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

The development and application of computational methods for studying molecular crystals, particularly density-functional theory (DFT), is a large and ever-growing field, driven by their numerous applications. Here we expand on our recent study of the importance of many-body van der Waals interactions in molecular crystals [Reilly and Tkatchenko, J. Phys. Chem. Lett., 4, 1028–1033, (2013)], with a larger database of 23 molecular crystals. Particular attention has been paid to the role of the vibrational contributions that are required to compare experiment sublimation enthalpies with calculated lattice energies, employing both phonon calculations and experimental heat-capacity data to provide harmonic and anharmonic estimates of the vibrational contributions. Exact exchange, which is rarely considered in DFT studies of molecular crystals, is shown to have a significant contribution to lattice energies, systematically improving agreement between theory and experiment. When the vibrational and exact-exchange contributions are coupled with a many-body approach to dispersion, DFT yields a mean absolute error (3.92 kJ/mol) within the coveted “chemical accuracy” target (4.2 kJ/mol). The role of many-body dispersion for structures has also been investigated for a subset of the database, showing good performance compared to X-ray and neutron diffraction crystal structures. The results show that the approach employed here can reach the demanding accuracy of crystal-structure prediction and organic material design with minimal empiricism

van der Waals dispersion interactions in molecular materials: beyond pairwise additivity

van der Waals (vdW) dispersion interactions are a key ingredient in the structure, stability, and response properties of many molecular materials and essential for us to be able to understand and design novel intricate molecular systems. Pairwise-additive models of vdW interactions are ubiquitous, but neglect their true quantum-mechanical many-body nature. In this perspective we focus on recent developments and applications of methods that can capture collective and many-body effects in vdW interactions. Highlighting a number of recent studies in this area, we demonstrate both the need for and usefulness of explicit many-body treatments for obtaining qualitative and quantitative accuracy for modelling molecular materials, with applications presented for small-molecule dimers, supramolecular host-guest complexes, and finally stability and polymorphism in molecular crystals

Mouvement de particules autour de l'orbite fermée chromatique dans un synchrotron

ACCCette note a pour but d'établir les expressions analytiques utilisées dans le code BETA[1] pour caratériser le mouvement des particules autour de l'orbite fermée chromatique dans un cyclotron. Elle détaille des calculs effectués depuis dix ans. Le formalisme utilisé est celui des aberrations au second ordre développé pour le code TRANSPORT[2]. Il conduit aux expressions de la fonction dispersion au second ordre. Des chromaticités au premier ordre et du "momentum compaction" au second ordre en fonction des termes de la matrice de transfert de la maille au second ordre

Interatomic Methods for the Dispersion Energy Derived from the Adiabatic Connection Fluctuation-Dissipation Theorem

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory (DFT) calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on \textit{ad hoc} assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula. Moreover, for a system of quantum harmonic oscillators coupled through a dipole--dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD correlation energy in the random-phase approximation. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy

Role of Dispersion Interactions in the Polymorphism and Entropic Stabilization of the Aspirin Crystal

Aspirin has been used and studied for over a century, but has only recently been shown to have an additional polymorphic form, known as form II. Since the two observed solid forms of aspirin are degenerate in terms of lattice energy, kinetic eects have been suggested to determine the metastability of the less abundant form II. Here, rst-principles calculations provide an alternative explanation based on free-energy dierences at room temperature. The explicit consideration of many-body van der Waals interactions in the free energy demonstrates that the stability of the most abundant form of aspirin is due to a subtle coupling between collective electronic uctuations and quantized lattice vibrations. In addition, a systematic analysis of the elastic properties of the two forms of aspirin rules out mechanical instability of form II as making it metastabl

Projet de hadrontherapie a Lyon - Revue de l'injection dans PIMMS et variantes: protons de 7 MeV, injection exterieure

Ce rapport passe en revue certaines etudes concernant l'injection dans le synchrotron, realisees sur la base du document PIMMS du Cern, dans le cadre et en tenant compte des specificites du projet de hadrontherapie Rhones-Alpes. Deux variantes sont aussi presentees, injection de protons de 7 MeV et injection par l'exterieur de l'anneau

Long-range correlation energy calculated from coupled atomic response functions

An accurate determination of the electron correlation energy is essential for describing the structure, stability, and function in a wide variety of systems, ranging from gas-phase molecular assemblies to condensed matter and organic/inorganic interfaces. Even small errors in the correlation energy can have a large impact on the description of chemical and physical properties in the systems of interest. In this context, the development of efficient approaches for the accurate calculation of the long-range correlation energy (and hence dispersion) is the main challenge. In the last years a number of methods have been developed to augment density functional approximations via dispersion energy corrections, but most of these approaches ignore the intrinsic many-body nature of correlation effects, leading to inconsistent and sometimes even qualitatively incorrect predictions. Here we build upon the recent 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.Comment: 15 pages, 3 figure

Electronic Properties of Molecules and Surfaces with a Self\uad-Consistent Interatomic van der Waals Density Functional.

How strong is the effect of van der Waals (vdW) interactions on the electronic properties of molecules and extended systems? To answer this question, we derived a fully self-consistent implementation of the density-dependent interatomic vdW functional of Tkatchenko and Scheffler [Phys. Rev. Lett. 102, 073005 (2009)]. Not surprisingly, vdW self-consistency leads to tiny modifications of the structure, stability, and electronic properties of molecular dimers and crystals. However, unexpectedly large effects were found in the binding energies, distances, and electrostatic moments of highly polarizable alkali-metal dimers. Most importantly, vdW interactions induced complex and sizable electronic charge redistribution in the vicinity of metallic surfaces and at organic-metal interfaces. As a result, a substantial influence on the computed work functions was found, revealing a nontrivial connection between electrostatics and long-range electron correlation effects

Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations

The random phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange energy, represents the state-of-the-art exchange-correlation functional within density-functional theory (DFT). However, the standard RPA practice -- evaluating both the exact-exchange and the RPA correlation energy using local or semilocal Kohn-Sham (KS) orbitals -- leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior is largely corrected by adding a "single excitation" (SE) contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent exact-exchange total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using Kohn-Sham orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of non-covalent intermolecular interactions.Comment: 5 pages, 4 figures, and an additional supplementary materia