Electrodynamic response and stability of molecular crystals

Abstract

We show that electrodynamic dipolar interactions, responsible for long-range fluctuations in matter, play a significant role in the stability of molecular crystals. Density functional theory calculations with van der Waals interactions determined from a semilocal "atom-in-a-molecule" model result in a large overestimation of the dielectric constants and sublimation enthalpies for polyacene crystals from naphthalene to pentacene, whereas an accurate treatment of nonlocal electrodynamic response leads to an agreement with the measured values for both quantities. Our findings suggest that collective response effects play a substantial role not only for optical excitations, but also for cohesive properties of noncovalently bound molecular crystals. Polyacene molecular crystals form a fundamental class of aromatic solids, and have been extensively studied as potential materials for organic electronics. [1][2][3] It is understood that the optical properties of polyacenes are very sensitive to longrange intra-and intermolecular electrodynamic interactions. This is reflected by shifts in the optical absorption frequencies upon increasing the molecule size or upon solid formation, 4 and is further exhibited by the visible color of oligoacene crystals, which changes from transparent in naphthalene and anthracene, to bright orange in tetracene, and deep blue in pentacene. 4,5 The optical absorption spectrum is directly related to the polarizability through the Kramers-Kronig transformation.6 Therefore, the observed changes in the optical spectrum upon crystallization of polyacenes are accompanied by a change in the molecular polarizability. In addition, these changes in polarization should directly impact the crystal lattice energy. However, the effect of electrodynamic intermolecular interactions on the cohesive properties of molecular crystals remains poorly understood. In this Rapid Communication, we show that the dipolar electrodynamic coupling between polyacene molecules reduces the solid dielectric constant by 15%, and has an impact of up to 0.5 eV per molecule on the computed van der Waals (vdW) energies and sublimation enthalpies of these molecular crystals. Our results imply that electrodynamic response is crucial for describing both the cohesive energy and the optical properties of molecular crystals, also providing strong quantitative support to empirical relations between stability and refractive index of molecular crystals. 7Polyacene crystals are extended aromatic networks characterized by polarizable π clouds. Therefore, an appreciable part of the crystal lattice energy stems from ubiquitous attractive vdW dispersion interactions. When studying the cohesion of molecular systems, for example, using densityfunctional theory (DFT) 8,9 or classical potentials, 10 the vdW energy is typically computed using effective polarizabilities for hybridized "atoms" inside a molecule. It is common to approximate the frequency-dependent polarizability of every atom using a single effective excitation frequency (also called t...

Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals

“…34,72 The importance of including manybody effects goes beyond cohesive energies; it has been recently shown that the prediction of the dielectric constants of the polyacene crystals is also significantly improved by the MBD method. 63 …”

“…63 To study the broad importance of phonon dispersion on the vibrational contributions unit-cell and supercell (of at least 9-10 Å length in each direction) calculations have been performed for the whole database of molecular crystals. The resulting vibrational contributions at 298 K are shown in Figure 2.…”

Current Understanding of Van der Waals Effects in Realistic Materials

“…Therefore, the observed changes in the optical spectrum upon crystallization of polyacenes are accompanied by a change in the molecular polarizability. These changes in polarization will also directly impact the crystal lattice energy [52].…”

“…In recent years, substantial progress has been achieved in the theoretical prediction of structures and stabilities of molecular crystals by using vdW-inclusive DFA approaches [43,44]. Today, the structures of (simple) organic molecular crystals can be predicted with an accuracy of 2-3% [45][46][47] and cohesive energies to 1-2 kcal/mol [43][44][45]48].…”

Ab initiophonon dispersion in crystalline naphthalene using van der Waals density functionals

“…More recently, the vibrational modes of gas-phase naphthalenein particular, infrared and Raman active modes-as well as the zone-center modes of crystalline naphthalene have also been reproduced successfully with ab initio methods 53,59,[64][65][66][67][68] , although the mode assignments depend somewhat on the level of theory and functional 53,68 . Finally, Schatschneider et al 69 and Reilly and Tkatchenko 70 used vdW-corrected DFT to obtain the zero-point energy and vibrational contribution (integrated over the Brillouin zone) to the lattice energy of several acenes, respectively, using the TkatchenkoScheffler pairwise approach; however, these studies did not provide any details of the phonon spectrum.…”