Showing papers on "Normal coordinates published in 1990"
TL;DR: In this paper, a rigorous derivation of the relationship between the vibrational coordinates belonging to two different electronic states of a polyatomic molecule is given, and it is shown that this transformation is generally nonlinear and nonorthogonal.
74 citations
TL;DR: A system of programs for treating normal coordinates of chain molecules is presented, applicable not only to specific research in vibrational spectroscopy, but also to casual calculations by nonspecialists.
15 citations
TL;DR: Using properties of shift- and rotation-invariance probability density distributions are derived for random straight lines in normal representation and found that in two-dimensional space the distribution of normal coordinates is uniform.
13 citations
TL;DR: In this paper, the ZFS part of a spin Hamiltonian is expressed in terms of the distortion along normal coordinates and the coefficients characteristic of a metal-ligand combination, which is particularly useful in the calculation of ZFS under non-axial distortions.
Abstract: A systematic approach is developed for the ZFS (zero-field splitting) parameters D and E in slightly distorted tetrahedral and octahedral complexes with spatially non-degenerate ground states. This approach is illustrated by treatment of the normal coordinate system. The ZFS part of a spin Hamiltonian is expressed in terms of the distortion along normal coordinates and the coefficients characteristic of a metal-ligand combination. This expression for a spin Hamiltonian clarifies the relation between the ZFS and the distortions of the coordination geometry from Td and Oh symmetries, and is particularly useful in the calculation of the ZFS under non-axial distortions. Some of the coefficients are derived for the ground A2 state (tetrahedral d7 and octahedral d3) ions in terms of the e σ and e π parameters of the angular overlap model. Satisfactory agreement is obtained in the application of the approach to Cs3CoCl5, Cs2CoCl4 and ruby.
6 citations
TL;DR: In this article, a detailed discussion of the dipole moment derivative with respect to normal coordinates, PQ, and in cartesian coordinates PX, for HCN is presented, and the definitive reason for the controversy about the relative signs of PQs is shown.
2 citations
TL;DR: A formalism is developed which can be used to compute the components of connections and curvature tensors relative to four-metrics with half-flat curvature.
Abstract: Orthonormal frames adapted to normal coordinate systems are considered. A formalism is developed which can be used to compute the components of connections and curvature tensors relative to such frames. An application to four-metrics with half-flat curvature is presented.
15 Apr 1990
TL;DR: In this article, a nonlinear transformation between the normal coordinates of an initial bound state of a symmetric bent triatomic molecule and the scattering coordinates of a dissociative state is given for describing the initial phase of dissociation reactions as well as the receding motion of the dissociating fragments on the repulsive potential surface.
Abstract: A nonlinear transformation between the normal coordinates of an initial bound state of a symmetric bent triatomic molecule and the scattering coordinates of a dissociative state is given. The transformation is appropriate for describing the initial phase of dissociation reactions as well as the receding motion of the dissociating fragments on the repulsive potential surface. This has certain advantages in comparison with a reaction path approach. As an application to a real system, an analytical expression is presented for the nonadiabatic electronic coupling term between states 2B2/2A′ and 2A1/2A′ of the H2O+ molecule, which decomposes into an atom and diatom fragment due to electronic predissociation.