  A comprehensive description of the optical cycle of spin defects in solids
requires the understanding of the electronic and atomistic structure of states
with different spin multiplicity, including singlet states which are
particularly challenging from a theoretical standpoint. We present a general
framework, based on spin-flip time-dependent density function theory, to
determine the excited state potential energy surfaces of the many-body singlet
states of spin defects; we then predict the vibrationally resolved absorption
spectrum between singlet shelving states of a prototypical defect, the
nitrogen-vacancy center in diamond. Our results, which are in excellent
agreement with experiments, provide an interpretation of the measured spectra
and reveal the key role of specific phonons in determining absorption
processes, and the notable influence of non-adiabatic interactions. The
insights gained from our calculations may be useful in defining strategies to
improve infrared-absorption-based magnetometry and optical pumping schemes. The
theoretical framework developed here is general and applicable to a variety of
other spin defects and materials.
