Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

Mechanical properties of SBR-networks: I. Determination of crosslink densities by stress-strain-measurements

The tube model is applied for the treatment of stress-strain measurements on SBR networks. It is shown that this theory allows the separation of crosslink and constraint contributions to the stress-strain behavior and, also, a reliable determination of crosslink densities. The consideration of dynamical contributions is discussed and a special numerical method is developed.     

Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals

Experimental and theoretical studies of electron densities and the corresponding derived entities such as electrostatic potentials have been the primary means of understanding the chemical nature and electronic properties of crystalline substances. Conventional crystal calculation methods such as the embedded cluster models are capable of performing calculations on small and medium-sized molecules, while periodic ab initio methods can treat crystals with up to 200 atoms per unit cell. A linear scaling method, viz. the molecular tailoring approach, has recently been developed for obtaining ab initio quality one-electron properties. In the present study, the molecular tailoring approach is employed to generate electron density, electrostatic potential and interaction density maps with the ibuprofen crystal as a test case. The interaction density and electrostatic potential maps produced in the present work succinctly bring out the actual crystalline environment around a given reference molecule by including the interactions with atoms in its neighborhood. The results obtained from the molecular tailoring approach may thus be expected to enhance our understanding of the environment in the crystalline material with reasonably small computational effort.Contribution to the Jacopo Tomasi Honorary Issue     

Excess thermodynamic properties of the 2-propanol + dichloromethane system at 25°C

Densities, viscosities, enthalpies, vapor-liquid equilibria, and surface tensions were determined at 25°C for the 2-propanol+dichloromethane system. From the experimental results excess volumes, viscosities, enthalpies, Gibbs energies, and excess surface tensions were calculated. An attempt has been made to explain the observed deviations from ideal behavior on the basis of intermolecular interactions.     

Speed of Sound, Isentropic Compressibilities, and Excess Molar Volumes of Binary Mixtures Containing p-Dioxane

The speed of sound u in and densities of eight binary mixtures of p-dioxane (p-C₄H₈O₂) with methylcyclohexane (c-C₆H₁₁CH₃), 1-chlorohexane (C₆H₁₃C1), 1-bromohexane (C₆H₁₃Br), p-xylene [C₆H₄(CH₃)₂], propylbenzene (C₆H₅C₃H₇), methyl acetate CH₃COOCH₃), butyl acetate (CH₃COOC₄H₉), and amyl acetate (CH₃COOC₅H₁₁) were measured over the whole composition range at 30°C. Isentropic compressibilities (K _S), Rao's molar sound functions (R), excess molar volumes (V ^E), excess isentropic compressibilities (K _S ^E ) together with relative change in volume V/₁₂ values, have been obtained for all measured mole fractions. The excess partial molar volume (V₁-V ₁ ⁰ ) of p-dioxane in different solvents have also been estimated. The experimental results have been analyzed in terms of the Prigogine–Flory–Patterson theory of solutions.     

Spin density distributions in radical anions of heterocyclic amine N-oxides

The unrestricted Hartree-Fock (UHF) method of Snyder and Amos is used to calculate, in the -electron approximation, the spin density distributions in radical anions of heterocyclic amine N-oxides. The computed spin densities are observed to be in good agreement with the experimental values. The computed spin density distribution of the radical anion of pyridine N-oxide is consistent with the greater susceptibility of pyridine N-oxide relative to pyridine to electrophilic nitration. Also, the calculations are consistent with the lower basicity of the N-oxides relative to the parent bases.     

Molar excess heat capacities and volumes for mixtures of alkanoates with cyclohexane at 25°C

Molar excess volumes V ^E at 25°C have been determined by vibrating-tube densimetry, as a function of mole fraction x for different series of an alkanoate (H _2m+1 C _m COOC _n H _2n+1 )+cyclohexane. Three types of alkanoates were investigated, i.e., methanoates (m=0, with n=3 and 4), ethanoates (m=1, with n=2, 3, and 4) and propanoates (m=2, with n=1, 2, and 3). In addition, a Picker flow calorimeter was used to obtain molar excess heat capacities C _p ^E at constant pressure at the same temperature. V ^E is positive for all systems and rather symmetric, with V ^E (x=0.5) amounting to almost identical values in a series of mixtures containing an alkanoate isomer of same formula (say C₄H₈O₂, C₅H₁₀O₂, or C₆H₁₂O₂). The composition dependence of C _p ^E is rather unusual in that two more or less marked minima are observed for most of the mixtures, especially when the alkanoate is a methanoate or an ethanoate. These results are discussed in terms of possible changes in conformation of both the ester and cyclohexane.     

The Many Measures of Molecular Dimensions

In contrast to the high precision with which masses of atoms and molecules can be specified, their external dimensions remain intrinsically fuzzy. Attention is directed to the difference between measurements of interatomic separations within molecules, that in many instances are cited with error bars of +/– 0.002 Å, and the available approximate magnitudes of over-all sizes, needed for estimating packing densities (in solids or liquids). The following account, is a critical examination of the underlying concepts and of the diversity of data in the literature, regarding internal dimensions (bond lengths), overall extensions, cross-sectional areas, and volumes of molecules that may be derived from a variety of experiments. Historical markers of the evolution of the underlying theories and experiments are included.