A new expression for the direct quantum mechanical evaluation of the thermal rate constant

Based on the formalism of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889(1983)], we derive a new expression for the thermal rate constant for a chemical reaction. The expression involves an unperturbed, i.e., reactant or product channel Boltzmann operator for the imaginary time propagation, making it possible to compute efficiently the rate constant for a range of temperatures. We illustrate numerical aspects with an extensive study of the one-dimensional Eckart barrier problem, as well as a study of the three-dimensional (J = 0) D + H2 problem.     

Second-order perturbation theory for the angular pair correlation function in molecular fluids

Second-order perturbation theory is used to calculate spherical harmonic coefficients of the angular pair correlation function g(rω₁ω₂) for a liquid in which the molecules interact with a pair potential that is the sum of Lennard-Jones and quadrupole-quadrupole parts. The theory is compared with both molecular dynamics results and with the predictions of the GMF ≡ LHNC, QHNC and first-order perturbation theories. Second-order perturbation theory gives excellent results for the harmonic coefficient g(224,r), but is poorer for g(222,r) and g(202,r).     

From solution-phase to solid-phase enyne metathesis: crossover in the relative performance of two commonly used ruthenium pre-catalysts

A crossover in the ability of two distinct ruthenium-based metathesis pre-catalysts to effect the synthesis of dialkenylboronic esters in solution and on the solid-phase was observed. Specifically, while the Grubbs 2nd generation pre-catalyst 3 affords a greater degree of conversion to product than the Hoveyda-Grubbs pre-catalyst 2 in a solution-phase enyne-metathesis reaction, this trend is reversed in the solid-phase variant. Systematic investigation showed this trend to be general, regardless of variations in the homoallylic alcohol and alkynylboronic ester components of the reaction, as well as in the type of solid support employed. Experiments to determine a mechanistic hypothesis for this trend highlighted the significance of the ruthenium remaining bound to the substrate after metathetic rearrangement and found the presence of phosphine ligand to be detrimental to the success of the solid-phase reaction. Therefore, these results suggest an expanded role for phosphine-free pre-catalysts, such as 2, in challenging solid-phase metathesis reactions.     

Monte Carlo study of the pair correlation function for a liquid with non-central forces

The pair correlation function g(R), giving the probability that the centers of two nonspherical molecules are a distance R apart irrespective of their orientations, has been studied by the Monte Carlo method. The pair potential model studied is of the type u_o + u_a, where u_o is the isotropic Lennard-Jones (12,6) potential and u_a is either a dipole-dipole, quadrupole-quadrupole, or anisotropic overlap interaction. Dipolar and quadrupolar forces are found to have a small effect on g(R), whereas anisotropic overlap forces have a large effect.