Lattice Energy Minimization Research Articles

Crystal structure predictions for molecules with soft degrees of freedom using intermonomer force fields derived from first principles.

A molecular crystal structure prediction (CSP) protocol used in the seventh blind test is presented. The seventh blind test was divided into two stages and included seven targets, with crystals containing from one to three molecules in asymmetric units, monomers built of up to 100 atoms, and all targets containing monomers with flexible degrees of freedom. Some targets were cocrystals and one target was a salt. These diverse targets were treated using a CSP protocol starting from finding the global and local minima conformations of the target molecule. Subsequently, an ab initio two-body rigid-monomer six-dimensional force field (aiFF) was developed for the global-minimum conformer. These aiFFs were then used in CSPs consisting of packing and lattice-energy minimization stages. Flexible-monomer CSPs were used for some targets. To describe the intramonomer FF, either generic empirical FFs or reparametrized FFs of this type were used, with some parameters fitted to ab initio energies of monomers in the latter case. A novel packing procedure was applied for two targets in stage 1. The success rate in the structure generation stage was 15% in submission phase and 54% in post-submission phase, while the corresponding values in the structure rating stage were 33% and 89%. We conclude that the inexpensive conformer-based approach with rigid-monomer CSPs can be recommended for investigations of crystals with flexible monomers. An advantage of this protocol is that it is fully based on first-principles quantum mechanics and generates tailor-made FFs suitable for use in subsequent molecular dynamics simulations investigating temperature-dependent effects. However, empirical intramonomer FFs reparametrized using ab initio data are not yet adequate for CSPs.

Intrinsic Defect and Deformation on Local Structure Caused by Rare‐Earth Ions in the Na3V2(PO4)2F3 Cathode Material

Na3V2(PO4)2F3 has been attracting a lot of attention as a positive electrode material for sodium‐ion batteries (SIBs). The deformation of local structure caused by rare‐earth ions and intrinsic defect properties in Na3V2(PO4)2F3 as a positive electrode for SIB have been investigated with atomistic simulation based on the lattice energy minimization. A good reproduction of the Na3V2(PO4)2F3 structure is obtained. It is revealed that Na Frenkel defect, which is formed by sodium interstitial and vacancy pair, is the most favorable type of intrinsic defect. This leads to the formation of stable sodium vacancy required for the Na‐ion diffusion. The results indicate that trivalent rare‐earth dopants at the V3+ site are the most energetically favorable dopants for Na3V2(PO4)2F3, and that the incorporation at the Na and P site could be used as a strategy to increase the sodium vacancy and interstitial, respectively. The deformation in the local structure by the rare‐earth ions doping at the V site is also investigated as helpful in improving the rate performance of SIBs.

Leucopterin, the white pigment in butterfly wings: structural analysis by PDF fit, FIDEL fit, Rietveld refinement, solid-state NMR and DFT-D.

Leucopterin (C6H5N5O3) is the white pigment in the wings of Pieris brassicae butterflies, and other butterflies; it can also be found in wasps and other insects. Its crystal structure and its tautomeric form in the solid state were hitherto unknown. Leucopterin turned out to be a variable hydrate, with 0.5 to about 0.1 molecules of water per leucopterin molecule. Under ambient conditions, the preferred state is the hemihydrate. Initially, all attempts to grow single crystals suitable for X-ray diffraction were to no avail. Attempts to determine the crystal structure by powder diffraction using the direct-space method failed, because the trials did not include the correct, but rare, space group P2/c. Attempts were made to solve the crystal structure by a global fit to the pair distribution function (PDF-Global-Fit), as described by Prill and co-workers [Schlesinger et al. (2021). J. Appl. Cryst. 54, 776-786]. The approach worked well, but the correct structure was not found, because again the correct space group was not included. Finally, tiny single crystals of the hemihydrate could be obtained, which allowed at least the determination of the crystal symmetry and the positions of the C, N and O atoms. The tautomeric state of the hemihydrate was assessed by multinuclear solid-state NMR spectroscopy. 15N CPMAS spectra showed the presence of one NH2 and three NH groups, and one unprotonated N atom, which agreed with the 1H MAS and 13C CPMAS spectra. Independently, the tautomeric state was investigated by lattice-energy minimizations with dispersion-corrected density functional theory (DFT-D) on 17 different possible tautomers, which also included the prediction of the corresponding 1H, 13C and 15N chemical shifts in the solid. All methods showed the presence of the 2-amino-3,5,8-H tautomer. The DFT-D calculations also confirmed the crystal structure. Heating of the hemihydrate results in a slow release of water between 130 and 250 °C, as shown by differential thermal analysis and thermogravimetry (DTA-TG). Temperature-dependent powder X-ray diffraction (PXRD) showed an irreversible continuous shift of the reflections upon heating, which reveals that leucopterin is a variable hydrate. This observation was also confirmed by PXRD of samples obtained under various synthetic and drying conditions. The crystal structure of a sample with about 0.2 molecules of water per leucopterin was solved by a fit with deviating lattice parameters (FIDEL), as described by Habermehl et al. [Acta Cryst. (2022), B78, 195-213]. A local fit, starting from the structure of the hemihydrate, as well as a global fit, starting from random structures, were performed, followed by Rietveld refinements. Despite dehydration, the space group remains P2/c. In both structures (hemihydrate and variable hydrate), the leucopterin molecules are connected by 2-4 hydrogen bonds into chains, which are connected by further hydrogen bonds to neighbouring chains. The molecular packing is very efficient. The density of leucopterin hemihydrate is as high as 1.909 kg dm-3, which is one of the highest densities for organic compounds consisting of C, H, N and O only. The high density might explain the good light-scattering and opacity properties of the wings of Pieris brassicae and other butterflies.

Defect and spectroscopy properties of Eu-doped RbBaPO4 phosphors: A computer simulation study

The effects of Eu incorporation in the RbBaPO4 structure was investigated using atomistic simulation based on lattice energy minimization combined with crystal field models. The defect study reveals that the most favorable intrinsic defect type is formed by the anti-site defect. The results revealed that Eu3+ prefers to enter the Ba site with a RbBa' anti-sites as charge compensation. Crystal field theory shows that the substitution of the Eu3+ ion for the Ba2+ ion in the anti-site defect accompanied by the local lattice deformation induces a local symmetry without the inversion center of the slightly distorted C4 type at the position of the impurity Eu3+ ion. The 7F1 and 7F2 energy sublevels as well as the 7F1 manifold were satisfactorily reproduced with a set of phenomenological charge factors and non-null crystal field parameters.

Analysis of diffuse scattering in electron diffraction data for the crystal structure determination of Pigment Orange 13, C32H24Cl2N8O2.

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single-crystal X-ray analysis of a tiny needle. The α phase was investigated using three-dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit-cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice-energy minimization with dispersion-corrected DFT. A four-layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X-ray powder data. Additionally, five further phases of P.O.13 are described.

Lattice defects in quinacridone

Various lattice defects in the αI-phase of quinacridone (C20H12N2O2) were simulated using lattice-energy minimizations. αI-Quinacridone forms a chain structure in P 1, Z = 1. The molecules are connected by hydrogen bonds along [010], by π-stacking along [100] and by weak van der Waals interactions along [001]. αI-Quinacridone is inherently nanocrystalline. Lattice defects were calculated in correspondingly large supercells with up to 4464 atoms, using a previously evaluated force field. Vacancies, vacancy aggregates and interstitial molecules are energetically very unfavourable. A misorientation of a single molecule (flip around [010] by 180°) causes an energy increase of 243.7 kJ mol−1. Various edge and screw dislocations were investigated. A screw dislocation along [010] causes an energy increase of ΔE = 38.0 kJ mol−1 per molecule, all other line dislocations are even worse. In contrast, the rotation of an entire chain around the chain axis [010] by 180° leads to only a very small energy increase (ΔE = 1.6 kJ mol−1) and the real crystals probably contain a high number of such defects. Various planar defects were calculated, including different stacking disorders and misfit-layer structures with two different types of layers having different lateral periodicities. Stacking faults along [001] with herringbone stacking instead of parallel stacking are energetically quite favourable (ΔE = 2.2 kJ mol−1); the same is true for domains with misoriented molecules in the [001] direction. As an example for a bulk defect, domains are calculated in which blocks of 4 × 4 chains are rotated by 180° around [010], which leads to an energy increase of only 1.1 kJ mol−1. Twinning by mirroring at the (001) plane is energetically favourable (ΔE = 0.9 kJ mol−1). This twinning was observed in an HRTEM image. It is probable that the crystallites also contain rotations of chains, layers or blocks around [010] by 180°, but these defects cause only a very slight modification of the molecular packing, which was not observable in the HRTEM image. The lattice defects in αI-quinacridone investigated here provide an insight into lattice defects, their energies and local structures. Similar lattice defects are expected to occur also in other similar organic chain structures.

Computer Modelling of Defects in Ba2YNbO6

The structural properties of Ba2YNbO6 were adjusted and compared with experimental data through an interatomic potential that was optimized here and is based on a model known as the shell model used in this work for oxygen ions. Intrinsic and extrinsic defects were calculated based on the minimization of the crystal lattice energy through computational modeling. Calculations showed that rare earth ions prefer to incorporate the Y3+ site and Mn4+ the Nb5+ site, thus being more energetically favorable.

Ambiguous structure determination from powder data: four different structural models of 4,11-di-fluoro-quinacridone with similar X-ray powder patterns, fit to the PDF, SSNMR and DFT-D.

Four different structural models, which all fit the same X-ray powder pattern, were obtained in the structure determination of 4,11-di-fluoro-quinacridone (C20H10N2O2F2) from unindexed X-ray powder data by a global fit. The models differ in their lattice parameters, space groups, Z, Z', molecular packing and hydrogen bond patterns. The molecules form a criss-cross pattern in models A and B, a layer structure built from chains in model C and a criss-cross arrangement of dimers in model D. Nevertheless, all models give a good Rietveld fit to the experimental powder pattern with acceptable R-values. All molecular geometries are reliable, except for model D, which is slightly distorted. All structures are crystallochemically plausible, concerning density, hydrogen bonds, intermolecular distances etc. All models passed the checkCIF test without major problems; only in model A a missed symmetry was detected. All structures could have probably been published, although 3 of the 4 structures were wrong. The investigation, which of the four structures is actually the correct one, was challenging. Six methods were used: (1) Rietveld refinements, (2) fit of the crystal structures to the pair distribution function (PDF) including the refinement of lattice parameters and atomic coordinates, (3) evaluation of the colour, (4) lattice-energy minimizations with force fields, (5) lattice-energy minimizations by two dispersion-corrected density functional theory methods, and (6) multinuclear CPMAS solid-state NMR spectroscopy (1H, 13C, 19F) including the comparison of calculated and experimental chemical shifts. All in all, model B (perhaps with some disorder) can probably be considered to be the correct one. This work shows that a structure determination from limited-quality powder data may result in totally different structural models, which all may be correct or wrong, even if they are chemically sensible and give a good Rietveld refinement. Additionally, the work is an excellent example that the refinement of an organic crystal structure can be successfully performed by a fit to the PDF, and the combination of computed and experimental solid-state NMR chemical shifts can provide further information for the selection of the most reliable structure among several possibilities.

Zeolite Phase Selectivity Using the Same Organic Structure-Directing Agent in Fluoride and Hydroxide Media

Force field-based calculations of all-silica zeolites show the role of fluoride as a structure-directing agent (SDA). Calculations of fully packed organic and fluoride SDAs were possible with an updated version of zeoTsda software, based on Monte Carlo+Lattice Energy Minimization. Comparison between fluoride-containing and fluoride-free calculations using the same organic SDA allowed us to predict which zeolite phase is obtained in fluoride and hydroxide media and also, through a new energy decomposition scheme, identify energetic contributions driving the synthesis outcome.

Effects of rare-earth doping and reduction processes in LiCaPO4 compound: A computer simulation study

We perform a computational study of rare earth (RE) doping of the LiCaPO4 structure using an atomistic simulation based on lattice energy minimisation. Particular attention is given to the effects of RE doping on the structure of LiCaPO4. It is found that RE3+ and RE2+ dopant ions have an energetic preference to be incorporated at the Ca2+ host site. Our simulations show that for the incorporation of the RE3+ ion, charge compensation by LiCa, antisite defects is more likely to occur. In addition, the bond valence sum (BVS) is obtained for the RE3+-O2- pair. To investigate Eu reduction doping mechanisms, three reduction mechanisms (open atmosphere, CO and a H2 reducing atmosphere) are considered. An H2 reducing atmosphere was found to be the most effective agent for Eu reduction. Our results reveal the possibility of the co-existence of both Eu3+ and Eu2+ ions in the host. In fact, a specific study of the lattice deformation by various types of defect mechanisms can improve the effective rate performance of LiCaPO4 for luminescent applications.

Defect and spectroscopy properties of Eu-doped LiMgPO4 phosphors

In this work we used atomistic simulation based on lattice energy minimization combined with crystal field models to study the effects of Eu incorporation in the LiMgPO4 structure. We showed that the most favorable intrinsic defect type is formed by the anti-site defect, in which Li+ and Mg2+ ions exchange positions. The results revealed that Eu3+ prefers to enter in the Mg site with a LiMg' anti-site charge compensation. The local structure of Eu3+ was used to obtain the crystal field parameters and 7F1 energy sub-levels. Also, we estimated the photoionization cross-section of localized traps in the bandgap and associated it with the presence of defects to understand the high sensitivity.

The Trivalent Rare‐Earth Dopant in the KBaPO4 and KSrPO4 Compounds: An Atomistic Simulation Study

KBaPO4 and KSrPO4 phosphates belong to an important group of luminescent materials that have a wide range of optical applications when doped with trivalent rare‐earth (RE) ions. An atomistic simulation technique based on lattice energy minimization is used to examine the intrinsic defect process and the incorporation of a variety of trivalent RE (RE = Yb3+, Dy3+, Tb3+, Sm3+, Pr3+, and Ce3+) dopant ions in KBaPO4 and KSrPO4. Calculations suggest that intrinsic defects such as the K’M antisite and K Frenkel are favorable, and also that the RE ions preferentially occupy divalent host sites in both structures. The K’Ba and K’Sr antisite defects are the most favorable charge compensation defect in KBaPO4 and KSrPO4, respectively. Structural and local changes caused by trivalent dopants are also investigated.

Atomistic simulation and spectroscopy study of the Eu-doped NaCdPO4 compound

Atomistic simulation based on lattice energy minimization was performed to study the defect process caused by europium in the NaCdPO4 structure. The calculations suggest that the most favorable intrinsic defect type is formed by cation anti-site defect, in which Na+ and Cd2+ ions exchange positions. The calculation also reveals that doping by Eu3+ on the Cd site is the most energetically favorable. Charge compensation by NaCdʼ anti-site defect is probable. Crystal field parameters are then calculated and used to obtain the 7F1 sublevels of the Eu3+, which we use to discuss the local symmetry of the Eu3+.

Identification of New Templates for the Synthesis of BEA, BEC, and ISV Zeolites Using Molecular Topology and Monte Carlo Techniques.

The presence of organic structure directing agents (templates) in the synthesis of zeolites allows the synthesis to be directed, in many cases, toward structures in which there is a large stabilization between the template and the zeolite micropore due to dispersion interactions. Although other factors are also important (temperature, pH, Si/Al ratio, etc.), systems with strong zeolite-template interactions are good candidates for an application of new computational algorithms, for instance those based in molecular topology (MT), that can be used in combination with large databases of organic molecules. Computational design of new templates allows the synthesis of existing and new zeolites to be expanded and refined. Three zeolites with similar 3-D large pore systems, BEA, BEC, and ISV, were selected with the aim of finding new templates for their selective syntheses. Using a training set of active and inactive templates (obtained from the literature) for the synthesis of target zeolites, it was possible to select chemical descriptors related to activity, meaning a good candidate template. With a discriminant function defined upon MT, the screening through a database of organic molecules led to a small subset (preselection) of candidate templates for the synthesis of BEA, BEC, and ISV. As far as we know, this is the first time that topological/topochemical descriptors, which do not consider 3-D information on the molecules, have been used to predict the activity of zeolite structure directing agents (SDAs). Following the prediction of SDAs using MT, an automated approach of sequential template filling of micropores based on a combination of Monte Carlo and lattice energy minimization was applied for all the candidate templates in the three zeolites. Two results can be obtained from this: an evaluation of the quality of the molecular topology QSAR models leading to the preselection of templates, and a final selection of candidate templates for the selective synthesis of BEA, BEC, and ISV. Regarding the latter, a good template will be that which maximizes the zeolite-template dispersion interactions with one, and only one, of the three zeolites. The presented methodology can be used to find alternative (maybe cheaper or perhaps more selective) templates than those already known.

Orientational disorder of monomethyl-quinacridone investigated by Rietveld refinement, structure refinement to the pair distribution function and lattice-energy minimizations.

The crystal structure of the organic pigment 2-monomethyl-quinacridone (Pigment Red 192, C21H14N2O2) was solved from X-ray powder diffraction data. The resulting average structure is described in space group P\overline 1, Z = 1 with the molecule on the inversion centre. The molecules are arranged in chains. The molecules, which have no inversion symmetry, show orientational head-to-tail disorder. In the average structure, the methyl group is disordered and found on both ends of the molecule with an occupancy of 0.5 each. The disorder and the local structure were investigated using various ordered structural models. All models were analysed by three approaches: Rietveld refinement, structure refinement to the pair distribution function (PDF) and lattice-energy minimization. All refinements converged well. The Rietveld refinement provided the average structure and gave no indication of a long-range ordering. The refinement to the PDF turned out to be very sensitive to small structural details, giving insight into the local structure. The lattice-energy minimizations revealed a significantly preferred local ordering of neighbouring molecules along the [0\bar 11] direction. In conclusion, all methods indicate a statistical orientational disorder with a preferred parallel orientation of molecules in one direction. Additionally, electron diffraction revealed twinning and faint diffuse scattering.

Computational modelling of intrinsic defects in the orthosilicates Y2SiO5 and Lu2SiO5

Atomistic computer modelling techniques were applied to study the intrinsic defects in the Y2SiO5 (YSO) and Lu2SiO5 (LSO) structures at 0 and 300 K temperatures. The approach used is based on the interatomic potentials model and lattice energy minimization. A set of potential parameters were obtained by empirical adjustment and reproduced the lattice parameters with values better than 0.98% and 2.24% for YSO and LSO, respectively. Intrinsic defects were performed using the well-known Mott-Littleton method. Two conditions were adopted to calculate defects: for unbonded condition, point defects (vacancies and interstitials) were calculated without possible interactions with each other; for bounded condition, point defects interact with each other through coulomb and short-range potentials. All possible configurations were tested for Frenkel and Schottky defects in unbounded condition and only the most favourable defect configuration was considered in bounded condition. Oxygen Frenkel type is the most favourable energetic defect in both structures at both temperatures. Bounded defects calculations showed that oxygen vacancy and interstitial located in first coordinate sphere have the lowest solution energy values for LSO. However, the most favourable defect positions are further apart in the YSO structure. The bounded condition was most favourable decreasing the energetic costs of the defect for all cases demonstrating that the interaction of O Frenkel pair should be consider in future works.

Ab Initio Prediction of Stable Crystal Structure of Procarbazine Molecule

The crystal structure of procarbazine molecule was predicted using first principles of quantum mechanics. The gas phase optimization was carried out by density functional theory and the resulted geometric coordinates were utilized for the search of hypothetical packings which reveals the possible stable conformers under a repulsion alone potential field with minimum cell volume. The thermodynamically favor structure was resulted from the lattice energy minimization of these hypothetical structures from the using the repulsion-dispersion potential field. The stability of global minimum structure was confirmed from the hydrogen bond interactions and second derivative properties.

Rare Earth Doping and Co‐Doping in Lithium Strontium Silicate: A Computational Study

Using atomistic simulations based on lattice energy minimization, rare earth doping and co‐doping in Li2SrSiO4 (LSSO) are investigated in terms of energetics. The doping effects are determined by the calculation of atomistic energetics, using potential parameters developed from an empirical potential by fitting. The potential parameters obtained in this way allowed us to reproduce the structural parameters, and the results showed good agreement with the experimental data. The results of these calculations indicate that the Li Frenkel and Li2O Schottky defects are the most favorable intrinsic defects, and also reveal that RE3+ = Ce, Pr, Sm, Eu, Dy, Er and RE2+ = Eu ions are most energetically favorable for incorporation at the Sr site. Charge compensation by VLi′ vacancy defects is the most probable route for RE3+ ion incorporation. The reduction–doping processes (Eu reduction) in a H2 reducing atmosphere were considered, and the effects of co‐doping on Eu reduction were also investigated.

Investigation of Europium dopant in the orthophosphate KMPO4 (M = Ba and Sr) compounds

Atomistic simulations based on lattice energy minimization are used to investigate trivalent and divalent Europium dopant ions in the structure of KMPO4 (M = Ba and Sr). Interatomic potentials are developed, and the structural properties calculated in this way show good agreement with experimental values. These calculations suggest that Eu3+ and Eu2+ ions are the most energetically provable to be incorporated at divalent (M = Ba and Sr) host sites. It is also predicted that the Eu divalent dopant is charge-compensated by KMʼ anti-site defects. Four reduction-doping process schemes (open atmosphere, CO, N2 and H2 reducing atmosphere) are investigated here, and it is observed that a CO reducing atmosphere is the most effective agent for Eu reduction. The results showed that the preferred host site, charge compensation and schemes for the reduction-doping process for Eu doping ions play important roles in an understanding of the luminescent properties of KMPO4 (M = Ba and Sr) phosphates.

A full palette: Crystal chemistry, polymorphism, synthetic strategies, and functional applications of lanthanide oxyhalides

Ionic compounds wherein lanthanide cations are arrayed alongside anions adopt a wide range of crystal structures as a result of the variation of ionic radii and electronic configurations across the lanthanide series. Owing to the constricted nature of 4f orbitals, local coordination environments and structural preferences in such compounds are primarily dictated by electrostatic interactions and steric considerations with the primary driving force being the minimization of the crystal lattice energy. In this review, we examine a broad class of dianionic rare-earth compounds, lanthanide oxyhalides that present a multidimensional design space for tuning of functional properties by dint of the possibilities for extensive alloying on cationic and anionic sublattices; the considerable span of ionic radii and hardness across the lanthanide series and down the halide group, respectively; a large tolerance window for point defects such as oxide and halide vacancies; as well as multiple accessible polymorphs. In addition to their structural versatility, control over functional properties is accessible based on alteration of microstructure and surface chemistry. Synthetic strategies for accessing atomistic, nanoscale, and mesoscale control are discussed using illustrative examples placing particular emphasis on non-hydrolytic sol—gel processes that provide access to well-defined solid-solution nanocrystals. The reactivity and post-synthetic modification of these compounds is further delineated. Methods for defining color centers within these compounds, cooperativity of the optical response of the color centers with the host lattice (determined by overlap integrals specific to each structure type and the polarization and ligand field effects of different halide ions) and adjacent color centers (reliant on energy transfer schema), and their practical application in phosphors are further detailed. Mechanisms facilitating down- and up-conversion of energy absorbed from incident electromagnetic radiation or high-energy particles are delineated with particular emphasis on X-ray and electron-beam excitation. The accessible energy conversion mechanisms, efficacious radiative recombination channels, and opportunities for systematically tuning color through compositional modulation have led to the emergence of these materials as potential candidates for phosphors. These materials have potential applications in solid-state lighting, radiation detection, and as the active elements of imaging devices. The tolerance towards large concentrations of anion vacancies and the facile diffusivity of anions in these compounds further underpins the function of lanthanide oxyhalides as ion conductors, gas sensors, and heterogeneous catalysts. Increasing interest has focused on utilization of well-defined color centers for quantum information science and multiplexed sensing in biological systems. Such applications require additional control of the positioning of dopant atoms and understanding of their interactions with the host lattice and other dopant atoms.