Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.     

Two-stage Off-Gel isoelectric focusing: protein followed by peptide fractionation and application to proteome analysis of human plasma

This paper presents the recently introduced Off-Gel electrophoresis (OGE) technology as a versatile tool to reproducibly fractionate intact proteins and peptides into discrete liquid fractions. The coupling of two stages of OGE, i.e., the separation of intact proteins in a first-stage followed by fractionation of peptides derived from each protein fraction after proteolysis in a second stage, results in an array of 15 x 15 fractions that are directly amenable to additional peptide fractionation like reverse-phase liquid chromatography (RPC). The analysis of all second-stage peptide fractions from only the first-stage protein fraction representing pH 5.0 -5.15 by on-line reverse-phase LC-tandem mass spectrometry resulted in the identification of 53 proteins (337 peptides), of which 10 were on different immunoglobulin (Ig) chains, with an input of only 1.5 mg human blood plasma proteins. Increasing the protein load to approximately 12 mg increased the number of identified proteins in the same protein fraction to 73 proteins (449 peptides), of which 15 were Ig-related. Immunodepletion of six of the most abundant proteins (albumin, transferrin, haptoglobin, IgG, IgA, and alpha-1-antitrypsin) prior to first-stage OGE with an input of 1.5 mg of protein (equivalent to approximately 10 mg nondepleted plasma) resulted in the identification of 81 proteins (660 peptides), of which three were still Ig fragments. The pI-based separation of peptides appears to be nonuniform based on the theoretically determined pI values of identified peptides. This observation specifically accounts for the neutral zone (pI 5-8) and can be accounted for by the physicochemical properties of the peptides given by their amino acid composition. The power of OGE separation of proteins and peptides is discussed with a focus on the use of the knowledge about the pI of proteins and peptides that assist the validation of correct identifications together with the retention time of peptides on RPC.     

Ab initio global potential-energy surface for H5(+) --> H3(+) + H2

An accurate global potential-energy surface (PES) is reported for H5(+) based on more than 100,000 CCSD(T)/aug-cc-pVTZ ab initio energies. This PES has full permutational symmetry with respect to interchange of H atoms and dissociates to H3(+) and H2. Ten known stationary points of H5(+) are characterized and compared to previous ab initio calculations. Quantum diffusion Monte Carlo calculations are performed on the PES to obtain the zero-point energy of H5(+) and the anharmonic dissociation energy (D0) of H5(+) --> H3(+) + H2. The rigorous zero-point state of H4D+ is also calculated and discussed within the context of a strictly classical approach to obtain the branching ratio of the reaction H4D+ --> H3(+) + HD and H2D+ + H2. Such an approach is taken using the PES and critiqued based on the properties of the quantum zero-point state. Finally, a simple procedure for adding the long range-interaction energy is described.     

“Short-bite” ligands in cluster synthesis

The short-bite ligands CH₂(PR ₂)₂ or CH(PR ₂)₃ (R = Me, Ph),RN(PX ₂)₂ (R=H, Me, Et;X = F, OR (R= Me, Et, i-Pr, Ph), Ph),RE(CH₂ ER₂)₂ (E = P, As;R = Me, Ph ), Ph₂ P(2-C₅H₄N) and related species are particularly versatile for the synthesis of di- and polynuclear complexes which frequently possess metal-metal bonds. In addition to homometallic products, these ligands often permit the directed synthesis of heterometallic complexes. Selected aspects of the chemistry of these complexes are also reviewed.     

Cyano-bridged hexanuclear Fe4M2 (M = Ni, Co, Mn) clusters: spin-canted antiferromagnetic ordering of Fe4Ni2 cluster

Heterobimetallic hexanuclear cyano-bridged complexes, [{Fe(Tp)(CN)3}4{M(MeCN)(H2O)2}(2)].10H2O.2MeCN [M = Ni (1), Co (2), Mn (3); Tp = hydrotris(1-pyrazolyl)borate], have been synthesized in H2O-MeCN solution. Complexes 1-3 are isostructural and hexanuclear with [{Fe(Tp)(CN)3}4{M(MeCN)(H2O)2}2] units linked by hydrogen bonds to form a 2D-structure in the solid state. Complex 1 is a canted antiferromagnet that undergoes a field-induced spin-flop-like transition at approximately 1 T and 2 K. At 4.45 K 1 has a transition to paramagnetic state of noninteracting S = 4 magnetic clusters. However, 2 and 3 show antiferromagnetic intracluster coupling. Facile loss of solvent from 2 alters the local symmetry resulting in changing the intracluster interaction from antiferro- to ferromagnetic.     

A group additivity approach for the estimation of heat capacities of organic liquids and solids at 298 K

A group additivity method is described which provides heat capacity estimates of the condensed phase. The data base consists of 810 liquids and 446 solids. Group values for carbon in various common substitution and hybridization states and for 47 functional groups are provided. The standard error of estimation using this approach on this data base is 19.5 (liquids) and 26.9 J/ (mole K) (solids). This can be compared to typical experimental uncertainties of 8.12 and 23,4 J/ (mole K) associated with these measurements, respectively. Experimental uncertainties were estimated from the numerical differences obtained for a given substance from multiple independent literature reports.     

Syntheses and photophysical properties of some 5(2)-aryl-2(5)-(4-pyridyl)oxazoles and related oxadiazoles and furans

A number of 5-aryl-2-(4-pyridyl)oxazoles, a 2-aryl-5-(4-pyridyl)oxazole, the related oxadiazole and furan, several 2-(4-pyridyl)cycloalkano[d]oxazoles, and many of their quaternary salts were prepared. No single standard synthesis was effective for preparation of more than a few of the 25 free bases described; methods often unique to a base were employed. Minor variations in structure sometimes produced large differences in absorption and emission wavelengths, as well as in the magnitude of the extinction coefficient. The salts are of interest as laser dyes, scintillation fluors, biological stains, and shifters for luminescent solar concentrators.     

Engineering the structure and magnetic properties of crystalline solids via the metal-directed self-assembly of a versatile molecular building unit

We report the supramolecular chemistry of several metal complexes of N-(4-pyridyl)benzamide (NPBA) with the general formula [Ma(NPBA)2AbSc], where M = Co2+, Ni2+, Zn2+, Mn2+, Cu2+, Ag+; A = NO3-, OAc-; S = MeOH, H2O; a = 0, 1, 2; b = 0, 1, 2, 4; and c = 0, 2. NPBA contains structural features that can engage in three modes of intermolecular interactions: (1) metal-ligand coordination, (2) hydrogen bonding, and (3) pi-pi stacking. NPBA forms one-dimensional (1-D) chains governed by hydrogen bonding, but when reacted with metal ions, it generates a wide variety of supramolecular scaffolds that control the arrangement of periodic nanostructures and form 1- (2-4), 2- (5), or 3-D (6-10) solid-state networks of hydrogen bonding and pi-pi stacking interactions in the crystal. Isostructural 7-9 exhibit a 2-D hydrogen bonding network that promotes topotaxial growth of single crystals of their isostructural family and generates crystal composites with two (11) and three (12) different components. Furthermore, 7-9 can also form crystalline solid solutions (M,M')(NPBA)2(NO3)2(MeOH)2 (M, M' = Co2+, Ni2+, or Zn2+, 13-16), where mixtures of Co2+, Ni2+, and Zn2+ share the same crystal lattice in different proportions to allow the formation of materials with modulated magnetic moments. Finally, we report the effects that multidimensional noncovalent networks exert on the magnetic moments between 2 and 300 K of 1-D (4), 2-D (5), and 3-D (7, 8, 10, and 13-16) paramagnetic networks.     

Origin of the acidity enhancement of formic acid over methanol: resonance versus inductive effects

Density functional theory calculations were employed to study the relative contribution of resonance versus inductive effects toward the 37 kcal/mol enhanced gas-phase acidity (DeltaH degrees (acid)) of formic acid (1) over methanol (2). The gas-phase acidities of formic acid, methanol, vinyl alcohol (5), and their vinylogues (6, 8, and 9) were calculated at the B3LYP/6-31+G level of theory. Additionally, acidities were calculated for the formic acid and vinyl alcohol vinylogues in which the formyl group and the vinyl group, respectively, were perpendicular to the rest of the conjugated system. Comparisons among these calculated acidities suggest that inductive effects are the predominant effects responsible for the enhanced acidity of formic acid over methanol, accounting for between roughly 62% and 65% of the total enhanced acidity; the remaining 38% to 35% of the acidity enhancement appears to be due to resonance effects. Further comparisons suggest that resonance effects are between roughly 58% and 65% of the 26 kcal/mol calculated acidity enhancement of vinyl alcohol over methanol, and the remaining 42% to 35% are due to inductive effects.     

An alternative multipolar expansion for intermolecular potential functions

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.