Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

Triangular symmetric molecules with mirror symmetry perpendicular to the threefold axis are forbidden to have a fixed electrical dipole moment. However, if the ground state is orbitally degenerate and lacks inversion symmetry, then a "quantum" dipole moment does exist. The system of three electrons in D3h symmetry is our example. This system is realized in triatomic molecules like Na3. Unlike the fixed dipole of a molecule like water, the quantum moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values ±μ0 along any direction of measurement in the plane. An electric field F in the plane leads to a linear Stark splitting ±μ0F. We introduce a toy model to study the effect of Jahn-Teller distortions on the quantum dipole moment. We find that the quantum dipole property survives when the dynamic Jahn-Teller effect is included if the distortion of the molecule is small. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. Coulomb correlations also give a partial suppression.