The influence of Coulombic interactions on thermal parameters for naphthalene and anthracene: a lattice-dynamical approach

Abstract

A lattice-dynamical calculation of thermal parameters is performed for naphthalene and anthracene in the external Born-von Karman formalism using 6-exp potential functions and electrostatic interactions in the form of an atomic point-charge model. Phonon dispersion curves and density-of-states functions are calculated with and without charges. In general, the effect of the Coulombic forces is small and sensibly affects optical branches linked to the Bu mode in both compounds, improving the agreement with the experimental data. The effect on thermal parameters is roughly opposite to that of molecular non-rigidity.

Transferability of deformation densities among related molecules: atomic multipole parameters from perylene for improved estimation of molecular vibrations in naphthalene and anthracene

“…The probable explanation, as demonstrated by Pawley (1967) and by Vovelle et al (1978), lies in the appreciable dispersion of the lattice frequencies with varying wavevector k. The major contributions to the mean-square libration amplitudes L, come from regions of the Brillouin zone with frequencies u~ much lower than those observed at k = 0. This conclusion is supported by the latticedynamical calculations of Gramaccioli & Filippini (1983) andof Criado (1989). Substituting, for example, the ax and bg (in-phase and out-of-phase libration) frequencies at k = 0 for non-rigid anthracene at 290 K from the former authors' Supplementary Table 2(a) into Cruickshank's equation (5), we obtain a value for Tr(L) of 20.9 deg 2, as cornpared with their calculated value of 36.8 deg 2 (Table 7).…”

“…Quantitatively, our experimental L tensor agrees best with the older calculations of Pawley (1967). These were based on the atom-atom potentials of Kitaigorodsky (1966), while the later studies used potential set IV of Williams (1967).A similar comparison with the libration components reported by Criado (1989), for both structures, is hampered by the difficulty in identifying the coordinate axes to which these components are referred.For a molecule librating in a harmonic potential with effective frequency u; about each of its inertial axes, the mean-square libration amplitudes, in radians 2, arewhere/, is the inertial moment about axis i. This is the form taken by equation (5) …”

“…Pawley, 1967;Filippini, Gramaciolli, Simonetta & Suffritti, 1973;Bokhenkov, Rodina, Sheka & Natkaniec, 1978;Vovelle, Chedin & Dumas, 1978;Natkaniec et al, 1980;Dorner et al, 1982). Among the calculated vibration tensors pertinent to the temperature ranges covered by our experimental studies are the results on anthracene by Pawley (1967) at 300 K and by Vovelle et al (1978), by Gramaccioli & Filippini (1983), and by Criado (1989) at 290 K, as well as the latter's results for naphthalene at 92 K. Also, Vovelle et al (1978) have plotted the calculated temperature dependence of L;;(mol) ~2 in naphthalene and listed both Tii(mol) I 2 and L;,(mol) ~ 2 for anthracene at 95 and 290 K. Their results agree remarkably well with the experimental curves in Figs. 4(b) and 5(b) except for the long-axis libration L~ in anthracene, which they calculate well above our experimental curve.…”

“…A similar comparison with the libration components reported by Criado (1989), for both structures, is hampered by the difficulty in identifying the coordinate axes to which these components are referred.…”

“…The X-ray results yield much smaller values of Tr(T) than any of the calculations; the agreement for Tr(L) is somewhat better. The disagreement in the mean-square translation amplitudes may be partly attributed to our failure to correct for thermal diffuse scattering, which causes a systematic underestimation of the crystallographically determined (1978); (c) Gramaccioli & Filippini (1983); (d) Criado (1989); (e) Brock & Dunitz (1982). atomic vibration amplitudes (Harada & Sakata, 1974).…”