Search

In this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth–death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the number of taxa existing at any time in the past in a tree of a known number of extant species, and given birth and death rates, and second, that of determining the TMRCA of two randomly selected taxa in an unobserved tree that is produced by a simple birth-only, or Yule, process. In the latter case, it is assumed that only the rate of bifurcation (speciation) and the size, or number of tips, are known. This is shown to lead to a closed-form analytical expression for the probability distribution of this parameter, which is arrived at based on the known mathematical form of the age distribution of Yule trees of a given size and branching rate, which is derived here de novo, and a similar distribution which additionally is conditioned on tree age. The new distribution is the exact Yule prior for divergence times of pairs of taxa under the stated conditions and is potentially useful in statistical (Bayesian) inference studies of phylogenies. [ABSTRACT FROM AUTHOR]

Polarized-ion models—with and without dipole reaction fields and charge-quadrupole interaction—are evaluated in calculating atomization energies, bond angles, and bending force constants of groups 2 and 12 dihalides. A study of the sensitivity to changes in the input parameters reveals a strong dependence on dipole polarizabilities. The charge–quadrupole bending terms of a multipole expansion are important for quasi-linear molecules, where the preceding terms in the expansion tend to cancel each other. They normally stabilize the linear geometry, but enhance bent structures, if a certain criterion for the ratio of quadrupole polarizabilities of metal and halide ions is fulfilled. The models explain the bent alkaline earth halides, but fail spectacularly for the group 12 halides—HgBr[sub 2] and HgI[sub 2] are even calculated as unstable relative to the constituent atoms. The unexpected weakness of ionic bonds is related to the large increase of the ionization energies by relativistic effects and the lanthanide contraction. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A thermodynamic treatment of the polarizable metal/electrolyte interface is presented and generalizes the classical electro-capillary equation, which interrelates variations in interfacial tension, cell potential, and solution composition, to include temperature changes. The result can be used in investigations of the structure of electrified interfaces; for example, in the calculation of entropy changes which occur in the solvent layer adjacent to the metal surface (inner or Stern layer) and, in particular, in the study of phase transitions in insoluble organic monolayers adsorbed at an electrochemical interface. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: Electrochemical measurements on pincer ligands bis‐N‐(2,5‐dimethoxyphenyl)pyridine‐2,6‐dicarbothioamide (pdcta) and 6‐(4,7‐dimethoxy‐2‐benzothiazolyl)‐N‐(2,5‐dimethoxyphenyl)‐2‐pyridinecarbothioamide (pbcta) in N,N‐dimethylformamide (DMF) and dimethylsulfoxide (DMSO) on a glassy carbon working electrode revealed sulfur centred electrochemical processes. Spectroscopic, elemental and electrochemical analyses indicated that pdcta coordinated to Pd(II) via a κ3‐SNS mode to give 1 whereas pbcta coordinated via a κ3‐SNN mode to give 2. Electrochemical measurements in DMF indicated that the reduction of Pd(II)→Pd(0) proceeded in a concerted manner in the 2, whereas reduction was resolved into the Pd(II)→Pd(I)→Pd(0) in the case of 1. In the presence of p‐toluenesulfonic acid, both palladium complexes displayed electro‐catalytic proton reduction in DMF, with associated overpotentials calculated to be 97 mV and 156 mV for 1 and 2, respectively. The data suggests that the κ3‐SNS pincer ligand enhances the activity of the Pd(II) towards proton reduction relative to 1. [ABSTRACT FROM AUTHOR]

The synthesis and crystal structures of bis-N-(2,5-dimethoxyphenyl)pyridine-2,6-dicarbothioamide (dicarbothioamide I) and 6-(4,7-dimethoxy-2-benzothiazolyl)-N-(2,5-dimethoxyphenyl)-2-pyridinecarbothioamide (L1) as well as the syntheses of the palladium(II) chloride and acetate pincer complexes are reported. The stability constant for the palladium complex formation at 25°C was found to be (2.04 ± 0.26) × 104 dm3 mol-1 and (2.30 ± 0.19) × 104 dm3 mol-1 with ΔfH = 8 ± 1 kJ mol-1, ΔfSθ = 108 ± 10 J K-1 mol-1, and ΔfH = 17 ± 4 kJmol-1 and ΔfSθ = 140 ± 20 JK-1mol-1 for the PdClL1 and Pd(OAc)L1, respectively. The kinetics of formation of the palladium(II) complexes were investigated and the mechanism is proposed to be associative in nature (ΔH‡1 = 34 ± 2 kJ mol-1 and AS‡1 = -113 ± 8JK-1 mol-1, and ΔH‡1 = 37 ± 3 kJ mol-1 and ΔS‡1 = -100 ± 8 JK-1mol-1 for the PdClL1 and Pd(OAc)L1 species, respectively). The electrochemical measurements of the acetonitrile solutions revealed irreversible electron transfers consistent with the electrochemical decomposition of the ligand and its coordination complexes. [ABSTRACT FROM AUTHOR]

This study assessed the relative merits of the Derjaguin-Landau-Verwey-Overbeek and Sogami-Ise theories for the description of the electrostatic interaction between like-charged colloid particles in an electrolyte solution, which differ qualitatively in their predictions of the nature of this interaction. The former implies a repulsion at all distances with a screened-Coulomb (or Yukawa-type) dependence on distance, whereas the latter leads to an electrolyte-mediated, long-range attraction. The Sogami-Ise result for the interaction potential depends critically on the notion that the electrostatic parts of the Helmholtz and Gibbs energies of an electrolyte solution are different. By elaborating on the thermodynamic implications of this assumption, it was determined that it leads to a conflict with well-established results, in particular the relation between osmotic pressure and solvent chemical potential, already at the Debye-Hückel level. For this reason alone, the Sogami-Ise theory is untenable. The condensation and ordering phenomena observed with charged colloids in low-ionic.strength solutions, which the Sogami-Ise theory was originally designed to explain, can be interpreted without the need to resort to longrange electrostatic attraction, as has been demonstrated in previously published work. [ABSTRACT FROM AUTHOR]

When dpktch was reacted with ZnCl2 in refluxing acetonitrile in air [ZnCl2(η3-dpktch)] was isolated in good yield. Infrared spectra suggest weaker binding of dpktch in [ZnCl2(η3-dpktch)] than in [CdCl2(η3-dpktch)]. 1H-NMR studies in non-aqueous media show that [ZnCl2(η3-dpktch)] is sensitive to changes in its environment and exchanges its amide proton. Electronic absorption spectral measurements confirmed the sensitivity of [ZnCl2(η3-dpktch)] to changes in its surroundings and show inter-conversion between two intra-ligand-charge-transfer transitions (ILCT) at 330 ± 2 nm and 404 ± 2 associated with [ZnCl2(η3-dpktch)] and its conjugate base. Thermo-optical measurements in non-aqueous dmf and dmso show facile inter-conversion between [ZnCl2(η3-dpktch)] and its conjugate base, respectively. Also, it is shown that protonation of dmf by [ZnCl2(η3-dpktch)] is exothermic (standard enthalpy of protonation ΔHθ = -40.7 ± 1.8 kJ mol-1), but endothermic for dmso (ΔHθ = +8.3 ± 1.5 kJ mol-1). Chemical stimuli in concentrations as low as 5.0 × 10-7 M can be detected and determined using [ZnCl2(η3-dpktch)] in non-aqueous media. X-ray crystallographic studies on a monoclinic, P21/n single crystal of [ZnCl2(η3-dpktch)] confirmed the N,N,O-coordination of dpktch and revealed interdigitated units of [ZnCl2(η3-dpktch)] connected via a web of hydrogen bonds. [ABSTRACT FROM AUTHOR]

The structure of dolomite, CaMg(CO3)2, was determined from 298 to 1466 K at a constant pressure of about 3 GPa using in situ synchrotron X-ray diffraction data to investigate the state of disorder. An order parameter s, defined as 2 xca - 1, varies from s = 1 (where xca = 1) for a completely ordered dolomite to s = 0 (where xca = 0.5) for a completely disordered dolomite. On heating, there is no measured change in s until the temperature is high enough to cause exchange of Ca2+ and Mg2+ cations. Significant disorder began to occur at about 1234 K [s = 0.83(1)] and increases along a smooth pathway to T = 1466 K [s = 0.12(5)]. The R3 ↔ R3c transition in dolomite is described by a modified Bragg-Williams thermodynamic model with the following molar free energy of disorder, Gd (T; s) = RTc[1 - s² + ½ a(s4- 1) - (T/Tc) {2 ln2 - (l+s) ln(1 + s) - (1 - s) ln(1 - s)}]. Using Tc = 1466 K and a = -0.29, this model provides an excellent agreement with experimental data. Moreover, the maximum enthalpy of disorder, Hd(s = 0) = RTc(1 - ½ a) ∼ 14 kJ/mol, agrees with published calorimetric data. A thermodynamic description of the aragonite + magnesite ↔ dolomite reaction boundary is also presented and it reproduces the main qualitative features correctly. [ABSTRACT FROM AUTHOR]

Mikanolide [systematic names: 1,10:2,3-diepoxy-6,8-dihydroxy-11-vinylgermacr-4-ene 12,14-di-γ-lactone and 7,10a-dimethyl-1a,1b,2a,6a,7,9a,10,10a-octahydro-4H-6,3-methenofuro[3,2-c]bisoxireno[f,h]oxacycloundecin-4,8(6H)-dione], C15H14O6, derived from a variety of Mikania micrantha growing in Portland, Jamaica, contains a methylcyclodecane ring fused to an unsaturated planar α,γ-lactone, an envelope-type near-planar vinyl-β,γ-lactone and two epoxide moieties. The crystal packing shows stacks of mikanolide molecules interlocked via a network of non-classical C-H…O hydrogen bonds between the lactone units. [ABSTRACT FROM AUTHOR]

We investigate the validity of employing a potential dependent polarizability in a model to determine atom in molecule (AIM) polarizabilities. It is found that the assumption of an electric potential dependent polarizability leads to a contravention of the principle of conservation of energy. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]