In this paper, structural, electronic, thermal and thermoelectric properties of Al$_{0.75}$B$_{0.25}$As under 0, 2, 4 and 6 GPa pressure have been investigated based on density functional theory. Values of band gaps under 4 and 6 GPa pressure have been increased. The values of group velocity have been increased with increment in pressures from 0 GPa, too. The value of band gap at 0 GPa using the GGA(PBE) exchange-correlation potential and the mBJ method are close to each other. It is due to the good muffin-tin radius selection for atoms of the compound. Thermal properties have been investigated by calculating the heat capacity at constant volume (phonon and electronic contributions) and Debye temperature. Heat capacity at constant volume has been reduced and Debye temperature increased in comparison with AlAs. In Seebeck coefficient charge carriers are holes. Electrical conductivity in most of temperatures and electronic thermal conductivity in all the temperatures show increment with the increase in temperature and pressure.

In this paper, structural, electronic, thermal and thermoelectric properties of Al$_{0.5}$B$_{0.5}$ As alloy at 0, 4 and 8 GPa pressure have been investigated. In electronic properties, the obtained band gaps in the present work with GGA(PBE) potential are close to the other works with the TB-mBJ method at 0 GPa pressure. Band gaps reduce by increasing pressure. Thermal properties consisting of phonon contribution of heat capacity at constant volumeand Debye temperature at 0, 4 and 8 GPa pressure in the temperature range of 0–1000 K have been calculated. The diagrams of Seebeck coefficient (S), electrical conductivity (σ ) divided by relaxation time ($\tau$ ), power factor (S$^2$σ/$\tau$), electronic thermal conductivity (κe) divided by relaxation time ($\tau$) and electronic contribution of heat capacity at a constant volume in the temperature range of 100–1000 K at 0, 4 and 8 GPa pressure have been plotted.

Based on the density functional theory (DFT), the structural, electronic, optical, magneto-optical and thermoelectric properties of KCaN$_2$-K, KCaN$_2$-Ca, KCaN$_2$-N Heuslerenes have been discussed. Energy changes in the volume of these compounds indicate the presence of their ground-state points. These three structures, KCaN$_2$-K, KCaN$_2$-Ca and KCaN2-N have magnetic moments 3.0, 3.0 and 1.0μB. The electronic results indicated that the KCaN2-K Heuslerene is a magnetic semiconductor and the other two are half-metallic with 100% spinpolarisation. Optical studies showed that in both directions of the incident light (along the x- and z-axes), these compounds have semiconductor behaviour.The highest light response occurs inKCaN2-K Heuslerene at the visible edge.KCaN2-Ca and KCaN$_2$-N Heuslerenes have the lowest optical energy loss function in the IR and visible regions. Also, magnetic behaviour of the KCaN$_2$-K, KCaN$_2$-Ca and KCaN2-N Heuslerenes causes a magnetic response tolight in theUVedge region and at higher energies to control the Kerr angle rotation and magnetic polarisation of light.