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Colour centres in diamond are attractive candidates for numerous quantumapplications due to their good optical properties and long spin coherencetimes. They also provide access to the even longer coherence of hyperfinecoupled nuclear spins in their environment. While the NV centre is wellstudied, both in experiment and theory, the hyperfine couplings in the morenovel centres (SiV, GeV, and SnV) are still largely unknown. Here we report onthe first all-electron \textit{ab-initio} calculations of the hyperfineconstants for SiV, GeV, and SnV defects in diamond, both for the respectivedefect atoms ($^{29}$Si, $^{73}$Ge, $^{117}$Sn, $^{119}$Sn), as well as for thesurrounding $^{13}$C atoms. Furthermore, we calculate the nuclear quadrupolemoments of the GeV defect. We vary the Hartree-Fock mixing parameter forPerdew-Burke-Ernzerhof (PBE) exchange correlation functional and show that thehyperfine couplings of the defect atoms have a linear dependence on the mixingpercentage. We calculate the inverse dielectric constant to predict an\textit{ab-initio} mixing percentage. The final hyperfine coupling predictionsare close to the experimental values available in the literature. Our resultswill help to guide future novel experiments on these defects.

All-electron $\mathrm{\textit{ab-initio}}$ hyperfine coupling of Si-, Ge- and Sn-vacancy defects in diamond