Free energy derivatives: A new method for probing the convergence problem in free energy calculations

The convergence behavior of free energy calculations has been explored in more detail than in any previously reported work, using a model system of two neon atoms in a periodic box of water. We find that for thermodynamic integration-type free energy calculations as much as a nanosecond or more molecular dynamics sampling is required to obtain a fully converged value for a single λ point of the integrand. The concept of “free energy derivatives” with respect to the individual parameters of the force field is introduced. This formalism allows the total convergence of the simulation to be deconvoluted into components. A determination of the statistical “sampling ratio” from these simulations indicates that for window-type free energy calculations carried out in a periodic waterbox of typical size at least 0.6 ps of sampling should be performed at each window (0.7 ps if constraint contributions to the free energy are being determined). General methods to estimate and reduce the error in thermodynamic integration and free energy perturbation calculations are discussed. We show that the difficulty in applying such methods is determining a reliable estimate of the correlation length from a short series of data. © 1994 by John Wiley & Sons, Inc.     

Styrene emulsion polymerization: Particle-size distributions

Data are presented on the time evolution of particle-size distributions (PSDs) in seeded and ab initio styrene emulsion polymerization systems. Initiation was by chemical reagent (potassium persulfate) or γ-radiation. The unswollen PSDs at various times during interval II of the polymerization were obtained by direct measurement of calibrated electron micrographs. Experimental results were fitted with the equations that describe the time evolution of an initial PSD. Analytic solutions to these equations that allow for entry, exit, and propagation of free radicals were obtained. The values of the rate coefficients for these processes used to fit the experimental data were in excellent agreement with those obtained from dilatometric kinetics experiments.     

Constrained phosphite ester complexes of π-cyclopentadienylmolybdenum tricarbonyl halides

The synthesis of complexes of the type π-C₅H₅Mo(CO)₂LX and π-C₅H₅Mo(CO)L₂X, where XCl, Br, or I and LP(OCH₂)₃CR (RCH₃, C₂H₅, or C₃H₇), is reported. Infrared and conductance data verified that all compounds existed as covalent species in solution. Each of the three π-C₅H₅Mo(CO)₂LCl complexes was isolated as an inseparable mixture of cis and trans isomeric forms. Only the trans forms of the remaining π-C₅H₅Mo(CO)₂LX complexes were observed in solution, as indicated by infrared and PMR spectra. All of the π-C₅H₅Mo(CO)L₂X compounds apparently exist in primarily one isomeric form in solution; their PMR spectra, which exhibited a sharp triplet resonance for the ?OCH₂? protons of the phosphite ligands and a single sharp π-C₅H₅ proton signal, indicated a predominantly trans arrangement of the phosphite ligands at room temperature.     

Synthesis of quinolines, 2-quinolones, phenanthridines, and 6(5h)-phenanthridinones via palladium[0]-mediated Ullmann cross-coupling of 1-bromo-2-nitroarenes with beta-halo-enals, -enones, or -esters

Palladium[0]-mediated Ullmann cross-coupling of 1-bromo-2-nitrobenzene (1 R = H) and its derivatives with a range of beta-halo-enals, -enones, or -esters readily affords the corresponding beta-aryl derivatives, which are converted into the corresponding quinolines, 2-quinolones, phenanthridines, or 6(5H)-phenanthridinones on reaction with dihydrogen in the presence of Pd on C or with TiCl(3) in aqueous acetone. [reaction: see text]     

Quantitative surface characterization using X-ray photoelectron spectroscopy

Use of X-ray Photoelectron Spectroscopy (XPS) for quantitative surface analysis is reviewed. Examples chosen are from our research on heterogeneous catalysts. XPS is useful for measuring distributions of oxidation states because of significant chemical shifts for many elements. However, linewidths complicate analysis of mixtures, necessitating the use of data analysis methodology. Use of factor analysis or deconvolution with non-linear least squares curve fitting gives useful protocols. Five important questions are posed, and some examples of solutions are presented: 1) How many components are present? 2) Where are they located? 3) What do they look like? 4) How much of each component is present? 5) How good is the answer?     

Acidities in cyclohexanediols enhanced by intramolecular hydrogen bonds

Equilibrium gas-phase acidities of the six isomeric cyclohexanediols were measured in a Fourier transform ion cyclotron resonance mass spectrometer. Although all six cyclohexanediols have the same functional groups and similar structures, the acidities vary over 11 kcal/mol. This large difference is due mostly to the balance between hydrogen bonding and geometric strain. To understand the origins of the acidity differences in more detail, the conformations and energetics of the cyclohexanediols were studied using density functional theory, which gave good agreement with the experimental acidities. Finally, methanol-methoxide and methanol-methanol interactions were used as a model for the hydrogen bonding.     

Two unusual, competitive mechanisms for (2-ethynylphenyl)triazene cyclization: pseudocoarctate versus pericyclic reactivity

The cyclization of (2-ethynylphenyl)triazenes in ODCB at 200 degrees C gives exclusively cinnolines, whereas addition of CuCl to 1,2-dichloroethane solutions of the triazenes at 50 degrees C results in the sole formation of isoindazoles. DFT calculations and deuterium labeling studies suggest the intermediacy of a 3-dehydrocinnolinium ion, produced through a pericyclic transition state. Calculations and trapping studies strongly implicate a carbene intermediate in isoindazole formation, which proceeds through a pseudocoarctate transition state.     

Metal salt catalyzed carbenoid—XIII: On the mechanisms of cyclopropanation and allylic CH insertions by diazo esters in the presence of olefins and homogeneous copper catalysts

Evidence is presented demonstrating the existence of two paths to the title processes which arise from a common intermediate. A rationale involving catalyzed addition of the diazo compound to the olefin and carbenoid addition to the olefin is proposed. The penultimate intermediate has one new CC bond formed. It is partitioned between products by forming the second CC bond or formation of a hydrocarbenoid allyl complex which collapses to the allylic CH insertion products. Cyclopropanation occurs stereospecifically. The proposed mechanism accounts for the stereospecificity of cyclopropanation, the variance of syn/anti ratios with catalyst concentration when diazoacetic ester is employed and optical inductions with chiral catalysts. The question of whether the alleged carbenoid and/or the penultimate intermediate contain N₂ is not answered although it is felt that a cupro-cyclobutane intermediate is the most probable intermediate before product partitioning.     

Kinetic study of anhydride formation during thermal degradation of isotactic and atactic polymethacrylic acid

A kinetic study of anhydride formation in isotactic and atactic polymethacrylic acids (PMA) has been performed at about 200° using a vacuum thermobalance. The results obey first order kinetics and show that the rate of water loss is about four times higher for the isotactic PMA than for the atactic isomer. The activation energies are almost identical (42 ± 1 kcal per mole); it is concluded that the arrangement of neighbouring carboxyl groups is more favourable for the formation of a cyclic anhydride by intramolecular reaction in the case of the isotactic PMA.