No, it is not correct to say that the valence orbital theory always requires half-filled orbitals in atoms, while molecular orbital (MO) theory does not have this requirement.
Valence orbital theory, also known as the valence bond theory, explains chemical bonding by the overlapping of atomic orbitals. It focuses on the concept of hybridization, where atomic orbitals mix to form new hybrid orbitals that participate in bonding. Valence bond theory does not require half-filled orbitals as a prerequisite for bonding. Instead, it emphasizes the overlap of atomic orbitals to form covalent bonds by sharing electron pairs.
On the other hand, molecular orbital theory describes bonding by considering the formation of molecular orbitals from the combination of atomic orbitals throughout the entire molecule. In MO theory, the atomic orbitals combine to form molecular orbitals, which can be bonding orbitals (lower in energy) or antibonding orbitals (higher in energy). Electrons fill the molecular orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
In MO theory, there is no strict requirement for half-filled orbitals. In fact, MO theory allows for the formation of stable bonds in molecules where the atomic orbitals are not necessarily half-filled. For example, in XeF2, the xenon atom contributes its filled 5p orbitals and vacant 5d orbitals to form molecular orbitals with fluorine atoms. This leads to the formation of sigma and pi bonds without the need for half-filled orbitals.
Similarly, in the case of H2-, MO theory explains the bonding by considering the combination of the atomic orbitals of two hydrogen atoms, resulting in the formation of a molecular orbital. The additional electron in H2- fills the antibonding molecular orbital, leading to a stable bond.
Both valence orbital theory and MO theory provide useful models for understanding chemical bonding, but they differ in their approach and level of complexity. Valence bond theory emphasizes localized electron pairs, while MO theory considers the delocalization of electrons over the entire molecule. Neither theory requires half-filled orbitals as a strict prerequisite for bonding.