B1u

B1u is a one-dimensional irreducible representation (irrep) used in molecular symmetry to label functions, orbitals, and vibrational modes. The “u” denotes ungerade parity, meaning the representation changes sign under inversion. The “B” indicates it belongs to a nondegenerate family in the group’s symmetry operations, and the numeral “1” distinguishes it from other B-type irreps within the same point group. B1u appears in several centrosymmetric point groups, most notably D2h and D4h, and its exact characters depend on the chosen axis conventions for a given group.

In practice, a molecular orbital or vibrational mode that transforms as B1u has odd parity with respect to inversion and follows a specific pattern of symmetry under the group's operations. B1u is used to classify electronic states and vibrational motions, and it informs selection rules in spectroscopy. For example, in infrared spectroscopy, a transition is allowed if the direct product of the initial state, the final state, and the dipole operator contains the totally symmetric representation; since the dipole operator components transform as x, y, or z, which themselves carry particular irreps, the involvement of B1u in the product determines infrared activity along certain directions within the molecule’s symmetry.

The interpretation of B1u depends on the specific point group and axis choices, so chemists consult the respective character table to identify which orbitals or motions have B1u symmetry and how this relates to observed spectra.