The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM)with themicroscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. $g$-tensor and $D$ tensor, has been determined by using the ORCA program package developed by F Neese $\it{et al}$. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor ($D^{SO}$) of the axial ZFS parameter $D$. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of $\rm{Mn}^{2+}$ ion in the host matrix.

The ceramics of spinel zinc orthotitanate (SZT) and perovskite zinc metatitanate (PZT) sintered at $800^{\circ}$C have been prepared using the high-energy ball milling technique. The structural and optical characterisation of the prepared samples has been performed using X-ray diffraction and Fourier transformation of infrared (FT-IR)spectroscopy analysis. The measurements of frequency-dependent dielectric constant of the PZT and SZT ceramics sintered at $800^{\circ}$C have been performed in the $(50−600)^{\circ}$C temperature range. Impedance spectroscopy studies have been reported for the prepared nanocrystalline ceramics. The empirical vibrational frequencies observed from the FT-IR spectra have been compared using the computational method of ORCA program package. Constraints for symmetry, bonds, angles or dihedral angles have not been applied in the geometry optimisation calculations. Hybrid three-parameter exchange-correlation functional of Becke, Lee, Yang, Parr with 20% amount of exact exchange and Ahlrichs triple-zeta valence (def2-TZVP) basis set with polarisation function have been investigated for all atoms without considering the relativistic effects.

In the present study, zero field splitting (ZFS) parameters are investigated for Mn(II) ion doped perovskites, viz. PbTiO$_3$, BaTiO$_3$ and SrTiO$_3$. The ZFS parameter and magnetisation induced in the host are investigated using quantum mechanical perturbation theory and classical statistics. A mathematical derivation is proposed to study magnetisation and ZFS due to charge distribution generated electric field and spin–orbit coupling (SOC). The computation of ZFS parameters is performed using non-hybrid functional unrestricted Kohn–Sham (UKS). The mathematical formulation is valid for perovskites in the non-ferroelectric state and finite temperature range. The contour plot and mesh surface of the spin–orbit interaction and induced magnetisation are reported.

The quantum chemical calculations of the magnetic parameters for the dopants manganese [Mn(II)] and cobalt [Co(II)] ion in the perovskite host ZnTiO$_3$ by computational program package of ORCA has been reported. All calculations are made in the distorted octahedron environment of the central metal ion Mn(II) and Co(II) about the oxygen anions. An attempt has been made to discuss the formation of orbitals in the interaction space by the power series method. The Hessian matrix as a function of electronic density distribution in active space has been constructed. The zero-field splitting (ZFS) parameters, $g$-tensors and absorption spectrum with the transition states are computed by quantum computational method. A comparative study of the density of states (DOS) for Mn(II) and Co(II) in the host is investigated in the present study.