Origin of Spontaneous Electric Dipoles in Homonuclear Niobium Clusters

Surprisingly large, spontaneous electric dipole moments recently observed in homonuclear niobium clusters below 100 K (Moro et al., 2003) are explained using first-principles electronic structure calculations. The calculated moments for ${\mathrm{N}\mathrm{b}}_n$ ($n\le 15$) generally agree with the experimental data. A strong correlation is found between the geometrical asymmetry of the cluster and electric dipole: its magnitude is proportional to the spread in the principal moments of inertia and its direction aligns with the axis of the largest principal moment. Charge deformation densities reveal directional, partially covalent bonds that stabilize structural asymmetry. Classical simulations of the deflection of a cluster in a molecular beam reveal that the electronic dipole may persist at higher temperatures, but is masked by the rotational dynamics of the cluster.

Figure 1

Comparison of the calculated dipole moments and “low-temperature” (50 K) experimental data from Fig. 2 of Ref. 1 ($1\mathrm{D}=0.20819e\AA$). Higher energy structures are labeled in alphabetical order, following the notation of Ref. 7.

Figure 2

The strong correlation between the dipole moment and asymmetry of the cluster, as quantified by the difference between the largest $I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and smallest $I_{\mathrm{m}\mathrm{i}\mathrm{n}}$ principal moments of inertia.

Figure 3

Charge deformation of ${\mathrm{N}\mathrm{b}}_3$ (0.5 D). Because of the mirror symmetry, the dipole moment (orange arrow) is restricted to lie on the symmetry axis.

Figure 4

Charge deformation for (a) ${\mathrm{N}\mathrm{b}}_{12}$ (2.3 D) and (b) ${\mathrm{N}\mathrm{b}}_{15}$ (no dipole). The direction of the dipole moment is represented by the orange arrow. Note the formation of covalent bonding. Unlike systems with a large dipole moment, no asymmetric covalency is seen in ${\mathrm{N}\mathrm{b}}_{15}$. Instead, the charge deformation density is entirely intra-atomic.

Figure 5

Classical deflection of a model $\mathrm{N}{\mathrm{b}}_{12}$ cluster with a dipole moment $\mu =2\mathrm{D}$ at 300 K (top) and 20 K (bottom). At higher temperatures, the rotational dynamics masks the permanent dipole moment.