Lattice Vibrations Of Molecular Crystals Research Articles

Anomalous Temperature Dependence of the Lowest-Frequency Lattice Vibration in Crystalline γ-Aminobutyric Acid.

Crystalline γ-aminobutyric acid (GABA) exhibits unusual thermal behavior in a low-frequency lattice vibration that occurs at 37.2 cm-1 at 290 K but decreases dramatically by 34.0% when the sample is cooled to 78 K. Lattice vibrations in molecular crystals are indicators of intermolecular force characteristics, and the extraordinary temperature sensitivity of this vibration offers new insight into the local environment within the solid. Solid-state density functional theory simulations of the GABA crystal have found this anomalous frequency shift is based in unexpected differences in the strengths of the intermolecular hydrogen bonds that are cursorily the same. This was accomplished through mapping of the potential energy surfaces governing the terahertz-frequency motions of the GABA solid and use of the quasi-harmonic approximation to model the response of all the lattice vibrations to temperature-induced unit cell volume changes brought about through the anharmonic character of the intermolecular interactions. The analysis reveals that the vibration in question is rotational in nature and involves the significant distortion of a specific weak intermolecular N-H···O hydrogen bond in the crystal that results in its unique thermal response.

Toward a Reliable Description of the Lattice Vibrations in Organic Molecular Crystals: The Impact of van der Waals Interactions.

This work assesses the reliability of different van der Waals (vdW) methods to describe lattice vibrations of molecular crystals in the framework of density functional theory (DFT). To accomplish this task, calculated and experimental lattice phonon Raman spectra of a pool of organic molecular crystals are compared. We show that the many-body dispersion (MBD@rsSCS) van der Waals method of Ambrosetti et al. and the pairwise method of Grimme et al. (D3-BJ) outperform the other tested approaches (i.e., the D2 method of Grimme, the TS method of Tkatchenko and Scheffler, and the nonlocal functional vdW-DF-optPBE of Klimeš et al.). For the worse-performing approaches the results could not even be fixed by the introduction of scaling parameters, as commonly used for high-energy intramolecular vibrations. Interestingly, when using the experimentally determined unit cell parameters, DFT calculations using the PBE functional without corrections for long-range vdW interactions provide spectra of similar accuracy as the MBD@rsSCS and D3-BJ simulations.

Lattice vibrations in molecular crystals: polymorphism and phase transitions

Lattice vibrations in molecular crystals: polymorphism and phase transitions

Infrared intensities of lattice vibrations in molecular crystals

From the dynamic multipoles model an expression is derived for the dipole moment derivative governing the intensity of infrared absorption by lattice modes in molecular crystals. The result depends on non-local susceptibilities which take proper account of the local electric field in a way consistent with dielectric theory. It is shown that the non-local rsponse follows naturally from microscopic lattice dynamical theory. It arises from dipolar coupling and is intimately connected with the delocalized exciton states produced by the same mechanism. Intensities calculated for the iodine crystal are inproved by including the local field, but a point quadrupole field proves too anisotropic to yield the measured intensity ratio. The treatment shows that infrared intensities can be used to obtain unique effective molecular polarizabilities.

Theory of infrared and Raman intensity of the lattice vibrations of molecular crystals. Application to solid ammonia and benzene

A theory of infrared and Raman intensity of lattice vibrations in molecular crystals is discussed. The effect of induction due to the molecular dipole and quadrupole fields is included. It is shown that both rotational and translational modes can contribute to the infrared and Raman intensity. Explicit expressions for the calculation of the dipole and polarizability derivatives with respect to the crystal normal coordinates are worked out. The theory is applied to polycrystalline ammonia and benzene and to single crystal benzene, and a good agreement is obtained. The influence of the eigenvectors on the calculated intensities is discussed.

Raman intensities of lattice vibrations in molecular crystals

An exact expression within the point-dipole rigid-molecule approximation is derived for the intensity of polarized Raman scattering from lattice modes in molecular crystals. By treating the local electric field properly, the method gives the contribution to the intensity from translational motions as well as rotational ones. The intensity varies as the fourth power of the local field correction for both types of motion. It also depends on the polarization vectors of the lattice modes and the effective molecular polarizability. Methods for obtaining these quantities are discussed. Numerical calculations for the pure rotational modes in hexachlorobenzene and naphthalene crystals show that the intensifies are very sensitive to the input data, making it difficult to draw conclusions from a comparison with measured intensifies.

Group theoretical analysis of lattice vibrations in molecular crystals

Computer programs have been developed by Warren and Worlton, for the external modes in ionic crystals where the principal axes of the radicals of groups coincide with the crystallographic axes. In this paper, we discuss the generalisation of these computer programs for molecular crystals where the principal axes do not coincide with the crystallographic axes and for molecular crystals with linear molecules having a redundant rotational degree of freedom. Our results are discussed for the q→O modes of solid NH3, N2 and CS2.

Dynamic multipoles in molecular crystals

The lattice energy of molecular crystals is expressed in terms of interactions between effective dynamical multipoles. The multipole moments are characteristic for a given molecule in a crystal; they depend on the arrangement of the molecules in the lattice and can be considered as self-consistent ones. The cohesive energy of the crystal is described as interactions between static multipoles, i.e., those parts of the multipoles which do not depend on displacements of molecules treated as rigid bodies. The remaining parts of the moments, depending on molecular displacements, represent the multipole moments induced by the lattice vibrations. The general equation for lattice vibrations in molecular crystals is derived and the dynamical matrix is expressed by the effective charge distributions and lattice sums. The conception of dynamical multipoles put forward in this paper relates frequencies and infrared intensities of lattice vibrations within the same model.

Anharmonicity in Crystal Vibrations

A scheme for the calculation of anharmonicity in crystal vibrations is developed for crystals with one molecule per unit cell. This method is applied to n-hexane crystal. It is found that the contribution from anharmonicity can be very important in lattice vibrations of molecular crystals. Hence, the use of harmonic crystal vibrations for evaluation of nonbonded potentials without an anharmonicity correction can lead to an inconsistent potential.

Optical Properties of Lattice Vibrations in Molecular Crystals

AbstractA classical microscopic theory is presented for the optical properties of lattice vibrations in molecular crystals, which are composed of electrically neutral molecules bound by van der Waals forces. It is shown, that Huang's theory, which until now has been applied to ionic crystals only, is also valid for molecular crystals. Finally, oscillator strengths as well as LO and TO frequencies are calculated for thiourea according to the “oriented gas” model. A comparison shows, that the calculated oscillator strengths have the same order of magnitude as those of α‐quartz.

Lattice Vibrations of Molecular Crystals. II. Cyanamide and Cyanamide-d2

The far-infrared spectra (33–500 cm−1) of crystalline cyanamide (NH2CN) and cyanamide-d2 have been recorded with polyethylene and silicon sample support plates. The laser Raman spectra have also been recorded from 40–1600 cm−1 for both molecules. No evidence was found for the inversion doubling and resultant low-frequency components of the NH2 and ND2 wagging frequencies previously proposed. While 14 of the predicted 15 infrared-active lattice modes were identified, only four of the predicted 24 Raman-active lattice modes were observed. Force constants were estimated from the observed infrared frequencies by use of modified Born–von Karman valence force field and Wilson-FG technique. Lastly, the distortion moment and effective charges were calculated using the method of Szigeti and Kurosawa. These results semiquantitatively reflect the difference in band intensities between the intra- and intermolecular vibrations.

Central force field approximation for the calculation of displacement lattice vibrations of molecular crystals

Displacement lattice vibration frequencies are calculated for a number of simple molecular crystals using a central force field approximation. The results are compared with experimental results. In the case of ammonia, where more experimental results are available, the calculation is extended to include electrostatic effects.

The crystal structure of hexam ethylenetetramine I. X -ray studies at 298, 100 and 34 °K

On account of its cubic molecular and crystal symmetry, hexamethylenetetramine is a key substance in the study of the lattice vibrations of molecular crystals; its anisotropic atomic-vibration amplitudes have been determined at 298, 100 and 34 °K from three-dimensional single crystal X-ray data. Two independent sets of experiments were done with Cu and Mo radiation; these led to results in very close agreement with one another (and with results derived from previous X-ray and neutron data at room temperature). Typical final discrepancy factors obtained from full-matrix least-squares refinements are 3.4 % for 95 Mo reflexions and 6.3 % for 44 Cu reflexions at 34 °K. The studies at the three temperatures provide direct support for the rotational-oscillation correction for atomic co-ordinates. The corrected weighted-mean dimensions from eight determinations are C—N = 1.476 ± 0.002 Å, ∠N—C—N = 113.6 ± 0.2°, ∠C—N—C = 107.2 ± 0.1°, and from the neutron study C—H = 1.088 ± 0.011 Å. The compact arrangement of molecules in the crystal is described.