High pressure differential thermal analysis of nematic compounds with different molecular shapes

By means of high pressure differential thermal analysis we measured the pressure/temperature phase diagrams of several nematic compounds with different molecular structures. Using pressures up to about 500 M Pa we found strongly nonlinear clearing curves. This behaviour is interpreted as changes from 'weak' intermolecular potentials to 'hard' potentials, or using thermodynarmic arguments, strong pressure dependence of the volume discontinuity at the clearing transitions.     

High pressure differential thermal analysis of nematic compounds with different molecular shapes

Abstract

By means of high pressure differential thermal analysis we measured the pressure/temperature phase diagrams of several nematic compounds with different molecular structures. Using pressures up to about 500 M Pa we found strongly nonlinear clearing curves. This behaviour is interpreted as changes from ‘weak’ intermolecular potentials to ‘hard’ potentials, or using thermodynarmic arguments, strong pressure dependence of the volume discontinuity at the clearing transitions.     

Interplay between structure and size in a critical crystal nucleus

We study the kinetics of crystal nucleation of an undercooled Lennard-Jones liquid using various path-sampling methods. We obtain the rate constant and elucidate the pathways for crystal nucleation. Analysis of the path ensemble reveals that crystal nucleation occurs along many different pathways, in which critical solid nuclei can be small, compact, and face centered cubic, but also large, less ordered, and more body centered cubic. The reaction coordinate thus includes, besides the cluster size, also the quality of the crystal structure.     

On the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2-sphere

Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time.     

Angular distribution in neutrino-induced single pion production processes

A partial wave decomposition of \({v \mathord{\left/ {\vphantom {v {\bar v}}} \right. \kern-0em} {\bar v}}\) single pion production is used for studying resonant and nonresonant contributions. The dominant resonance excitation is dynamically described by a semirelativistic quark model. Nonresonant background is considered to arise from Born-terms diminuished by the lowest order partial waves (which are determined by resonances alone.) The method permits evaluation of interferences between resonance and background amplitudes as well as, more importantly, among resonances themselves. Predicted interference patterns are reflected by the pion angular distribution coefficients which compare well with recent data. Results obtained this way are also in agreement with momentum transfer measurements if higher resonance excitation form factors are chosen to resemble those tested in pion photoproduction, rendering simultaneously any nonresonant background small.     

Integral approximations for molecular orbital theory

The electron repulsion integrals arising in LCAO-MO theory are approximated by replacement of the product of two orbitals on different centers by linear combinations of one-center products. The approximation differs from those previously proposed in that the coefficients of the various terms are determined by requiring agreement for certain integrals, and in the emphasis of the role of symmetry in selecting the one-center products. For two-center integrals, the new approximation is significantly better than older approximate methods. Reasons are given for expecting this improvement to extend also to multi-center integrals.

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Zusammenfassung Es wird ein Verfahren zur näherungsweisen Berechnung von Elektronenwechselwirkungsintegralen der LCAO-MO-Theorie beschrieben, bei welchem das Produkt zweier Zustandsfunktionen an verschiedenen Zentren durch eine Linearkombination von Produkten am gleichen Zentrum ersetzt wird. Der Unterschied zu ähnlichen Ansätzen liegt in der Justierung der Koeffizienten. Für Zweizentrenintegrale liefert die hier vorgeschlagene Methode bedeutend bessere Ergebnisse als das Mulliken-Verfahren.

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Résumé Les intégrales de répulsion électroniques intervenant dans la théorie LCAO MO sont calculées d'une manière approchée en remplaçant le produit de deux orbitales sur des centres différents par des combinaisons linéaires de produits à un centre. Cette approximation diffère de celles proposées auparavant par la détermination des coefficients des différents termes au moyen de l'ajustement de certaines intégrales et par l'importance du rôle de la symétrie dans le choix des produits monocentriques. Cette nouvelle approximation est bien meilleure que les anciennes en ce qui concerne les intégrales bi-centriques. Nous donnons des raisons d'espérer que cette amélioration s'étendra aux intégrales polycentriques.

     

Theory of intermolecular interactions: The long range terms in the dipole–dipole,monopoles–dipole,and monopoles–bond polarizabilities approximations

The problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.     

Molecular geometries and moments from the maximum overlap criterion

The maximized overlap population, defined as Σ_μ≠νP_μνS_μν, and a related quantity, Σ_μ,νP_μνS²_μν are computed for a series of configurations. The extremum of both approximate molecular geometries, the latter with an accuracy suitable for predictive value. The maximum overlap orbitals predict dipole and quadrupole moments that give reasonable agreement with experimental values.