Enthalpy of formation of the cyclopentadienyl radical: photoacoustic calorimetry and ab initio studies

The gas-phase C-H bond dissociation enthalpy (BDE) in 1,3-cyclopentadiene has been determined by time-resolved photoacoustic calorimetry (TR-PAC) as 358 +/- 7 kJ mol(-1). Theoretical results from ab initio complete basis-set approaches, including the composite CBS-Q and CBS-QB3 procedures, and basis-set extrapolated coupled-cluster calculations (CCSD(T)) are reported. The CCSD(T) prediction for the C-H BDE of 1,3-cyclopentadiene (353.3 kJ mol(-1)) is in good agreement with the TR-PAC result. On the basis of the experimental and the theoretical values obtained, we recommend 355 +/- 8 kJ mol(-1) for the C-H BDE of 1,3-cyclopentadiene and 271 +/- 8 kJ mol(-1) for the enthalpy of formation of cyclopentadienyl radical.     

Internal energy content of n-butylbenzene, bromobenzene, iodobenzene and aniline molecular ions generated by two-photon ionization at 266 nm. A photodissociation study

A technique to investigate photodissociation kinetics on a nanosecond time scale has been devised for molecular ions generated by multiphoton ionization (MPI) using mass-analyzed ion kinetic energy spectrometry. The branching ratio or rate constant has been determined for the photodissociation of the n-butylbenzene, bromobenzene, iodobenzene, and aniline molecular ions generated by MPI at 266 nm. The ion internal energies have been estimated by comparing the measured kinetic data with the previous energy dependence data. The analysis has shown that only those molecular ions generated by two-photon ionization contribute to the photodissociation signals. Around half of the available energy has been found to remain as molecular ion internal energy in the two-photon ionization process. Copyright 1999 John Wiley & Sons, Ltd.     

Density functional theory study of adsorption of OOH on Pt-based bimetallic clusters alloyed with Cr, Co, and Ni

The adsorption of OOH, the main product of the first step in the O₂ reduction on Pt(1 1 1) surfaces, is studied on Pt-based bimetallic three-atom clusters. Cr, Co, and Ni are better adsorption sites for OOH than Pt, but the strong adsorption might not favor the dissociation of OOH. However, the presence of Cr, Co, or Ni in the vicinity of a Pt atom increases its electron density, enhancing the Pt ability to transfer electrons to oxygenated species. Thus, Cr, Co, or Ni in the subsurface, rather than on the exposed surface, may contribute favorably to catalyze the O₂ reduction.     

Performance of multiplicity-based energy correctors for molecules containing second-row elements

We introduce a posteriori multiplicity-based corrections to ab initio energies in order to reproduce experimental atomization energies. This simple approach, as compared to the alternative ones to improve density functionals and standard correlated methods, requires less computational resources than higher levels of theory. We extend our approach to include molecules containing second-row elements. Molecules are taken from the Gaussian sets for which experimental values are known with errors of less than 1 kcal/mol. We postulate that inexpensive multiplicity-based corrections can account for effects that are not accounted because of the low level of theory of the method or because of the small basis used for the calculations.     

Perfluorobutyric Acid and Its Monohydrate: A Chirped Pulse and Cavity Based Fourier Transform Microwave Spectroscopic Study

Rotational spectra of perfluorobutyric acid (PFBA) and its monohydrate were studied with a broadband chirped pulse and a narrow‐band cavity based Fourier transform microwave spectrometer, and high‐level ab initio calculations. Extensive conformational searches were performed for both the acid and its monohydrate at the MP2/6‐311++G(2d,p) level of theory. Two and three conformers were predicted to exist for PFBA and its monohydrate, respectively. One set of rotational transitions was observed and assigned for each, PFBA and its monohydrate. Based on the measured broadband spectra, we confidently conclude that only one dominant conformer exists in each case. The orientation of the hydroxyl group in PFBA was determined by using isotopic analysis. Comparison of the observed transition intensities and the calculated electric dipole moment components allowed us to identify the most stable monohydrate conformation, which takes on an insertion hydrogen‐bonding topology. Comparisons to the shorter chain analogues, that is, trifluoroacetic acid, perfluoropropionic acid, and their monohydrates, are made to elucidate the general trend in their conformational preference and binding topologies.     

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.     

Eulerian polynomials via the Weyl algebra action

Journal of Algebraic Combinatorics - Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family...     

Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Energy correctors for accurate prediction of molecular energies

Energy correctors are introduced for the calculation of molecular energies of compounds containing first row atoms (Li-F) to modify ab initio molecular orbital calculations of energies to better reproduce experimental results. Four additive correctors are introduced to compensate for the differences in the treatment of molecules with different spin multiplicities and multiplicative correctors are also calculated for the electronic and zero-point vibrational energies. These correctors, individually and collectively yield striking improvements in the atomization energies for several ab initio methods. We use as training set the first row subset of molecules from the G1 basis of molecules; when the correctors are applied to other molecules not included in the training set, selected from the G3 basis, similar improvements in the atomization energies are obtained. The special case of the B3PW91/cc-pVTZ yields an average error of 1.2 kcal/mol, which is already within a chemical accuracy and comparable to the Gaussian-n theories accuracy. The very inexpensive B3PW91/6-31G** yields an average error of 2.1 kcal/mol using the correctors. Methods considered unsuitable for energetics such as HF and LSDA yield corrected energies comparable to those obtained with the best highly correlated methods.