A Glivenko-Cantelli Theorem and Strong Laws for L-Statistics

We prove a weighted Glivenko-Cantelli theorem and apply it to study the rate of convergence in the strong law for L-statistics.     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.     

A growing string method for determining transition states: comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.     

The Stereochemistry of simple enols in solution

On the basis of their ¹H n.m.r. spectra it is concluded that vinyl alcohol and $\text{trans}$-1-propenol exist mainly in the $\text{syn}$-conformation and that $\text{cis}$-1-propenol and 2-methyl-1-propenyl exist mainly in the $\text{anti}$ conformation.     

Aquation of α-cis-chloroaquoethylenediamine-N,N'-diacetatocobalt(III) in aqueous and in mixed solvents: A mechanistic study

Summary The displacement of chloride ligands from -cis-chloro-aquoethylenediamine-N,N-diacetatocobalt(III) in nonacidic aqueous solutions was followed conductimetrically at 30–45° and the products of aquation were characterised by conductance, spectral and ion-exchange techniques. The rate constants for aquation in aqueous media and in 1 : 4 v : v mixed solvents at 25° are: 4.0 × 10^–5 s^–1 in H₂O, 2.71 × 10^–5 s^–1 in MeOH : H₂O, 2.74 × 10^–5 s^–1 in EtOH: H₂,O and 2.58 × 10^–5 s^–1 n in Me₂CO : H₂O. The corresponding H* and S* values have also been evaluated. Solvent polarity has a marked influence on the rate of chloride ion release. The aquation rate constants and the activation parameters have been correlated with solvent parameters,e.g. D, Y-values, Dimroth's E_T and Kosower's Z-values and, based on these correlations, a dissociative interchange (I_d) mechanism is proposed rather than dissociative as observed for some other cobalt(III) complexes.Senior author.     

Evidence in support of levitation effect as the reason for size dependence of ionic conductivity in water: a molecular dynamics simulation

We report extensive molecular dynamics simulations of (i) model ions in water at high concentrations as a function of the size and charge of the ion as well as (ii) realistic simulation of Cl- and Br- ions at low concentrations in water at room temperature. We also analyze existing experimental data in light of the results obtained here. The halide ion simulations have been carried out using the interaction potentials of Koneshan et al. (J. Phys. Chem. B 1998, 102, 4193). We compute structural and dynamical properties of ions in water and explore their variation with size and charge of the ion. We find that ions of certain intermediate sizes exhibit a maximum in self-diffusivity in agreement with previous experimental measurements and computer simulations. We analyze molecular dynamics trajectories in light of the previous understanding of the levitation effect (LE) and the recent suggestion that ionic conductivity has its origin in LE (J. Phys. Chem. B 2005, 109, 8120). We report the distribution of void and neck radii that exist amidst water. Our analysis suggests that the ion with maximum self-diffusivity is characterized by a lower activation energy and a single-exponential decay of F(s)(k,t). The behavior of these and other related quantities of the ion with maximum self-diffusivity are characteristic of the anomalous regime of the LE. The simulation results of Br- and Cl- ions in water also yield results in agreement with the predictions of LE. A plot of experimental conductivity data in the literature for alkali ions in water by Kay and Evans (J. Phys. Chem. 1966, 70, 2325) also yields a lower activation energy for the ion with maximum conductivity in excellent agreement with the LE. To the best of our knowledge, none of the existing theories predict a lower activation energy for the ion with maximum conductivity.     

Enhanced reducibility of Ce1-xTixO2 compared to that of CeO2 and higher redox catalytic activity of Ce1-x-yTixPtyO2-delta compared to that of Ce1-xPtxO2-delta

Nanocrystalline Ce(1)(-)(x)Ti(x)O(2) (0 < or = x < or = 0.4) and Ce(1-)(x)(-)(y)Ti(x)Pt(y)O(2)(-)(delta) (x = 0.15, y = 0.01, 0.02) solid solutions crystallizing in fluorite structure have been prepared by a single step solution combustion method. Temperature programmed reduction and XPS study of Ce(1)(-)(x)Ti(x)O(2) (x = 0.0-04) show complete reduction of Ti(4+) to Ti(3+) and reduction of approximately 20% Ce(4+) to Ce(3+) state compared to 8% Ce(4+) to Ce(3+) in the case of pure CeO(2) below 675 degrees C. The substitution of Ti ions in CeO(2) enhances the reducibility of CeO(2). Ce(0.84)Ti(0.15)Pt(0.01)O(2)(-)(delta) crystallizes in fluorite structure and Pt is ionically substituted with 2+ and 4+ oxidation states. The H/Pt atomic ratio at 30 degrees C over Ce(0.84)Ti(0.15)Pt(0.01)O(2)(-)(delta) is 5 and that over Ce(0.99)Pt(0.01)O(2)(-)(delta) is 4 against just 0.078 for 8 nm Pt metal particles. Carbon monoxide and hydrocarbon oxidation activity are much higher over Ce(1-)(x)(-)(y)Ti(x)Pt(y)O(2) (x = 0.15, y = 0.01, 0.02) compared to Ce(1)(-)(x)Pt(x)O(2) (x = 0.01, 0.02). Synergistic involvement of Pt(2+)/Pt degrees and Ti(4+)/Ti(3+) redox couples in addition to Ce(4+)/Ce(3+) due to the overlap of Pt(5d), Ti(3d), and Ce(4f) bands near E(F) is shown to be responsible for improved redox property and higher catalytic activity.     

One-pot synthesis of furo[2,3-h]quinoline and furo[2,3-h]isoquinoline derivatives using Fischer carbene complex

A new route for the synthesis of furo[2,3-h]quinoline and furo[2,3-h]isoquinoline derivatives have been explored through the coupling of carbene complexes with pyridine-bridged enynes. This reaction process, involving the annulation of both furan and benzene ring on to a pre-existing pyridine ring is highly efficient in the presence of triphenylphosphine as ligand additive.     

The first examples of anthracene capped chiral carbohydrate derived dendrimers: synthesis, fluorescence and chiroptical properties

The first examples of anthracene capped chiral dendrimers derived from a 1,3,5-trisubstituted aromatic core and carbohydrate units in the interior and periphery are described. Excimer formation was evident from the fluorescence spectrum, and both fluorescence and chiroptical properties indicated that the dendrimer does not undergo aggregation in the ground state.     

Lewis acid-mediated highly regioselective SN2-Type ring-opening of 2-aryl-N-tosylazetidines and aziridines by alcohols

Lewis acid-mediated highly regioselective SN2-type ring-opening of 2-aryl-N-tosylazetidines with alcohols to afford various 1,3-amino ethers in excellent yields with good enantiomeric excess is described. Similar SN2-type ring-opening of chiral 2-phenyl-N-tosylaziridine with various alcohols produces the corresponding nonracemic 1,2-amino ethers in excellent yields and good ee. The mechanism of the ring-opening of aziridines and azetidines via an SN2 pathway is supported by the formation of nonracemic amino ethers.