Search results for "Normal coordinates"
showing 4 items of 4 documents
Vibrational Energy Levels via Finite-Basis Calculations Using a Quasi-Analytic Form of the Kinetic Energy
2015
A variational method for the calculation of low-lying vibrational energy levels of molecules with small amplitude vibrations is presented. The approach is based on the Watson Hamiltonian in rectilinear normal coordinates and characterized by a quasi-analytic integration over the kinetic energy operator (KEO). The KEO beyond the harmonic approximation is represented by a Taylor series in terms of the rectilinear normal coordinates around the equilibrium configuration. This formulation of the KEO enables its extension to arbitrary order until numerical convergence is reached for those states describing small amplitude motions and suitably represented with a rectilinear system of coordinates. …
Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations
2015
We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\ensuremath{\alpha}$ and shift ${\ensuremath{\beta}}^{i}$ on the respective time slice, as they are fixed to Gaussian normal coordinates while leaving the coordinate label…
Inelastic neutron scattering study of proton dynamics in Ca(OH)2 at 20 K
1995
Abstract Inelastic neutron scattering (INS) spectra of Ca(OH) 2 at 20 K are presented from 30 to 4000 cm −1 for a powder sample, from 30 to 12000 cm −1 for an oriented single-crystal. INS band splitting due to the lattice density-of-states is observed. Polarization effects reveal the orientation of atomic displacements for each mode and a new band assignment scheme is proposed. For the single-crystal, the v OH mode and overtones are observed. This oscillator shows only moderate anharmonicity. Spectrum simulation reveals that INS spectral intensities are not consistent with simple normal coordinates and harmonic force-fields for Ca(OH) 2 entities. A new dynamical model is proposed, including…
Expressions of Effective Hamiltonian Parameters of XY4 Molecules in the Tetrahedral Formalism
1998
We have derived expressions of second-order effective Hamiltonian parameters of XY4 molecules in the tetrahedral formalism (1992, J. P. Champion et al., "Spectroscopy of the Earth's Atmosphere and Interstellar Medium: Spherical Top Spectra," Academic Press, San Diego). They are written as a function of the force constants of the potential expanded in terms of the dimensionless normal coordinates. These expressions can be used in the isolated band scheme as well as in the polyad one. The ambiguity of the effective Hamiltonian parameters is treated. Relations between the parameters for q2 and q4 terms and Hecht's anharmonicity constants (1960, K. T. Hecht, J. Mol. Spectrosc. 5, 355-389) in th…