Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals

The performance of non-empirically tuned long-range corrected hybrid functionals for the prediction of vertical ionization potentials (IPs) and electron affinities (EAs) is assessed for a set of 24 organic acceptor molecules. Basis set-extrapolated coupled cluster singles, doubles, and perturbative triples [CCSD­(T)] calculations serve as a reference for this study. Compared to standard exchange-correlation functionals, tuned long-range corrected hybrid functionals produce highly reliable results for vertical IPs and EAs, yielding mean absolute errors on par with computationally more demanding <i>GW</i> calculations. In particular, it is demonstrated that long-range corrected hybrid functionals serve as ideal starting points for non-self-consistent <i>GW</i> calculations

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

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

Accurate Valence Ionization Energies from Kohn–Sham Eigenvalues with the Help of Potential Adjustors

An accurate yet computationally very efficient and formally well justified approach to calculate molecular ionization potentials is presented and tested. The first as well as higher ionization potentials are obtained as the negatives of the Kohn–Sham eigenvalues of the neutral molecule after adjusting the eigenvalues by a recently [Görling Phys. Rev. B 2015, 91, 245120] introduced potential adjustor for exchange-correlation potentials. Technically the method is very simple. Besides a Kohn–Sham calculation of the neutral molecule, only a second Kohn–Sham calculation of the cation is required. The eigenvalue spectrum of the neutral molecule is shifted such that the negative of the eigenvalue of the highest occupied molecular orbital equals the energy difference of the total electronic energies of the cation minus the neutral molecule. For the first ionization potential this simply amounts to a ΔSCF calculation. Then, the higher ionization potentials are obtained as the negatives of the correspondingly shifted Kohn–Sham eigenvalues. Importantly, this shift of the Kohn–Sham eigenvalue spectrum is not just ad hoc. In fact, it is formally necessary for the physically correct energetic adjustment of the eigenvalue spectrum as it results from ensemble density-functional theory. An analogous approach for electron affinities is equally well obtained and justified. To illustrate the practical benefits of the approach, we calculate the valence ionization energies of test sets of small- and medium-sized molecules and photoelectron spectra of medium-sized electron acceptor molecules using a typical semilocal (PBE) and two typical global hybrid functionals (B3LYP and PBE0). The potential adjusted B3LYP and PBE0 eigenvalues yield valence ionization potentials that are in very good agreement with experimental values, reaching an accuracy that is as good as the best <i>G</i>₀<i>W</i>₀ methods, however, at much lower computational costs. The potential adjusted PBE eigenvalues result in somewhat less accurate ionization energies, which, however, are almost as accurate as those obtained from the most commonly used <i>G</i>₀<i>W</i>₀ variants

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

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 <i>Z</i>′ = 2 structure with <i>P</i>1̅ symmetry and a scaffold packing motif, which has not been reported previously

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD­(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD­(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree–Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates

The Malaria Pigment Hemozoin Comprises at Most Four Different Isomer Units in Two Crystalline Models: Chiral as Based on a Biochemical Hypothesis or Centrosymmetric Made of Enantiomorphous Sectors

Hemozoin is a crystalline byproduct formed upon hemoglobin digestion in <i>Plasmodium</i>-infected blood cells. Based on X-ray powder diffraction (XRPD), hemozoin and its synthetic analogue β-hematin are very similar in structure, consisting of cyclic dimers (cd) of ferriprotoporphyrin IX [Fe­(3+)-PPIX] molecules coordinated via Fe–O­(propionate) bonds. Enantiofacial symmetry of Fe­(3+)-PPIX implies formation of four different stereoisomeric dimers, two centrosymmetric (1̅), labeled cd1̅₁ and cd1̅₂, and two enantiomeric, cd2­(+) and cd2(−), in which the Fe­(3+)­PPIX moieties are related by pseudo-2-fold symmetry. Only the cd1̅₁ stereoisomer was reported as the repeat unit in the initial structural elucidation of β-hematin and refinement of hemozoin. Our recent study of β-hematin, employing a combination of XRPD and density functional theory (DFT), revealed besides the published phase, characterized in terms of a disordered cd1̅₁/cd2­(±) mixture, which is diffractionally equivalent to a cd1̅₁/cd1̅₂ mixture, a minor phase considered to comprise mainly cd1̅₂ dimers. As a consequence single-phase β-hematin powders were recently reanalyzed in terms of a cd1̅₁/cd1̅₂ mixture, yielding an average occupancy ≅ 75:25. Here, we present evidence enhancing the biphase model of β-hematin. The primary focus is on a reexamination of the hemozoin structure in light of a biochemically based dimerization mechanism that we recently hypothesized. We suggest that upon hemoglobin degradation, the heme byproduct retains the O₂ molecule bound to Fe on the <i>Re</i> side of the heme until Fe–O­(propionate) coordination between such heme molecules occurs across their unbound <i>Si</i> sides yielding the cd2­(+) dimer. We report Rietveld refinement of the hemozoin structure using data measured on an all-in-vacuum powder diffractometer assuming the following models: cd1̅₁, cd1̅₂, cd2­(+), and the two mixtures cd1̅₁/cd1̅₂ and cd1̅₁/cd2­(+). The best figures of merit were obtained for the mixture cd1̅₁/cd2­(+) with a 50:50 occupancy, followed by the cd1̅₁/cd1̅₂ mixture with an occupancy ≅ 75:25, which we interpret as a structure that comprises the cd1̅₁, cd2­(+), cd2(−), and cd1̅₂ isomers with occupancies ≅ 58:17:17:8. In this model system, the cd1̅₁ “host” molecule is uniformly distributed throughout the crystal, whereas the enantiomeric molecules cd2­(+) and cd2(−) are preferentially occluded in different crystalline sectors, which are thus enantiomorphous, related by overall centrosymmetric symmetry. Various arguments appear to favor the 50:50 cd1̅₁/cd2­(+) mixture, namely, a hemozoin crystal of overall chiral symmetry, consistent with our hypothesis. However, we cannot overrule the alternative model

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods

Comparison of <i>ab initio</i> electron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree–Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of <i>GW</i> Methods

The performance of different <i>GW</i> methods is assessed for a set of 24 organic acceptors. Errors are evaluated with respect to coupled cluster singles, doubles, and perturbative triples [CCSD­(T)] reference data for the vertical ionization potentials (IPs) and electron affinities (EAs), extrapolated to the complete basis set limit. Additional comparisons are made to experimental data, where available. We consider fully self-consistent <i>GW</i> (sc<i>GW</i>), partial self-consistency in the Green’s function (sc<i>GW</i>₀), non-self-consistent <i>G</i>₀<i>W</i>₀ based on several mean-field starting points, and a “beyond <i>GW</i>” second-order screened exchange (SOSEX) correction to <i>G</i>₀<i>W</i>₀. We also describe the implementation of the self-consistent Coulomb hole with screened exchange method (COHSEX), which serves as one of the mean-field starting points. The best performers overall are <i>G</i>₀<i>W</i>₀+SOSEX and <i>G</i>₀<i>W</i>₀ based on an IP-tuned long-range corrected hybrid functional with the former being more accurate for EAs and the latter for IPs. Both provide a balanced treatment of localized vs delocalized states and valence spectra in good agreement with photoemission spectroscopy (PES) experiments