Dynamic effects on the periselectivity, rate, isotope effects, and mechanism of cycloadditions of ketenes with cyclopentadiene

The cycloadditions of cyclopentadiene with diphenylketene and dichloroketene are studied by a combination of kinetic and product studies, kinetic isotope effects, standard theoretical calculations, and trajectory calculations. In contrast to recent reports, the reaction of cyclopentadiene with diphenylketene affords both [4 + 2] and [2 + 2] cycloadducts directly. This is surprising, since there is only one low-energy transition structure for adduct formation in mPW1K calculations, but quasiclassical trajectories started from this single transition structure afford both [4 + 2] and [2 + 2] products. The dichloroketene reaction is finely balanced between [4 + 2] and [2 + 2] cycloaddition modes in mPW1K calculations, as the minimum-energy path (MEP) leads to different products depending on the basis set. The MEP is misleading in predicting a single product, as trajectory studies for the dichloroketene reaction predict that both [4 + 2] and [2 + 2] products should be formed. The periselectivity does not reflect transition state orbital interactions. The (13)C isotope effects for the dichloroketene reaction are well-predicted from the mPW1K/6-31+G** transition structure. However, the isotope effects for the diphenylketene reaction are not predictable from the cycloaddition transition structure and transition state theory. The isotope effects also appear inconsistent with kinetic observations, but the trajectory studies evince that nonstatistical recrossing can reconcile the apparently contradictory observations. B3LYP calculations predict a shallow intermediate on the energy surface, but trajectory studies suggest that the differing B3LYP and mPW1K surfaces do not result in qualitatively differing mechanisms. Overall, an understanding of the products, rates, selectivities, isotope effects, and mechanism in these reactions requires the explicit consideration of dynamic trajectories.     

Summation methods of Coulomb interactions in computer simulations of a system with one—dimensional periodic boundary conditions

The Ewald-type method, its modified version and the Lekner-type method for summing Coulomb interactions in a system periodic along one direction are presented and compared. Advantages and disadvantages of these methods are discussed, and the methods are tested in molecular dynamics simulations of acetone molecules confined to cylindrical silica pores.     

Electrostatic interactions in molecular dynamics simulation of a three-dimensional system with periodicity in one direction

The Mellin transform and Poisson summation formula are used to derive an expression for the Coulomb interaction energy of a three-dimensional system with periodicity in one direction. Initially, calculations are performed for interactions characterized by any inverse power and, using the analytical continuation of the energy function, one obtains the final expression for the interaction energy of charges. We consider also a special case when two different charges are located on a line parallel to the periodicity direction. The energy and force expressions are identical to those obtained from the Lekner summation which is simply a sum over reciprocal lattice terms. The convergence behaviour of the Lekner summation is compared with that based on the Ewald type approach.     

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.     

Isotope effects, dynamics, and the mechanism of solvolysis of aryldiazonium cations in water

The mechanism of the heterolytic solvolysis of p-tolyldiazonium cation in water was studied by a combination of kinetic isotope effects, theoretical calculations, and dynamics trajectories. Significant (13)C kinetic isotope effects were observed at the ipso (k(12)C/k(13)C = 1.024), ortho (1.017), and meta (1.013) carbons, indicative of substantial weakening of the C(2)-C(3) and C(5)-C(6) bonds at the transition state. This is qualitatively consistent with a transition state forming an aryl cation, but on a quantitative basis, simple S(N)1 heterolysis does not account best for the isotope effects. Theoretical S(N)2Ar transition structures for concerted displacement of N(2) by a single water molecule lead to poor predictions of the experimental isotope effects. The best predictions of the (13)C isotope effects arose from transition structures for the heterolytic process solvated by clusters of water molecules. These structures, formally saddle points for concerted displacements on the potential energy surface, may be described as transition structures for solvent reorganization around the aryl cation. Quasiclassical dynamics trajectories starting from these transition structures afforded products very slowly, compared to a similar S(N)2 displacement, and the trajectories often afforded long-lived aryl cation intermediates. Critical prior evidence for aryl cation intermediates is reconsidered with the aid of DFT calculations. Overall, the nucleophilic displacement process for aryldiazonium ions in water is at the boundary between S(N)2Ar and S(N)1 mechanisms, and an accurate view of the reaction mechanism requires consideration of dynamic effects.