Dispersion-inclusive Density Functional Theory Research Articles

Structure of Graphene Grown on Cu(111): X-Ray Standing Wave Measurement and Density Functional Theory Prediction.

We report the quantitative adsorption structure of pristine graphene on Cu(111) determined using the normal incidence x-ray standing wave technique. The experiments constitute an important benchmark reference for the development of density functional theory approximations able to capture long-range dispersion interactions. Electronic structure calculations based on many-body dispersion-inclusive density functional theory are able to accurately predict the absolute measure and variation of adsorption height when the coexistence of multiple moiré superstructures is considered. This provides a structural model consistent with scanning probe microscopy results.

Ab Initio Crystal Structure Prediction of the Energetic Materials LLM-105, RDX, and HMX.

Crystal structure prediction (CSP) is performed for the energetic materials (EMs) LLM-105 and α-RDX, as well as the α and β conformational polymorphs of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), using the genetic algorithm (GA) code, GAtor, and its associated random structure generator, Genarris. Genarris and GAtor successfully generate the experimental structures of all targets. GAtor's symmetric crossover scheme, where the space group symmetries of parent structures are treated as genes inherited by offspring, is found to be particularly effective. However, conducting several GA runs with different settings is still important for achieving diverse samplings of the potential energy surface. For LLM-105 and α-RDX, the experimental structure is ranked as the most stable, with all of the dispersion-inclusive density functional theory (DFT) methods used here. For HMX, the α form was persistently ranked as more stable than the β form, in contrast to experimental observations, even when correcting for vibrational contributions and thermal expansion. This may be attributed to insufficient accuracy of dispersion-inclusive DFT methods or to kinetic effects not considered here. In general, the ranking of some putative structures is found to be sensitive to the choice of the DFT functional and the dispersion method. For LLM-105, GAtor generates a putative structure with a layered packing motif, which is desirable thanks to its correlation with low sensitivity. Our results demonstrate that CSP is a useful tool for studying the ubiquitous polymorphism of EMs and shows promise of becoming an integral part of the EM development pipeline.

Fine Tuning the Intermolecular Interactions of Water Clusters Using the Dispersion-Corrected Density Functional Theory.

Dispersion-inclusive density functional theory (DFT) methods have unequivocally demonstrated improved performances with respect to standard DFT approximations for modeling large and extended molecular systems at the quantum mechanical level. Yet, in some cases, disagreements with highly accurate reference calculations, such as CCSD(T) and quantum Monte Carlo (MC) calculations, still remain. Furthermore, the application of general-purpose corrections, such as the popular Grimme's semi-classical models (DFT-D), to different Kohn-Sham exchange-correlation functionals sometimes leads to variable and inconsistent results, which recommend a careful prior evaluation. In a recent study, we proposed a simple optimization protocol for enhancing the accuracy of these DFT-D methods by following an alternative and system-specific approach. Here, adopting the same computational strategy, we show how the accurate MC intermolecular interactions of a large set of water clusters of variable sizes (i.e., 300 (H2O)n structures, n = 9, 15, 27) can be reproduced remarkably well by dispersion-corrected DFT models (i.e., B3LYP-D4, PBE-D4, revPBE(0)-D4) upon re-optimization, reaching a mean absolute error per monomer of ~0.1 kcal/mol. Hence, the obtained results support the use of this procedure for fine-tuning tailored DFT-D models for the accurate description of targeted molecular systems.

Performance of Dispersion-Inclusive Density Functional Theory Methods for Energetic Materials.

Molecular crystals of energetic materials (EMs) are denser than typical molecular crystals and are characterized by distinct intermolecular interactions between nitrogen-containing moieties. To assess the performance of dispersion-inclusive density functional theory (DFT) methods, we have compiled a data set of experimental sublimation enthalpies of 31 energetic materials. We evaluate the performance of three methods: the semilocal Perdew-Burke-Ernzerhof (PBE) functional coupled with the pairwise Tkatchenko-Scheffler (TS) dispersion correction, PBE with the many-body dispersion (MBD) method, and the PBE-based hybrid functional (PBE0) with MBD. Zero-point energy contributions and thermal effects are described using the quasi-harmonic approximation (QHA), including explicit treatment of thermal expansion, which we find to be non-negligible for EMs. The lattice energies obtained with PBE0+MBD are the closest to experimental sublimation enthalpies with a mean absolute error of 9.89 kJ/mol. However, the state-of-the-art treatment of vibrational and thermal contributions makes the agreement with experiment worse. Pressure-volume curves are also examined for six representative materials. For pressure-volume curves, all three methods provide reasonable agreement with experimental data with mean absolute relative errors of 3% or less. Most of the intermolecular interactions typical of EMs, namely nitro-amine, nitro-nitro, and nitro-hydrogen interactions, are more sensitive to the choice of the dispersion method than to the choice of the exchange-correlation functional. The exception is π-π stacking interactions, which are also very sensitive to the choice of the functional. Overall, we find that PBE+TS, PBE+MBD, and PBE0+MBD do not perform as well for energetic materials as previously reported for other classes of molecular crystals. This highlights the importance of testing dispersion-inclusive DFT methods for diverse classes of materials and the need for further method development.

3D Electron Diffraction Structure Determination of Terrylene, a Promising Candidate for Intermolecular Singlet Fission.

Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri‐condensed naphthalene analogues, which has eluded structure determination for 65 years. The structure was determined by direct methods using electron diffraction data and corroborated by dispersion‐inclusive density functional theory optimizations. Terrylene crystalizes in the monoclinic space group P21/a, arranging in a sandwich‐herringbone packing motif, similar to analogous compounds. Having solved the crystal structure, we use many‐body perturbation theory to evaluate the excited‐state properties of terrylene in the solid‐state. We find that terrylene is a promising candidate for intermolecular singlet fission, comparable to tetracene and rubrene.

Electronic property trends of single-component organic molecular crystals containing C, N, O, and H

Organic molecular crystals have shown promise in optoelectronic application due to their potential for exhibiting low excitation energies and high charge carrier mobilities. In order to uncover physicochemical trends that will enable optimization of the electronic properties of these materials, high-throughput dispersion-inclusive density functional theory (DFT + vdW) and fragment-orbital density functional theory (FO-DFT) was used to calculate the electronic properties of 831 single-component organic molecular crystals (OMCs) comprised of C, H, O, and/or N atoms. The resulting data was analyzed using structure-dependent property distributions, Pearson correlation coefficient matrices, Euclidean distances, T-tests, and P-values. It is shown that the atomic species, crystalline space group, and molecular topology control the optical band gap (Egopt) value, the dispersion of the HOMO and LUMO derived bands, the intermolecular electronic coupling, and the difference between the molecular HOMO-LUMO gap value and crystalline band gap value. Detailed statistical treatment of qualitative and quantitative descriptors shows some new and many expected structure–property relationships. The structure–property data has been organized in the free access Organic Molecular Crystal Properties Database (OMCPD) available at www.organiccrystalbandgaps.org.

Area-selective atomic layer deposition enabled by competitive adsorption

In this work, we investigate the atomic layer deposition (ALD) of ZrO2 thin films on Cu and SiO2 substrates, using Zr[N(C2H5CH3)]4 as the thin-film precursor, and H2O or O2 as the coreactants. Here, we introduce 3-hexyne as a coadsorbate molecule during the thin-film precursor half-cycle and examine its effect on the selectivity of growth. We find that 3-hexyne strongly inhibits growth on Cu, while having essentially no effect on the growth on SiO2. Calculations using dispersion-inclusive density functional theory verify that 3-hexyne undergoes sp → sp2 rehybridization on Cu, which results in strong chemisorption on the metal surface, while only binding weakly to SiO2 via nonbonded van der Waals/dispersion interactions. After 10 cycles of ALD using 3-hexyne as the coadsorbate, we observed the deposition of ∼1.5 nm of ZrO2 on SiO2. On a Cu substrate, we only detected <0.15 nm of ZrO2 after the same number of cycles of ALD. At this point in the process, we find evidence of the formation of cuprous oxide (Cu2O) from in situ x-ray photoelectron spectroscopy and a significant increase in the roughness of the Cu substrate. We conclude that both factors likely contribute to the loss of selectivity due to the formation of sites (e.g., Cu2O) that bind 3-hexyne less strongly and/or an increase in the density of highly reactive sites (e.g., steps, kinks) that promote dissociative chemisorption of the thin-film precursor.

Deep Molecular Orbital Driven High-Temperature Hydrogen Tautomerization Switching.

Hydrogen tautomerization molecular switches, a promising class of molecular components for the construction of complex nanocircuits, have been extensively studied using low-temperature scanning tunneling microscopy. However, these molecules are generally only reliably controllable in cryogenic environments, obstructing their utility in real devices. Here, we use dispersion-inclusive density functional theory and systematically investigate the adsorption and tautomerization behaviors of porphycene on six transition-metal surfaces. Among these surfaces, we found that hydrogen tautomerization on the Pt(110) surface corresponds to the largest switching barrier, allowing a controllable transition at high temperature. The switching behavior is closely related to the exceptional degree of charge transfer in the HOMO-2 orbital, illustrating the important role of deep orbital-surface interactions in porphycene molecular switching. Our work provides an in-depth understanding of the porphycene tautomerization mechanism and highlights new research avenues toward the practical application of molecular switches.

Anomalous pressure dependence of the electronic properties of molecular crystals explained by changes in intermolecular electronic coupling

Optimization of the electronic properties of crystalline organic semiconductors is important for the evolution of organic optoelectronic devices. One method of tuning the electronic properties is by applying external pressure to semiconducting molecular crystals. A recent dispersion-inclusive density functional theory (DFT) investigation regarding the effect of pressure up to 20 GPa on herringbone polycyclic aromatic hydrocarbons (PAHs) has revealed anomalous pressure dependence of the electronic properties of six systems [J. Phys. Chem. C 122, 23828 (2018)]. Here, we use intermolecular electronic coupling values (Hab), calculated by fragment orbital DFT (FO-DFT) to elucidate the pressure dependence of the electronic properties. We show that discontinuities in the pressure dependence of the band structures are correlated with pressure-dependent discontinuities in the electronic couplings of certain molecular dimers. Hab is shown to be a useful descriptor for gaining insight into the pressure dependence of the electronic properties of crystalline organic semiconductors.

High-Throughput Pressure-Dependent Density Functional Theory Investigation of Herringbone Polycyclic Aromatic Hydrocarbons: Part 2. Pressure-Dependent Electronic Properties

Understanding the effect intermolecular interactions have on the electronic properties of highly conjugated/aromatic organic networks is important for optimizing these materials for optoelectronic device applications. Here, dispersion inclusive density functional theory (DFT + vdW) is used to study the effect of pressure up to 20 GPa on the intermolecular interactions of 40 herringbone polycyclic aromatic hydrocarbons. In the first part of this two-part study (10.1021/acs.jpcc.8b07209), we reported the pressure-induced structural changes. Here, we elucidate the relation between those structural changes and the electronic properties, where it is shown that increased pressure leads to variations in the intermolecular interactions and molecular conformations, resulting in alterations of the band dispersion, band gap (magnitude as well as direct/indirect), and semiconductor polarity (n-type vs p-type). Specifically, increased pressure increases the C–H···π and π···π interactions, typically leading to increase...

Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation.

We present Genarris, a Python package that performs configuration space screening for molecular crystals of rigid molecules by random sampling with physical constraints. For fast energy evaluations, Genarris employs a Harris approximation, whereby the total density of a molecular crystal is constructed via superposition of single molecule densities. Dispersion-inclusive density functional theory is then used for the Harris density without performing a self-consistency cycle. Genarris uses machine learning for clustering, based on a relative coordinate descriptor developed specifically for molecular crystals, which is shown to be robust in identifying packing motif similarity. In addition to random structure generation, Genarris offers three workflows based on different sequences of successive clustering and selection steps: the "Rigorous" workflow is an exhaustive exploration of the potential energy landscape, the "Energy" workflow produces a set of low energy structures, and the "Diverse" workflow produces a maximally diverse set of structures. The latter is recommended for generating initial populations for genetic algorithms. Here, the implementation of Genarris is reported and its application is demonstrated for three test cases.

GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction.

We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. The experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with P1̅ symmetry and a scaffold packing motif, which has not been reported previously.

Origins and dissociation of pyramidal dislocations in magnesium and its alloys

Alloying magnesium (Mg) with rare earth elements such as yttrium (Y) has been reported to activate the pyramidal <c + a> slip systems and improve the plasticity of Mg at room temperature. However, the origins of such dislocations and their dissociation mechanisms remain poorly understood. Here, we systematically investigate these mechanisms using dispersion-inclusive density-functional theory, in combination with molecular dynamics simulations. We find that <c + a> dislocations form more readily on the pyramidal I plane than on the pyramidal II plane in Mg. The addition of Y atoms in Mg facilitates the dissociation of <c + a> dislocations on pyramidal II, leading to the easier formation of the pyramidal II than pyramidal I in Mg-Y alloy. Importantly, in pyramidal II slip plane, a flat potential-energy surface (PES) exists around the position of stable stacking fault energy (SFE), which allows cooperative movement of atoms within the slip plane. Alloying Mg with Y atoms increases the range of the PES, and ultimately promotes different sliding pathways in the Mg-Y alloy. These findings are consistent with experimentally observed activation of the pyramidal II <c + a> slip system in Mg-Y alloys, and provide important insight into the relationship between dislocation structure and macroscopic enhancement of plasticity.

Unusual physical behaviour and polymorphic phase transitions in crystalline bicyclic anhydrides

Bicyclic anhydrides function as versatile building blocks for polymeric materials, but molecular crystals of these monomeric units demonstrate interesting physicochemical properties. Here, we investigate two pairs of crystalline bicyclic anhydrides, where each pair contains a saturated and unsaturated component. One pair (RTM3/RTM4) is built around bicyclo[2.2.2]octane-2-endo,3-endo-dicarboxylic acid anhydride (BA) and another pair (BCA1/BCA2) consists of a BA-core with alkyl substituents. Differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD) and reflective melting point determination shows that both components in the RTM3/RTM4 pair undergo reversible, polymorphic temperature-induced phase transitions to the same space group while the BCA1/BCA2 pair does not. The melting point (MP) behavior of the BCA1/BCA2 pair is interesting because it contradicts typical alkane/alkene MP trends, as the un-saturated component (BCA1) has the higher MP. Lattice enthalpies calculated via dispersion inclusive density functional theory (DFT+vdW) help to elucidate this unusual MP behavior. In addition, Hirshfeld surface analysis of both pairs demonstrates that variations in the intermolecular close contacts may have an effect as to whether the saturated or unsaturated component will exhibit the higher MP. Finally, BCA1 is found to possess unique liquid–solid phase transition properties for a single component organic molecular crystal (OMC), as it is supercoolable over a ∼60 K range.

Effect of packing motifs on the energy ranking and electronic properties of putative crystal structures of tricyano-1,4-dithiino[c]-isothiazole.

We present an analysis of putative structures of tricyano-1,4-dithiino[c]-isothiazole (TCS3), generated within the sixth crystal structure prediction blind test. Typical packing motifs are identified and characterized in terms of distinct patterns of close contacts and regions of electrostatic and dispersion interactions. We find that different dispersion-inclusive density functional theory (DFT) methods systematically favor specific packing motifs, which may affect the outcome of crystal structure prediction efforts. The effect of crystal packing on the electronic and optical properties of TCS3 is investigated using many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation (BSE). We find that a structure with Pna21 symmetry and a bilayer packing motif exhibits intermolecular bonding patterns reminiscent of π-π stacking and has markedly different electronic and optical properties than the experimentally observed P21/n structure with a cyclic dimer motif, including a narrower band gap, enhanced band dispersion and broader optical absorption. The Pna21 bilayer structure is close in energy to the observed structure and may be feasible to grow.

Effect of crystal packing on the excitonic properties of rubrene polymorphs

Singlet fission (SF), the conversion of one singlet exciton into two triplet excitons, may lead to the realization of high efficiency organic photovoltaics by generating two carriers from one photon. Recently, SF has been observed in molecular crystals of rubrene. While the orthorhombic form of rubrene is most often observed under ambient conditions, metastable monoclinic and triclinic polymorphs are known. Here, dispersion-inclusive density functional theory (DFT) is used to investigate the relative stability of all three phases. Many-body perturbation theory is then employed to study the effect of crystal structure on the electronic and excitonic properties. Band structures are calculated within the GW approximation and optical properties are calculated by solving the Bethe–Salpeter equation (BSE). We find that crystal packing significantly affects the electronic and excitonic properties of rubrene. Based on our calculations, the triclinic and especially the monoclinic forms of rubrene are expected to exhibit higher SF efficiencies than the orthorhombic form.

Low-Cost Quantum Chemical Methods for Noncovalent Interactions.

The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chemistry, ranging from supramolecular host-guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster "low-cost" methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular-orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree-Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10-30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.

High-Throughput Investigation of the Geometry and Electronic Structures of Gas-Phase and Crystalline Polycyclic Aromatic Hydrocarbons

The quest for cheap, light, flexible materials for use in electronics applications has resulted in the exploration of soft organic materials as possible candidates, and several polycyclic aromatic hydrocarbons (PAHs) have been shown to be versatile (semi)conductors. In this investigation, dispersion inclusive density functional theory is used to explore all of the current crystalline PAHs within the Cambridge Structure Database (CSD) from both structural and electronic standpoints. Agreement is achieved between the experimental and calculated crystalline structures, as well as the electronic properties. Specifically, variation between the mass densities, unit cell parameters, and intermolecular close contact fractions were within +5%, ±2%, and ±1% of experiment, respectively. It is found that a simple addition of a ∼1 eV constant to the DFT-PBE gaps provides good agreement with the experimental optical gaps of both gas phase (within ±2.6%) and crystalline (within ±3.5%) PAHs. Structural and electronic ana...

Size Effects in the Interface Level Alignment of Dye-Sensitized TiO2 Clusters.

The efficiency of dye-sensitized solar cells (DSCs) depends critically on the electronic structure of the interfaces in the active region. We employ recently developed dispersion-inclusive density functional theory (DFT) and GW methods to study the electronic structure of TiO2 clusters sensitized with catechol molecules. We show that the energy level alignment at the dye-TiO2 interface is the result of an intricate interplay of quantum size effects and dynamic screening effects and that it may be manipulated by nanostructuring and functionalizing the TiO2. We demonstrate that the energy difference between the catechol LUMO and the TiO2 LUMO, which is associated with the injection loss in DSCs, may be reduced significantly by reducing the dimensions of nanostructured TiO2 and by functionalizing the TiO2 with wide-gap moieties, which contribute additional screening but do not interact strongly with the frontier orbitals of the TiO2 and the dye. Precise control of the electronic structure may be achieved via "interface engineering" in functional nanostructures.

Understanding molecular crystals with dispersion-inclusive density functional theory: pairwise corrections and beyond.

CONSPECTUS: Molecular crystals are ubiquitous in many areas of science and engineering, including biology and medicine. Until recently, our ability to understand and predict their structure and properties using density functional theory was severely limited by the lack of approximate exchange-correlation functionals able to achieve sufficient accuracy. Here we show that there are many cases where the simple, minimally empirical pairwise correction scheme of Tkatchenko and Scheffler provides a useful prediction of the structure and properties of molecular crystals. After a brief introduction of the approach, we demonstrate its strength through some examples taken from our recent work. First, we show the accuracy of the approach using benchmark data sets of molecular complexes. Then we show its efficacy for structural determination using the hemozoin crystal, a challenging system possessing a wide range of strong and weak binding scenarios. Next, we show that it is equally useful for response properties by considering the elastic constants exhibited by the supramolecular diphenylalanine peptide solid and the infrared signature of water libration movements in brushite. Throughout, we emphasize lessons learned not only for the methodology but also for the chemistry and physics of the crystals in question. We further show that in many other scenarios where the simple pairwise correction scheme is not sufficiently accurate, one can go beyond it by employing a computationally inexpensive many-body dispersive approach that results in useful, quantitative accuracy, even in the presence of significant screening and/or multibody contributions to the dispersive energy. We explain the principles of the many-body approach and demonstrate its accuracy for benchmark data sets of small and large molecular complexes and molecular solids.