Anthony M. Reilly

Long-range correlation energy calculated from coupled atomic response functions

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Many-Body Dispersion Interactions in Molecular Crystal Polymorphism

Polymorphs of molecular crystals are often very close in energy, yet they may possess very different physical and chemical properties. The understanding of polymorphism is therefore of great importance for a variety of applications, ranging from drug design to nonlinear optics and hydrogen storage. While the crystal structure prediction blind tests conducted by the Cambridge Crystallographic Data Centre have shown steady progress toward reliable structure prediction for molecular crystals, several challenges remain, including molecular salts, hydrates, and flexible molecules with several stable conformers. The ability to identify and rank all of the relevant polymorphs of a given molecular crystal hinges on an accurate description of their relative energetic stability. Hence, a first-principles quantum mechanical method that can attain the required accuracy of around 0.1–0.2 kcalmol 1 would clearly be an indispensable tool for polymorph prediction. In this work, we show that accounting for the nonadditive many-body dispersion (MBD) energy beyond the standard pairwise approximation is crucial for the correct qualitative and quantitative description of polymorphism in molecular crystals. We demonstrate this through three fundamental and stringent benchmark examples: glycine, oxalic acid, and tetrolic acid. These systems represent a broad class of molecular crystals, comprising hydrogenbonded (H-bonded) networks of amino acids and carboxylic acids. Among the first-principles methods, density functional theory (DFT) is the most widely used approach in the study of polymorphism in molecular crystals. However, most common exchange-correlation functionals (including hybrid functionals) are based on semi-local electron correlation, and thereby fail to capture the contribution of dispersion interactions to the stability of molecular crystals. These ubiquitous noncovalent interactions are quantum mechanical in nature and correspond to the multipole moments induced in response to instantaneous fluctuations in the electron density. To incorporate these long-range electron correlation effects within DFT, significant progress has been made by using the standard C6/R 6 pairwise additive expression for the dispersion energy. Indeed, DFT with pairwise dispersion terms can yield accurate results when the energy differences between molecular crystal polymorphs are sufficiently large. Notably, Neumann et al. have achieved the highest success rate in the last two blind tests using such methods. However, these pairwise dispersion approaches, even when used in conjunction with state-of-the-art functionals, are still unable to reach the level of accuracy required to describe polymorphism in many relevant molecular crystals, including glycine and oxalic acid. Recently, a novel and efficient method for describing the many-body dispersion (MBD) energy has been developed, building upon the Tkatchenko–Scheffler (TS) pairwise method. Within the TS approach, the effective dispersion coefficients (C6) are calculated from the DFTelectron density, hence the effect of the local environment of an atom in a molecule is accurately accounted for by construction. The MBD method presents a two-fold improvement over the TS approach by including: 1) the long-range electrodynamic screening through the self-consistent solution of the dipole– dipole electric-field coupling equations for the effective polarizability, and 2) the non-pairwise-additive many-body dispersion energy to infinite order through diagonalization of the Hamiltonian corresponding to a system of coupled fluctuating dipoles. The inclusion of the MBD energy in DFT leads to a significant improvement in the binding energies between organic molecules, and for the cohesion of the benzene and oligoacene molecular crystals. The MBD energy, like the TS energy, can be added to any DFT functional, requiring only the adjustment of a single rangeseparation parameter per functional. [*] N. Marom, J. R. Chelikowsky Center for Computational Materials Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, TX 78712 (USA) E-mail: noa@ices.utexas.edu

Electrodynamic response and stability of molecular crystals

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.

First-principles modeling of molecular crystals: structures and stabilities, temperature and pressure

The understanding of the structure, stability, and response properties of molecular crystals at finite temperature and pressure is crucial for the field of crystal engineering and their application. For a long time, the field of crystal‐structure prediction and modeling of molecular crystals has been dominated by classical mechanistic force‐field methods. However, due to increasing computational power and the development of more sophisticated quantum‐mechanical approximations, first‐principles approaches based on density functional theory can now be applied to practically relevant molecular crystals. The broad transferability of first‐principles methods is especially imperative for polymorphic molecular crystals. This review highlights the current status of modeling molecular crystals from first principles. We give an overview of current state‐of‐the‐art approaches and discuss in detail the main challenges and necessary approximations. So far, the main focus in this field has been on calculating stabilities and structures without considering thermal contributions. We discuss techniques that allow one to include thermal effects at a first‐principles level in the harmonic or quasi‐harmonic approximation, and that are already applicable to realistic systems, or will be in the near future. Furthermore, this review also discusses how to calculate vibrational and elastic properties. Finally, we present a perspective on future uses of first‐principles calculations for modeling molecular crystals and summarize the many remaining challenges in this field. WIREs Comput Mol Sci 2017, 7:e1294. doi: 10.1002/wcms.1294

Modeling crystal growth from solution with molecular dynamics simulations: Approaches to transition rate constants

The feasibility of using the molecular dynamics (MD) simulation technique to study crystal growth from solution quantitatively, as well as to obtain transition rate constants, has been studied. The dynamics of an interface between a solution of Lennard-Jones particles and the (100) face of an fcc lattice comprised of solute particles have been studied using MD simulations, showing that MD is, in principle, capable of following growth behavior over large supersaturation and temperature ranges. Using transition state theory, and a nearest-neighbor approximation growth and dissolution rate constants have been extracted from equilibrium MD simulations at a variety of temperatures. The temperature dependence of the rates agrees well with the expected transition state theory behavior.

Simulating thermal motion in crystalline phase-I ammonia

Path-integral molecular dynamics have been used to simulate the phase-I crystalline form of ammonia, using an empirical force field. This method allows quantum-mechanical effects on the average geometry and vibrational quantities to be evaluated. When these are used to adjust the output of a high-temperature density functional theory simulation, the results are consistent with those given by the most recent structural refinement based on powder neutron diffraction data. It is clear that the original refinement overestimated thermal motion, and therefore also overestimated the equilibrium N-{H/D} bond length.

Sixth blind test of organic crystal-structure prediction methods.

Over the past 15 years progress in predicting crystal structures of small organic molecules has been charted by a series of blind tests hosted by the Cambridge Crystallographic Data Centre. This letter announces a sixth blind test to take place between September 2014 and August 2015, giving details of the target systems and the revised procedure. We hope that as many methods as possible will be assessed and benchmarked in this new blind test.

Temperature- and pressure-dependent densities, self-diffusion coefficients, and phase behavior of monoacid saturated triacylglycerides: toward molecular-level insights into processing.

Using molecular-dynamics (MD) simulations the densities and self-diffusion coefficients of a range of liquid monoacid triacylglycerides (TAGs) have been studied as a function of temperature and, for the first time, pressure. While offset by their ambient properties, the response of the TAGs to temperature and pressure is qualitatively similar. Application of pressure was found to significantly increase densities and reduce diffusion of the TAG molecules, suggesting that it may have as much a role in processing and crystallizing TAGs as supercooling does. A solution of glycerol tripalmitate and glycerol trihexanoate was also studied, showing that application of pressure should lead to a significant decrease in the saturation point of the solution, which is an important consideration for processing TAGs. Different solid/liquid interfaces of glycerol tripalmitate have also been investigated. Although crystal growth could not be observed, dissolution of one interface was seen in the MD simulations. The results suggest that over moderate distances the melting of TAGs may be cooperative in nature, rather than involving dissolution of individual TAG molecules.

Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. I. Study of positional parameters

Molecular-dynamics-derived numerical probability density functions (PDFs) have been used to illustrate the effect of different models for thermal motion on the parameters refined in a crystal structure determination. Specifically, anharmonic curved or asymmetric PDFs have been modelled using the traditional harmonic approximation and the anharmonic Gram-Charlier series treatment. The results show that in cases of extreme anharmonicity the mean and covariance matrix of the harmonic treatment can deviate significantly from physically meaningful values. The use of a Gram-Charlier anharmonic PDF gives means and covariance matrices closer to the true (numerically determined) anharmonic values. The physical significance of the maxima of the anharmonic distributions (the most probable or mode positions) is also discussed. As the data sets used for the modelling process are theoretical in origin, these most probable positions can be compared to equilibrium positions that represent the system at the bottom of its potential-energy surface. The two types of position differ significantly in some cases but the most probable position is still worthy of report in crystal structure determinations.