Barium titanate is one of the most studied perovskite materials due to its substitution ability at both nodes of the crystal lattice, high dielectric constant, and stability. It has many outstanding characteristics, especially ferroelectric and dielectric properties, which can be improved by alloying, making this material suitable for a wide range of applications. In this paper, the effect of Rh doping on the structural, optical properties and electronic density of states of this compound is investigated. According to our calculations, Rh doping is a method that helps to increase the ability of BaTiO₃ to absorb more light and reduce the excess potential required for water oxidation. Calculations of the electronic density of states were carried out using the hybrid functional HSE06. The analysis of optical properties was performed on the basis of matrix elements with a transient dipole moment. Studies have confirmed that the (001) BaTiO₃ surface with terminated TiO₂ has significant potential for use as a catalyst. Rh doping leads to an expansion of the spectrum of absorbed light over the entire visible range.

The advancement of effective, durable, and economically viable photocatalytic systems aimed at solar-driven water splitting into hydrogen and oxygen represents a strategically vital pathway for future fuel and chemical production from renewable sources. Water splitting is a promising strategy for the sustainable production of renewable hydrogen and for addressing the global energy and environmental crisis. However, the large-scale application of this method is limited by the low efficiency and high cost of solar water splitting systems. The search for economical, efficient, and stable photocatalysts is crucial in the development of solar water splitting technologies. Perovskite-based photocatalysts have recently attracted considerable attention for use in solar water splitting processes due to their simple structure and flexible composition. BaTiO₃ is a promising photocatalyst because of its adjustable electronic structure. Initially considered a poor photocatalyst due to its wide band gap, this material has become the focus of various strategies aimed at reducing the band gap. In this paper, we study the effect of Rh doping on the electronic structure of the (001) BaTiO₃ perovskite surface. Theoretical results show that Rh atoms can occupy both sites simultaneously, or only Ti sites, or Ba sites. The electronic structure was modeled for two conditions. When Rh atoms occupy one Ba position and one Ti position, the electronic structure shows the presence of an acceptor level within the band gap above the Fermi level, effectively reducing the band gap of the material.

The search for efficient photocatalysts for sustainable hydrogen production has driven growing interest in barium titanate (BaTiO₃)-based materials, particularly through polymorph control, surface engineering, and nonmetal and transition-metal doping. In this work, we provide an atomic-scale understanding of structural modifications in nitrogen-, fluorine-, and rhodium-doped BaTiO₃ using Density Functional Theory (DFT), as well as pristine and fluorine-substituted BaTiO₃ using reactive force-field molecular dynamics (ReaxFF-MD) simulations. DFT results for pristine and doped tetragonal BaTiO₃, as well as pristine hexagonal BaTiO₃, reveal that nitrogen and rhodium substitutions enhance the covalent character of Ti-N and Rh-O bonds and promote the redistribution of electron density, as evidenced by noncovalent interaction (NCI) and critical point (QTAIM) analyses, whereas fluorine substitution leads to more ionic Ti-F bonding. ReaxFF-MD simulations of pristine and fluorine-substituted BaTiO₃ in contact with water molecules demonstrate that fluorine substitution suppresses interfacial O-H bond formation and promotes ordered molecular hydration layers near titanium sites, as reflected in bond statistics and radial distribution functions. This study provides molecular insights into the role of N, F, and Rh doping in BaTiO₃ using DFT, and the role of fluorine doping in BaTiO₃ at the water–solid interface using ReaxFF-MD simulations, demonstrating that this integrated computational approach provides a solid basis for the rational design of next-generation materials for energy-related applications. Direct calculations of photocatalytic activity, charge transfer rates, and ferroelectric polarization effects were not performed in this work and remain important directions for future study.

This study explores the probability density distribution of gas molecules (hydrogen, neon, helium, argon, and oxygen) under optimal operating conditions. The research aims to analyze the impact of temperature, pressure, and altitude on the behavior and concentration of gas, particularly focusing on Maxwell-Boltzmann and barometric distributions. Case studies of the analysis of the probability density distribution of gas molecules using the Python programming language were presented. The analysis revealed that increasing temperature leads to an increase in the average and most probable molecular velocities, accompanied by a flattening of the Maxwell-Boltzmann distribution curve. At a constant temperature of T = 80 K, hydrogen exhibits significantly higher average velocities compared to heavier molecules such as neon and helium. Overall, the velocity distribution of gas molecules is influenced by the molecular mass and the thermodynamic state parameters. The proposed visualization methodology for Maxwell-Boltzmann distributions offers valuable applications for university educators and students. Keywords: Maxwell distribution, Python, models, distribution function, Boltzmann distribution.

In this work, the diagram of diamond deformation under tension oriented in the direction [111] in the temperature range from 1 to 1700 K is studied in the framework of classical molecular dynamics. The ideal diamond structure is considered, as well as a structure containing a relatively high concentration of defects. To study the elasticity of structures obtained at different temperatures during stretching, anisotropic modeling was performed at atmospheric pressure and the values of deformation and density of the structure over time were calculated. The elasticity of both structures is shown in a wide range of strain values characteristic of each temperature value. It is also shown that a diamond can achieve a plastic state in a narrow range of tensile strength before complete destruction at high temperatures.