Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory.

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Inverted Lowest Singlet and Triplet Excitation Energy Ordering of Graphitic Carbon Nitride Flakes.

In organic light-emitting diodes (OLEDs), only 25% of electrically generated excitons are in a singlet state, S1, and the remaining 75% are in a triplet state, T1. In thermally activated delayed fluorescence (TADF) chromophores the transition from the nonradiative T1 state to the radiative S1 state can be thermally activated, which improves the efficiency of OLEDs. Chromophores with inverted energy ordering of S1 and T1 states, S1 < T1, are superior to TADF chromophores, thanks to the absence of an energy barrier for the transition from T1 to S1. We benchmark the performance of time-dependent density functional theory using different exchange-correlation functionals and find that scaled long-range corrected double-hybrid functionals correctly predict the inverted singlet-triplet gaps of N-substituted phenalene derivatives. We then show that the inverted energy ordering of S1 and T1 is an intrinsic property of graphitic carbon nitride flakes. A design strategy of new chromophores with inverted singlet-triplet gaps is proposed. The color of emitted light can be fine-tuned through flake size and amine substitution on flake vertices.

First-Principles Assessment of CdTe as a Tunnel Barrier at the α-Sn/InSb Interface.

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as ß-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between α-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [ npj Computational Materials 2020, 6, 180]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for α-Sn and CdTe. For CdTe, the z-unfolding method [ Advanced Quantum Technologies 2022, 5, 2100033] is used to resolve the contributions of different kz values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/α-Sn, InSb/CdTe, and CdTe/α-Sn, as well as in trilayer interfaces of InSb/CdTe/α-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the α-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments.

Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization.

The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.

True molecular conformation and structure determination by three-dimensional electron diffraction of PAH by-products potentially useful for electronic applications.

The true molecular conformation and the crystal structure of benzo[e]dinaphtho[2,3-a;1',2',3',4'-ghi]fluoranthene, 7,14-diphenylnaphtho[1,2,3,4-cde]bisanthene and 7,16-diphenylnaphtho[1,2,3,4-cde]helianthrene were determined ab initio by 3D electron diffraction. All three molecules are remarkable polycyclic aromatic hydrocarbons. The molecular conformation of two of these compounds could not be determined via classical spectroscopic methods due to the large size of the molecule and the occurrence of multiple and reciprocally connected aromatic rings. The molecular structure of the third molecule was previously considered provisional. These compounds were isolated as by-products in the synthesis of similar products and were at the same time nanocrystalline and available only in very limited amounts. 3D electron diffraction data, taken from submicrometric single crystals, allowed for direct ab initio structure solution and the unbiased determination of the internal molecular conformation. Detailed synthetic routes and spectroscopic analyses are also discussed. Based on many-body perturbation theory simulations, benzo[e]dinaphtho[2,3-a;1',2',3',4'-ghi]fluoranthene may be a promising candidate for triplet-triplet annihilation and 7,14-diphenylnaphtho[1,2,3,4-cde]bisanthene may be a promising candidate for intermolecular singlet fission in the solid state.

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 ß 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 ß 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.

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.

Best practices for first-principles simulations of epitaxial inorganic interfaces.

At an interface between two materials physical properties and functionalities may be achieved, which would not exist in either material alone. Epitaxial inorganic interfaces are at the heart of semiconductor, spintronic, and quantum devices. First principles simulations based on density functional theory (DFT) can help elucidate the electronic and magnetic properties of interfaces and relate them to the structure and composition at the atomistic scale. Furthermore, DFT simulations can predict the structure and properties of candidate interfaces and guide experimental efforts in promising directions. However, DFT simulations of interfaces can be technically elaborate and computationally expensive. To help researchers embarking on such simulations, this review covers best practices for first principles simulations of epitaxial inorganic interfaces, including DFT methods, interface model construction, interface structure prediction, and analysis and visualization tools.

Structure prediction of epitaxial inorganic interfaces by lattice and surface matching with Ogre.

We present a new version of the Ogre open source Python package with the capability to perform structure prediction of epitaxial inorganic interfaces by lattice and surface matching. In the lattice matching step, a scan over combinations of substrate and film Miller indices is performed to identify the domain-matched interfaces with the lowest mismatch. Subsequently, surface matching is conducted by Bayesian optimization to find the optimal interfacial distance and in-plane registry between the substrate and the film. For the objective function, a geometric score function is proposed based on the overlap and empty space between atomic spheres at the interface. The score function reproduces the results of density functional theory (DFT) at a fraction of the computational cost. The optimized interfaces are pre-ranked using a score function based on the similarity of the atomic environment at the interface to the bulk environment. Final ranking of the top candidate structures is performed with DFT. Ogre streamlines DFT calculations of interface energies and electronic properties by automating the construction of interface models. The application of Ogre is demonstrated for two interfaces of interest for quantum computing and spintronics, Al/InAs and Fe/InSb.

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.

Machine Learned Model for Solid Form Volume Estimation Based on Packing-Accessible Surface and Molecular Topological Fragments.

We present a machine learned model for predicting the volume of a homomolecular crystal based on the single-molecule structure, implemented in the open-source Python package for Molecular Volume Estimation (PyMoVE). The model is based on two descriptors: the volume enclosed by the packing-accessible surface and molecular topological fragments. To calculate the volume enclosed by the molecular surface, we have developed a new "projected marching cubes" algorithm. The new algorithm achieves a higher accuracy with a smaller number of elements than the traditional marching cubes algorithm, the marching tetrahedron variant, and Monte Carlo methods. The packing-accessible surface is then calculated using an optimized probe radius. The molecular topological fragments are used to construct a representation that captures the bonding environments of the atoms in the molecule. Feature selection is used to determine which fragments to include in the model. The accuracy and robustness of the model may be attributed to including both geometric and chemical features. The volume enclosed by the packing-accessible surface accounts for the presence of voids and sterically hindered regions as well as for the effect of conformational changes. The molecular topological fragments account for the effect of intermolecular interactions on the packing density. The model is trained on a dataset of structures extracted from the Cambridge Structural Database. Excellent performance is demonstrated for three validation sets of unseen data.

Ogre: A Python package for molecular crystal surface generation with applications to surface energy and crystal habit prediction.

We present Ogre, an open-source code for generating surface slab models from bulk molecular crystal structures. Ogre is written in Python and interfaces with the FHI-aims code to calculate surface energies at the level of density functional theory (DFT). The input of Ogre is the geometry of the bulk molecular crystal. The surface is cleaved from the bulk structure with the molecules on the surface kept intact. A slab model is constructed according to the user specifications for the number of molecular layers and the length of the vacuum region. Ogre automatically identifies all symmetrically unique surfaces for the user-specified Miller indices and detects all possible surface terminations. Ogre includes utilities to analyze the surface energy convergence and Wulff shape of the molecular crystal. We present the application of Ogre to three representative molecular crystals: the pharmaceutical aspirin, the organic semiconductor tetracene, and the energetic material HMX. The equilibrium crystal shapes predicted by Ogre are in agreement with experimentally grown crystals, demonstrating that DFT produces satisfactory predictions of the crystal habit for diverse classes of molecular crystals.

Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence.

Singlet fission (SF) is a photophysical process considered as a possible scheme to bypass the Shockley-Queisser limit by generating two triplet-state excitons from one high-energy photon. Polyacene crystals, such as tetracene and pentacene, have shown outstanding SF performance both theoretically and experimentally. However, their instability prevents them from being utilized in SF-based photovoltaic devices. In search of practical SF chromophores, we use many-body perturbation theory within the GW approximation and Bethe-Salpeter equation to study the excitonic properties of a family of pyrene-stabilized acenes. We propose a criterion to define the convergence of exciton wave-functions with respect to the fine k-point grid used in the BerkeleyGW code. An open-source Python code is presented to perform exciton wave-function convergence checks and streamline the double Bader analysis of exciton character. We find that the singlet excitons in pyrene-stabilized acenes have a higher degree of charge transfer character than in the corresponding acenes. The pyrene-fused tetracene and pentacene derivatives exhibit comparable excitation energies to their corresponding acenes, making them potential SF candidates. The pyrene-stabilized anthracene derivative is considered as a possible candidate for triplet-triplet annihilation because it yields a lower SF driving force than anthracene.

Evolutionary niching in the GAtor genetic algorithm for molecular crystal structure prediction.

The goal of molecular crystal structure prediction (CSP) is to find all the plausible polymorphs for a given molecule. This requires performing global optimization over a high-dimensional search space. Genetic algorithms (GAs) perform global optimization by starting from an initial population of structures and generating new candidate structures by breeding the fittest structures in the population. Typically, the fitness function is based on relative lattice energies, such that structures with lower energies have a higher probability of being selected for mating. GAs may be adapted to perform multi-modal optimization by using evolutionary niching methods that support the formation of several stable subpopulations and suppress the over-sampling of densely populated regions. Evolutionary niching is implemented in the GAtor molecular crystal structure prediction code by using techniques from machine learning to dynamically cluster the population into niches of structural similarity. A cluster-based fitness function is constructed such that structures in less populated clusters have a higher probability of being selected for breeding. Here, the effects of evolutionary niching are investigated for the crystal structure prediction of 1,3-dibromo-2-chloro-5-fluorobenzene. Using the cluster-based fitness function increases the success rate of generating the experimental structure and additional low-energy structures with similar packing motifs.

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.

On the possibility of singlet fission in crystalline quaterrylene.

Singlet fission (SF), the spontaneous down-conversion of a singlet exciton into two triplet excitons residing on neighboring molecules, is a promising route to improve organic photovoltaic (OPV) device efficiencies by harvesting two charge carriers from one photon. However, only a few materials have been discovered that exhibit intermolecular SF in the solid state, most of which are acene derivatives. Recently, there has been a growing interest in rylenes as potential SF materials. We use many-body perturbation theory in the GW approximation and the Bethe-Salpeter equation to investigate the possibility of intermolecular SF in crystalline perylene and quaterrylene. A new method is presented for determining the percent charge transfer (%CT) character of an exciton wave-function from double-Bader analysis. This enables relating exciton probability distributions to crystal packing. Based on comparison to known and predicted SF materials with respect to the energy conservation criterion (ES-2ET) and %CT, crystalline quaterrylene is a promising candidate for intermolecular SF. Furthermore, quaterrylene is attractive for OPV applications, thanks to its high stability and narrow optical gap. Perylene is not expected to exhibit SF; however, it is a promising candidate for harvesting sub-gap photons by triplet-triplet annihilation.

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.