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