Molecular force fields of ethyl bromide: Normal coordinate analysis of d0, d2, d3, and d5 species

A normal coordinate analysis of ethyl bromide and some deuterated derivatives was carried out using the MUBFF and GHFF fields. The results are discussed in relation to the recently published force field of ethyl chloride.     

The 13C NMR spectrum of coumarandione

A re-examination of the ¹³C NMR spectra of coumarandione and isatin with the aid of proton-coupled ¹³C NMR spectra and selective proton decoupling experiments is reported.     

Has Bell's inequality a general meaning for hidden-variable theories?

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in measurement results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning.     

Asymptotic expansion of Feynman amplitudes

Employing the technique of Mellin transforms to scalar convergent Feynman amplitude in the Schwinger integral representation, we determine its asymptotic expansion for large Euclidean momenta. The determination of the coefficients of the expansion is effected via the use of generalized Taylor operators.     

Ko and λ production at the CERN ISR

Transverse momentum distributions of $\text{λ}{}^{\mathrm{o}}\text{,}\text{λ}{}^{\mathrm{o}}$, and K^o, produced in pp collisions at x = 0, have obtained at the CERN ISR. The K^o yield is in agreement with published K⁺, K^? results, obtained at this centre-of-mass energy (√s≈44 GeV). The results on $\text{λ}{}^{\mathrm{o}}\text{and}\text{λ}{}^{\mathrm{o}}$ production obtained in this experiment are compared with results obtained at lower centre-of-mass energies.     

A study of the photoneutron contribution to the giant dipole resonance of nuclei in the 64 ≦ A ≦ 86 mass region

The partial photoneutron cross sections [σ(γ, n) + σ(γ, pn)] and σ(γ, 2n) of ⁶⁴Zn, Ga, ^70,72,74,76Ge, ⁷⁵As and ^76,78,80,82Se were measured with a monochromatic photon beam and a high efficiency neutron detecting system in the photon-energy range 8 ≦ E ≦ 30 Me V. Integrated cross sections are discussed. The evolution of the GDR as observed through the neutron exit channel only, is tentatively interpreted either in terms of isospin splitting or in terms of the dynamic collective model.     

Sufficient conditions for optimality of threat strategies in a differential game

The problem of defining threat strategies in nonzero-sum games is considered, and a definition of optimal threat strategies is proposed in the static case. This definition is then extended to differential games, and sufficient conditions for optimality of threat strategies are derived. These are then applied to a simple example. The definition proposed here is then compared with the definition of threat strategies given by Nash.     

Neutron scattering study of 49 K phase transition in TTF-TCNQ

Elastic neutron scattering measurements show the existence of three low temperature phase transitions in TTF-TCNQ and are interpreted within the framework of a recent theoretical investigation by Bak and Emery. Direct evidence for the new 49 K transition is presented in addition to the 38 and 54 K transitions reported previously.     

Nova methodus adhibendi approximationem molecularium orbitalium ad plures iuxtapositas unitates

Résumé L'étude de la structure électronique d'une chaîne constituée par la répétition d'un motif polyatomique et l'interprétation des propriétés du polymère ainsi formé sont grandement facilités, s'il est possible de ramener les termes d'interaction entre unités voisines à un paramètre d'interaction unique. Ce problème a été traité en méthode des orbitales moléculaires par un procédé qui permet de tenir compte des modifications du monomère à l'intérieur du polymère et ne néglige que de faibles contributions.L'interaction entre deux monomèresi etj est représentée par la sous-matriceB _ij de dimensionn ×n formée par les termes non-diagonaux correspondants de la matrice-énergie. Par des transformations unitaires appropriées, il est possible de mettre sous forme diagonale les sousmatricesB _ij entre monomères voisins. En général, la diagonale de la matrice transformée contient un terme prépondérant qu'on peut considérer comme mesurant l'interaction (i, j). Une application numérique a été effectuée dans le cas d'un polymère fictif formé par des molécules H₂ et dans le cas d'un polymère peptidique formé par des groupements HNCO en interaction par l'intermédiaire de liaisons hydrogène. La validité des approximations introduites selon l'importance de l'interaction peut être vérifiée sur l'exemple d'un dimère dont les deux unités sont placées à des distances variables. Dans le cas d'un polymère les transformations effectuées conduisent à remplacer les orbitales atomiques du monomère par des orbitales s'étendant sur deux unités voisines; en prenant comme motif structural de la chaîne le monomère double formé par deux unités successives, on peut représenter l'interaction entre deux motifs adjacents par un seul terme.La réduction de la matriceB _ij à un seul terme fournit des bandes d'énergie dont la position est en très bon accord avec celles obtenues directement par les techniques classiques de calcul de l'état solide [7].

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The study of the electronic structure of a chain formed by repetition of polyatomic monomers and the interpretation of the resulting polymer are made much easier if the interaction terms relating to neighbouring units can be reduced to a single parameter. This problem has been treated in the MO scheme by a procedure which makes it possible to take into account the modifications of the monomer within the polymer and only neglects minor contributions.The interaction between two monomersi andj is represented by then ×n submatrixB _ij formed by the corresponding non diagonal terms of the energy matrix. By appropriate unitary transformations it is possible to bring the submatricesB _ij of neighbouring monomers to a diagonal form. In general, one of the diagonal elements thus obtained is much higher than the others, and can be taken as a measure of thei-j interaction. A numerical application has been made in the case of a fictitious polymer formed by H₂ molecules, and in the case of a polypeptide formed by HNCO groups interacting through hydrogen bonds. The validity of the approximations introduced for different values of interaction can be tested on a dimer whose units are placed at different distances. In the case of a polymer the transformations mentioned above require that the atomic orbitals of a monomer be replaced by orbitals extending over two neighbouring units. Taking as a new unit the corresponding pair of monomers, the interaction between the units can be represented by a single term. The reduction of theB _ij matrices to a single term each gives energy bands whose positions are in perfect agreement with those obtained directly by the classical techniques of solid-state physics [7].

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Zusammenfassung Das Studium der elektronischen Struktur von linearen Polymeren vereinfacht sich sehr, wenn die Wechselwirkung zwischen benachbarten Monomeren durcheinen Parameter beschrieben werden kann. Entsprechend wird im MO-Schema ein Verfahren entwickelt, das auf der Veränderung der Monomeren im Polymeren fußt.Die Wechselwirkung zwischen zwei Monomereni, j des Polymer wird durch eine aus Nichtdiagonalelementen der Hamiltonmatrix bestehende UntermatrixB _ij beschrieben. Für alle benachbarten Monomerenpaare lassen sich diese durch unitäre Transformationen diagonalisieren. I. a. ist eines der so erhaltenen Diagonalelemente vonB merklich größer und dient als Maß für die Wechselwirkung der beiden Monomeren. Angewendet wird die Methode auf ein fiktives Polymer aus H₂-Molekülen und auf ein Polymer aus durch H-Brücken verbundenen Peptidgruppen. Der Einfluß der Näherungen wird zunächst an einem Dinieren für verschiedene Abstände getestet.Im Falle eines Polymeren sind als Monomere Einheiten von zwei benachbarten Molekülen mit entsprechend ausgedehnten Orbitalen zu betrachten. Die Rechnung führt hier auf Energiebänder, deren Lage voll mit der nach klassischen Methoden der Festkörperphysik [7] erhaltenen übereinstimmt.

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Gratias agimus Cl. Vir.Raphaeli Del Re, qui nos, quod ad usum linguae latinae attinet, consilio benigne adiuvit.