We carry out a complete treatment of the leading-order relativistic one-electron contributions, arising from the Breit-Pauli Hamiltonian, to the g-tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the F-2(-), Cl-2(-), Br-2(-), and I-2(-). series, using analytical response theory calculations with. a multiconfigurational self-consistent field reference state. The results are compared to available experimental data. (C) 2004 American Institute of Physics.