The vibrational frequencies of CaO2, ScO2, and TiO2: a comparison of theoretical methods

The vibrational frequencies of several states of␣CaO₂, ScO₂, and TiO₂ are computed using density functional theory (DFT), the Hartree-Fock approach, second-order M?ller-Plesset perturbation theory (MP2), and the complete-active-space self-consistent-field theory. Three different functionals are used in the DFT calculations, including two hybrid functionals. The coupled cluster singles and doubles approach including the effect of connected triples, determined using perturbation theory, is applied to selected states. The Becke-Perdew 86 functional appears to be the most cost-effective method of choice, although even this functional does not perform well for one state of CaO₂. The MP2 approach is significantly inferior to the DFT approaches. Received: 3 September 1997 / Accepted: 8 December 1997     

Gaseous H5P2O8- ions: a theoretical and experimental study on the hydrolysis and synthesis of diphosphate ion

The structure and reactivity of gaseous H5P2O8- ions obtained from the chemical ionization (CI) of an H4P2O7/H2O mixture and from electrospray ionization (ESI) of CH3CN/H2O/H4P2O7 solutions were investigated by Fourier transform ion cyclotron (FTICR) and triple quadrupole mass spectrometry. Theoretical calculations performed at the B3LYP/6-31+G* level of theory and collisionally activated dissociation (CAD) mass spectrometric results allowed the ionic population obtained in the CI conditions to be structurally characterized as a mixture of gaseous [H3P2O7...H2O]-, [H3PO4...H2PO4]-, and [PO3...H3PO4...H2O]- clusters. The energy profile emerging from theoretical calculations affords insight into the mechanism of diphosphate ion hydrolysis and synthesis.     

On the determination of deformation from strain

The problem of finding a deformation corresponding to a given Cauchy–Green strain is approached with a procedure that employs the Gram decomposition of the deformation gradient. It is shown that the rotation occurring in that decomposition can be obtained by solving a system of partial differential equations in the group of rotations or in its Lie algebra. The equivalence between the integrability conditions of these two systems and those of the systems of equations arising in the usual procedures for determining a deformation from the strain is proved. Examples of application of the proposed procedure are given.     

One-Dimensional Ising Models with Long Range Interactions: Cluster Expansion,Phase-Separating Point

We consider the phase separation problem for the one-dimensional ferromagnetic Ising model with long-range two-body interaction, J(n) = n ^?2+α , where ${n\in {\rm {I\!N}}}$ denotes the distance of the two spins and ${\alpha \in [0,\alpha_+[}$ with α ₊ = (log 3)/(log 2) ?1. We prove that when α = 0 the localization of the phase separation fluctuates macroscopically with a non-uniform explicit limiting law, while when 0 < α < α ₊ the macroscopic fluctuations disappear and mesoscopic ones appear with a gaussian behavior when conveniently scaled. The mean magnetization profile is also given.     

Study of a Long Range Perturbation of a One-Dimensional Kac Model

We consider a one dimensional ferromagnetic Ising spin system with interactions that correspond to a 1/r ² long range perturbation of the usual Kac model. We apply a coarse graining procedure widely used for higher-dimensional finite range Kac potentials to describe the basic properties of the system and the relation with the mean field theory.     

Low temperature kinetics, crossed beam dynamics and theoretical studies of the reaction S((1)D) + CH4 and low temperature kinetics of S((1)D) + C2H2

The reaction between sulfur atoms in the first electronically excited state, S((1)D), and methane (CH(4)), has been investigated in a complementary fashion in (a) crossed-beam dynamics experiments with mass spectrometric detection and time-of-flight (TOF) analysis at two collision energies (30.4 and 33.6 kJ mol(-1)), (b) low temperature kinetics experiments ranging from 298 K down to 23 K, and (c) electronic structure calculations of stationary points and product energetics on the CH(4)S singlet potential energy surface. The rate coefficients for total loss of S((1)D) are found to be very large (ca. 2 × 10(-10) cm(3) molec(-1) s(-1)) down to very low temperatures indicating that the overall reaction is barrier-less. Similar measurements are also performed for S((1)D) + C(2)H(2), and also for this system the rate coefficients are found to be very large (ca. 3 × 10(-10) cm(3) molec(-1) s(-1)) down to very low temperatures. From laboratory angular and TOF distributions at different product masses for the reaction S((1)D) + CH(4), it is found that the only open reaction channel at the investigated collision energies is that leading to SH + CH(3). The product angular, T(θ), and translational energy, P(E'(T)), distributions in the center-of-mass frame are derived. The reaction dynamics are discussed in terms of two different micromechanisms: a dominant long-lived complex mechanism at small and intermediate impact parameters with a strongly polarized T(θ), and a direct pickup-type (stripping) mechanism occurring at large impact parameters with a strongly forward peaked T(θ). Interpretation of the experimental results on the S((1)D) + CH(4) reaction kinetics and dynamics is assisted by high-level theoretical calculations on the CH(4)S singlet potential energy surface. The dynamics of the SH + CH(3) forming channel are compared with those of the corresponding channel (leading to OH + CH(3)) in the related O((1)D) + CH(4) reaction, previously investigated in crossed-beams in other laboratories at comparable collision energies. The possible astrophysical relevance of S((1)D) reactions with hydrocarbons, especially in the chemistry of cometary comae, is discussed.