Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

Abstract

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal–organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0–300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal–organic crystal are off by up to 100%.

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors

“…Although the majority of studies on crystals reporting computed elastic constants ignore thermal effects, there are some notable recent exceptions involving calculations of temperature dependence of elastic properties using the quasi‐static approximation (QSA), which evaluates derivatives of the internal energy of a crystal at a fixed volume obtained via a quasi‐harmonic analysis (QHA). Materials for which these relatively time‐consuming calculations of thermoelastic behavior have been performed include urea, [52] deutero‐ammonia, [53] the mineral forsterite α‐Mg 2 SiO 4 , [54] organic semiconductors rubrene and BTBT ([1]benzothieno[3,2‐b]‐[1]benzothiophene), [55] and the elastically flexible copper(II) acetylacetonate [56] …”

Structure–Thermomechanical Property Correlation in Polymorphic Molecular Crystals Probed by the Nanoindentation Technique

“…For example, the order of compressibility along different directions has been found to follow the order of the TE coefficients (α) along the same axes. , That is, the direction with large α tends to be more compressible. Computational studies also showed that the elastic moduli ( E ) decrease with decreased temperature in an anisotropic manner and that the magnitude of the anisotropy is significantly affected by thermal expansion . More recently, Rather et al reported that in a mechanically bending crystal, the unit cell parameters at the concave and convex sides have some resemblance to those in the contraction and expansion induced by thermal treatment .…”

“…Computational studies also showed that the elastic moduli (E) decrease with decreased temperature in an anisotropic manner and that the magnitude of the anisotropy is significantly affected by thermal expansion. 19 More recently, Rather et al reported that in a mechanically bending crystal, the unit cell parameters at the concave and convex sides have some resemblance to those in the contraction and expansion induced by thermal treatment. 15 These recent results suggest an underlying relationship between thermal expansion and the mechanical properties of molecular crystals although some differences are expected.…”

On the use of a volume constraint to account for thermal expansion effects on the low-frequency vibrations of molecular crystals

“…While effective, unless simplified Gru ¨neisen parameters are used, 19,20 these simulations require a full vibrational analysis to be performed on at least four geometries optimised in the compression and expansion regimes. [21][22][23] Such analysis can be cost prohibitive for large unit cells containing hundreds of atoms, particularly if accurate DFT-D forces or supercells are desired. [24][25][26] Clearly then, it is worth considering simpler avenues to accomplish the same goal.…”