Giuseppe Filippini

A Statistical Study of Density and Packing Variations among Crystalline Isomers

Abstract Crystal structures of groups of isomeric hydrocarbons, oxahydrocarbons and azahydrocarbons have been retrieved from the Cambridge Structural Database. Correlations among crystal and molecular descriptors were sought, with particular attention to factors affecting crystal density. Packing coefficients do not differ much from 0.74, so organic molecules have roughly the same packing efficiency as a close packed assembly of spheres. Molecular shape factors associated with high crystal density are difficult to identify. However, crystal density is higher for compact polycyclic molecules, since they have smaller molecular volumes. Also, flat, rigid molecules pack better than flexible, twisted ones. On the other hand, substituents such as alkyl or nitrile groups tend to lower the packing efficiency. High crystal density does not necessarily lead to high lattice energy, and, in particular, hydrogen bonding seems to have no immediate effect on crystal density. Results of bivariate statistics were confirmed by principal component analysis. These results may be of interest for practical applications in crystal chemistry and crystal physics.

Solid-State Behaviour of the Dichlorobenzenes: Actual, Semi-Virtual and Virtual Crystallography

The crystal structures of the low-melting 1,2- and 1,3-dichlorobenzene isomers in monoclinic space group P21/n and monoclinic space group P21/c, resp., were detd. by x-ray anal. and in situ crystn. techniques. Attempts to predict these structures in advance by force-field calcns. were not successful, although the known crystal structures of two of the three polymorphs of the 1,4-isomer were successfully a posteriori predicted. Calcd. lattice energies were supplemented with estd. lattice-vibrational entropies obtained in the rigid-body approxn. Energy calcns. for actual and virtual crystal structures indicate that the higher m.p. of the 1,4-isomer can be largely attributed to more efficient crystal packing.

Molecular Shape and Crystal Packing: a Study of C12H12 Isomers, Real and Imaginary

Isomeric C12H12 hydrocarbon molecules with widely different constitution and shape are analysed for their packing ability. Some correspond to known compounds with known crystal structures, but some are invented hypothetical molecules designed to have low packing efficiency. For each isomer, a large number of close-packed, low-energy crystal structures was generated by computer, with lattice energies within a range of a few kJ mol−1. Molecules with linear chains, triple bonds and Me groups tend to have larger molecular volume, lower lattice energy and lower crystal density than cyclic or cage isomers. The calculated crystal structures for each isomer show an inverse relationship between packing energy and cell volume. Although the slope dE/dV varies from molecule to molecule, the product of slope and free space stays roughly constant; less efficient crystal packings thus appear to be less sensitive to an increase in cell volume. Lattice-vibrational frequencies and the corresponding contributions to thermal vibrational entropy were estimated for real and virtual crystal structures. For a given isomer, as expected, a higher entropy goes with a larger cell volume, but different isomers show different entropy/volume relationships. At 300 K, TΔS differences among computational polymorphs may compete with ΔH differences, thus making the lattice-vibrational entropy estimation a relevant factor in crystal-structure prediction.

Lattice-dynamical calculations for tetracene and pentacene

Abstract Lattice-dynamical, calculations for evidently non-rigid molecules of aromatic hydrocarbons have been carried out on tetracene and pentacene. In these substances, “out-of plane” vibrations mix extensively with lattice vibrations, and significant differences can be noted between results from a “rigid-body” and a “non-rigid” treatment. For tetracene crystals, whose Raman spectral data are given in the literature, the agreement with experiment is satisfactory. This confirms the validity of such procedures for interpreting and/or predicting spectroscopic behaviour, starting from empirical atom—atom potentials and valence force fields.

The crystal structure of 1,3,5-triammo-2,4,6-trimtrobenzene: Centrosymmetric or non-centrosymmetric?

Abstract The crystal structure of the title compound (TATB) has been determined as centrosymmetric (space group P1, Z = 2) by X-ray diffraction, and yet the solid substance displays non-negligible second-harmonic generation. The contradiction is analyzed by means of potential energy calculations for the crystal packing of TATB, using a set of newly calibrated empirical potentials for the NO·H-N hydrogen bond. It is shown that two non-centrosymmetric (P1) crystal structures are energetically similar to the one with P1, Z = 2, and that libration or reorientation of the whole molecule in its plane within the crystal may be possible, especially at high temperatures. An explanation of the unusual optical behaviour of TATB is attempted in the light of these results.

Thermodynamic functions for crystals of “rigid” hydrocarbon molecules: A derivation via the Born-von Karman procedure

Abstract Thermodynamic functions for crystals of some “rigid” hydrocarbons have been evaluated using for external lattices vibration modes a density of states derived through a Born-von Karman treatment. For this purpose, force constants have been obtained from different sets of semi-empirical potential functions: the agreement with experimental data is satisfactory.

A simplified force field for non-planar vibrations in aromatic polycyclic hydrocarbons

A simplified force field for general application to aromatic polycyclic hydrocarbons concerning ‘out-of-plane’ vibration is presented and discussed. A discriminating fit to frequencies obtained from the vapour phase and the crystal is relevant in this case, and harmonic lattice dynamical calculations have been applied for this purpose. On the whole, satisfactory results can be obtained even from very simple fields, involving two to five torsional coordinates, with no interaction constants: for each molecule, the force constants can be evaluated from geometrical considerations and Kekule structures. Examples of application to isolated molecules and crystals of benzene, naphthalene, anthracene, phenanthrene and pyrene, including some deuterium analogues, are given: the average disagreement between observed and calculated frequencies is 13 cm-1 for the five parameter field.

Use of anisotropic atom-atom potential functions in lattice-dynamical calculations for solid nitrogen

For solid nitrogen, a set of ‘anisotropic’ atom-atom semi-empirical potential functions, which are easily derived from the usual ‘6-exp’ or ‘12-6’, eliminates the difficulties encountered in demonstrating the stability of the γ-phase in lattice-dynamical calculations according to the Born-von Karman procedure. Negative eigenvalues of the dynamical matrices in certain regions of the Brillouin zone disappear, the agreement with experimental data improves and the α-γ transition is foreseen.

X-ray diffraction and packing analysis on vintage crystals: Wilhelm Koerner's nitrobenzene derivatives from the School of Agricultural Sciences in Milano.

The crystal structures of six nitrotoluene derivatives, synthesized by Wilhelm Koerner about a century ago and retrieved from a depository at the University of Milano, were determined. The correct assignment of molecular structures is verified. The geometry of the nitro groups and factors affecting the orientation of nitro groups with respect to the benzene ring are discussed, also using an auxiliary set of crystal structures retrieved from the Cambridge Structural Database. The crystal packings have been analyzed, and lattice energies have been calculated by atom-atom potential methods and by the newly proposed Pixel method. This method allows a more complete description of intermolecular potentials in terms of the interaction between molecular electron densities and separate Coulombic, polarization, dispersion and overlap repulsion energies. Lattice vibrations and external entropies were calculated by lattice-dynamical procedures. The results of the Pixel energy calculations allow a reliable, quantitative assessment of the relative importance of stacking interactions and hydrogen bonding in the rationalization of the recognition modes of nitrobenzene derivatives, which is impossible to attain using only qualitative atom- atom geometry concepts.

Application of semiempirical atom–atom potentials to crystals of acetylene

Semiempirical atom–atom potentials of the ’6‐exp’ and ’Lennard‐Jones’ type have been applied to crystals of acetylene, in order to account for various experimental data, such as sublimation energy, unit cell parameters, lattice vibration frequencies, etc. Most potentials which are generally satisfactory for hydrocarbons, do not account for the lattice vibration frequencies in acetylene: for the cubic phase, a good fit to several experimental data can be obtained using appropriate functions, provided that the sublimation energy is substantially lowered with respect to the experimental value. However, no potentials of this kind, at least in the very extensive range so far tried, can account for the properties and the very existence of the orthorhombic phase, as it is described in the literature. Before pointing to an inadequacy of the present form of these potentials, there is anyway the need of remeasuring the sublimation energy of acetylene, as well as collecting and refining single crystal data also for ...