Ab-initio density-functional lattice-dynamics studies of ice

We present the results of first-principles computational studies of the dynamical properties of hexagonal ice using both the ab-initio pseudopotential method and the full-potential augmented plane-wave method. Properties obtained using both the generalized gradient approximation (GGA) and the meta-GGA in density-functional theory are compared. The lattice-dynamical properties of the structures are obtained using a finite-difference evaluation of the dynamical matrix and force-constant matrix from atomic forces. Phonon dispersion is evaluated by the direct determination of the force-constant matrix in supercells derived from the primitive molecule unit cells with the assumption that force constants are zero beyond the second molecular nearest neighbors. The k-dependent phonon frequencies are then obtained from the force-constant matrix and dispersion relations, and the Brillouin-zone integrated density of states is evaluated. The importance of phonon dispersion in the various regions of the phonon spectra is then assessed and compared to existing neutron-scattering data. Frozen-phonon calculations are used to compare phonon frequencies evaluated in both the GGA and meta-GGA. PACS Nos.: 61.12Ex, 63.20Dj

A Comparative Study of the BJH- and MCYL-Type Potentials Applied to the Gaseous Water Dimer

Various refined potentials describing the intra- and inter-molecular force fields of water molecules arc used to calculate the properties of the gas-phase water dimer. The intra-molecular parts have been taken from spectroscopic or quantum-chemical sources. The minimum energy structure was found iteratively using the first derivatives of the potential; the force-constant matrix was constructed by numerical difierentation. A quite close agreement between the Bopp-Jancso-Heinzinger and the Matsuoka-Clementi-Yoshimine-Lie potentials is found. The treatment is applied to seven observed water-dimer isotopomeric isomerizations

Calculationof Equilibrium Isotope Effects in a Conformationally Mobile Carbocation

The rapid, degenerate 1,2-hydride shift in 2,3-dimethyl-2-butyl cation in stable solution in SbF5/SO2C1F was perturbed by deuterium and 13C leading to splittings observed by 13C NMR spectroscopy over a range of temperatures. Accurate values for equilibrium isotope effects were obtained from these data. Theoretical calculations of the equilibrium isotope effects were performed using the Gaussian-86 program to obtain an optimized geometry and the Cartesian force constant matrix, followed by the program QUIVER which applies the Bigeleisen-Mayer method. When all of the conformers, which are in rapid equilibrium, were considered specifically, quite good agreement between theory and experiment was obtained.

Die Anwendbarkeit verschiedener Näherungsmethoden zur Berechnung von Kraftkonstanten bei Säkulargleichungen der Ordnung n > 2 / The Applicability of Different Approximation Methods for the Calculation of Force Constants in Secular Equations of Order n > 2

Force constants for molecules with secular equations of order n > 2 have been determined with the help of various approximation methods based on the General Valence Force Field. The applicability of the approximations have been tested empirically. It cannot be predicted with certainty whether any approximation method yields reliable force constants. Some methods have been found to be inapplicable. The calculation of off-diagonal force constants with any approximation method is impossible. The principle of the quasi-determination of off-diagonal force constant matrix elements from the form of the G matrix on which most approximation methods are based, is critically discussed. It is shown that diagonal force constants calculated with approximation methods are more reliable if the coupling between the vibrations in the same species is low. The application of approximation methods for the determination of force constants without critical consideration is not meaningful.