Search results for "Tetrahedron"
showing 10 items of 75 documents
Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models
1997
Abstract A new algebraic treatment of a three-oscillator system, called 3d formalism, is proposed. First, arbitrary tensor operators, expressed in terms of elementary creation and annihilation boson operators, are built within the standard algebraic chain u (3) ⊃ so (3) ⊃ so (2). Their matrix elements are next derived in a standard basis. Some applications, which require few adaptions or extensions, are proposed. They allow one to recover, for instance, Hecht's and tetrahedral Hamiltonians associated with threefold degenerate modes of spherical molecules and the vibron model Hamiltonian introduced for diatomic molecules.
Calculated rJ2-type effective dipole moment parameters for fundamental bands of tetrahedral XY4 molecules
1991
Abstract Formulas in terms of basic molecular constants are presented for effective dipole moment parameters which are responsible for second-order corrections to the line intensities of fundamental bands of tetrahedral XY 4 molecules. Two cases have been considered. In the first case all bands were considered as separate bands. In the second case the ν 2 and ν 4 bands were considered as interacting bands. The influence of effective Hamiltonian transformations on effective dipole moment parameters has been studied. Numerical calculations of effective dipole moment parameters for the ν 2 and ν 4 bands of 12 CH 4 have been performed. There is reasonable agreement between calculated and fitted…
Model calculations of phase diagrams of magnetic alloys on the body-centered-cubic lattice.
1987
We treat a model for a binary (AB) alloy, where species A is magnetic (Ising spin σi = ± 1) while species B is not, and repulsive interactions are assumed between first and second neighbors of the same kind, in addition to a nearest-neighbor ferromagnetic exchange interaction. Both the mean-field approximation, the cluster variation (CV) method in the tetrahedron approximation and the Monte Carlo (MC) method are applied; comparing the phase diagrams obtained by the various approximations their accuracy is tested. It is shown that the CV method is in rather close agreement with the MC method for the present problem.
First Assignment and Line Strengths of the 4ν4 Band of 12CH4 near 1.9 μm
2001
Abstract The investigation of the methane spectrum in the region 1.6–2 μm has provided the first assignment and analysis of the 4ν 4 band near 1.9 μm. Hamiltonian and dipole moment operators written in tetrahedral formalism and adapted to the extrapolation method have been used to fit the spectra recorded at the Kitt Peak National Observatory/National Solar Observatory. Nearly 190 line positions and 160 measured intensities have been modeled with standard deviations of 0.107 cm −1 and 18.5%, respectively.
Simultaneous Determination of Force Constants and Dipole Moment Derivatives of Methane.
1998
The expressions of the effective Hamiltonian and dipole moment spectroscopic parameters in the tetrahedral formalism are used simultaneously to fit the force field and dipole moment derivatives of the methane molecule. Data, the so-called "observed parameters," are the values of the spectroscopic parameters determined from the frequencies and line strengths analyses. The ambiguities of most parameters (in the polyad scheme) are treated consistently with the Hamiltonian reduction chosen in the frequency analyses. As an illustration, the method is applied to the tetrahedral XY4 isotopic species only. The quadratic and cubic force field constants have been determined in addition to the linear …
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
2018
We consider inequalities of the Poincare–Steklov type for subspaces of \(H^1\)-functions defined in a bounded domain \(\varOmega \in \mathbb {R}^d\) with Lipschitz boundary \(\partial \varOmega \). For scalar valued functions, the subspaces are defined by zero mean condition on \(\partial \varOmega \) or on a part of \(\partial \varOmega \) having positive \(d-1\) measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of \(\partial \varOmega \) (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincare type inequalities for domains typically used in finite …
Speed-dependent broadening and line mixing in CH4 perturbed by Ar and N2 from multispectrum fits
2000
International audience; Speed-dependent broadenings and shifts have been determined for the P and R branches of the nu3 band of CH4 perturbed by Ar and N2 using a multispectrum fitting analysis of high-resolution tunable difference-frequency laser spectra recorded at pressures 3, the tetrahedral fine structure components in each J manifold are collisionally coupled and exhibit significant interference. The coupled lines are treated using a speed-dependent first-order line-mixing profile and are compared to a speed-independent full relaxation matrix inversion procedure with off-diagonal coupling elements calculated from an atom-atom Lennard-Jones potential model.
Intermediate Range Order in Silicate Melts and Glasses: Computer Simulation Studies
2002
ABSTRACTWe present the results of large scale computer simulations to discuss the structural and dynamic properties of silicate melts with the compositions (Na2O)(2·SiO2), (Na2O)(20·SiO2) and (Al2O3)(2·SiO2). We show that these systems exhibit additional intermediate range order as compared to silica (SiO2) where the characteristic intermediate length scales stem from the tetrahedral network structure. Furthermore we show that the sodium dynamics in the sodium silicate systems exhibits a very peculiar feature: the long–time decay of the incoherent intermediate scattering function can be described by a Kohlrausch law with a constant exponent β for q > qth whereby qth is smaller than the l…
The dynamics of melts containing mobile ions: computer simulations of sodium silicates
2003
We present the results of large-scale computer simulations in order to discuss the structural and dynamic properties of sodium silicate melts with the compositions (Na2O)2(SiO2) (NS2) and (Na2O)20(SiO2) (NS20). We show that, compared to silica (SiO2), these systems exhibit additional intermediate range order on intermediate length scales that stem from the tetrahedral network structure. By means of intermediate-scattering functions, we characterize the dynamics of sodium in the system under consideration. Whereas in NS2 the incoherent scattering functions for Na decay much faster to zero than the coherent ones for Na–Na, in NS20 this different behaviour of the incoherent and coherent functi…
Tetraaryl-methane analogues in group 14—V. Distortion of tetrahedral geometryin terms of through-space π–π and π–σ interactions andNMR sagging in ter…
1998
Abstract 44 members of thecompound series Ph4−nMRn (M=Si, Ge, Sn, Pb; R=o-, m-, p-Tol; n=0–4) were synthesized (15 newcompounds). The crystal structures of Ph3Sn (o-Tol) and PhSn (o-Tol)3 were determined and compared to 16 known structures. Subject to the distanced (M–C), an interplay between through-space π–π repulsion and π–σ attraction leads to either elongated or compressed tetrahedral geometry. 29 Si-, 119 Sn- and 207 Pb-NMR chemical shifts were determined in solution and in the solid state.73 Ge chemical shifts were measured only in solution. Anupfield or downfield sagging of the chemical shifts along each series is rationalized in terms of a π–σcharge transfer which is constrained by…