Spin splitting in monoperiodic systems described by magnetic line groups.

In this paper we report the classification of all the 81 magnetic line group families into seven spin splitting prototypes, in analogy to the similar classification previously reported for the 1651 magnetic space groups, 528 magnetic layer groups, and 394 magnetic rod groups. According to this classification, electrically induced (Pekar-Rashba) spin splitting is possible in the antiferromagnetic structures described by magnetic line groups of type I (no anti-unitary operations) and III, both in the presence and in the absence of the space inversion operation. As a specific example, a group theoretical analysis of spin splitting in CoO (8, 8) nanotube is carried out and its predictions are confirmed byab initiodensity functional theory calculations.

First-Principles Calculations of Phonons and Thermodynamic Properties of Zr(Hf)S2 -Based Nanotubes.

Comparative hybrid density functional calculations on the structure, stability, and phonon frequencies of monolayers and single-walled nanotubes are performed for Zr(Hf)S2 disulfides. The first-principles calculations of HfS2 -based nanotubes are made for the first time. The symmetry analysis of infrared and Raman active vibrational modes in ZrS2 and HfS2 nanotubes is made using the induced representations of the isogonal point groups of line groups. It is shown that the number of infrared and Raman active modes is constant for NTs with the same chirality type. The correlation of the phonon modes of the nanotubes of relatively large diameters with those of monolayer is analyzed. The thermodynamic functions of monolayers and nanotubes with various chirality and diameters are calculated on the basis of the obtained phonon frequencies. It is established that the phonon contribution to the nanotube strain energy is small, but may be important for an accurate estimate of the stability of the nanotubes of small diameters. The calculated results show that the thermal contributions to Helmholtz free energy are positive; thereby they slightly reduce the stability of ZrS2 and HfS2 nanotubes at elevated temperatures. © 2019 Wiley Periodicals, Inc.

Infrared and Raman active vibrational modes in MoS2 -based nanotubes: Symmetry analysis and first-principles calculations.

The possibility to use the axial point group dynamical representations for the infrared and Raman active modes classification in nanotubes is analyzed. The method proposed allows one to obtain the results of phonon symmetry analysis for nanotubes in Mulliken designations, which are traditional for molecules and crystallographic point groups. The approach suggested is applied to the phonon symmetry analysis in the single-wall carbon and MoS2 -based nanotubes. First-principles calculations of phonons in a bulk MoS2 crystal and a monolayer S-Mo-S are made. The results obtained are in reasonable agreement with the existing experimental data and other published results. The first-principles calculations of the phonon frequencies for armchair and zigzag MoS2 nanotubes are performed for the first time. It is shown that the number of infrared and Raman active modes becomes fixed starting from the relatively small nanotube diameters. The correlation of the phonon modes of MoS2 nanotubes with diameters up to 3.64 nm with phonon modes of the S-Mo-S monolayer is analyzed. It is demonstrated that the interpretation of the nature of nanotube A-type modes in the crystallographic factorization of the line group L = TF is the same as for m = 0 modes in the "polymer type" factorization L = ZP where P is the subgroup of the isogonal point group F, T is the translation subgroup of line group and the cyclic group Z includes the one-dimensional translations and the rotations around the screw axes or the reflections in the glide planes. © 2018 Wiley Periodicals, Inc.

Temperature dependence of thermodynamic properties of MoS2 monolayer and single-wall nanotubes: Application of the developed three-body force field.

MoS2 nanostructures, especially mono-, multilayer nanothin films as well as single- and multiwall nanotubes are rather interesting popular objects in nanomaterials chemistry. The thermodynamic properties of inorganic nanotubes, and the temperature dependence of their properties can be efficiently investigated by first-principles and molecular mechanics methods in the framework of harmonic approximation. At the same time, only thin single-wall nanotubes are available for the first-principles calculations. The classical mechanics is suitable to simulate very large atomic systems and their phonon frequencies, but developing sufficiently accurate force field is rather tedious work. Herein, we report the force field fitted to the experimental and first-principles data on the structure of 2H- and 3RMoS2 polytypes of bulk crystal, structure of monolayer and several bilayers, vibrational frequencies of 2HMoS2 bulk and monolayer, relative energetic stability of polytypes experimental and first-principles data, elastic constants, strain energy of a (12, 12) MoS2 nanotube. The thermodynamic functions and their temperature dependence for the armchair and zigzag nanotubes are calculated within the formalism of molecular mechanics using elaborated interatomic potential. The results of molecular mechanics and first-principles method application to the thinnest nanotubes are compared.

Phonon spectra, electronic, and thermodynamic properties of WS2 nanotubes.

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.

First-principles modeling of hafnia-based nanotubes.

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.

Temperature dependence of strain energy and thermodynamic properties of V2 O5 -based single-walled nanotubes: Zone-folding approach.

A zone-folding approach is applied to estimate the thermodynamic properties of V2 O5 -based nanotubes. The results obtained are compared with those from the direct calculations. It is shown that the zone-folding approximation allows an accurate estimation of nanotube thermodynamic properties and gives a gain in computation time compared to their direct calculations. Both approaches show that temperature effects do not change the relative stability of V2 O5 free layers and nanotubes derived from the α- and γ-phase. The internal energy thermal contributions into the strain energy of nanotubes are small and can be ignored. © 2016 Wiley Periodicals, Inc.

Application of zone-folding approach to the first-principles estimation of thermodynamic properties of carbon and ZrS2 -based nanotubes.

A zone-folding (ZF) approach is applied for the estimation of the phonon contributions to thermodynamic properties of carbon-and ZrS2 -based nanotubes (NTs) of hexagonal morphology with different chiralities. The results obtained are compared with those from the direct calculation of the thermodynamic properties of NTs using PBE0 hybrid exchange-correlation functional. The phonon contribution to the stability of NTs proved to be negligible for the internal energy and small for the Helmholtz free energy. It is found that the ZF approach allows us an accurate estimation of phonon contributions to internal energy, but slightly overestimates the phonon contributions to entropy. © 2015 Wiley Periodicals, Inc.

Theoretical Study of α-V2O5 -Based Double-Wall Nanotubes.

First-principles calculations of the atomic and electronic structure of double-wall nanotubes (DWNTs) of α-V2 O5 are performed. Relaxation of the DWNT structure leads to the formation of two types of local regions: 1) bulk-type regions and 2) puckering regions. Calculated total density of states (DOS) of DWNTs considerably differ from that of single-wall nanotubes and the single layer, as well as from the DOS of the bulk and double layer. Small shoulders that appear on edges of valence and conduction bands result in a considerable decrease in the band gaps of the DWNTs (up to 1 eV relative to the single-layer gaps). The main reason for this effect is the shift of the inner- and outer-wall DOS in opposite directions on the energetic scale. The electron density corresponding to shoulders at the conduction-band edges is localized on vanadium atoms of the bulk-type regions, whereas the electron density corresponding to shoulders at the valence-band edges belongs to oxygen atoms of both regions.

Quantum Chemical Study of Water Adsorption on the Surfaces of SrTiO3 Nanotubes.

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.

TiS2 and ZrS2 single- and double-wall nanotubes: first-principles study.

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.

BaTiO3-based nanolayers and nanotubes: first-principles calculations.

The first-principles calculations using hybrid exchange-correlation functional and localized atomic basis set are performed for BaTiO(3) (BTO) nanolayers and nanotubes (NTs) with the structure optimization. Both the cubic and the ferroelectric BTO phases are used for the nanolayers and NTs modeling. It follows from the calculations that nanolayers of the different ferroelectric BTO phases have the practically identical surface energies and are more stable than nanolayers of the cubic phase. Thin nanosheets composed of three or more dense layers of (0 1 0) and (0 1 1[overline]) faces preserve the ferroelectric displacements inherent to the initial bulk phase. The structure and stability of BTO single-wall NTs depends on the original bulk crystal phase and a wall thickness. The majority of the considered NTs with the low formation and strain energies has the mirror plane perpendicular to the tube axis and therefore cannot exhibit ferroelectricity. The NTs folded from (0 1 1[overline]) layers may show antiferroelectric arrangement of Ti-O bonds. Comparison of stability of the BTO-based and SrTiO(3)-based NTs shows that the former are more stable than the latter.

First-principles calculations on thermodynamic properties of BaTiO3 rhombohedral phase.

The calculations based on the linear combination of atomic orbitals have been performed for the low-temperature phase of BaTiO(3) crystal. Structural and electronic properties, as well as phonon frequencies were obtained using hybrid PBE0 exchange-correlation functional. The calculated frequencies and total energies at different volumes have been used to determine the equation of state and thermal contribution to the Helmholtz free energy within the quasiharmonic approximation. For the first time, the bulk modulus, volume thermal expansion coefficient, heat capacity, and Grüneisen parameters in BaTiO(3) rhombohedral phase have been estimated at zero pressure and temperatures form 0 to 200 K, based on the results of first-principles calculations. Empirical equation has been proposed to reproduce the temperature dependence of the calculated quantities. The agreement between the theoretical and experimental thermodynamic properties was found to be satisfactory.

First-principles calculations on the four phases of BaTiO3.

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.

Faster proton transfer dynamics of water on SnO2 compared to TiO2.

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.

Surface protonation at the rutile (110) interface: explicit incorporation of solvation structure within the refined MUSIC model framework.

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.

Comparisons of multilayer H2O adsorption onto the (110) surfaces of alpha-TiO2 and SnO2 as calculated with density functional theory.

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.