We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory (DFT) calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number N = 1, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.
Aldegunde, J., & Hutson, J. M. (2009). Hyperfine energy levels of alkali-metal dimers: Ground-state homonuclear molecules in magnetic fields. Physical Review A - Atomic, Molecular, and Optical Physics, 79(1). https://doi.org/10.1103/PhysRevA.79.013401