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For the first time, the dependences of the strain energy and the band gap of achiral nanotubes obtained by folding monolayers of gallium(II) sulfides and selenides on their diameter have been calculated nonempirically. The calculations were performed using the CRYSTAL17 software package using an atomic basis set within the hybrid density functional theory with a thirteen-percent Hartree–Fock exchange. To take into account the dispersion interactions between the layers in the crystal, the Grimme empirical correction is included in the calculations. As a result of simulation of nanotubes with different chirality and different diameters, the minimum diameters of single-walled nanotubes, at which the integrity of chemical bonds on their outer surface is preserved, are established. It is shown that the dependence of the strain energy on the diameter satisfies the classical law of inverse squares and is the same for nanotubes of the zigzag and armchair types.

We used hybrid density functional theory to investigate 50% cubic solid solutions based on Fe-doped LaGaO3 and LaAlO3. The supercell composed of 8 primitive cells was used. All the possible configu...

A force field is proposed that reproduces with a high accuracy a large number of properties of the bulk crystal MoS2 phases, monolayers, and nanotubes. The reproduced values are both the experimental results and the results of quantum chemical calculations. The elaborated interaction potential can be useful primarily for investigation of multiwall MoS2 nanotubes and their thermodynamic properties, especially, since the potential is able to reproduce the frequencies of the crystal phonon spectrum. In this study the proposed potential is applied to simulate the temperature dependence of a number of properties of the armchair and zigzag nanotubes. The calculations have been performed using molecular mechanics method within the framework of quasi harmonic approximation which is carried out through the estimation of the temperature dependence of the Helmholtz free energy.

Adsorption of water on (001)-terminated α-V2O5 surface has been investigated in the framework of density functional theory. According to our calculations, molecular adsorption is preferred, and two types of adsorption sites (Lewis acid center on V atom and Lewis base center on O atoms) have been found. Water adsorption on Lewis acid site does not change the electronic structure of V2O5 surface. Adsorption on Lewis base site is less favorable but reduces the band gap value by half (from 2.5 to 1.3 eV). The reason of this decreasing is the localization of the non-bonding 1b2 electron state of water molecule within the forbidden gap of V2O5 surface. The idealized structure of V2O5∙nH2O xerogel has been computationally studied at n = 0 and 1. It is proved that only Lewis base sites are suitable for water positions. At n = 1, the water absorption energy in xerogel is close to adsorption energy of water on the oxygen atoms of α-V2O5 surface. The presence of the non-bonding states of physically absorbed water in the forbidden gap is also found in the xerogel case. This results in decreasing of the band gap from 2.7 eV to 0.7 eV.

Hybrid density functional theory calculations are performed for the first time on the phonon dispersion and thermodynamic properties of WS2-based single-wall nanotubes. Symmetry analysis is presented for phonon modes in nanotubes using the standard (crystallographic) factorization for line groups. Symmetry and the number of infra-red and Raman active modes in achiral WS2 nanotubes are given for armchair and zigzag chiralities. It is demonstrated that a number of infrared and Raman active modes is independent on the nanotube diameter. The zone-folding approach is applied to find out an impact of curvature on electron and phonon band structure of nanotubes rolled up from the monolayer. Phonon frequencies obtained both for layers and nanotubes are used to compute the thermal contributions to their thermodynamic functions. The temperature dependences of energy, entropy, and heat capacity of nanotubes are estimated with respect to those of the monolayer. The role of phonons in the stability estimation of nanotubes is discussed based on Helmholtz free energy calculations. © 2017 Wiley Periodicals, Inc.

Using the laser ablation method, films comprised of alternating layers of AgI and (GeSe 2 ) 30 (Sb 2 Se 3 ) 30 (AgI) 40 glass were obtained. Individual layer thickness amounts to 10 ÷ 15 nm, and the total number of layers is about 100. X-ray diffraction (XRD) and film conductivity measurements were carried out during several cycles of heating up to 200 °C and cooling to room temperature. It was established that after three cycles of thermal processing specific lateral conductivity of the film is equal to 0.3 S cm − 1 and conductivity activation energy is equal to 0.07 eV at room temperature. Attempts to explain such a high conductivity value based on XRD results did not yield satisfactory results. However, our first-principle calculations within the density functional theory (DFT) showed that in the free layer composed of four AgI planes a rearrangement occurs, resulting in formation of the stable structure of two silver planes on the inside and two iodine planes on the outside (I–Ag–Ag–I). Rearrangement of similar stack of eight or twelve atomic planes results in formation of two or three I–Ag–Ag–I layers loosely bound to each other, accordingly. This suggests that increase in specific conductivity growth of multilayer film as a consequence of cyclic heating and cooling may be connected with AgI stratification on its boundary with chalcogenide glass and following stabilization of layered phases mentioned above. The existence of an empty space between the layers that is constrained by iodine ion planes should facilitate silver ion diffusion along the layers.

The properties of multi-walled MoS2 nanotubes have been investigated by the first principles calculations and by molecular mechanics (MM) simulations using a revised three-body force field. The density functional theory (DFT) calculations have been performed on single-, double- and triple-walled MoS2 nanotubes. The new version of the force field is able to reproduce the structure integrity of the MoS2 nanotubes at temperatures up to 700 K through the molecular dynamics simulations. Comparison of the results of first principles and MM simulations of the multi-walled nanotubes demonstrates satisfactory agreement. The results of DFT and MM simulations indicate that the difference between chirality indices of adjacent shells of a multi-walled nanotube is the main factor that determines a possibility of the nanotube to be synthesized. The structure of zigzag 12-walled nanotubes with chirality indices difference 12 and 13, simulated by MM method and using the proposed force field, is the most close to the structure of experimentally detected nanotubes.

Calculations of the cubic models of two solid solutions LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 have been performed within the hybrid density functional theory. Multiple configurations have been considered for the solid solutions resulting from a different distribution of Fe atoms over the p-metal (Ga or Al) positions accounting for different spin orientation for Fe atoms themselves. It was demonstrated that 27 structures for both LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 should be treated to account for all the possible configurations in case of cubic 2 × 2 × 2 supercell. Optimized geometry, energy, and electron properties were calculated for all the obtained configurations. Statistical weights and probabilities were estimated for each symmetry non-equivalent configuration of the solid solutions within the canonical ensemble. A new parameterization for the dilute Ising model has been proposed. In this model, we account for non-magnetic contributions, which are absent in the simple Ising model, using the lattice approach based on the concept of interchange energy. Two model parameters (the magnetic coupling constant and interchange energy) were fitted to the calculated total energies of all considered configurations of both solid solutions. The dilute Ising model confirmed the benefit of Fe-clustering in doped lanthanum gallate against aluminate. Different signs of the estimated interchange energy enable us to explain the reasons for such differences.

MoS

Adsorption of Rb+ to the quartz(101)–aqueous interface at room temperature was studied with specular X-ray reflectivity, resonant anomalous X-ray reflectivity, and density functional theory. The interfacial water structures observed in deionized water and 10 mM RbCl solution at pH 9.8 were similar, having a first water layer at height of 1.7 ± 0.1 A above the quartz surface and a second layer at 4.8 ± 0.1 A and 3.9 ± 0.8 A for the water and RbCl solutions, respectively. The adsorbed Rb+ distribution is broad and consists of presumed inner-sphere (IS) and outer-sphere (OS) complexes at heights of 1.8 ± 0.1 and 6.4 ± 1.0 A, respectively. Projector-augmented planewave density functional theory (DFT) calculations of potential configurations for neutral and negatively charged quartz(101) surfaces at pH 7 and 12, respectively, reveal a water structure in agreement with experimental results. These DFT calculations also show differences in adsorbed speciation of Rb+ between these two conditions. At pH 7, the lowe...

First principles periodic calculations based on the density functional theory within the localized atomic orbital approach (DFT-LCAO) using the hybrid exchange–correlation potential PBE0 have been performed in order to simulate the structural and electronic properties of both stoichiometric and nonstoichiometric [001]-oriented four-faceted SrTiO3 (STO) nanowires (NW) of cubic structure. Their diameters have been varied from 0.3 up to 2.4 nm with a corresponding consequent change of NW cross-section from 2 � 2t o 5� 5 extension of the lattice constant in bulk. Energetic stability of STO NW (both stoichiometric and non-stoichiometric) has been found to increase with the decrease of their formation energies together with the increase of NW diameter. The electronic structure calculations have shown that the width of the band gap changes in STO NWs of different structural types as compared to that in bulk being consequently reduced with the growth of NW diameter although the character of such a decrease depends on the morphology of the nanowire. Analysis of these changes shows that stoichiometric and non-stoichiometric TiO2-terminated strontium titanate nanowires can be quite promising candidates for further applications in photocatalytic processes under solar irradiation whereas SrO-terminated NWs are rather not suitable for this purpose.

We have performed first-principles calculations to study the atomic and electronic structures of single wall nanotubes (NTs) of two possible chirality types rolled up from monolayers of α- and γ-V2O5 phases. We have used a hybrid exchange–correlation PBE0 functional within density functional theory and a basis set of localized atomic orbitals. A dispersion correction has been taken into account. All the lattice parameters and atomic positions have been totally optimized. The strain energies calculated for the nanotubes folded from the layers of both phases along the [100] direction are close to zero. This reflects the unique flexibility of the layers for folding in the [100] direction. The electronic structure of the nanotubes of both phases appeared to be similar to that of the parent layer. It was found that for both considered phases, the nanotubes of the same chirality are energetically equivalent but the shape of γ-NTs is closer to the cylindrical form than that of α-NTs. Young's moduli calculated for (6,0) α- and γ-NTs were found to be 172 GPa and 148 GPa, respectively. The phonon mode frequencies of (6,0) α- and γ-NTs have been calculated and compared with those of α- and γ-V2O5 free layers.

Hybrid density functional theory calculations were performed for the first time on structure, stability, phonon frequencies, and thermodynamic functions of hafnia-based single-wall nanotubes. The nanotubes were rolled up from the thin free layers of cubic and tetragonal phases of HfO2 . It was shown that the most stable HfO2 single-wall nanotubes can be obtained from hexagonal (111) layer of the cubic phase. Phonon frequencies have been calculated for different HfO2 nanolayers and nanotubes to prove the local stability and to find the thermal contributions to their thermodynamic functions. The role of phonons in stability of nanotubes seems to be negligible for the internal energy and noticeable for the Helmholtz free energy. Zone folding approach has been applied to estimate the connection between phonon modes of the layer and nanotubes and to approximate the nanotube thermodynamic properties. It is found that the zone-folding approximation is sufficiently accurate for heat capacity, but less accurate for entropy. The comparison has been done between the properties of TiO2 , ZrO2 , and HfO2 . © 2017 Wiley Periodicals, Inc.

Hybrid density functional theory calculations are performed for the first time to compare the stability, structural and electronic properties of monolayers and single-wall nanotubes based on pure Mo(W)S(Se)2 and mixed (Janus) Mo(W)SSe dichalcogenides. The stability, structural and electronic properties of Mo and W dichalcogenide nanotubes have been compared at different wall compositions, chiralities and diameters using the same calculation scheme. Different types of mixed nanotubes are considered – with S or Se atoms on the outer (inner) shell of the nanotube. It was found that nanotubes Se(out)WS(in) with average diameter (Davr) greater than ≈40 A have the negative strain energy. Our calculations show that the band gap is direct for zigzag MS2 and S(out)MSe(in) nanotubes (M = Mo, W) but it becomes indirect in armchair nanotubes. For the MSe2 and Se(out)MS(in) nanotubes of both chiralities, the band gap is mostly direct, except the armchair tubes with Davr

We have performed first-principles calculations of the atomic and electronic structures and stability of three (α, β and γ) layered V 2 O 5 phases and their free layers within the same computational approach. In computations, we have used a hybrid exchange–correlation functional within the density functional theory and a basis set of localized atomic orbitals. All the lattice parameters and the atomic positions have been totally optimized and the phonon frequencies at the Γ-point of the Brillouin zone have been obtained. The calculated relative stability of considered bulk phases decreases as α > γ > β. The calculated relative stability of layers differs from that of bulk phases and decreases as β > α ⩾ γ. The possibility of the folding of V 2 O 5 layers into nanotubes is discussed.

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of bulk phases, nanolayers, and nanotubes based on titanium and zirconium disulfides. Calculations have been performed on the basis of the localized atomic functions by means of the CRYSTAL-2009 computer code. The full optimization of all atomic positions in the regarded systems has been made to study the atomic relaxation and to determine the most favorable structures. The different layered and isotropic bulk phases have been considered as the possible precursors of the nanotubes. Calculations on single-walled TiS2 and ZrS2 nanotubes confirmed that the nanotubes obtained by rolling up the hexagonal crystalline layers with octahedral 1T morphology are the most stable. The strain energy of TiS2 and ZrS2 nanotubes is small, does not depend on the tube chirality, and approximately obeys to D(-2) law (D is nanotube diameter) of the classical elasticity theory. It is greater than the strain energy of the similar TiO2 and ZrO2 nanotubes; however, the formation energy of the disulfide nanotubes is considerably less than the formation energy of the dioxide nanotubes. The distance and interaction energy between the single-wall components of the double-wall nanotubes is proved to be close to the distance and interaction energy between layers in the layered crystals. Analysis of the relaxed nanotube shape using radial coordinate of the metal atoms demonstrates a small but noticeable deviation from completely cylindrical cross-section of the external walls in the armchair-like double-wall nanotubes.

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO(3) crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange-correlation density functional theory (DFT) functionals for four stable phases of BaTiO(3). A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO(3). The comparative phonon symmetry analysis in BaTiO(3) four phases has been made basing on the site symmetry and irreducible representation indexes for the first time.

Plane wave density functional theory (DFT) calculations have been performed to study the atomic structure, preferred H2O adsorption sites, adsorption energies, and vibrational frequencies for water adsorption on the α-quartz (101) surface. Surface energies and atomic displacements on the vacuum-reconstructed, hydrolyzed, and solvated surfaces have been calculated and compared with available experimental and theoretical data. By considering different initial positions of H2O molecules, the most stable structures of water adsorption at different coverages have been determined. Calculated H2O adsorption energies are in the range −55 to −65 kJ/mol, consistent with experimental data. The lowest and the highest O−H stretching vibrational bands may be attributed to different states of silanol groups on the water-covered surface. The dissociation energy of the silanol group on the surface covered by the adsorption monolayer is estimated to be +80 kJ/mol. The metastable states for the protonated surface bridging O...

The study of the bulk and surface properties of cubic (fluorite structure) HfO 2 and UO 2 was performed using the hybrid Hartree–Fock density functional theory linear combination of atomic orbitals simulations via the CRYSTAL06 computer code. The Stuttgart small-core pseudopotentials and corresponding basis sets were used for the core–valence interactions. The influence of relativistic effects on the structure and properties of the systems was studied. It was found that surface properties of Mott–Hubbard dielectric UO 2 differ from those found for other metal oxides with the closed-shell configuration of d -electrons.

Mono- and bilayer adsorption of H2O molecules on TiO2 and SnO 2 (110) surfaces has been investigated using static planewave density functional theory (PW DFT) simulations. Potential energies and structures were calculated for the associative, mixed, and dissociative adsorption states. The DOS of the bare and hydrated surfaces has been used for the analysis of the difference between the H2O interaction with TiO2 and SnO 2 surfaces. The important role of the bridging oxygen in the H2O dissociation process is discussed. The influence of the second layer of H2O molecules on relaxation of the surface atoms was estimated.

We have studied the adsorption of water molecules on the inner and outer surfaces of nanotubes generated by rolling (001) layers of SrTiO3 cubic crystals. The stability and the atomic and electronic structures of the adsorbed layers are determined by using hybrid density functional theory. The absorption energy and the preferred adsorbate structure are essentially governed by the nature of the surface of the nanotube. Dissociative adsorption prevails on the outer nanotube surfaces. The stability of the adsorbed layers on the inner surfaces is related to the possibility of the formation of hydrogen bonds between water molecules and surface oxygen atoms, and depends on the surface curvature. The presence of water molecules on the inner surface of the nanotubes leads to an increase of the electronic band gap. Externally TiO2 -terminated nanotubes could be used for the photocatalytic decomposition of water by ultraviolet radiation.

Adsorption of Zn{sup 2+} at the rutile TiO{sub 2} (110)-aqueous interface was studied with Bragg-reflection X-ray standing waves (XSW), polarization-dependent surface extended X-ray absorption fine structure (EXAFS) spectroscopy, and density functional theory (DFT) calculations to understand the interrelated issues of adsorption site, its occupancy, ion-oxygen coordination and hydrolysis. At pH 8, Zn{sup 2+} was found to adsorb as an inner-sphere complex at two different sites, i.e., monodentate above the bridging O site and bidentate between two neighboring terminal O sites. EXAFS results directly revealed a four or fivefold first shell coordination environment for adsorbed Zn{sup 2+} instead of the sixfold coordination found for aqueous species at this pH. DFT calculations confirmed the energetic stability of a lower coordination environment for the adsorbed species and revealed that the change to this coordination environment is correlated with the hydrolysis of adsorbed Zn{sup 2+}. In addition, the derived adsorption locations and the occupancy factors of both sites from three methods agree well, with some quantitative discrepancies in the minor site location among the XSW, EXAFS, and DFT methods. Additional XSW measurements showed that the adsorption sites of Zn{sup 2+} were unchanged at pH 6. However, the Zn{sup 2+} partitioning between the two sitesmore » changed substantially, with an almost equal distribution between the two types of sites at pH 6 compared to predominantly monodentate occupation at pH 8.« less

Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO2 (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H2O present. A classical interatomic force field has been developed to describe bulk SnO2 and SnO2-H2O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystal structure and elastic constants of SnO2 are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H2O molecules agree well between the ab initio and force field predictions. H2O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.

Liu and co-workers [Phys. Rev. B 82, 161415 (2010)] discussed the long-standing debate regarding whether H${}_{2}$O molecules on the defect-free (110) surface of rutile (\ensuremath{\alpha}-TiO${}_{2}$) sorb associatively, or there is dissociation of some or all first-layer water to produce hydroxyl surface sites. They conducted static density functional theory (DFT) and DFT molecular dynamics (DFT-MD) investigations using a range of cell configurations and functionals. We have reproduced their static DFT calculations of the influence of crystal slab thickness on water sorption energies. However, we disagree with several assertions made by these authors: (a) that second-layer water structuring and hydrogen bonding to surface oxygens and adsorbed water molecules are ``weak''; (b) that translational diffusion of water molecules in direct contact with the surface approaches that of bulk liquid water; and (c) that there is no dissociation of adsorbed water at this surface in contact with liquid water. These assertions directly contradict our published work, which compared synchrotron x-ray crystal truncation rod, second harmonic generation, quasielastic neutron scattering, surface charge titration, and classical MD simulations of rutile (110) single-crystal surfaces and (110)-dominated powders in contact with bulk water, and (110)-dominated rutile nanoparticles with several monolayers of adsorbed water.

Proton jump processes in the hydration layer on the iso-structural TiO(2) rutile (110) and SnO(2) cassiterite (110) surfaces were studied with density functional theory molecular dynamics. We find that the proton jump rate is more than three times faster on cassiterite compared with rutile. A local analysis based on the correlation between the stretching band of the O-H vibrations and the strength of H-bonds indicates that the faster proton jump activity on cassiterite is produced by a stronger H-bond formation between the surface and the hydration layer above the surface. The origin of the increased H-bond strength on cassiterite is a combined effect of stronger covalent bonding and stronger electrostatic interactions due to differences of its electronic structure. The bridging oxygens form the strongest H-bonds between the surface and the hydration layer. This higher proton jump rate is likely to affect reactivity and catalytic activity on the surface. A better understanding of its origins will enable methods to control these rates.

The detailed solvation structure at the (110) surface of rutile (alpha-TiO2) in contact with bulk liquid water has been obtained primarily from experimentally verified classical molecular dynamics (CMD) simulations of the ab initio-optimized surface in contact with SPC/E water. The results are used to explicitly quantify H-bonding interactions, which are then used within the refined MUSIC model framework to predict surface oxygen protonation constants. Quantum mechanical molecular dynamics (QMD) simulations in the presence of freely dissociable water molecules produced H-bond distributions around deprotonated surface oxygens very similar to those obtained by CMD with nondissociable SPC/E water, thereby confirming that the less computationally intensive CMD simulations provide accurate H-bond information. Utilizing this H-bond information within the refined MUSIC model, along with manually adjusted Ti-O surface bond lengths that are nonetheless within 0.05 A of those obtained from static density functional theory (DFT) calculations and measured in X-ray reflectivity experiments (as well as bulk crystal values), give surface protonation constants that result in a calculated zero net proton charge pH value (pHznpc) at 25 degrees C that agrees quantitatively with the experimentally determined value (5.4+/-0.2) for a specific rutile powder dominated by the (110) crystal face. Moreover, the predicted pHznpc values agree to within 0.1 pH unit with those measured at all temperatures between 10 and 250 degrees C. A slightly smaller manual adjustment of the DFT-derived Ti-O surface bond lengths was sufficient to bring the predicted pHznpcvalue of the rutile (110) surface at 25 degrees C into quantitative agreement with the experimental value (4.8+/-0.3) obtained from a polished and annealed rutile (110) single crystal surface in contact with dilute sodium nitrate solutions using second harmonic generation (SHG) intensity measurements as a function of ionic strength. Additionally, the H-bond interactions between protolyzable surface oxygen groups and water were found to be stronger than those between bulk water molecules at all temperatures investigated in our CMD simulations (25, 150 and 250 degrees C). Comparison with the protonation scheme previously determined for the (110) surface of isostructural cassiterite (alpha-SnO2) reveals that the greater extent of H-bonding on the latter surface, and in particular between water and the terminal hydroxyl group (Sn-OH) results in the predicted protonation constant for that group being lower than for the bridged oxygen (Sn-O-Sn), while the reverse is true for the rutile (110) surface. These results demonstrate the importance of H-bond structure in dictating surface protonation behavior, and that explicit use of this solvation structure within the refined MUSIC model framework results in predicted surface protonation constants that are also consistent with a variety of other experimental and computational data.

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of nanotubes based on titanium and zirconium disulfides. The full optimization of all atomic positions in the considered systems has been performed to study the atomic relaxation and to determine the most favorable nanostructures. Our calculations on single-wall TiS2 and ZrS2 nanotubes confirmed that the nanotubes obtained by rolling of the hexagonal layers of 1T crystalline polymorphs with the octahedral morphology (and with the layer group Pm1) are the most stable. However, it is also possible to obtain the relatively stable nanotubes with lepidocrocite morphology by rolling up layers of the metastable tetragonal or orthorhombic phases. The strain energy of TiS2 is almost the same as that of ZrS2 but it is greater than the strain energy of TiO2 and ZrO2 nanotubes. However, the formation energy of the sulfide nanotubes is considerably less than the formation energy of the oxide nanotubes.

Hybrid functional of the density functional theory has been applied for investigations of the electronic and atomic structure of nanotubes (NTs) based on cubic and orthorhombic strontium zirconate. The full optimization of all atomic positions in the considered systems has been performed to study the atomic relaxation and to determine the most favourable nanostructures. The stability of the single-walled nanotubes of chiralities (n, 0) and (n, n) for the cubic, and (n1, 0) and (0, n2) for the orthorhombic SrZrO3 has been investigated in dependence on their diameter, the number of layers (2 or 4) in the slab, and the outer surface termination (SrO or ZrO2). The spontaneous splitting of the SrO-terminated (n, n) 4-layer nanotubes folded from the cubic phase into the two separated NTs has been found. The NTs folded from the orthorhombic phase, generally, preserve the atomic distortions inherent to the bulk SrZrO3 orthorhombic phases. However, the concrete NT surface structure depends on the chirality, the number of layers and termination type.

The electronic structures of four well-known modifications of crystalline SrZrO3 with different symmetries, namely, the cubic (Pm3m), tetragonal (I4/mcm), and two orthorhombic (Cmcm, Pbnm) modifications, are calculated in the framework of the density-functional theory in the basis set of the linear combination of atomic orbitals (LCAO). A comparative analysis of the electronic properties of the crystals under consideration is performed on the basis of the calculated band structures and densities of states (the total densities of states and the densities of states projected onto the atomic states). The calculated relative stabilities of the different modifications are in good agreement with the experimental data on the phase transitions in the SrZrO3 crystal: the low-temperature modifications with lower symmetry are more stable. The ionicities of chemical bonding in different modifications of crystalline SrZrO3 are compared by analyzing the Mulliken populations and constructing the localized Wannier functions for the occupied energy bands.