A Density Functional Theory Study of New Boron Nanotubes

Using first-principles calculations, a series of new boron nanotubes (BNTs), which show various electronic properties, were theoretically predicted. Stable nanotubes with various chiral vectors and diameters can be formed by rolling up the boron sheet with relative stability [H. Tang and S. I. Beigi, Phys. Rev. B 82, 115412 (2010).]. By increasing the diameter for BNT, the stability is enhanced. The calculated density of states and band structures demonstrate that all the predicted BNTs are metallic, regardless of their diameter and chirality. The multicentre chemical bonds of the relatively stable boron sheet and BNTs are analysed using the deformation electron density. Within our study, the BNTs all have metallic conductive characteristics, in addition to having a low effective quality and high carrier concentration, which are very good nanoconductive material properties and could be combined to form high-power electrodes for lithium-ion batteries such as those used in many modern electronics.

Charge density study of hydrogen [(2,4-diaminopyrimidin-1-io)methyl]phosphonate monohydrate

The crystal structure and charge density of hydrogen (2,4-diaminopyrimidin-1-io)methyl]phosphonate monohydrate, C5H9N4O3P·H2O, have been determined by means of single-crystal X-ray diffraction. Diffraction data were collected at 105 K with Mo Kα radiation to a resolution of sin θ/λ = 1.08 Å−1. A four-circle diffractometer equipped with a CCD area detector was used to collect 50 161 reflections over 3 d. 6082 unique reflections with I > 3σ(I) were used in the multipole model to map the deformation electron density and gave the final statistical factors R(F) = 0.0329, wR(F) = 0.0235 and g.o.f. = 1.37. Structure determination revealed that two O atoms in the crystal structure of the title compound act as hydrogen-bond acceptors for more than one hydrogen bond. Examination of deformation electron density maps showed preferential polarization of the lone-pair electron density of the two O atoms into the shortest hydrogen bonds.

Electron density in the sodium vanadium oxide bronze β-Na x V2O5 at 9 K

The crystal structure and electron density in sodium vanadium oxide bronze, β-Na x V2O5 [x = 0.282 (3)], have been studied by accurate Mo Kα X-ray diffraction measurements at 9.6 (3) K. No noticeable difference in the crystal structures at room temperature and 9.6 K has been observed. No superstructure reflections, previously found by Kanai, Kagoshima & Nagasawa [(1982), J. Phys. Soc. Jpn, 51, 697–698], have been detected at low temperature. Analysis of the deformation electron density has revealed the presence of the quasi-two-dimensional sheets of the —V—O—V—O— bonds in the structure. The electron density in the different chemical bonds within each of the three crystallographically independent VO6 polyhedra noticeably varies, although there is no clear evidence that the three crystallographically independent V atoms have different valence states.

Experimental electron density of urea–phosphoric acid (1/1) at 100 K

The deformation electron density of the urea–phosphoric acid adduct has been studied from 100 K X-ray and neutron diffraction experiments. Data were interpreted according to the Hirshfeld model. The long hydrogen bonds show characteristics of electrostatic interaction. Deformation density maps on the short hydrogen bond shows hydrogen more strongly bonded to urea than to phosphoric acid, and peak maxima at almost midway between the two O—H bonds.

X-ray study of deformation density and spontaneous polarization in ferroelectric NaNO2

The deformation electron density of ferroelectric sodium nitrite has been determined from X-ray diffraction data at 30 K, using Hirshfeld deformation functions. Owing to the strong correlation between odd terms of the deformation coefficients, constraints were imposed in the refinement. The net charges for Na, N and O atoms were estimated to be 0.27, 0.20 and −0.24 e, respectively. The calculated spontaneous polarization using these net charges and atomic dipole terms, 7.8 µC cm−2, is much closer to the recently measured value, 12 µC cm−2, as compared with the value calculated from the formal point charges (74 µC cm−2).

Synchrotron X-ray analysis of the electron density in HoFe2

Structure factors for a small holmium diiron HoFe2 Laves crystal were measured with focused λ = 0.75 Å synchrotron X-radiation using a fast avalanche photodiode (APD) counter. The deformation electron density (Δρ) maps are remarkable for significant excess electron density midway between the Ho atoms, which is not dissimilar to the peaks attributed to classic `covalent bonding' in C and Si crystals. These residual electrons accumulate at the centres of the kagomé net hexagons and form, with the Fe atoms, a triangular lattice which is characterized by more stable magnetic order than the kagomé net. Similar peaks occur along the Ho–Fe and Fe–Fe contacts. These results confirm the hypothesis that 5d electrons of the rare-earth atoms are important in the spin-coupling mechanism for HoFe2-type compounds. The 5d electrons are far less localized than the 4f electrons, and considerable 5d–5d and 5d–3d orbital overlap occurs between neighbouring atoms. Aspherical electron density near the Ho nuclei can be associated with the Ho 4f subshell electrons. Strong depletions of the Δρ near the atoms along the Ho–Ho, Ho–Fe and Fe–Fe vectors are indications of exchange repulsion. The effect of anharmonicity on the Δρ is insignificant.

Transferability of Multipole Charge-Density Parameters: Application to Very High Resolution Oligopeptide and Protein Structures

Crystallography at sub-atomic resolution permits the observation and measurement of the non-spherical character of the electron density (parameterized as multipoles) and of the atomic charges. This fine description of the electron density can be extended to structures of lower resolution by applying the notion of transferability of the charge and multipole parameters. A database of such parameters has been built from charge-density analysis of several peptide crystals. The aim of this study is to assess for which X-ray structures the application of transferability is physically meaningful. The charge-density multipole parameters have been transferred and the X-ray structure of a 3_{10} helix octapeptide Ac-Aib_2-L-Lys(Bz)-Aib_2-L-Lys(Bz)-Aib_2-NHMe refined subsequently, for which diffraction data have been collected to a resolution of 0.82 Å at a cryogenic temperature of 100 K. The multipoles transfer resulted in a significant improvement of the crystallographic residual factors wR and wR free. The accumulation of electrons in the covalent bonds and oxygen lone pairs is clearly visible in the deformation electron-density maps at its expected value. The refinement of the charges for nine different atom types led to an additional improvement of the R factor and the refined charges are in good agreement with those of the AMBER molecular modelling dictionary. The use of scattering factors calculated from average results of charge-density work gives a negligible shift of the atomic coordinates in the octapeptide but induces a significant change in the temperature factors (\Delta B ≃ 0.4 Å2). Under the spherical atom approximation, the temperature factors are biased as they partly model the deformation electron density. The transfer of the multipoles thus improves the physical meaning of the thermal-displacement parameters. The contribution to the diffraction of the different components of the electron density has also been analyzed. This analysis indicates that the electron-density peaks are well defined in the dynamic deformation maps when the thermal motion of the atoms is moderate (B typically lower than 4 Å^2). In this case, a non-truncated Fourier synthesis of the deformation density requires that the diffraction data are available to a resolution better than 0.9 Å.