We carried out a combined experimental and theoretical study of grain boundaries in polycrystalline diamond, aimed at achieving the conditions in which grain boundaries are equilibrated. Raman spectra of compacted at high-pressure and high-temperature diamond powders allow us to identify signals from $s{p}^{2}$-bonded atoms, in addition to a strong peak at 1332 cm${}^{\ensuremath{-}1}$, corresponding to $s{p}^{3}$-bonded carbon. To verify our interpretation of the experiment, $\ensuremath{\Sigma}$5 (001) twist grain boundaries of polycrystalline diamond were studied by means of molecular dynamics simulations using the technique proposed by von Alfthan et al. [Phys. Rev. Lett. 96, 055505 (2006)]. We find that grain-boundary (GB) configurations, from which one atom is removed, have significantly lower energy compared to those obtained with conventional techniques. These calculated GBs are highly ordered, a few monolayers thick, in agreement with experimental observations, and are primarily $s{p}^{2}$ bonded. This paper underlines the importance of varying the number of atoms within GBs in molecular dynamics simulations to correctly predict the GB ground-state structure.