Independent Atom Model Research Articles

Rescattering photoelectron spectroscopy of the CO2 molecule: Progress towards experimental discrimination between theoretical target-structure models

Author(s): Okunishi, M; Ito, Y; Sharma, V; Aktar, S; Ueda, K; Lucchese, RR; Dnestryan, AI; Tolstikhin, OI; Inoue, S; Matsui, H; Morishita, T | Abstract: Photoelectron momentum distributions (PEMDs) generated in strong-field ionization of randomly oriented CO2 molecules by intense infrared laser pulses at 1300-, 1450-, and 1650-nm wavelengths are measured experimentally and analyzed theoretically. The experimental PEMDs extracted along the outermost backward rescattering caustic are well reproduced by theoretical calculations based on the recently derived factorization formula with an analytical returning photoelectron wave packet (RWP). The sensitivity of the theoretical results to the target structure models used in the calculations is investigated. It is shown that RWPs obtained in the single-active-electron (SAE) approximation and by the Hartree-Fock method have only minor differences. On the other hand, differential cross sections (DCSs) for elastic scattering of a photoelectron on the parent molecular ion calculated by ab initio, SAE, and independent-atom model methods are considerably different. This difference almost disappears after averaging over molecular orientations, so the present experiment does not enable us to discriminate between the different target structure models. However, we show that such a discrimination should become possible by measuring PEMD with aligned molecules. This will provide an access to the rich target structure information contained in the DCS.

Theoretical study on positron scattering by benzene over a broad energy range

In this paper two theoretical methodologies, the Schwinger multichannel (SMC) method and the independent atom model with the screening corrected additivity rule (IAM-SCAR), were employed to study positron scattering by benzene over a broad impact energy range. The SMC calculations were carried out in the static plus polarization approximation, accounting for the elastic channel, for impact energies up to 20 eV. The IAM-SCAR method covered energies up to 1000 eV to provide total, elastic, ionization, excitation, and positronium formation cross sections. In the low-energy region we discuss how the description of the polarization effects affects the cross sections. In particular, our calculations support the existence of a bound state in the positron scattering by benzene, in agreement with previous predictions by Young and Surko [Phys. Rev. A 77, 052704 (2008)].

Proton-impact-induced electron emission from biologically relevant molecules studied with a screened independent atom model

We use the recently introduced independent-atom-model pixel counting method to calculate proton-impact net ionization cross sections for a large class of biologically relevant systems including pyrimidines, purines, amino acids, and nucleotides from 10 keV to 10 MeV impact energy. Overall good agreement with experimental data, where available, is found. A scaling prescription that involves coefficients derived from the independent atom model is shown to represent the cross section results better than scalings based on the number of (bonding) valence electrons of the target molecules. It is shown that the scaled net ionization cross sections of the proton-nucleotide collision systems can be represented in terms of a simple analytical formula with four parameters to within 3% accuracy.

Excitation, ionization, neutralization and anionic production in collisions of C+, N+ and CnN+ (n = 1–3) with He atoms at 2.2 a.u. velocity; cross sections and dissociation branching ratios

We present measurements of absolute cross sections for projectile ionization and electron capture for C+, N+ and CnN+ (n = 1–3) projectiles impinging on He atoms with velocity v = 2.2 a.u. Single and multiple electron processes are considered, as well as projectile dissociative excitation in the case of incident molecular cations. The measurements are compared to Classical Trajectory Monte Carlo (CTMC) calculations for C+, N+ + He collisions in the framework of the independent electron approximation. CnN+ + He systems are described by means of the independent atom and electron (IAE) model which represents the molecule as a set of independent atoms. The impact parameter probabilities for excitation, ionization and electron transfer in C, C+, N–He collisions, underlying the IAE calculations, are also obtained by means of CTMC computations. A good agreement is generally found between measured and calculated cross sections, except for anionic production of C− and CnN−. The internal energy deposit due to electron excitation in CnN+ is also calculated with the IAE/CTMC model and compared to semi-empirical estimates based on either measured dissociation branching ratios for C2N+ and C3N+ (IdBarkach et al 2018 Mol. Astrophys. 12 25) or measured fragments kinetic energy release for CN+. Finally, measured dissociation branching ratios of excited CnN− and CnNQ+ species, with 1 ≤ n ≤3 and 0 ≤ Q ≤ 4, are reported.

Experimental and theoretical analysis for total electron scattering cross sections of benzene.

Measurements of the total electron scattering cross sections (TCSs) from benzene, in the impact energy range of 1-1000 eV, are presented here by combining two different experimental systems. The first utilizes a magnetically confined electron transmission beam for the lower energies (1-300 eV), while the second utilizes a linear transmission beam apparatus for the higher energies (100-1000 eV). These cross sections have also been calculated by means of two different theoretical methods, the Schwinger Multichannel with Pseudo Potential (SMCPP) procedure, employing two different approaches to account for the polarization of the target for impact energies between 0.1 and 15 eV, and the Independent Atom Model with the Screening Corrected Additivity Rule including Interference effect (IAM-SCAR+I) paradigm to cover the 10-10 000 eV impact energy range. The present results are compared with available theoretical and experimental data, with the level of accord being good in some cases and less satisfactory in others, and some predicted resonances have been identified. In particular, we found a π* shape resonance at 1.4 eV and another feature in the energy region 4.6-4.9 eV interpreted as a π* resonance (2B2g symmetry), which is a mixture of shape and a core excited resonance, as well as a Feshbach resonance at 5.87 eV associated with the 3s (a1g) Rydberg state. A Born-type formula to extrapolate TCS values for energies above 10 000 eV is also given. This study provides a complete set of TCS data, with uncertainty limits within 10%, ready to be used for modeling electron transport applications.

Theoretical and experimental cross sections for electron scattering from halothane

We report a joint theoretical and experimental study on elastic scattering of electrons from halothane (CF3CHBrCl). The theoretical differential, integral and momentum transfer cross sections were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP), and with the independent atom model with screening corrected additivity rule including interference effects (IAM-SCAR+I). The differential cross sections measurements were conducted for incident electron energies of 10, 20, 30 and 50 eV, while the scattered electron angular range varied from 7° to 100°. At these energies the present experimental differential cross sections are in reasonable agreement with both SMCPP and IAM-SCAR+I calculations. As expected, the two theoretical methodologies agree well with each other as the electron impact energy increases. We also discuss the presence of low-energy resonances and a bound anion state identified in our SMCPP calculations.

Electron scattering from 1-butanol at intermediate impact energies: Total cross sections.

We report experimental measurements of the absolute total cross sections (TCSs) for electron scattering from 1-butanol at impact energies in the range 80-400 eV. Those measurements were conducted by considering the attenuation of a collimated electron beam, at a given energy, through a gas cell containing 1-butanol, at a given pressure, and through application of the Beer-Lambert law to derive the required TCS. We also report theoretical results using the Independent-Atom Model with Screening Corrected Additivity Rule and Interference approach. Those results include the TCS, the elastic integral cross section (ICS), the ionization total ICS, and the sum over all excitation process ICSs with agreement at the TCS level between our measured and calculated results being encouraging.

Calculation of electron scattering cross sections for Anthracene, Pyridine and Warfarin molecules over energy range 10–30000 eV

This paper reports electron impact total cross section, total elastic, total inelastic and differential cross sections for molecules Anthracene, Pyridine and Warfarin having been computed using the independent atom model with screening-corrected additivity rule over an incident energy range of 10–30000 eV. The calculations are performed with relativistic (Dirac) partial-wave for scattering by applying a local central interaction potential V(r). A model spherical complex optical potential is used for calculations. Good agreement is achieved in intermediate and high-energy zones.

Ab Initio Fragment Method for Calculating Molecular X-ray Diffraction.

A fragment-based approach for the prediction of elastic X-ray scattering is presented. The total diffraction pattern is assembled from anisotropic form factors calculated for individual molecular fragments, optionally including corrections for pairwise interactions between fragments. The approach is evaluated against full ab initio scattering calculations in the peptide diphenylalanine, and the optimal selection of fragments is examined in the ethanol molecule. The approach is found to improve significantly on the independent atom model while remaining conceptually simple and computationally efficient. It is expected to be particularly useful for macromolecules with repeated subunits, such as peptides, proteins, DNA, or RNA and other polymers, where it is straightforward to define appropriate fragments.

Extension of the transferable aspherical pseudoatom data bank for the comparison of molecular electrostatic potentials in structure-activity studies.

The transferable aspherical pseudoatom data bank, UBDB2018, is extended with over 130 new atom types present in small and biological molecules of great importance in biology and chemistry. UBDB2018 can be applied either as a source of aspherical atomic scattering factors in a standard X-ray experiment (dmin ≃ 0.8 Å) instead of the independent atom model (IAM), and can therefore enhance the final crystal structure geometry and refinement parameters; or as a tool to reconstruct the molecular charge-density distribution and derive the electrostatic properties of chemical systems for which 3D structural data are available. The extended data bank has been extensively tested, with the focus being on the accuracy of the molecular electrostatic potential computed for important drug-like molecules, namely the HIV-1 protease inhibitors. The UBDB allows the reconstruction of the reference B3LYP/6-31G** potentials, with a root-mean-squared error of 0.015 e bohr-1 computed for entire potential grids which span values from ca 200 e bohr-1 to ca -0.1 e bohr-1 and encompass both the inside and outside regions of a molecule. UBDB2018 is shown to be applicable to enhancing the physical meaning of the molecular electrostatic potential descriptors used to construct predictive quantitative structure-activity relationship/quantitative structure-property relationship (QSAR/QSPR) models for drug discovery studies. In addition, it is suggested that electron structure factors computed from UBDB2018 may significantly improve the interpretation of electrostatic potential maps measured experimentally by means of electron diffraction or single-particle cryo-EM methods.

Ab Initio Computation of Rotationally-Averaged Pump-Probe X-ray and Electron Diffraction Signals.

We develop a new algorithm for the computation of the rotationally averaged elastic molecular diffraction signal for the cases of perpendicular or parallel pump-probe geometries. The algorithm first collocates the charge density from an arbitrary ab initio wave function onto a Becke quadrature grid [A. Becke, J. Chem. Phys. 1988 , 88 , 2457 ], providing a high-fidelity multiresolution representation of the charge density. A double sum is then performed over the Becke grid points, and the interaction between points computed using the scattering kernels of Williamson and Zewail [J. C. Williamson and A. H. Zewail, J. Phys. Chem. 1994 , 98 , 2766 ]. These kernels analytically average over the molecular orientations with the cos2 γ selection factor appropriate for one-photon dipole absorption in a perpendicular pump-probe geometry. We show that the method is converged with small grids containing <500 points/atom. We implement the algorithm on a GPU for increased efficiency and emonstrate the algorithm for molecules with up to a few dozen atoms. We explore the accuracy of the independent atom model (IAM) by comparison with our new and more accurate method. We also investigate the possibility of detecting signatures of electronic transitions in polyatomic pump-probe diffraction experiments.

Structure and electrostatic properties of the pyrimethamine-3,5-dihydroxybenzoic acid cocrystal in water solvent studied using transferred electron-density parameters.

Pyrimethamine is an antimalarial drug. The cocrystal salt form of pyrimethamine with 3,5-dihydroxybenzoic acid in water solvent has been synthesized, namely 2,4-diamino-5-(4-chlorophenyl)-6-ethylpyrimidin-1-ium 3,5-dihydroxybenzoate hemihydrate, C12H14ClN4+·C7H5O4-·0.5H2O. X-ray diffraction data were collected at room temperature. Refinement of the crystal structure was carried out using the classical Independent Atom Model (IAM), while the electrostatic properties were studied by transferring electron-density parameters from an electron-density database. The Cl atom was refined anharmonically. The results of both refinement methods were compared. Topological analyses were carried out using Bader's theory of Atoms in Molecules (AIM). The three-dimensional Hirshfeld surface analysis and the two-dimensional fingerprint maps of individual molecules revealed that the crystal structures are dominated by H...O/O...H and H...H contacts. Other close contacts are also present, including weak C...H/H...C contacts. Charge transfer between the pyrimethamine and 3,5-dihydroxybenzoic acid molecules results in a molecular assembly based on strong intermolecular hydrogen bonds. This is further validated by the calculation of the electrostatic potential based on transferred electron-density parameters. The current work proves the significance of the transferability principle in studying the electron-density-derived properties of molecules in cases where high-resolution diffraction data at low temperature are not available.

Aspherical scattering factors for SHELXL - model, implementation and application.

A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.

Stopping power of cluster ions in a free-electron gas from partial-wave analysis

A nonlinear model for the stopping power of cluster ions based on partial-wave analysis is developed through the generalization of the induced density approach (IDA) model for the interaction of homo- and heteronuclear molecular ions with a free-electron gas (IDAMol). We apply IDAMol to the energy loss of ${{\mathrm{H}}_{2}}^{+}$ dimers in ${\mathrm{SiO}}_{2}$ and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, where we find that the results are consistent with established linear (dielectric) models at higher speeds, as expected for small perturbations (small values of the projectile charge or high velocities). Specifically at low projectile energies, however, it is important that IDAMol goes beyond perturbation theory. This feature appears to be central for a good description of negative and positive vicinage effects, a measure of the deviation from the independent-atom model. The focus of this work, however, is the investigation of enhanced nonlinear effects. Here we present experimental results for a heteronuclear cluster ion namely ${\mathrm{HeH}}^{+}$ on ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, in the energy range of few tens of keV/u using the medium energy ion scattering technique. The IDAMol results are corroborated by the experimental data and time-dependent density-functional calculations for this case. Strong nonlinearities are observed for the energy loss of the fragment ${\mathrm{H}}^{+}$ due to the higher charge of its He companion.

Total cross section measurements for electron scattering from dichloromethane.

Using our magnetically confined electron transmission apparatus, we report the results of total cross sections (TCSs) for electron scattering from dichloromethane (CH2Cl2). The energy range of this study is 1-300 eV. Wherever possible, the present data are compared to earlier measured TCSs of Wan et al. [J. Chem. Phys. 94, 1865 (1991)] and Karwasz et al. [Phys. Rev. A 59, 1341 (1999)] and to the corresponding theoretical independent atom model with screening corrected additivity rule and interference term (IAM-SCAR+I) results of Krupa et al. [Phys. Rev. A 97, 042702 (2018)] and a spherical complex optical potential formulation calculation of Naghma et al. [J. Electron Spectrosc. Relat. Phenom. 193, 48 (2014)]. Within their respective uncertainties, the present TCS and those of Karwasz et al. are found to be in very good agreement over their common energy range. However, agreement with the results of Wan et al. is quite poor. The importance of the experimentally inherent 'missing angle' effect (see later) on the measured TCS is investigated and found to be significant at the lower energies studied. Indeed, when this effect is accounted for, agreement between our measured TCSs and the corrected IAM-SCAR+I+rotations calculation results are, for energies above about 3 eV, in good accord (to better than 8%). Finally, we observe two σ * shape resonances, consistent with the earlier electron transmission spectroscopy results of Burrow et al. [J. Chem. Phys. 77, 2699 (1982)], at about 2.8 eV and 4.4 eV incident electron energy, in our measured TCS.

Low to intermediate energy elastic electron scattering from dichloromethane (CH2Cl2)

We report a theoretical-experimental investigation of electron scattering by dichloromethane (CH2Cl2) in the low- and intermediate energy ranges. Experimental elastic differential cross sections (DCS), in the incident electron energy range of 0.5–800 eV and scattering angle range of 10°–130°, were measured using a crossed beam relative flow technique. Integral and momentum-transfer cross sections were determined from the experimental DCS. Theoretical elastic differential, integral, and momentum-transfer, as well as grand-total, and total absorption cross sections were also calculated for impact energies ranging from 0.5 to 500 eV. A complex optical Hartree–Fock potential represented the electron-target interaction and a single-center expansion method combined with a Padé approximation was used to solve the scattering equations. Three resonances: a 2A1 C–Cl kσ* resonance centered at about 3.5 eV, a 2B2 C–Cl kσ* resonance centered at about 5 eV and a broad 2A1 C–H kσ* resonance at about 10 eV were detected in our calculation. Further calculations of DCS were performed at an intermediate energy range of 50–800 eV, using the independent-atom model in which the atomic complex optical potential and partial-wave method were used to obtain atomic scattering amplitudes. Comparisons of our experimental and theoretical data with very recent experimental and theoretical results are made.

Structure refinement from ‘digital’ large angle convergent beam electron diffraction patterns

We use semi-automated data acquisition and processing to produce digital large angle CBED (D-LACBED) patterns. We demonstrate refinements of atomic coordinates and isotropic Debye–Waller factors for well-known materials using simulations produced with a neutral, spherical independent atom model. We find that atomic coordinate refinements in Al2O3 have sub-pm precision and accuracy. Isotropic DWFs are accurate for Cu, a simple fcc metal, but do not agree with X-ray measurements of GaAs or Al2O3. This lack of agreement is probably caused by bonding and change transfer between atoms. While it has long been appreciated that CBED is sensitive to bonding, examination of D-LACBED data shows that some regions exhibit large changes in diffracted intensity from small changes in the periodic crystal potential. Models of bonding will be essential to fully interpret D-LACBED data.

On avoiding negative electron density in Gram-Charlier refinements of anharmonic motion: the example of glutathione

Abstract The structure of glutathione, γ-l-Glutamyl-l-cysteinyl-glycine (C10H17N3O6S), was studied by multi-temperature single-crystal X-ray diffraction. Residual density maps from conventional independent atom model refinement gave indication of anharmonic motion in the molecule. This was further investigated by invariom refinement with anisotropic displacement parameters for all atoms, which described asphericity due to chemical bonding and lone pairs; afterwards only the residual-density signal of anharmonic motion remained. Treating anharmonicity with third-order Gram-Charlier displacement parameters led to regions with unphysical negative electron density. In contrast, a maximum entropy method (MEM) determination of the electron density successfully takes the features into account. Respective difference electron density plots (MEM minus prior and [Invariom+GC] minus invariom) agree well with each other. Challenges in treating and understanding the phenomenon are discussed. A procedure is proposed how unphysical negative electron density can be avoided. It is closely related to the free lunch algorithm.

Tightly binding valence electron in aluminum observed through X-ray charge density study

Accurate and high reciprocal resolution experimental structure factors of aluminum were determined from a synchrotron powder X-ray diffraction data measured at 30 K with sin θ/λ < 2.31 Å−1. The structure factors have small deviations from independent atom model in sin θ/λ < 0.83 Å−1. Theoretical structure factors were prepared using density functional theoretical calculations by full potential linearized augmented plane wave method. The deviation between experimental and theoretical data was also observed at around sin θ/λ ≈ 0.4 Å−1. The charge density was determined by an extended Hansen-Coppens multipole modeling using experimental and theoretical structure factors. Charge density maxima at tetrahedral site were observed in both experimental and theoretical deformation density. The charge-density difference peaks indicating directional bonding formation were observed in the difference density between experiment and theory. The present study reveals tight binding like character of valence electron of aluminum. The fact will provide a crucial information for development of high-performance aluminum alloy.

Total electron scattering cross section from sevoflurane by 1–300 eV energy electron impact

We report on novel total electron scattering cross section (TCS) measurements for electrons scattering from sevoflurane, at incident electron impact energies in the range 1–300 eV. The experimental results, obtained from a newly implemented magnetic beam apparatus based in Madrid, are compared with theoretical results from the independent atom model with screening corrected additivity rule including interference effects and rotational excitation (IAM-SCAR+I+R). A very good level of agreement has been found between the present experimental and theoretical data at above about 20 eV electron impact and to within the experimental uncertainties.