Some aspects of the crystal structure of illite are not understood properly yet, in spite of its abundance and significance as a component of soils, sediments, and low-grade metamorphic rocks. The present study aimed to explore the role of hydronium cations in the interlayer space of illite in a theoreticalexperimental approach in order to clarify previous controversial reports. The infrared spectroscopy of this mineral has been studied experimentally and by means of atomistic calculations at the quantum mechanical level. The tetrahedral charge is critical for the stability of the hydronium cations, the presence of which has probably been underestimated in previous studies. In the present study, computational studies have shown that the hydronium cations in aqueous solutions are likely to be intercalated in the interlayer space of illite, exchanging for K cations. During the drying process these cations are stabilized by hydrogen bonds in the interlayer space of illite.

A detailed structural characterization of organo-clays is a key in understanding their properties. In this work, mono-, di-, tri-, and tetra-butylammonium (nBA; n = 1–4) cations intercalated in the layered clay mineral montmorillonite (Mnt) have been studied for the first time by combining a theoretical approach based on density functional theory (DFT) and infrared spectroscopy. The DFT calculations revealed the detailed structure and position of nBA cations in the interlayer space. A relation between the basal spacing (d001 parameter) and the cation size and structure was found, and explained with respect to the structure, composition, and size of the organic cations. Hydrogen bonds between -NHx/-CH3/-CH2 groups of the nBA cations and oxygen atoms of the basal planes of the Mnt layers were found to be an important factor for the arrangement and energetic stabilization of cations in the interlayer space. The N-H-O hydrogen bonds are stronger than C-H-O hydrogen bonds and the stabilization decreases with decreased number of bands. Analysis of DFT-calculated vibrational modes helped in understanding a problematic region of the experimental infrared spectra (4000–3000 cm-1), in which assignment of all vibrational modes unambiguously was not possible because of a significant overlap of broad bands.

The aims of this study were to obtain accurate structural information on the dimethyl sulfoxide (DMSO) and dimethylselenoxide (DMSeO) kaolinite intercalates, paying close attention to the hydrogen-bond geometries, and to provide a detailed interpretation of the individual vibrational modes of intercalates under study and relate their energies to the formation of the hydrogen bonds. Accurate positions of all the atoms in the structures of kaolinite:dimethylsulfoxide (K:DMSO) and kaolinite:dimethylselenoxide (K:DMSeO) intercalates have been obtained by the total energy minimization in solid state at density functional theory (DFT) level of the theory. The bond distances and angles in the kaolinite 1:1 layer are in good agreement with those reported in the most recent single-crystal refinement of kaolinite. Computed geometries of DMSO and DMSeO agree well with the high-quality diffraction data and independent theoretical ab initio calculations. The organic molecules are fixed in the interlayer space mainly by three moderately strong O-H⋯O hydrogen bonds, of different strengths, with the O⋯O contact distances being within 2.739–2.932 Å (K:DMSO) and 2.681–2.849 Å (K:DMSeO). Substantially weaker C-H⋯O and O-H⋯S(Se) contacts play only a supporting role. The optimized atomic coordinates were used to calculate the individual vibrational modes between 0 and 4000 cm−1. The maximum red shifts of the OH-stretching modes caused by the formation of the O-H⋯O hydrogen bonds were 407 cm−1 (K-DMSO) and 537 cm−1 (K-DMeSO), respectively. The Al-O-H bending modes are spread over the large interval of 100–1200 cm−1, but the dominant contributions are concentrated between 800 and 1200 cm−1. Theoretically calculated energies of the OH- and CH-stretching modes show good agreement with the previously published figures obtained from the infrared and Raman spectra of these intercalates.

Vibrational spectra of two kaolinite-dimethylsulfoxide intercalates, obtained using inelastic neutron scattering (INS), were analyzed with a view to understanding the dynamics of the hydrogen atoms in the structure. The main focus was on the spectral region 0–1700 cm−1, which is difficult to analyze using optical spectroscopy. The experimental vibrational spectra of kaolinite:dimethylsulfoxide and kaolinite:d6-dimethylsulfoxide collected using two different spectrometers were interpreted by means of the solid-state DFT calculations. Calculated spectra were obtained by both normal-mode analysis and molecular dynamics going beyond the harmonic approximation. The Al-O-H bending modes were found to be spread over the large interval 100−1200 cm−1, with the dominant contributions located between 800 and 1200 cm−1. The shape of the individual hydrogen spectrum depends on whether or not the respective hydrogen atom is involved in an O-H⋯O hydrogen bond and on its strength. The modes corresponding to the in-plane movements of the inner-surface hydrogen atoms are well defined and always appear at the top of the intervals of energy transfer. In contrast, the modes generated by the out-of-plane movements of the hydrogen atoms are spread over large energy intervals extending down to the region of external (lattice) modes. The C-H modes are concentrated mainly in the three regions 1200–1450 cm−1, 800–1100 cm−1, and 0–400 cm−1. While the first two regions are typical of the various deformational modes of methyl groups, the low-energy region is populated by the modes corresponding to the movements of the whole dimethylsulfoxide molecule.

The capability of borospherene to detect radioactive pollutants (radon and radium) is investigated utilizing density functional theory and nonequilibrium Green's function regime. The quantum transport is evaluated by calculating the density of states, chemical potential, transmission and molecular energy spectra, highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap, electron densities, current–voltage curve, and differential and quantum conductance. LUMO-mediated transmission is observed in all the cases. The conduction considerably declines in B40 molecular junction doped with radioactive pollutants in comparison to pure B40 molecular junction. This decrease in conduction is due to reduced electron density and higher chemical potential in doped B40 junctions. Due to different values of current and differential conductance, we propose utilization of B40 in detecting the presence of radioactive pollutants in underground water. Also, all molecular junctions assay lifting of Coulomb blockade at equilibrium state; thus, these devices can be effectively utilized in single-electron transistor applications.

Effective and accurate high-degree spline interpolation is still a challenging task in today’s applications. Higher degree spline interpolation is not so commonly used, because it requires the knowledge of higher order derivatives at the nodes of a function on a given mesh.

In this article, our goal is to demonstrate the continuity of the piecewise polynomials and their derivatives at the connecting points, obtained with a method initially developed by Beaudoin (1998, 2003) and Beauchemin (2003). This new method, involving the discrete Fourier transform (DFT/FFT), leads to higher degree spline interpolation for equally spaced data on an interval $[0,T]$. To do this, we analyze the singularities that may occur when solving the system of equations that enables the construction of splines of any degree. We also note an important difference between the odd-degree splines and even-degree splines. These results prove that Beaudoin and Beauchemin’s method leads to spline interpolation of any degree and that this new method could eventually be used to improve the accuracy of spline interpolation in traditional problems.

3-[1-[4-(2-Methylpropyl)phenyl]ethyl]-6-(4-fluorophenyl)-1,2,4-triazolo[3,4-b]-1,3,4-thiadiazole (C21H21FN4S) has been synthesized as a member of a series of triazolothiadiazoles having NSAIDs moieties with cytotoxic activity. The crystal structure of this new compound has been solved and refined using conventional laboratory X-ray powder diffraction data and optimized using density functional techniques. The final structure solution was achieved by Rietveld refinement using soft restraints on all non-H atom bond lengths and angles. This compound crystallizes in $P\bar{1}\;$ space group, with the unit cell parameters a = 5.5880(4) Å, b = 9.3074(7) Å, c = 19.497(4) Å, α = 99.311(10)°, β = 91.925(9)°, γ = 98.199(6)°, and V = 988.8(2) Å3. To complement and verify the structure solution of the compound, the density functional theory (DFT) calculations were performed by using the local density approximation and the generalized gradient approximation for exchange-correlation energy. In order to see the effect of the van der Waals interactions on the electronic structure, the relevant structure was also optimized with B3LYP-D2, PBE-D2, and optB88-vdW functionals. The refined crystal structure was confirmed by the DFT calculations. The best agreement with the experimental structure was achieved by optB88-vdW functional.

Sn–Sb alloy is an ideal candidate for lead-free solder; however, its performance has been inferior to that of Sn–Pb alloy. Here, the authors used ab initio molecular dynamics simulation to investigate the interatomic interaction in Sn–Sb-based lead-free solders. By calculating the electron density distribution, bond population, and partial density of states, the authors found that the Sn–Sb bonds are a mixture of nonlocalized metal and localized covalent bonds. The covalent bond between Sn and Sb is easy to break at higher temperatures, so Sn–Sb (6.4 wt%) had better fluidity than other studied Sn–Sb alloys. Furthermore, adding Cu or Ag into Sn–Sb alloys can decrease the strength of covalent bonds and stabilize the metal bonds, which improves the metallicity and wettability of the Sn–Sb–Cu and Sn–Sb–Cu–Ag systems when the temperature increases. These results are all in good agreement with experimental findings and have significant value for the development of new solder alloys.

The stability of organoclays prepared from smectites and organic cations depends on the type of used cation, among other factors. This study provides a prediction of the structure, stability and dynamic properties of organoclays based on montmorillonite (Mt) intercalated with two types of organic cations – tetrabutylammonium (TBA) and tetrabutylphosphonium (TBP) – using first-principle density functional theory. The results obtained from simulations were also used in the interpretation of the experimental infrared spectrum of the TBP-Mt organoclay. Analysis of interatomic distances showed that weak C–O···H hydrogen bonds were important in the stabilization of both TBA- and TBP-Mt models, with slightly stronger hydrogen bonds for the TBP cation. Calculated intercalation and adsorption reaction energies (ΔEint//ΔEads*/ΔEads**) confirmed that TBP-Mt structures (–72.4//–32.8/–53.8 kJ/mol) were considerably more stable than TBA-Mt structures (–56.7//–22.6/–37.4 kJ/mol). The stronger interactions of the alkyl chains of the TBP cation with Mt basal surfaces in comparison to those of the TBA cation were also correlated with the positions of the calculated bands of the C–H stretching vibrations.

The low-charge dioctahedral 2:1 phyllosilicates are an important group of clay minerals that have a low degree of cation substitution and very weak interlayer interatomic interactions which are difficult to reproduce with quantum mechanical calculations. In order to study the crystallographic properties of these compounds with density functional theory (DFT) quantum-mechanical methods, an optimization of norm-conserving pseudopotentials of Al, Si, O, H and Na atoms has been carried out, and an optimization of the cutoff radii of the basis sets has been accomplished. Crystallographic properties and vibrational stretching frequencies of the OH groups, ν(OH), have been calculated, being consistent with previous computational and experimental results. All frequencies can be related to the different molecular environment of the OH groups. The effect of octahedral Fe3+ substitution on the ν(OH) frequency is reproduced. Several configurations of cation substitutions and interlayer cation (IC) positions are studied in low-charge dioctahedral 2:1 phyllosilicates, such as Al4(Si7–xAlx)O20(OH)4Nax, with x = 0.25, 0.50 and 0.75, indicating that the IVAl3+ is highly dispersed and the IC tends to be in the substituted ditrigonal hole. For the Al4(Si7Al)O20(OH)4Na composition, the trans-vacant form is more stable than the cis-vacant one.

We have studied the structures of Al/Si disordered leucite and bicchulite with a quantum mechanical version of the virtual crystal approximation, VCA. In leucite, the average tetrahedron has a composition of (AlSi2)O4, while bicchulite represents an extreme case with (Al2Si)O4 tetrahedra. Both structures are well described with the VCA. In conjunction with an earlier study, where we have shown that the (AlSi)O4 tetrahedra in gehlenite and Al,Si-disordered octahedra are also well reproduced, we have now established that the VCA gives a reliable description of the averaged structure of disordered aluminosilicates over the whole compositional range. The current calculations confirm that Al/Si ordering is not driving the cubic to tetragonal phase transformation in leucite. In bicchulite, the model calculations are consistent with hydrogen on Wyckoff position 8c, in agreement with the result of a single crystal X-ray diffraction study, but in variance with results based on a neutron powder diffraction study.

The [AlO4/M+]0 (where M = H, Li, Na and K) defects in α-quartz have been investigated by ab initio calculations at the density functional theory (DFT) level, using the CRYSTAL06 code, 72-atom supercells, and all-electron basis sets. Our DFT calculations yielded substantially improved results than previous cluster calculations with minimal basis sets. For example, the [AlO4/M+(a<)]0 defects with M = H, Li and Na have been shown to be more stable than their [AlO4/M+(a>)]0 structural analogues (where a> and a< denote the location of the charge-compensating ion on the long-bond and short-bond side respectively), correctly predicting the common occurrence of paramagnetic [AlO4/M+(a>)]+ centres. In addition, the [AlO4/K+]0 defects have been investigated for the first time and are shown to be stable in quartz. Moreover, our calculations confirm previous suggestions that incorporation of the [AlO4/M+]0 defects results in significant structural relaxations that extend at least to the nearest Si atoms and give Li—O and Na—O bond distances in better agreement with the experimentally obtained values. The present theoretical results on the [AlO4/M+]0 defects provide a more complete picture for the coupled Al3+—M+ substitutions and hence new insights into crystal-chemical controls on the uptake of Al in quartz.

The influence of hydrostatic compression on the charge transport properties of an excellent 2,6-diphenylanthracene (2,6-DPA) semiconducting single crystal was investigated up to 10 GPa by performing density-functional calculations together with the tight binding approximation. In this pressure region the lattice constants a, b and c decrease by up to 0.948 Å (5.23%), 1.30 Å (17.26%), and 0.711 Å (11.34%), respectively, while the monoclinic angle β increases by 3.4°. The unit-cell volume decreases by increasing pressure, and the volume decreases by 30.5% at 10 GPa. In comparison, the C–C and C–H intermolecular distances within and between the herringbone layers reduced by 16–19% and 16–24%, respectively, in the same pressure ranges. The results indicate that under high pressure, the molecular planes of the crystal become more and more parallel to each other due to molecular rearrangement in the 2,6-DPA crystal. The band gap decreases with increasing pressure due to decreasing intermolecular separation between neighboring molecules. Finally, the results indicate an improvement of the hole mobility of 2,6-DPA single crystals under hydrostatic pressure.

The structure of Cs2AlF5 obtained by thermal dehydration of Cs2AlF5•H2O is determined ab initio from powder diffraction data, space group Pmn21, a = 6.36216 (17) Å, b = 12.7523 (4) Å, c = 11.4102 (3) Å, and Z = 6. Contrarily to most A2MF5 compounds presenting MF5cis or trans-chains of corner-sharing MF6 octahedra, Cs2AlF5 is characterized by the rare occurrence of the face-sharing anion Al2F93− combined with an isolated AlF63− octahedron, the sum leading to Al3F156−. The structure of Cs3Al2F9 [space group P63/mmc, a = 6.2535 (2) Å, c = 14.7193 (6) Å, Z = 2] is confirmed to be isostructural with Cs3Fe2F9, built up from the same M2F93− dimers (M = Fe, Al). Both crystal structures are optimized by energy minimization density funtional theory (DFT) in the solid state using a hybrid PBE0 functional, and their relations with the hexagonal perovskites and elpasolites are discussed.

The recently discovered compound BeP2N4 that crystallizes in the phenakite-type structure has potential application as a high strength optoelectronic material. Therefore, it is important to analyze experimentally the electronic structure, which was done in the present work by monochromated electron energy-loss spectroscopy. The detection of Be is challenging due to its low atomic number and easy removal under electron bombardment. We were able to determine the bonding behavior and coordination of the individual atomic species including Be. This is evident from a good agreement between experimental electron energy-loss near-edge structures of the Be-K-, P-L2,3-, and N-K-edges and density functional theory calculations.

We present a theoretical framework for calculating probe-position-dependent electron energy-loss near-edge structure for the scanning transmission electron microscope by combining density functional theory with dynamical scattering theory. We show how simpler approaches to calculating near-edge structure fail to include the fundamental physics needed to understand the evolution of near-edge structure as a function of probe position and investigate the dependence of near-edge structure on probe size. It is within this framework that density functional theory should be presented, in order to ensure that variations of near-edge structure are truly due to local electronic structure and how much from the diffraction and focusing of the electron beam.