An improved computer program for calculating formation constants of ligand complexes from pH data

Several improvements are made to available computer programs for calculating formation constants from pH data. The most important features are wide portability of program among computers, ability to optimize any parameter in the model equations and to fix any parameters (including stepwise formation constants) to a constant, and options to allow for variations in thermodynamic activity of ions and to fit pH after fitting the volume of added reagent. The latter feature was used with synthetic data to explore the effects of random errors in either reagent volume or pH or both. Whereas fits to reagent volume will usually be more accurate for systems with pK_a values near 7, this is not the case for systems with pK_a values which differ by > 2.0 from 7.     

Incidence modules for symplectic spaces in characteristic two

We study the permutation action of a finite symplectic group of characteristic 2 on the set of subspaces of its standard module which are either totally isotropic or else complementary to totally isotropic subspaces with respect to the alternating form. A general formula is obtained for the 2-rank of the incidence matrix for the inclusion of one-dimensional subspaces in the distinguished subspaces of a fixed dimension.     

Radiating shock measurements in the Z-pinch dynamic hohlraum

The Z-pinch dynamic hohlraum is an x-ray source for high energy-density physics studies that is heated by a radiating shock to radiation temperatures >200 eV. The time-dependent 300-400 eV electron temperature and 15-35 mg/cc density of this shock have been measured for the first time using space-resolved Si tracer spectroscopy. The shock x-ray emission is inferred from these measurements to exceed 50 TW, delivering >180 kJ to the hohlraum.     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

Catalytic, asymmetric transannular aldolizations: total synthesis of (+)-hirsutene

We report an asymmetric, catalytic transannular aldolization that provides polycyclic products useful for natural product synthesis. We found that a proline-derivative catalyzes the transannular aldol reaction of 1,4-cyclooctanediones to the corresponding cyclic beta-hydroxy ketones in good yields and with high enantioselectivities. The utility of our reaction has been demonstrated in a total synthesis of (+)-hirustene.     

Theoretical studies of five-membered ring ketene acetals

Cyclic ketene acetals are a class of organic molecules characterized by a nucleophilic exo-methylene carbon attached to a carbon with two adjacent O, N, or S atoms. We have carried out a systematic computational study of a series of five-membered cyclic acetals like 2-methylene-1,3-dioxolane and its OS, SS, NO, NS, and NN analogs as well as all the protonated species. The calculations were performed at the MP2 level using a triple zeta plus polarization basis set. The nucleophilicity was discussed in terms of geometrical factors, calculated atomic charges, calculated chemical shifts, and proton affinities. All the six neutral species were strong nucleophiles. The NN analog was predicted to be the strongest and the SS analog the weakest nucleophile.     

Constrained dynamics of localized excitations causes a non-equilibrium phase transition in an atomistic model of glass formers

Recent progress has demonstrated that trajectory space for both kinetically constrained lattice models and atomistic models can be partitioned into a liquid-like and an inactive basin with a non-equilibrium phase transition separating these behaviors. Recent work has also established that excitations in atomistic models have statistics and dynamics like those in a specific class of kinetically constrained models. But it has not been known whether the non-equilibrium phase transitions occurring in the two classes of models have similar origins. Here, we show that the origin is indeed similar. In particular, we show that the number of excitations identified in an atomistic model serves as the order parameter for the inactive-active phase transition for that model. In this way, we show that the mechanism by which excitations are correlated in an atomistic model - by dynamical facilitation - is the mechanism from which the active-inactive phase transition emerges. We study properties of the inactive phase and show that it is amorphous lacking long-range order. We also discuss the choice of dynamical order parameters.     

Dual-etalon frequency-comb cavity ringdown spectrometer

We have demonstrated a spectroscopic technique for simultaneously obtaining broad spectral bandwidth and high frequency resolution absorption measurements, with 5 μs temporal resolution, continuously for tens of microseconds in an apparatus with no active stabilization. The technique utilizes two passive air-gap etalons to imprint two frequency comb patterns onto a single pulsed light source. The air-gap etalons also serve as cavity ringdown cells increasing the sensitivity of the absorption spectroscopy by increasing the interrogation path length. Here, we demonstrate the operation of the spectrometer utilizing a ~0.15 cm(-1) bandwidth pulsed dye laser and two nearly identical 300 MHz free-spectral range confocal air-gap etalons each with a finesse of ~1 × 10(5), to investigate the (1,1,3) overtone of water and the R(7) transition of the O(2) b(1)Σ(g)(+)←X(3)Σ(g)(-) (2,0) band with high spectral resolution.     

Basis for Breakup States of Three Identical Particles

 A new basis for expanding three-body momentum-space states for three identical particles is studied. The basis states are simultaneously eigenstates of the total angular momentum and the total antisymmetrization operator. The total kinetic energy and two Dalitz-Fabri variables are chosen as the remaining three continuous variables. Zernike polynomials are used as a basis set for a generalized Fourier expansion in the Dalitz-Fabri variables. Born approximations to the nucleon-deuteron breakup amplitude (zero total orbital angular momentum) are calculated for Malfliet-Tjon I–III potentials and displayed in a Dalitz plot that shows the global structures of the reaction probabilities. Numerical results are presented, which indicate favorable convergence properties of the generalized Fourier expansion. These results suggest that the new basis set may be attractive in more realistic calculations. Received July 28, 2000; accepted in final form January 29, 2001