Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: a first application to aromatic hydrocarbons

Abstract

Evaluation of temperature factors from a harmonic lattice-dynamical theory of molecular crystals has been applied to some aromatic hydrocarbons in the non-rigid case: i.e. mixing of lattice vibrations with the lowestfrequency internal modes. The calculations start from known atomic coordinates, unit-cell parameters and symmetry operations, using Cail fano-Neto potentials for in-plane modes, Williams IVa potentials for intermolecular interactions, and an overall value of 0.9 nN A for any twisting around C-C bonds. Molecular motions inside the crystal are described on the basis of normal coordinates of the isolated molecule, by applying Gwinn's method. For some molecules (benzene and naphthalene) the rigid-body approximation is adequate for the carbon-atom framework, and practically no coupling occurs between the lattice vibrations and the internal motion. For anthracene and phenanthrene, there are differences between rigid-body and non-rigid estimates of temperature factors. Molecular vibration tensors T, L, and S can be calculated, and also a general molecular displacement matrix (tensor). including even the internal modes (W), which permits extension of the rigid-body analysis to non-rigid molecules.

Lattice dynamics and thermal crystallographic parameters in phenothiazine

“…A great variety of potential parameters are available in the literature to describe the interactions of C and H atoms. We have selected set IVa of Williams (1967) which has been used successfully for obtaining thermal crystallographic parameters in aromatic hydrocarbons (Filippini, Gramaccioli, Simonetta & Suffritti, 1973;Gramaccioli & Filippini, 1983). We have also tested Williams (1972) parameters and Mirskaya, Kozlova & Bereznitskaya (1974) parameters; even though both of them predicted an equilibrium configuration as close to the experimental one as the first set, calculated thermal parameters were slightly worse for the Williams (1972) set, and rather worse (some diagonal thermal parameters twice their experimental values) for the Mirskaya et al parameters, indicating that lattice-dynamics calculations are more critical with respect to potential parameters than packing calculations.…”

Thermal motion analysis in [5]-, [6]- and [7]-circulene crystals: a harmonic lattice-dynamical calculation

“…Lattice-dynamical calculations in the harmonic approximation have been performed following a previously described procedure (Gramaccioli & Filippini, 1983, 1985aWillis & Pryor, 1975); details of the Brillouin-zone sampling are given in Filippini et al (1976). Empirical atom-atom van der Waals potentials were chosen according to Mirsky (1978); the internal field was assumed following Neto, Scrocco & Califano (1966) for the 'in-plane' movements and Filippini, Simonetta & Gramaccioli (1984) for the 'out-of-plane' displacements.…”

“…Lattice-dynamical calculations for crystals of aromatic hydrocarbons have been carried out by several authors with substantial success (Pawley, 1967;Filippini, Gramaccioli, Simonetta & Suffritti, 1973Bonadeo & Burgos, 1982;Gramaccioli & Filippini, 1983, 1985aFilippini & Gramaccioli, 1986; in most cases, the agreement between the observed and calculated IR-and Raman-active frequencies, phonon-dispersion curves, thermodynamic functions, and atomic diplacement parameters is very good. The aim of these calculations is on the one side to extend the range of applicability of the available semiempirical force fields and on the other side to provide a comparison with experimentally determined a.d.p.…”

A test of chlorine and fluorine nonbonded potential functions with lattice-dynamical calculations

“…Empirical 6-exp atom-atom potential-energy models proved to be very reliable (Pertsin & Kitaigorodsky, 1987). The method has recently been applied to silicates (Pilati, Bianchi & Gramaccioli, 1990), and the effects of molecular non-rigidity have also been considered (Gramaccioli, Filippini & Simonetta, 1982;Gramaccioli & Filippini, 1983;Filippini, 1990).…”