la condition d'existence et les propriétés de ces états-ci. On démontre aussi que, pour des états pareils, certains opérateurs peuvent avoir des fonctions propres en commun avec l'Hamiltonien. Pour cette raison on les appelle constantes du mouvement locales. Comme les constantes du mouvement ordinaires, elles simplifient le problème des valeurs propres. En particulier on étudie par cette méthode-ci le potentiel q/r2. Finalement on discute l'application des résultats obtenus à la diffusion de résonance et au calcul de nombre des états liés.
    Abstract: Es wird der Begriff eines lokal entarteten Hamilton-Operators definiert. Es wird bewiesen, dass ein solcher Hamilton-Operator, mit Rücksicht auf eine spezielle Quantenzahl, nur in einem einzigen Niveau entartet ist. Einige Beispiele von Einteilchensystemen werden untersucht und mit dem Keplerproblem verglichen. In diesen Beispielen befindet sich das entartete Niveau an dem Grenzwert für grosse Abstände der potentiellen Energie. Die Existenzbedingungen und die Eigenschaften dieser Zustände werden abgeleitet. Es wird auch bewiesen, dass für solche Zustände, gewisse Operatoren mit dem Hamilton-Operator gemeinsamen Eigenfunktionen haben können. Aus diesem Grund werden sie als lokale Bewegungskonstanten bezeichnet. Wie gewöhnliche Bewegungskonstanten können sie das Eigenwertproblem vereinfachen. Insbesondere wird das Potential q/r2 mit diesen Methoden studiert. Schliesslich werden die Anwendungen der Resultäte auf Resonanzstreuung und auf die Berechnung der Anzahl der gebundenen Zustände angedeutet.
    Notes: The concept of a locally degenerate Hamiltonian is defined. It is shown that such a Hamiltonian is, with respect to a particular quantum number, degenerate in a single level only. Some examples of single-particle systems suggested by a study of the stereographic projection are examined, a comparison being made with the Kepler problem. It is found, in these examples, that the degenerate level lies at the limiting value of the potential energy at large distances and the condition for the existence and the properties of these states are deduced. It is also shown that for such states certain operators may have eigenfunctions in common with the Hamiltonian and for this reason they are called local constants of the motion. Like ordinary constants of the motion, they help to simplify the eigenvalue problem and, in particular, the singular inverse square law potential is studied by this approach. Finally, the application of the results to resonance scattering (by bound states near the continuum) and to the calculation of the number of bound states is indicated.
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  • 49
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    International Journal of Quantum Chemistry 1 (1967), S. 561-575 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On étudie la structure électronique de l'adénine, de la guanine, de la cytosine, de la thymine et de l'uracile dans leurs états fondamentaux, ionisés, excités singulets et triplets, par les méthodes SCF—CI et SCF “couche ouverte”. Les états singulets correspondent d'une façon satisfaisante aux maxima des bandes d'absorption. La différence des énergies des deux premiers états singulets de l'adénine est très petite. La méthode “couche ouverte” donne le měme potentiel d'ionisation relatif que la méthode SCF. Les énergies des états triplets coincident presque dans les deux méthodes. Les énergies de transition au premier état triplet des pyrimidines sont plus grandes que celles des purines. L'énergie de séparation singulet-triplet des purines s'accorde aux valeurs expérimentales.
    Abstract: Die π-Elektronstruktur des Adenins, Guanins, Cytosins, Thymins und Uracils in ihren Grundzuständen, ionisierten Zuständen, angeregten Singulett- und Triplett-Zuständen wird vermittelst der SCF—CI und der SCF “offene Schale”-Methoden untersucht. Die Singulettzustände stimmen mit den Maxima der Absorptionsbanden gut überein. Die Energiedifferenz zwischen den zwei ersten Singulettzustände des Adenins ist sehr klein. Die “offene Schale”-Methode ergibt dieselbe relative Ionisierungsspannung als die SCF-Methode. Die Energien der Triplettzustände fallen in den beiden Methoden beinahe zusammen. Die Übergangsenergien zum ersten Triplett-zustand der Pyrimidine sind grösser als die der Purine. Die Singulett-Triplett-Trennungsenergie der Purine stimmt mit den experimentellen Tatsachen überein.
    Notes: The π-electron structure of adenine, guanine, cytosine, thymine and uracil in their ground, ionized, singlet and triplet excited states are investigated by means of the SCF—CI and SCF open-shell methods. The calculations for singlets fit the maxima of the absorption bands well. The energy difference between the first and the second singlet states of adenine is found to be very small. The open-shell method leads to the same relative ionization potential as does the SCF (with the integrals empirically corrected). The calculated energies of the triplet states almost coincide in the SCF open-shell and the SCF—CI approximation. The calculated transition energies to the first triplet state of the pyrimidines are higher than in the case of the purines. The value of the singlet-triplet separation energy of purines is in agreement with experimental data.
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  • 50
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    International Journal of Quantum Chemistry 1 (1967), S. 591-594 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Employant une fonction d'onde d'électrons libres on a évalué la section efficace d'excitation au premier état excité et celle d'ionisation du benzène dans une collision inélastique avec des électrons rapides. Dans le procès d'ionisation la section efficace est maximum quand l'électron secondaire quitte la molécule avec une énergie cinétique d'environ 3 eV. Si l'énergie de l'électron incident dépasse 20 eV la section efficace d'ionisation est plus grande que celle d'excitation et vice versa.
    Abstract: Mit einer Freielektronenfunktion wird der Wirkungsquerschnitt für die Anregung des ersten angeregten Zustands und der für die Ionisierung des Benzols abgeschätzt. In dem Ionisierungsprozess hat der Wirkungsquerschnitt ein Maximum, wenn das sekundäre Elektron das Molekül mit einer kinetischen Energie von ungefähr 3 eV verlässt. Wenn die Energie des einfallenden Elektrons grösser als 20 eV ist, wird der Querschnitt für Ionisierung grösser als der für Anregung, und umgekehrt.
    Notes: Using a free-electron wave function the cross section for the excitation of the first excited state and that for the ionization of benzene in the inelastic collision with fast electrons have been estimated. In the ionization process the cross section has been found to be maximum when the secondary electron moves away with a kinetic energy of about 3 eV. For incident-electron energy above 20 eV the cross section for ionization is larger than that for excitation, while below it the reverse is the case.
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  • 51
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    International Journal of Quantum Chemistry 1 (1967), S. 605-613 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: A time-saving way of programming an SCF method for molecules (SCF—MO—LCGO method) is proposed, which is based on an economic way of handling the two-electron-multicenter integrals.
    Abstract: On présente un programme efficace pour des calculs SCF moléculaires, dont l'efficacité dépend d'un traitement rationnel des intégrales à deux centres.
    Notes: Es wird eine rechenzeitsparende Programmierung eines SCF-Verfahrens für Moleküle (SCF—MO—LCGO-Verfahren) angegeben, die auf einer rationellen Behandlung der Zweielektronen-Mehrzentrenintegrale beruht.
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  • 52
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    International Journal of Quantum Chemistry 3 (1969), S. 749-749 
    ISSN: 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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  • 53
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    International Journal of Quantum Chemistry 3 (1969), S. 751-751 
    ISSN: 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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  • 54
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    International Journal of Quantum Chemistry 3 (1969), S. 767-780 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The explicit form of a projection operator constructed from a linearly dependent set is found. The relationships with canonical orthonormalization and with the cofactor matrix of the set's metric matrix are discussed. Similar expressions are obtained for the inner projection of a positive definite operator using a linearly dependent set.
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  • 55
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    International Journal of Quantum Chemistry 3 (1969), S. 851-871 
    ISSN: 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: Potential curves that show the energy dependence of hydrogen bonds between carbonyl and hydroxyl groups on the O—H bond length, on the distance between the molecules, and on the angle between the functional groups have been calculated with the CNDO/2 method. The results are presented for a small model system-formaldehyde/water - and for the dimer of formic acid. Good agreement is obtained with the available experimental data. The influence of the molecular geometry on the calculated results is discussed.
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  • 56
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    International Journal of Quantum Chemistry 3 (1969), S. 889-891 
    ISSN: 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: 2-butene has been investigated for different nuclear positions taking all 32 electrons into account, using the SCF-MO-LC(LCGO) method. The calculations show that the energy of the trans-form is 1.1 kcal/mol lower than that of the cis-form. The potential curve between these two forms is shown graphically. The ionization energy was estimated to be 9.0 eV.
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  • 57
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    International Journal of Quantum Chemistry 3 (1969), S. 969-981 
    ISSN: 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 is given of the current status of our work on electron transport properties and Fermi surfaces in simple metals. A simple classical model is proposed to extend existing theory to account for the effects of electron-impurity interactions on the behavior of magnetoacoustic absorption and the size and shape of the Fermi surface in the alkali metal potassium. The theoretical prediction is compared with measurements of the magnetoacoustic absorptionand Fermi surface diameters in potassium crystals of different impurity levels. An attempt is made to explain, on the basis of the theory of electron-impurity interactions, the decrease by 9% in the Fermi diameter and the departure by 53% in the phase factors of the impure potassium crystal. The results are compared with observations on a zone refined potassium crystal which satisfies the nearly-free-electron model.
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  • 58
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    International Journal of Quantum Chemistry 3 (1969), S. 945-968 
    ISSN: 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 long-range interaction energies for different dissociation products of the HeH+ molecule have been calculated using the Rayleigh-Schrödinger perturbation theory up to the third order in the energy. The calculations were carried out for the ground state (He(ls2) + H+), the first excited state (H(ls) + He+(ls)) and the second excited state Π(H(2pπ) + He+(ls)). The unperturbed states correspond to the dissociation products denoted in parentheses. Assuming the overlap to be zero, expanding the interaction potential in the inverse powers of the internuclear distance R and using the familiarly known perturbation-variational technique, the coefficients of various powers of R-1 in the energy expansion were evaluated. They correspond to different multipole-multipole interactions. The potential energy curves of all three states under consideration were calculated for large values of R. Also calculated were the multipole polarizabilities of the hydrogen atom in the is and 2pπ states and of the helium atom in the ground state.
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  • 59
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    International Journal of Quantum Chemistry 3 (1969), S. 1027-1043 
    ISSN: 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 wave function defining a quantum-mechanical system is considered as the Laplace transform of some distribution and the consequent form of the Variational Principle derived; an integral equation defines the eigenfunctions of a certain subclass. The model of the hydrogen-like atom is used to test the theory; the eigenfunctions and associated energy levels of the ground and excited states are obtained for arbitrary values of the orbital quantum number.
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  • 60
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    International Journal of Quantum Chemistry 3 (1969), S. 1061-1064 
    ISSN: 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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  • 61
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    International Journal of Quantum Chemistry 3 (1969), S. 795-822 
    ISSN: 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 correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented. The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the Clebsch-Gordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applied to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the Appendix.
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  • 62
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    International Journal of Quantum Chemistry 1 (1967), S. 637-640 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: The (Li2H)+ has been investigated ab initio in the linear configuration, with the H atom in the middle of the system, for five different distances RLiH, taking all six electrons into account, using the Allgemeines Programmsystem/SCF—MO—LC(LCGO) Verfahren. A bond distance RLiH of 3.14 a.u., a total energy of -15.289 a.u., and an ionization energy of 15.1 eV were found. Comparing the results of SCF investigations, the formation energy of (Li2H)+ from LiH and Li+ was computed to be 59.7 kcal/mole (2.58 eV). Using the energy curve near the minimum, a force constant for the symmetric vibration of k = 0.13777 × 106 dyn/cm and a frequency ω = 577.9 cm-1 were found.
    Abstract: En tenant compte de tous les six électrons on a fait des calculs pour le (Li2H)+ dans le cas linéaire pour cinq distances différentes RLiH et avec l'atome H au milieu. On trouve au minimum une énergie totale de -15,289 u.a. et une distance de liaison RLiH de 3,14 u.a. L'énergie d'ionization correspondante est 15,1 eV. L'énergie de formation du LiH et du Li+ a été obtenue en comparant les calculs SCF des trois systèmes, ce qui donne 59,7 kcal/mole (2,58 eV). La courbe de potentiel près du minimum donne une constante de force de vibrations symmétriques de 0,13777 × 106 dyn/cm, ce qui correspond à une fréquence de 577,9 cm-1.
    Notes: Das (Li2H)+ wurde unter Berücksichtigung aller 6 Elektronen mit dem Allgemeinen Programmsystem/SCF—MO—LC(LCGO) Verfahren im linearen Fall für 5 verschiedene Abstände RLiH berechnet, wobei das H-Atom in der Mitte lag. Es ergab sich im Minimum eine Gesamtenergie von -15,289 a.E. der Bindungsabstand RLiH berechnet sich zu 3,14 a.E. Die Ionisierungsenergie beträgt dabei 15,1 eV. Die Bildungsenergie aus LiH und Li+ ergibt sich beim Vergleich der SCF-Rechnungen an den beteiligten Systemen zu 59,7 kcal/mol (2,58 eV). Aus der Potentialkurve in der Nähe des Minimums berechnet sich die Kraftkonstante der symmetrischen Schwingung zu k = 0,13777 × 106 dyn/cm, aus der eine Frequenz ω = 577,9 cm-1 resultiert.
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  • 63
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    International Journal of Quantum Chemistry 3 (1969), S. 25-32 
    ISSN: 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 calculating wave functions for an electron-nucleon system by a variational method originally suggested by Born and Oppenheimer [1] is rigorously investigated. As an application we sketch the calculation of a simple nonadiabatic wave function for the system.
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  • 64
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    International Journal of Quantum Chemistry 3 (1969), 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: An adiabetic theory of spin lattice relaxation is proposed. It is shown that if one takes account of the adiabatic adaptation of the electrons to the motion of the ionic complex the motor of the relaxation is not the crystalline potential modulation but the fluctuation of the effective magnetic field produced by the complex near the paramagnetic system.
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  • 65
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    International Journal of Quantum Chemistry 3 (1969), S. 1069-1070 
    ISSN: 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
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum theory of the Faraday effect or magnetic rotatory power is set up for diamagnetic molecules and is based upon a variation-perturbation method which, unlike the usual Dirac perturbation theory, needs only the knowledge of the wave function ψ0(0) of the ground state of the non-perturbed molecule. The principle of this theory includes in the expression of the perturbed wave function, vectors which characterize the contribution of the different fields of perturbation. The quantities which descríbe the Faraday effect, obtained from the calculation of the electric and magnetic macroscopic dipole moments, are expressed from ψ0(0) and the vectors precedently introduced. They are determined by a variation calculus.
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  • 67
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Les réactions de la 2-chloropurine et d'autre bases, catalysées par la xanthine oxidase, ont été étudiées avec des méthodes différentes basées sur l'idée des orbitales molécularies, telles que HMO, ω-SCF—HMO, et PPP. Ces études not démontré l'importance des indices de réactivité électronique pour comprendre les réactions d'enzymes. De plus il paraît possible de prédire la spécificité de l'enzyme d'une analyse systématique de la différence entre les sites de réactions prédits et observés dans des substrats avec des substituants 2- et 8-oxy.Les concepts de densité d'obritale de frontière, de superdélocalisabilité et d'énergie de localisation se sont avérés tres utiles. Les Méthodes différentes ont donné en général dees résultats consistants.
    Abstract: Ein genauses Studium der durch Xanthine-Oxidas katalysierten Reaktionen von 2-Chloropurin und anderen Basen mittels verschiedenen MO-Methoden, wie HMO, ω-SCF—HMO, PPP, zeigt dass die Enzymreaktionen in der Sprache von elektronischen Reaktivitätsindizes beschrieben werden können. Es scheint möglich das Enzymspezifizität von einer systematischen Analysis der Verschiedenheit zwischen theoretisch berechnbeten und observierten Reaktionslagen in Substraten Mit 2- und 8-oxy Substituenten vorherzusagen.De Regriffe der Grenzorbitaldichte, des Superdelokalisabilitäts und der Lokalisierungsenergie sind sich sehyr nützlich rewiesen. Verschiedence MO-Methoden gaben im allgemeinen übereinstimmende Resultate.
    Notes: A detailed study to the xanthine oxidase-catalyzed reactions of 2-chloropurine and other substrate bases with various molecular-orbital techniques such as HMO, ω-SCF—HMO, and ppp semiempirical SCF—LCAO—MO has shown that the enzyme reactions can be understood in terms of electronic reactivity indices. Furthermore, it appeared possible to suggest the enzyme specificity from a systematic analysis of discrepancy between mo theoretically predicted and observed reaction sites in substrates with 2- and 8-oxy substituents. In other words, the discrepancy does not necessarily indicate the failure of the MO melthodes for such substrates, but it is possible to utilize the result in correlating with binding specificity of the ES complex. This has been done specifically for 2-chloropurine.Among several electronic reacxtivity indices, frontier orbital density, superdelocalizability, and localization energy have been proved to be very useful. Diferent MO methods gave, in general, consistent results.
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  • 68
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On a examiné l'application de la méthode de Pariser-Parr-Pople aux systèmes avec des liaisons d'hydrogène. La courbe de potentiel pour le mouvement du proton a été calculée. La validité des résultats obtenus a été discutée.
    Abstract: Es wurde die Anwendung der Pariser-Parr-Pople Methode auf Systemen mit Wasserstoffbrücken untersucht. Die Potentialkurven für die Bewegung des Protons wurde berechnet und die Zuverlüssigkeit der erhaltenen Resultate diskutiert.
    Notes: In this work, the application of the Pariser-Parr-Pople scheme to hydrogen-bonded systems containing π electrons has been examined. The potential energy curves for the movement of the hydrogen atom in the bond have been calculated, and the reliability of the results obtained from this method, applied in this manner, have been discussed.
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  • 69
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    International Journal of Quantum Chemistry 2 (1968), S. 5-21 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On a étudié la structure électronique du cation de la proflavine par la méthode SCF-ASMO-CI avec les approximations de Pariser-Parr-Pople. On démontre que la bande à 445 mμ peut ětre attributée à la transition 1A1 → 1B1 polarisée le long de l'axe long de la molécule. Les bandes au voisinage de 260 mμ, qui sont composées de trois bandes d'absorption, sont attribuées à l'essai aux transitions 1A1 → 1B1, 1B1 → 1B1, et 1A1 → 1A1.Il est bien connu que la dimérisation des cations des acridines colorées varie avec la concentration. Les distances intermoléculaires dans ces dimères ont été estimées des déplacements des bandes provenant de la formation des dimères. On démontre que la contribution essentielle de l'interaction moléculaire est l'interaction électrostatique dipǒle-dipǒle.En employant ces résultats-ci on discute certains modèles pour la liaison entre l'ADN et les acridines colorées.
    Abstract: Die Elektronstruktur des Proflavinkations wurde mit der SCF-ASMO-CI Methode und den Pariser-Parr-Pople Approximationen untrsucht. Es wird gezeigt dass das Band an 445 mμ dem 1A1 → 1B1-Übergang, der längs der Molekülachse polarisiert ist, zugeschrieben werden kann. Die Bänder in der Nachbarschaft von 260 mμ, die aus drei Absorptionsbänder bestehen, werden versuchsweise den 1A1 → 1B1, 1A1 → 1B1, und 1A1 → 1A1-Übergänge zugeschrieben.Es ist wohlbekannt, dass die Dimerisation der Akridinfarben mit det Konzentration wechselt. Die Intermolekularabstände in diesen Dimeren wurden von den Bandenverschie-bungen abgeschätzt. Es wird gezeigt, dass der Hauptbeitrag zur molekularen Wechselwirkung die elektrostatische Dipol-Dipolwechselwirkung ist.Von der Standpunkt dieser Resultate aus, wurden gewisse Modellen für die Bindung zwischen die DNA-Moleküle und die Akridin-Farben diskutiert.
    Notes: The electronic structure of the proflavine cation is studied by the SCF-ASMO-CI method using the Pariser-Parr-Pople approximations. It is shown that the band at 445 mμ may be assigned to the 1A1 → 1B1, transition polarized along the long axis of the molecule. The bands in the neighbourhood of 260 mμ, which are composed of three absorption bands, are tentatively assigned to the 1A1 → 1B1, 1A1 → 1B1, and 1A1 → 1A1 transitions, respectively, in order of decreasing wavelength. The spectrum of the acridine orange cation may be understood to have the same assignment as that of the proflavine cation.The acridine dye cations are well known for their dimerization with concentration. The intermolecular distances in these dimers are estimated from the band shifts due to the formation of dimers, using the exciton theory. The main contribution to the molecular interaction is shown to be the electrostatic dipole-dipole interaction.Since the first excitation band of the dye molecule which exhibits a remarkable change due to the formation of the DNA-acridine dye complex, is suggested to be polarized along the long axis, preference of the outside stacking or the intercalation model is qualitatively discussed from the spectral shift of the acridine dye bound to the DNA, assuming simple models.
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    International Journal of Quantum Chemistry 2 (1968), S. 55-67 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On propose une approximation pour la solution du problème SCF pour les systèmes à couches incomplètes. On donne les équations et on discute les résultats.
    Abstract: Eine Näherung zur Lösung des SCF-Verfahrens für Systeme mit räumlich ungepaarten Elektronen wird vorgeschlagen. Die Gleichungen werden hergeleitet und die Ergebnisse diskutiert.
    Notes: An approximate solution of the SCF problem for systems with unpaired electrons (open-shell) is proposed. The equations are given and the results are discussed.
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  • 72
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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
    Description / Table of Contents: La méthode AMO, modifiée à l'aide d'un “paramètre” d'échelle a été appliquée à l'état 1sσ2pσ1∑u+ de la molécule d'hydrogène. On emploie une méthode pour étendre le domaine du “paramètre de mélange” dans le plan complexe. Tous les paramètres employés ont été complètement variés. Pour les grandes séparations internucléaires on obtient une amélioration considérable de l'énergie totale. Les résultats obtenus ont été comparés aux ceux de Kolos et Wolniewicz en fonction de la distance internucléaire R. Pour R = 12 u.a. la différence entre les deux énergies n'est que 18% de la différence correspondante pour R = 2.43 u.a. Pour la distance internucléaire à l'équilibre on trouve 2.140 u.a. ce qui n'est pas en très bon accord avec la valeur 2.429 u.a., obtenue par les deux autres auteurs.Dans la limite des atomes séparés l'état en question ne donne pas H+ + H-, bien que le caractère ionique de la fonction d'onde soit dominant dans la région 3 ≦ R ≦ 8 u.a.
    Abstract: Es wurde eine Version der AMO-Methode mit einen Koordinatenstreckungsparameter auf den 1sσ2pσ1∑u+ Zustand des Wasserstoffmoleküls angewendet. Alle eingeführten Parameter wurden vollstündig variiert. Für grosse Kernabstände, R, wurde dadurch eine ansehnliche Verbesserung der berechneten Energiewerte erhalten. Die hier berechnete Potentialkurve wurde mit der von Kolos und Wolniewicz berechneten verglichen. Für r = 12 a.E. ist die Energie-differenz nur 18% von der für R = 2.43 a.E. erhaltenen. Für den Gleichgewichtskernabstand gab unsere Berechnung 2.140 a.E., was in schlechter Übereinstimmung mit dem von Kolos und Wolniewicz erhaltenen Abstand, 2.429 a.E. steht.In der Grenze getrennter Atome wurde der hier behandelte Zustand nicht in H+ + H- dissoziiert, obgleich der Ionencharacter der Wellenfunktion im Intervall 3 ≦ R ≦ 8 a.E. dominierend sei.
    Notes: A scaled version of the AMO method is applied to the 1sσ2pσ 1∑u+ state of the hydrogen molecule. A method to extend the domain of the mixing parameter λ to the whole complex plane is described and applied in the present calculation. All the parameters introduced have been varied completely. A considerable improvement in the computed energy values is found for large internuclear separations R. The comparison between our potential energy curve and the accurate curve calcualted by Kolos and Wolniewicz is studied and, for example, for R = 12 a.u. the energy difference is only 18% of that for R = 2.43 a.u. The equilibrium separation is found to be 2.140 a.u. in poor agreement with 2.429 a.u. obtained by the previously mentioned authors.In the separated atom limit, the state under consideration does not dissociate into H+ + H-, although the ionic character of the wave function is dominating in the region 3 ≦ R ≦ 8 a.u. The connections with earlier calculations and methods, especially the scaled version of the MO-LCAO approximation, are also pointed out and discussed.
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  • 73
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Des méthodes différentes pour le calcul des énergies d'interaction intermoléculaire ont été comparées dans une application a des configurations de type ADN à deux chaines. L'interaction totale a été décomposée en parties différentes pour permettre des combinaisons optimales des méthodes existantes. On propose une méthode nouvelle pour calculer l'interaction de dispersion entre les électrons σ d'une molécule et les électrons π d'une autre. Les résultats ont été condensés dans un grand nombre de tablaux.
    Abstract: Methoden für die Berechnung intermolekulare Wechselwirkungsenergien werden in Anwendungen auf Konfigurationen von DNA-Typ zwischen Basen verglichen. Die Gesamtwechselwirkung wird in solche Teilen zerlegt, die optimale Kombinationen der existierenden Methoden gestatten. Es wird eine neue Methode für die Berechnung der Dispersionswechselwirkung zwischen den σ-Elektronen eines Moleküls und den π-Elektronen eines anderen vorgeschlagen. Die Resultate sind in Tabellen zusammengefasst.
    Notes: Methods for calculating intermolecular interaction energies are evaluated in a specific application to double-stranded DNA-like configurations between bases. The total interaction is decomposed in such a way, that existing methods can be hybridized so that each method can be utilized to its best advantage. In addition, a new method is suggested for the computation of the dispersion interaction between the σ-electron system of one molecule and the π-electron system of the other. Results of various approaches applied to base pairs and double-stranded dimers are summarized and compared in a number of tables.
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  • 74
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 2 (1968), S. 333-339 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Une méthode qui converge rapidement pour l'état fondamental de l'atome de hélium, a été appliquée aux états excités S. Cette méthode est basée sur un développement de la fonction d'onde en puissances de \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {r_1^2 + r_2^2} $\end{document}, In (r12 + r22), \documentclass{article}\pagestyle{empty}\begin{document}$ w = r_{12} /\sqrt {r_1^2 + r_2^2} $\end{document}. Des charges nucléaires effectives différentes ont été employées pour les deux électrons. Des résultats très satisfaisants ont été obtenus pour les valeurs moyennes de plusieurs opérateurs.
    Abstract: Eine Methode, die sehr schnell für den Grundzustand des Helium-atoms konvergiert, wurde zu den angeregten S-Zuständen ausgedehnt. Diese Methode ist auf eine Entwicklung der Wellenfunktion in Potenzen von \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {r_1^2 + r_2^2} $\end{document}, In (r12 + r22), \documentclass{article}\pagestyle{empty}\begin{document}$ w = r_{12} /\sqrt {r_1^2 + r_2^2} $\end{document} basiert. Verschiedene effektive Kernladungen wurden für die zwei Elektronen benützt. Sehr befriedigende Resultate wurden für die Erwartungswerteverschiedener Operatoren erhalten.
    Notes: A rapidly convergent method, which has previously been applied to the ground state of the helium atom, has been extended to excited S states. This method is based on an expansion of the wave function in powers of \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {r_1^2 + r_2^2} $\end{document}, ln (r12 + r22), \documentclass{article}\pagestyle{empty}\begin{document}$ w = r_{12} /\sqrt {r_1^2 + r_2^2} $\end{document}. Different effective nuclear charges are used for the inner and the outer electrons. Very satisfactory results are obtained for expectation values of various operators.
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  • 75
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    International Journal of Quantum Chemistry 2 (1968), S. 349-357 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Le nombre total d'associations atomiques différentes pour une molécule à N atomes est plus petit qu'un nombre AN (obtenu si tous les atomes sont différents) et plus grand qu'un nombre PN (obtenu si tous les atomes sont identiques). PN peut ětre calculé d'un problème classique de la théorie des nombres. AN peut ětre réduit à une certaine expression qui peut ětre évaluée à l'aide du langage non-numérique FORMAC. De la relation PN ≦ 2N-1 ≦ AN on obtient une estimation approximative de l'ordre de grandeur des nombres cherchés. Le nombre Z(G)N de toutes les associations atomiques de grade (nombre “d'unions partielles”) G pour N atomes peut ětre calculé à l'aide d'une formule récursive.
    Abstract: Die Zahl sämtlicher verschiedener Atomassoziationen für ein N-atomiges Molekül liegt zwischen einer unteren Schranke PN (alle Atome identisch) und einer oberen Schranke AN (alle Atome verschieden). Zur Berechnung von PN kann ein klassisches zahlentheoretisches Problem herangezogen werden. AN kann als ein Operator-Ausdruck dargestellt werden, der mit einem einfachen FORMAC-Program ausgewertet wird. Es gilt PN ≦ 2N-1 ≦ AN, was einen ungefähren Eindruck von den zu erwartenden Grössenordnungen gibt. Die Zahl Z(G)N aller Atomassoziationen von N Atomen des Grades (Zahl der “Teil-vereinigungen”) G kann mit einer Rekursionsformel berechnet werden.
    Notes: The total number of different possible atomic associations of an N-atomic molecule lies between a value PN (all N atoms identical) and AN (all atoms different). PN may be obtained reducing the problem to a classical problem in number theory. AN may be given as an operator expression which can be evaluated using the non-numerical programming language FORMAC. The relation PN ≦ 2N-1 ≦ AN gives a rough estimate for the orders of magnitude to be expected. The number Z(G)N of all atomic associations of grade (number of “partial unions”) G for N atoms can be computed using a recursive formula.
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  • 76
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    International Journal of Quantum Chemistry 2 (1968), S. 359-369 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On fait un commentaire sur un développement multipolaire de la force à longue portée entre deux atomes d'hydrogéne, obtenu antérieurement. L'énergie de perturbation du second ordre sans échange, est calculée exactement dans le cadre de l'approximation de Unsöld. On traite aussi deux atomes de hélium ainsi que d'autres interactions d'électrons de type s. On propose une méthode approximative pour estimer la force interatomique entre deux atomes en général.Es wurde eine Bemerkung über eine vorher erhaltene Multipolentwicklung der zwischen-atomaren Kraft zwei entfernter Wasserstoffatomen gemacht. Die Störungsenergie zweiter Ordnung ohne Austausch wurde im Rahmen der Unsöldapproximation genau ausgewertet. Eine Erweiterung wurde an Heliumatome und andere s-Elektronwechsel-wirkungen gemacht. Eine annähernde Methode für die Abschätzung der interatomaren Kraft zwischen zwei Atomen wird vorgeschlagen.
    Notes: A comment is made on the multipolar expansion formula of the long-range force between hydrogen atoms previously obtained. The second-order perturbation energy neglecting exchange in the framework of the Unsöld approximation is evaluated exactly. An extension is made to helium atoms, and to other s-electron interactions. An approximate method is suggested to estimate the interatomic force between two atoms in general.
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  • 77
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    International Journal of Quantum Chemistry 2 (1968), S. 391-396 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: La courbe de potentiel pour l'état 1s2s 3∑g+ de la molécule d'hydrogène a été calculée dans l'approximation AMO à l'aide d'un facteur de “scaling”. On note des déviations d'une courbe ordinaire. Les résultats présentés ici sont en meilleur accord avec les données expérimentales que ceux de l'état 1sσ2pσ 1∑u+, étudié dans un article antérieur.
    Abstract: Die Potentialkurve des 1s2s 3∑g+ Zustands des Wasserstoffmoleküls wurde in der AMO-Annäherung berechnet. Abweichungen von einer gewöhnlichen Potentialkurve wurden bemerkt. Die Übereinstimmung mit den Messergebnissen ist für den 1s2s 3∑g+ Zustand besser als für den in einer vorläufigen Abhandlung berechneten 1sσ2pσ 1∑u+ Zustand.
    Notes: The potential energy curve for the 1s2s 3∑g+ state of the hydrogen molecule is calculated in a scaled version of the AMO approximation. Deviations from a simple potential curve occur. The agreement with experimental data is found to be better for the present state than for the 1sσ2pσ 1∑u+ state studied in a previous paper.
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  • 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
    Description / Table of Contents: Des expressions analytiques des facteurs de diffusion des rayons x et des électrons pour un système atomique ont été deduites dans le cas où la fonction d'onde du système est écrite comme une somme de déterminants de Slater de spin-orbitales. La partie radiale d'orbitale est développée en termes d'orbitales de type Slater (STO). Les expressions ainsi obtenues ont été employées pour calculer les facteurs de diffusion cohérente et incohérente des rayons x et des électrons, ainsi que les intensités pour tous les atomes neutres jusqu'au krypton (Z = 36) et pour quelques ions positifs et négatifs d'interět chimique. Les résultats obtenus ont été employés pour examiner la valeur des fonctions d'onde de Hartree-Fock pour le calcul des “propriétés à un électron” des systèmes atomiques à plusieurs électrons.
    Abstract: Analytische Ausdrücke für die Röntgenstrahl- und Elektronenstreuungsfaktoren für ein atomares System wurden für Wellenfunktionen die als eine Summe von Slaterdeterminanten von Spinorbitalen geschrieben sind hergeleitet. Das Radialteil der Orbitalen wurde als eine Summe von Slatertyporbitalen (STO) geschrieben. Die so herge-leiteten Ausdrücke wurden für die Berechnung der Streuungsfaktoren koherenter und inkoherenter Röntgenstrahlen und Elektronen, als auch Intensitäten für alle neutrale Atome bis zu Krypton (Z = 36) und für einige positiven und negativen Ionen chemisches Interesse angewendet. Die erhaltenen Resultate wurden für die Prüfung der Güte der Hartree-Fock-Wellenfunktionen für die Berechnung “Ein-Elektron-Eigenschaften” von Viel-elektronenatome benutzt.
    Notes: Analytical expressions are developed for the x-ray and electron scattering factors for a many-electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater-type orbitals (STO's). The expressions so developed have been used to calculate the coherent and incoherent x-ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree-Fock wave functions for the evaluation of “one-electron properties” of many-electron atomic systems.
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  • 79
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    International Journal of Quantum Chemistry 2 (1968) 
    ISSN: 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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  • 80
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: En mécanique quantique des systèmes à plusieurs particules il est très important de distinguer entre états à couches complètes et états à couches incomplètes, cela en particulier si l'on s'intéresse au problème de la corrélation. Les définitions habituelles permettent une telle classification seulement dans le cas des états pour lesquels une description par un modèle à particules indépendantes est acceptable. On propose ici une classification dans le cadre d'une mécanique quantique rigoureuse, indépendante d'un modèle quelconque. On établit une distinction entres états à couches complètes et plusieurs sortes d'états à couches incomplètes. On formule des conditions suffisantes, permettant de reconnaǐtre des états à couches complètes, en fonction des invariants unitaires des matrices-densité à une particule.
    Abstract: In der Quantentheorie der Mehrteilchensysteme ist es wichtig-insbesondere im Hinblick auf das Korrelationsproblem-zwischen Zuständen mit offenen und solchen mit abgeschlossenen Schalen zu unterscheiden. Die üblichen Definition für diese beiden Arten von Zuständen sind aber nur für solche Zustände sinnvoll, die sich durch ein Modell der unabhängigen Teilchen beschreiben lassen. Hier werden dagegen im Rahmen einer strengen quantenmechanischen Beschreibung Definitionen angegeben, die unabhängig von irgendwelchen Modellvorstellungen sind. Man kann zwischen “Zuständen mit abgeschlossenen Schalen” und verschiedenen Typen von “Zuständen mit offenen Schalen” unterscheiden. Hinreichende Kriterien, ausdrückbar durch unitäre Invarianten der Einteilchendichtematrix, für “Zustände mit abgeschlossenen Schalen” werden angegeben.
    Notes: The distinction between open- and closed-shell states is quite important in few-particle quantum mechanics-especially in view of the correlation problem. The current definitions of such states and of shells in general are, however, only meaningful if one can assume that the independent particle model is a valid description of the state under consideration. Definitions are given in terms of rigorous quantum-mechanical concepts which allow a classification of states irrespective of any model assumptions. Closed-shell states and different types of open-shell states are distinguished. Sufficient criteria for a state to be a closed-shell state are derived in terms of unitary invariants of the one-particle density matrix of this state.
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  • 81
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Dans le premier article de cette série nous avons développé une classification rigoureuse d'états de type couche complète et incomplète. Dans le présent article nous appliquons cette méthode aux états atomiques, qui peuvent être classifiés dans la limite Z → ∞ des séries isoélectroniques, parce qu'on en connaît la fonction d'onde exacte. Nous donnons des nombres d'occupation de la matrice-densité du premier ordre pour un nombre d'états des atomes de la première ligne dans la limite Z → ∞, et nous classifions les états correspondants.Pour Z fini on peut définir une classification dans le cadre de la théorie des perturbations grâce à un théorème sur la stabilité d'un état à couches complètes en fonction de petites perturbations. Pour les états à couches incomplètes il n'existe en général pas de stabilité correspondante.
    Abstract: Die strengen definitionen der Zustände mit abgeschlossenen und offenen Schalen, die im ersten Artikel dieser Reihe eingeführt worden sind, wurden auf Atomzustände angewendet. Diese können in der Grenze Z → ∞ der isoelektronischen Reihen klassifiziert werden, weil die exakte Wellenfunktion in dieser Grenze bekannt ist. Besetzungszahlen der Einteilchendichtematrix werden für eine Reihe von Zuständen der Atome der ersten Zeile in der Grenze Z → ∞ gegeben und die entsprechenden Zustände werden klassifiziert.Für endliche Z ist eine Klassifikation für Zustände mit abgeschlossenen Schalen möglich im Rahmen einer Störungstheorie, wobei ein Satz über der Stabilität eines Zustands mit abgeschlossenen Schalen mit Rücksicht auf kleine Störungen benützt wird. Für Zustände mit offenen Schalen gibt es im allgemeinen keine solche Stabilität.
    Notes: The system developed in the first paper of this series for the classification of states as open- or closed-shed type is applied to atomic states. These may be classified in the isoelectronic limit (Z → ∞) from knowledge of the true wave function in this limit. One-matrix occupation numbers are tabulated for a number of states of the first-row atoms in the limit Z → ∞ and the states classified.A classification for finite Z is possible in the framework of the Z-dependent perturbation theory by use of a thoerem for the stability of a closed-shed with respect to small perturbations. Such a stability does not hold in general for open-shel states.
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  • 82
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    International Journal of Quantum Chemistry 2 (1968), S. 599-605 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: La formule approximative de Preuss pour les surfaces d'énergie des molécules à plusieurs centers fait usage des “associations atomiques” pour le calcul de certaines constantes. Un programme LISP a été développé pour calculer toutes les “associations atomiques” d'une molécule donnée, en tenant compte des dégénérescences de permutation possibles. A titre d'exemple on donne les “associations atomiques” de l'alcool de méthyle. La plus grande molécule étudiée jusqu'ici est l'alcool d'éthyle, done les 289 associations différentes ont été obtenues en 3 minutes, y compris le temps de compilation. Sans tenir compte de la dégénerescence de permutation on aurait dù considérer 21147 “associations atomiques” pour cette molécule-ci, ce qui aurait été impossible à cause limitations de l'ordinateur en question.
    Abstract: Eine von H. Preuss angegebene Näherungsformel für die Energiehyperfläche von mehrzentrigen Molekülen benutzt zur Berechnung der in ihr vorkommenden Konstanten die sogenannten Atomassoziationen des Moleküls. Es wurde ein LISP-Programm ent-wickelt, das die Berechnung sämtlicher verchiedener Atomassoziationen eines Moleküls unter Berücksichtigung eventuell vorhandener Permutationsentartung durchführt. Als Beispiel werden die Atomassoziationen von Methylalkohol angegeben. Das grösste bis jetzt behandelte Molekül ist das Äthylalkohol-Molekü. Seine 289 verschiedenen Atom-assoziationen wurden in 3 min Rechenzeit einschliesslich Kompilationszeit erhalten. Ohne Berücksichtigung der Permutationsentartung hätten fü dieses Molekü 21147 Atom-assoziationen berücksichtigt werden müssen, was die durch Speicherkapazität und Rechengeschwindigkeit gesetzten Grenzen weit überstiegen hätte.
    Notes: Preuss's approximation formula for energy surfaces of multicentered molecules uses the “atomic associations” of the molecule to calculate certain constants. A LISP program was developed which calculates all atomic associations of a given molecule taking into consideration possible permutation degeneracy. As an example the atomic associations of methyl alcohol are listed. The largest molecule under study so far is ethyl alcohol. Its 289 different atomic associations were obtained in 3 min including compilation time. Not using the permutation degeneracy one would have had to consider 21147 atomic associations for this molecule, a task unfeasible from memory space and computing time limitations.
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  • 83
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    International Journal of Quantum Chemistry 2 (1968), S. 761-784 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Des bornes supérieures et inférieures pour les polarisabilités et pour les interactions à longue distance des atomes et des molécules sont déduites en usant des inégalités pour opérateurs.Les formules pour les forces de dispersion et les forces non-additives à trois corps, sont données en termes des S(k) rapportés, par régles de somme, avec des propriétés des systèmes séparés.Quelques approximations déjà connues sont obtenues, mais avec information additionelle sur leur nature, ainsi que plusieurs inégalités nouvelles. Leur intérět est qu'elles donnent des bornes explicites et rigoureuses renfermant des quantités accessibles à partir des données experimentales.
    Abstract: Obere und untere Grenzen für die Polarisierbarkeiten und für die “long-range” Wechselwirkungen zwischen Atomen und Molekülen wurden mittels Operatorungleichungen hergeleitet. Die Formeln für die Dispersionskräfte und die nichtadditiven Dreikörperkräfte sind in den S(k), die durch Summenregeln mit den Eigenschaften der getrennten Systeme in Verbindung stehen, ausgedrückt.Einige schon bekannte Annäherungen wurden erhalten, aber mit zusätzlicher Information über ihre Beschaffenheit. Mehrere neuen Ungleichungen wurden hergeleitet, die explizite und strenge Grenzen geben, welche in solchen Grössen ausgedrückt sind, die aus experimentellen Tatsachen berechnet werden können.
    Notes: Upper and lower bounds to polarizabilities, and long-range interactions of atoms and molecules are derived using operator inequalities.The formulae for the dispersion and the three-body non-additive forces are given in terms of the S(k), related by sum rules to properties of the separated systems.Some known approximations are obtained but with additional information about their nature, as well as several new inequalities. Their interest is that they give explicit and rigorous bounds involving quantities available from experimental data.
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  • 84
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    International Journal of Quantum Chemistry 2 (1968), S. 801-805 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: L'approximation d'une combinaison linéaire des orbitales de Slater en termes de fonctions Gaussiennes est un problème d'optimisation multi-paramétrique. On présente des formules pour l'évaluation du gradient de recouvrement dans un espace paramétrique, et une méthode alternative pour l'évaluation du gradient, qui posséde une application générale. Cette technique permet l'évaluation exacte d'une dérivée sans dérivation et programmation de son expression analytique.
    Abstract: Die Entwicklung der Gaussfunktionen einer Linearkombination von Slaterfunktionen ist eine Optimalisierungsproblem von manchen Parametern. Ausdrücke für die Berechnung des Gradients der Überlappungsintegrale in einem Parameterraum werden hier angegeben. Eine andere Methode der Berechnung des Gradients, die allgemeine Anwendbarkeit besitzt, wird auch beschrieben. Diese Technik lässt die exakte Berechnung einer Ableitung zu, ohne seinen analytischen Ausdruck zu derivieren und programmieren.
    Notes: The approximation of a linear combination of Slater-type orbitals in terms of Gaussian functions is a many-parameter optimization problem. Formulas for computation of the gradient of the overlap in parameter space are reported. An alternative method of computing the gradient is described, which is of general applicability. This technique permits the exact evaluation of a derivative, without derivation and programming of its analytic expression.
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    International Journal of Quantum Chemistry 2 (1968), S. 857-866 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: L'effet de corrélation pour les systémes atomiques de trois et quatre éléctrons a été considéré en modifiant les potentiels des interactions éléctroniques dans les équations de Hartree-Fock. Les énergies de corrélation obtenues pour Li, Be+, B2+, Li-, Be et B+ différent moins que 25 pour cent des valeurs exacts.
    Abstract: Der Korrelationseffekt für drei und vier Elektronen-Atom-Systeme wurde mit Hilfe der Modifikation der elektronischen Wechselwirkungspotentiale in der Hartree-Fock Gloichnung berücksichtigt. Die Differenzen zwischen den exakten und berechneten Korrelationsenergiewerten für Li, Be+, B2+, Li-, Be und B+ sind niedriger als 25%.
    Notes: The correlation effect for three- and foru-electron atomic systems has been taken into account by modifying the potentials of the electron interactions appearing in the Hartree-Fock equations. The correlation energies obtained for Li, Be+, B2+, Li-, Be and B+ differ by less than 25 percent from the exact values.
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  • 86
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    International Journal of Quantum Chemistry 3 (1969) 
    ISSN: 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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  • 87
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    International Journal of Quantum Chemistry 3 (1969), S. 247-247 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 88
    ISSN: 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: Several classes of functions related to the Gaussian have been used with success as basis sets for the representation of atomic and molecular orbitals.We have compared the representation of a hydrogen 1s orbital by a sum of Gaussian lobe functions with its expansion in eigenfunctions of the three-dimensional isotropic harmonic oscillator. The lobe functions are shown to achieve better expectation values of the energy, with fewer terms. The lobe functions have the further computational advantage of not containing high powers of the radius.It is concluded that the lobe functions are a superior basis set for use in calculations of the electronic structure of atoms and molecules.
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  • 89
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    International Journal of Quantum Chemistry 3 (1969), S. 373-376 
    ISSN: 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 Ill.
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  • 90
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    International Journal of Quantum Chemistry 3 (1969), S. 371-373 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the familiar Temple, Stevenson-Crawford, and Weinstein lower bound formulas for eigenvalues are consequences of a much stronger general lower bound formula and the weak “Eckart criterion” for the overlap of the approximate and true wave functions.
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  • 91
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    International Journal of Quantum Chemistry 3 (1969), S. 397-415 
    ISSN: 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: Two-center one-electron integrals needed in certain molecular correlated wave function calculations, using one-center expansion approximation, have been studied. The form of the basic correlated function used in this study is \documentclass{article}\pagestyle{empty}\begin{document}$$ h(r_{12}) = r_{12}^n e^{ - \zeta r_{12} } $$\end{document} The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r1, r2, and r12. Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.
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  • 92
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have studied the validity of the traditional model of a dimer that has been treated exactly by Merrifield and Fulton and Gouterman, solving the vibronic coupled equations by a numerical method. This model takes into account the modification of the nuclear equilibrium configuration, but it neglects the variation of the force constant when the monomer is electronically excited from the fundamental to a given excited state (the corresponding electronic potentials are both considered as harmonic). We have shown by inspection of the absorption and fluorescence spectra calculated by solving the vibronic equation exactly that the variation force constant cannot be neglected, even if it is weak, particularly in the weak coupling region. The weak, intermediate and strong coupling criteria have been deduced, for the model studied, by examination of the dimeric electronic potential surfaces for different cases of intermolecular interactions.
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  • 93
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    International Journal of Quantum Chemistry 3 (1969), S. 485-487 
    ISSN: 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 emphasized that for the theoretical consideration of many problems of defect centers in crystals (especially of problems which need the correct asymptotic behavior of the wave functions) the semiempirical approach can be effective. As an example the spontaneous radiative time decay of the excited F-center in alkali halides is calculated by using the experimental energies of absorption and emission bands.
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  • 94
    ISSN: 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: Pauling's formulas for the calculation of matrix elements for valence bond functions are derived using a simple substitutional process. The results generalize and simplify the formulas. In particular, the formulas do not depend upon orthogonality of atomic orbitals nor upon the nature of the choice of bond structures (canonical or not). The results are particularly adaptable to automatic computation.
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  • 95
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    International Journal of Quantum Chemistry 3 (1969), S. 593-610 
    ISSN: 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 formalism of the variational theory of the Faraday effect established in the first part of this paper is now applied to the actual computation of the Verdet constant of the hydrogen molecule, of water and of some saturated hydrocarbons. The numerical results have a correct order of magnitude and even, for hydrogen, are rather close to the experimental value.
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  • 96
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    International Journal of Quantum Chemistry 3 (1969), S. 781-793 
    ISSN: 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: Radiation damping of three atoms in a radiation field is studied for both a linear and closed-chain configuration. One atom of the system is initially excited. Use is made of the Heitler-Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two-atom system, and the results are extended to cover larger rings.
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  • 97
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    International Journal of Quantum Chemistry 3 (1969), S. 873-879 
    ISSN: 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 system C2H5+ has been investigated as ethyl cation and as protonated ethylene using the SCF-MO-LC(LCGO) method. Equilibrium distances and angles have been estimated by different potential curves. No difference in total energy was found between the π- and the σ-complex.
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  • 98
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    International Journal of Quantum Chemistry 3 (1969), S. 903-911 
    ISSN: 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 how the leading term for very large R of the Casimir-Polder potential, that is the term varying as R-7, arises in second-order perturbation theory applied to the interaction Hamiltonian - \documentclass{article}\pagestyle{empty}\begin{document}$ - \sum\limits_\sigma {\frac{1}{2}\alpha (\sigma){\rm E}^{ \bot ^2 } (\sigma)} $\end{document}. The generalization to anisotropic molecules is calculated and the angular dependence of the long range intermolecular potential in this case is given explicitly in terms of the principal polarizabilities and their corresponding directions of the two molecules.
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  • 99
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    International Journal of Quantum Chemistry 3 (1969), S. 1058-1061 
    ISSN: 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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    International Journal of Quantum Chemistry 3 (1969), S. 1064-1066 
    ISSN: 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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