  Artificial atom qubits in diamond have emerged as leading candidates for a
range of solid-state quantum systems, from quantum sensors to repeater nodes in
memory-enhanced quantum communication. Inversion-symmetric group IV vacancy
centers, comprised of Si, Ge, Sn and Pb dopants, hold particular promise as
their neutrally charged electronic configuration results in a ground-state spin
triplet, enabling long spin coherence above cryogenic temperatures. However,
despite the tremendous interest in these defects, a theoretical understanding
of the electronic and spin structure of these centers remains elusive. In this
context, we predict the ground- and excited-state properties of the neutral
group IV color centers from first principles. We capture the product
Jahn-Teller effect found in the excited state manifold to second order in
electron-phonon coupling, and present a non-perturbative treatment of the
effect of spin-orbit coupling. Importantly, we find that spin-orbit splitting
is strongly quenched due to the dominant Jahn-Teller effect, with the lowest
optically-active $^3E_u$ state weakly split into $m_s$-resolved states. The
predicted complex vibronic spectra of the neutral group IV color centers are
essential for their experimental identification and have key implications for
use of these systems in quantum information science.
