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Theoretical studies of the optical and EPR spectra for VO$^{2+}$ in Na$_{3}$C$_{6}$H$_{5}$O$_{7}\cdot 2$H$_{2}$O single crystal

On the basis of the perturbation formulas for a $d^{1}$ configuration ion in a tetragonal crystal field, the three optical absorption bands and electron paramagnetic resonance (EPR) parameters ($g$ factors $g_{i}$ and hyperfine structure constants $A_{i}$ for $i = \|$ and $\perp$, respectively) of VO$^{2+}$ in Na$_{3}$C$_{6}$H$_{5}$O$_{7}\cdot2$H$_{2}$O single crystals were studied using the perturbation theory method. By simulating the calculated optical and EPR spectra to the observed values, local structure parameters and negative signs of the hyperfine structure constants $A_{i}$ of the octahedral (VO$_{6}$)$^{8-}$ cluster in trisodium citrate dehydrate single crystal can be obtained.