  Recently there has been much interest in using Group IV elements from the
Periodic Table to fabricate and study X$V$ color centers in diamond where X =
Si, Ge, Sn, or Pb and $V$ is a carbon vacancy. These Group IV color centers
have a number of interesting spin and optical properties which could
potentially make them better candidates than N$V^-$ centers for important
applications in quantum computing and quantum information processing.
Unfortunately, the very same ion implantation process that is required to
create these X$V$ color centers in diamond necessarily also produces many
carbon vacancies ($V_{\rm C}$) which can form complexes with these color
centers ($V_{\rm C}-$X$V$) that can dramatically affect the properties of the
isolated X$V$ color centers. The main focus of this work is to use
density-functional theory (DFT) to study the thermodynamics and kinetics of the
formation of these $V_{\rm C}-$X$V$ complexes and to suggest experimental ways
to impede this process such as varying the Fermi level of the host diamond
material through chemical doping or applying an external electrical bias. We
also include a discussion of how the simple presence of many $V_{\rm C}$ can
negatively impact the spin coherence times ($T_2$) of Group IV color centers
through the presence of acoustic phonons.
