Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene

Abstract

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.

Can we trust the experiment? Anisotropic displacement parameters in 1-(halomethyl)-3-nitrobenzene (halogen = Cl or Br)

“…Here, one finds the expected result that the quasiharmonic approximation improves on the amplitude of the ADPs by incorporating temperature effects, thereby leading to larger values. However, in this case, the approach results in a clear overestimation (slope = 1.185), as also frequently seen (George et al, 2017).…”

“…Careful diffraction experiments on crystals of reasonable quality provide reliable intensity data from which atomic positions and anisotropic displacement parameters (ADPs) can be derived almost routinely. The alternative route towards ADPs, namely, their calculation from first principles, has made good progress (George et al, 2015a(George et al, ,b, 2016(George et al, , 2017Deringer et al, , 2017Baima et al, 2016;Lane et al, 2012;Madsen et al, 2013;Pozzi et al, 2013;Dittrich et al, 2012).…”

Discovering structure–property relationships for the phonon band structures of hydrocarbon-based organic semiconductor crystals: the instructive case of acenes

“…The DFT calculations were carried out using the PBE functional 52 , the standard pseudopotentials 53 for the projector-augmented wave method 54 , and a plane wave energy cutoff of 900 eV. Given its outstanding performance compared to other a posteriori van der Waals corrections for calculating the properties of low-frequency phonons in organic semiconductors [40][41][42][43] , we employed the D3 van der Waals correction 55 with Becke-Johnson damping 56 (D3-BJ).…”

A New Tool for Validating Theoretically Derived Anisotropic Displacement Parameters with Experiment: Directionality of Prolate Displacement Ellipsoids

“…Within the last few years, anisotropic displacement parameters (ADPs) have been successfully predicted by means of ab initio electronic-structure theory and validated, too, for a variety of different compounds. [1][2][3][4][5][6][7][8][9][10] In particular, such theoretical approaches based on density-functional theory (DFT) can be a useful tool for molecular crystallography concerned with structural refinement, complementing the experiment in difficult situations where the experiment alone faces resolution limits or contrast problems. Despite reaching "neutron quality" in many cases, at least in terms of visual inspection of theoretically and experimentally derived ORTEP plots, the quest for suitable tools capable of correctly (or conveniently) measuring the quality of theoretically calculated anisotropic displacement parameters arises.…”

“…Alternatively, a displacement ellipsoid may be characterized by its volume, shape and directionality. As for the former two aspects, it has been proposed to compare the mainaxis components of the theoretical displacement matrices with the experimental counterparts using a linear fit between both quantities 3,5,6 such that the resulting correlation function of the scatter plot yields the mean deviation from the experimental values. The ratio between the main axes describes the shape; flat "saucer-type" ellipsoids are addressed as oblate, elongated "cigar-shaped" ellipsoids as prolate.…”