Independent Atom Model Research Articles

Ionisation of atoms determined by kappa refinement against 3D electron diffraction data.

Conventional refinement strategies used for three-dimensional electron diffraction (3D ED) data disregard the bonding effects between the atoms in a molecule by assuming a pure spherical model called the Independent Atom model (IAM) and may lead toan inaccurate or biased structure. Here we show that it is possible to perform a refinement going beyond theIAM with electron diffraction data. We perform kappa refinement which models charge transfers between atoms while assuming a spherical model. We demonstrate the procedure by analysing five inorganic samples; quartz, natrolite, borane, lutecium aluminium garnet, and caesium lead bromide. Implementation of kappa refinement improved the structure model obtained over conventional IAM refinements and provided information on the ionisation of atoms. The results were validated against periodic DFT calculations. The work presents an extension of the conventional refinement of 3D ED data for a more accurate structure model which enables charge density information to be extracted.

The Hydrogen-Bond Continuum in the Salt/Cocrystal Systems of Quinoline and Chloro-Nitrobenzoic Acids.

This study investigates the hydrogen-bond geometry in six two-component solid systems composed of quinoline and chloro-nitrobenzoic acids. New X-ray diffraction studies were conducted using both the conventional independent-atom model and the more recent Hirshfeld atom-refinement method, with the latter providing precise hydrogen-atom positions. The systems can be divided into salts (the hydrogen atom transferred to the quinoline nitrogen), cocrystals (the hydrogen atom retained by the acid), and intermediate structures. Solid-state NMR experiments corroborated the X-ray diffraction-derived H-N distances. DFT calculations, using five functionals including hybrid B3LYP and PBE0, showed varying energy profiles for the hydrogen bonds, with notable differences across functionals. These calculations revealed different preferences for salt or cocrystal structures, depending on the functional used. Path-integral molecular dynamics simulations incorporating nuclear quantum effects demonstrated significant hydrogen-atom delocalization, forming a hydrogen-bond continuum, and provided average N-H distances in excellent agreement with experimental results. This comprehensive experimental and theoretical approach highlights the complexity of multicomponent solids. The study emphasizes that the classification into salts or cocrystals is frequently inadequate, as the hydrogen atom is often significantly delocalized in the hydrogen bond. This insight is crucial for understanding and predicting the behavior of such systems in pharmaceutical applications.

Hirshfeld atom refinement and dynamical refinement of hexagonal ice structure from electron diffraction data.

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural parameters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O-H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O-H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled - with extinction correction or with dynamical refinement. The latter led to an improvement of the O-H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

TAAM refinement on high-resolution experimental and simulated 3D ED/MicroED data for organic molecules.

3D electron diffraction (3D ED), or microcrystal electron diffraction (MicroED), has become an alternative technique for determining the high-resolution crystal structures of compounds from sub-micron-sized crystals. Here, we considered L-alanine, α-glycine and urea, which are known to form good-quality crystals, and collected high-resolution 3D ED data on our in-house TEM instrument. In this study, we present a comparison of independent atom model (IAM) and transferable aspherical atom model (TAAM) kinematical refinement against experimental and simulated data. TAAM refinement on both experimental and simulated data clearly improves the model fitting statistics (R factors and residual electrostatic potential) compared to IAM refinement. This shows that TAAM better represents the experimental electrostatic potential of organic crystals than IAM. Furthermore, we compared the geometrical parameters and atomic displacement parameters (ADPs) resulting from the experimental refinements with the simulated refinements, with the periodic density functional theory (DFT) calculations and with published X-ray and neutron crystal structures. The TAAM refinements on the 3D ED data did not improve the accuracy of the bond lengths between the non-H atoms. The experimental 3D ED data provided more accurate H-atom positions than the IAM refinements on the X-ray diffraction data. The IAM refinements against 3D ED data had a tendency to lead to slightly longer X-H bond lengths than TAAM, but the difference was statistically insignificant. Atomic displacement parameters were too large by tens of percent for L-alanine and α-glycine. Most probably, other unmodelled effects were causing this behaviour, such as radiation damage or dynamical scattering.

Electron scattering beyond the independent atom model: Quantum fluctuation of the Coulomb potential.

In the past century, electron scattering has mostly served as a powerful tool to measure the microscopic structure of gases, liquids, and solids in either a static or time-resolved manner. One common basis for these works is the independent atom model, which directly relates electron scattering signals to the atomic structure of matter. In this perspective, we explore the information content of electron scattering that goes beyond the independent atom model. We show that the small-angle limit of the electron scattering signal encodes the quantum mechanical fluctuation of the long-range Coulomb potential. This quantum fluctuation, described by the second moment of the dipole operator, is the root cause of the intermolecular van der Waals forces.

Dynamical refinement with multipolar electron scattering factors.

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Extracting the electronic structure signal from X-ray and electron scattering in the gas phase.

X-ray and electron scattering from free gas-phase molecules is examined using the independent atom model (IAM) and ab initio electronic structure calculations. The IAM describes the effect of the molecular geometry on the scattering, but does not account for the redistribution of valence electrons due to, for instance, chemical bonding. By examining the total, i.e. energy-integrated, scattering from three molecules, fluoroform (CHF3), 1,3-cyclohexadiene (C6H8) and naphthalene (C10H8), the effect of electron redistribution is found to predominantly reside at small-to-medium values of the momentum transfer (q ≤ 8 Å-1) in the scattering signal, with a maximum percent difference contribution at 2 ≤ q ≤ 3 Å-1. A procedure to determine the molecular geometry from the large-q scattering is demonstrated, making it possible to more clearly identify the deviation of the scattering from the IAM approximation at small and intermediate q and to provide a measure of the effect of valence electronic structure on the scattering signal.

Elastic and electronically inelastic scattering of electrons by the pyrazine molecule.

We report on elastic and electronically inelastic integral and differential cross sections as well as ionization and total cross sections for electron collisions with the pyrazine molecule. The Schwinger multichannel method is applied in calculations carried out according to the minimal orbital basis for single configuration interactions strategy from the 1-channel up to 139-channels close-coupling level of approximation. With these calculations we have obtained integral and differential cross sections as well as excitation functions for elastic electron scattering and, also, integral and differential cross sections for electronic excitation from the ground state to the 3B1u, 3B2u, 3B3u, 1B1u, 1B2u and 1B3u excited states of pyrazine by electron impact. By summing the total ionization cross section obtained by means of the binary-encounter-Bethe model to these elastic and electronically inelastic contributions, we provided an estimate for the total cross section describing the electron-pyrazine interaction process. The independent atom model with the screening-corrected additivity rule plus interference terms method was also used in the present study to determine elastic integral and differential as well as ionization and total cross sections for electron collisions from pyrazine. The present results were, whenever possible, critically compared to the experimental and theoretical data available in the literature. In general, the overall agreement between the present results and the experiment is quite encouraging.

Investigating theoretical and experimental cross sections for elastic electron scattering from isoflurane.

We present a comprehensive analysis of elastic electron scattering from isoflurane in the intermediate energy range of 50-300 eV. This research is motivated by the significant impact of this molecule on global warming effects. We conducted this investigation through experimental measurements using a crossed-beam apparatus and covering a wide angular range from 25 to 125 degrees. Relative differential cross sections (DCSs) were obtained and subsequently normalized on an absolute scale by using the relative flow technique, with argon as the reference gas. These DCS values were then extrapolated and integrated to determine the experimental integral cross sections (ICSs). Additionally, we employed the independent atom model and the screening corrected additivity rule with incorporated Interference effects (IAM-SCAR+I) to calculate the theoretical differential and integral cross-sections. Remarkably, the calculated cross sections align closely with the experimental measurements across the entire energy and angular range. Furthermore, this study involved a comparison of the DCSs for isoflurane with previously published DCS values for two other volatile anesthetics, sevoflurane and halothane.

Simulational and theoretical study of electron scattering cross section by Chlormethine-DNA complex

Studying phenomena happening in therapies to conquer cancer has been the aim of extensive research projects in recent years. One of the most practical treatments is utilizing electrons as interacting particles in body tissues. So, studying electron interactions with biological molecules is highly important. Chlormethine as an alkylating agent has always been used since the initial era of cancer chemotherapy. The drug makes interstrand and intrastrand covalent cross-links between two constituents in DNA. In this paper the physical interaction of electrons with Chlormethine drug was reported for the first time. Molecular dynamic (MD) simulations and free energy calculations were carried out to investigate near approach binding of the drug with DNA. Electron scattering cross sections on the system of DNA bases along with Chlormethine as an anticancer drug taken from MD simulations are studied in this paper. Calculations include relativistic Dirac partial-wave which is combined with a local interaction potential. Electron scattering is modelled by the independent atom model (IAM) considering a screening corrected coefficient over an energy range.

Collisions of low- to intermediate-energy electrons with acetonitrile

A systematic investigation was carried out on the elastic scattering of low- to intermediate-energy electrons ( = 0.1–1000 eV eV) by acetonitrile (CH3CN). We calculated differential (DCS), integral (ICS), momentum-transfer (MTCS), and total absorption cross sections from 0.1 to 1000 eV energy range using an absorption-effects-implemented ePolyScat-E3 suite of codes, which applies the Schwinger variational method combined with the Padé-approximants technique. Also, the screen-corrected independent atom model was used to compute DCSs, ICSs, and MTCSs from 10–1000 eV impact energies. Present results are compared to other theoretical and experimental data when available. In general, our DCS and MTCS results show a good agreement with available data, however, the ICSs and the resonance features exhibit fair accordance. Our results show two shape-resonance structures: one at about 3.4 eV and a second at about 7 eV. They are labeled as and , and comprise the and scattering channels, respectively.

Indium Kα radiation from a MetalJet X-ray source: comparison of the Eiger2 CdTe and Photon III detectors.

The MetalJet source makes available new Kα radiation wavelengths for use in X-ray diffraction experiments. The purpose of this paper is to demonstrate the application of indium Kα radiation in independent-atom model refinement, as well as approaches using aspherical atomic form factors. The results vary greatly depending on the detector employed, as the energy cut-off of the Eiger2 CdTe provides a solution to a unique energy contamination problem of the MetalJet In radiation, which the Photon III detector cannot provide.

Scattering of electron and positron by HCN: a theoretical investigation

A theoretical investigation of differential, integrated elastic, inelastic, transport (momentum transfer & viscosity), grand total (elastic+inelastic) and total ionisation cross-sections along with the Sherman functions for the scattering of electron and positron by hydrogen cyanide (HCN) in the energy range 1 e V − 1 MeV are presented in this report. We perform calculations using the single scattering independent atom model (IAM) and IAM with screening correction (IAMS). The scattering observables are calculated using a complex optical model potential in the framework of the Dirac partial wave analysis (DPWA). The inclusion of screening correction to the IAM appreciably improves the cross-sections, especially at low-impact energies. Our calculated results are compared with the available experimental and theoretical works found in the literature. Our present computational data agree well with prior results.

Combined experimental and theoretical study on the elastic electron scattering cross sections of ethanol

Combined theoretical and experimental studies on the elastic scattering of electrons on ethanol were performed in the energy range of 30–800 eV. The differential elastic electron scattering cross sections (DCS) of ethanol were measured for scattering angles of 30° to 150° using the relative flow technique and nitrogen (N2) as the reference gas. From these experimental DCS, integral elastic and momentum transfer cross sections were estimated. The comparison of the experimental results from the present work to those of other groups showed good agreement within the experimental uncertainty. In addition to the experimental determination, the DCS of ethanol were calculated by applying the independent atomic model with screening-corrected additivity rule and the modified independent atomic model. These theoretical calculations reproduced the experimental data well within the experimental uncertainty, with agreement better at high electron energies as was expected.Graphical abstract

Hirshfeld Atom Refinement of Metal-Organic Complexes: Treatment of Hydrogen Atoms Bonded to Transition Metals.

Hydrogen positions in hydrides play a key role in hydrogen storage materials and high-temperature superconductors. Our recently published study of five crystal structures of transition-metal-bound hydride complexes showed that using aspherical atomic scattering factors for Hirshfeld atom refinement (HAR) resulted in a systematic elongation of metal-hydrogen bonds compared to using spherical scattering factors with the Independent Atom Model (IAM). Even though only standard-resolution X-ray data was used, for the highest-quality data, we obtained excellent agreement between the X-ray and the neutron-derived bond lengths. We present an extended version of this study including 10 crystal structures of metal-organic complexes containing hydrogen atoms bonded to transition-metal atoms for which both X-ray and neutron data are available. The neutron structures were used as a benchmark, and the X-ray structures were refined by applying Hirshfeld atom refinement using various basis sets and DFT functionals in order to investigate the influence of the technical aspects on the length of metal-hydrogen bonds. The result of including relativistic effects in the Hamiltonian and using a cluster of multipoles simulating interactions with a crystal environment during wave function calculations was examined. The effect of the data quality on the final result was also evaluated. The study confirms that a high quality of experimental data is the key factor allowing us to obtain significant improvement in transition metal (TM)-hydrogen bond lengths from HAR in comparison with the IAM. Individual adjustments and better choices of the basis set can improve hydrogen positions. Average differences between TM-H bond lengths obtained with various DFT functionals upon including relativistic effects or between double-ζ and triple-ζ basis sets were not statistically significant. However, if all bonds formed by H atoms were considered, significant differences caused by different refinement strategies were observed. Finally, we examined the refinement of atomic thermal motions. Anisotropic refinement of hydrogen thermal motions with HAR was feasible only in some cases, and isotropically refined hydrogen thermal motions were in similar agreement with neutron values whether obtained with HAR or with the IAM.

Comparative study of photoelectron momentum distributions from Kr and CO2 near a backward rescattering caustic by carrier-envelope-phase mapping

We study carrier-envelope-phase- (CEP-) dependent photoelectron momentum distributions (PEMDs) of Kr atoms and randomly oriented ${\mathrm{CO}}_{2}$ molecules exposed to sub-two-cycle intense infrared fields with linear polarization. The adiabatic theory predicts that, at fixed laser parameters (intensity, pulse duration, and CEP), the PEMDs for targets with equal ionization potentials considered across a backward rescattering caustic have identical shapes and only their absolute values depend on the target. We choose Kr and ${\mathrm{CO}}_{2}$ as targets with almost identical ionization potentials (approximately $14$ eV) to explore this behavior of PEMDs. We find that the measured PEMDs for Kr and ${\mathrm{CO}}_{2}$ have cutoff structures, which are associated with the caustics, with identical decaying profiles. We also reveal that CEP-dependent PEMDs around the cutoff exhibit target dependence, reflecting the differences in the differential cross sections (DCSs) of elastic rescattering and tunneling ionization rates. Furthermore, we extract the DCSs from the measured PEMDs around the cutoffs at different CEPs based on the adiabatic theory. The extracted DCSs agree with ones calculated by using the single-active-electron (SAE) scattering model, which includes all multiple-scattering processes, with orientation averaging for ${\mathrm{CO}}_{2}$. In contrast, the independent-atom model, which only considers single-scattering processes, cannot reproduce the extracted DCSs of ${\mathrm{CO}}_{2}$ at low scattering momenta. This finding indicates that multiple scattering is not negligible in the momentum range of 1.5--2.5 a.u. The extracted DCSs also show interference features assigned to multicenter scattering of O-O and C-O. These results confirm that the signature of electron interference is retained after orientation averaging, indicating that the internuclear distances of the constituent atoms can be retrieved from the CEP-dependent PEMDs for randomly oriented molecules using the SAE model.

Dynamical diffraction of high-energy electrons by light-atom structures: a multiple forward scattering interpretation.

Because of the strong electron-atom interaction, the kinematic theory of diffraction cannot be used to describe the scattering of electrons by an assembly of atoms due to the strong dynamical diffraction that needs to be taken into account. In this paper, the scattering of high-energy electrons by a regular array of light atoms is solved exactly by applying the T-matrix formalism to the corresponding Schrödinger's equation in spherical coordinates. The independent atom model is used, where each atom is represented by a sphere with an effective constant potential. The validity of the forward scattering approximation and the phase grating approximation, assumed by the popular multislice method, is discussed, and an alternative interpretation of multiple scattering is proposed and compared with existing interpretations.

Aspherical atom refinements on X-ray data of diverse structures including disordered and covalent organic framework systems: a time-accuracy trade-off.

Aspherical atom refinement is the key to achieving accurate structure models, displacement parameters, hydrogen-bond lengths and analysis of weak interactions, amongst other examples. There are various quantum crystallographic methods to perform aspherical atom refinement, including Hirshfeld atom refinement (HAR) and transferable aspherical atom model (TAAM) refinement. Both HAR and TAAM have their limitations and advantages, the former being more accurate and the latter being faster. With the advent of non-spherical atoms in Olex2 (NoSpherA2), it is now possible to overcome some limitations, like treating disorder, twinning and network structures, in aspherical refinements using HAR, TAAM or both together. TAAM refinement in NoSpherA2 showed significant improvement in refinement statistics compared with independent atom model (IAM) refinements on a diverse set of X-ray diffraction data. The sensitivity of TAAM towards poor data quality and disorder was observed in terms of higher refinement statistics for such structures. A comparison of IAM with TAAM and HAR in NoSpherA2 indicated that the time taken by TAAM refinements was of the same order of magnitude as that taken by IAM, while in HAR the time taken using a minimal basis set was 50 times higher than for IAM and rapidly increased with increasing size of the basis sets used. The displacement parameters for hydrogen and non-hydrogen atoms were very similar in both HAR and TAAM refinements. The hydrogen-bond lengths were slightly closer to neutron reference values in the case of HAR with higher basis sets than in TAAM. To benefit from the advantages of each method, a new hybrid refinement approach has been introduced, allowing a combination of IAM, HAR and TAAM in one structure refinement. Refinement of coordination complexes involving metal-organic compounds and network structures such as covalent organic frameworks and metal-organic frameworks is now possible in a hybrid mode such as IAM-TAAM or HAR-TAAM, where the metal atoms are treated via either the IAM or HAR method and the organic part via TAAM, thus reducing the computational costs without compromising the accuracy. Formal charges on the metal and ligand can also be introduced in hybrid-mode refinement.

Accurate Crystal Structures of C12H9CN, C12H8(CN)2, and C16H11CN Valence Isomers Using Nonspherical Atomic Scattering Factors.

Fourteen crystal structures, mostly from good-quality datasets but including some marginal and twinned exemplars, from a series of novel polycyclic benzo- and naphtho-fused organic nitriles are presented and accurately described, including some related structures of a bromo-substituted and partially hydrogenated analogues. These structures represent a considerable increase in the number of published structures within their archetypes. This work highlights the significant advancement in structural refinement software proffered by NoSpherA2, which enables Hirshfeld Atom Refinement (HAR) of the structures within Olex2 v1.5. This results in the determination of C-H bond lengths with near to neutron diffraction accuracies at far lower experimental cost, and with an average improvement in C-C bond precision of 42% compared to Independent Atom Model refinements. H-atoms (apart from disordered components) refined well with anisotropic displacement parameters. Nonclassical H-bonding (C-H···N≡C) in this series is analyzed, and dipolar nitrile-nitrile interactions (C≡N···C≡N) in three major motifs described by (Wood, P. A. Acta Cryst. B, 2008, 64, 393-396) are found in 9 out of 13 nitrile-containing compounds of this series, a much higher proportion than the global average of 21% of nitrile-containing compounds. The HAR/NoSpherA2 approach shows increasing benefits with better data quality without apparent discontinuities.

New refinement strategies for a pseudoatom databank – toward rapid electrostatic interaction energy estimations

Pseudoatom databanks, collections of parameters from the multipole model of electron densities for various atom types, are used to replace the Independent Atom Model with the more accurate Transferable Aspherical Atom Model (TAAM) in crystal structure refinements. The databanks are also employed to reconstruct the electron density of a molecule, crystal or biomacromolecular complex in a fast yet accurate way and compute various properties such as the energy of electrostatic interactions, for example. A even faster but similarly accurate model for estimations of electrostatic energy exists called aug-PROmol [Bojarowski, Kumar & Dominiak (2016). ChemPhysChem, 17, 2455–2460]. A model analogous to aug-PROmol cannot be built from the current pseudoatom databanks, as they perform badly when truncated to the monopole level. Here, new strategies for multipole model refinements were sought, leading to better parametrization at the monopole level. This would allow the creation of a pseudoatom databank in a single route of model parametrization, which would be suitable for both crystal structure refinement and rapid electrostatic energy calculations. Here it is shown that the cumulative approach to multipole model refinements, as opposed to simultaneous or iterative refinements of all multipole model parameters (Pv , κ, Plm , κ′), leads to substantially different models of electron density. Cumulative refinement of two blocks of parameters, the first with Pv and κ and then the second with Plm and κ′, leads to the P v κ|P lm κ′ model having promising properties. The P v κ|P lm κ′ model is as good as the University at Buffalo DataBank (UBDB) in X-ray structure TAAM refinements and electrostatic energy estimations, especially for less polar molecules. When truncated to the monopole level, the P v κ model has a chance to replace aug-PROmol in fast yet accurate electrostatics energy calculations, although some improvements in κ parametrization for polar functional groups are still needed. The P v κ model is also a source of point charges which behave similarly to restrained electrostatic potential (RESP) charges in electrostatic interaction energy estimations.