Ab initio calculations on nuclear quadrupole interactions of ^69,71Ga and ¹⁴N nuclei in GaN of ionic crystal

This paper presents the results of our calculation of nuclear quadrupole coupling constant (NQCC) of ^69,71Ga and ¹⁴N on wurtzite GaN crystal using the Hartree-Fock Roothaan Molecular Cluster procedure. We employed Ga₄N₄H₁₈ cluster as well as the (GaN₄)^9- and the (NGa₄)⁹⁺ clusters surrounded by 1160 external Ga³⁺ and N^3- ions in 15 Å radius lattice to simulate the covalent bonding and ionic bonding among the constituent atoms in the solid-state system and to calculate the electronic structure and the associated nuclear quadrupole interaction properties of ¹⁴N and ^69,71Ga. The nuclear quadrupole coupling constant (NQCC) e²qQ/h for ⁶⁹Ga with a value of its Q as 0.168 barns was found to be 2.98 MHz in the (GaN₄)^9- cluster and 34.43 MHz in the Ga₄N₄H₁₈ cluster. The e²qQ/h for the ¹⁴N in the (NGa₄)⁹⁺ cluster representing the ionic bonding was found to be 0.0303 MHz using the nuclear quadrupole moment of ¹⁴N nucleus as 0.0193 barns. The calculated NQI parameters from the (GaN₄)^9- and the (NGa₄)⁹⁺ clusters agree well with the experimental values indicating the existence of the significant ionic bonding between the constituent atoms in the solid-state system.