A length descriptor to measure the linear and third-order nonlinear optical responses of atomic-cluster isomers

Atomic clusters, a form of matter intermediate between atomic and condensed states, exhibit remarkable geometrical and chemical-compositional flexibilities. Unlike inorganic crystals and organic molecules, atomic clusters do not conform to the well-established multi-level model developed decades ago for predicting nonlinear optical properties. As a result, they present opportunities to achieve currently unattainable nonlinear optical performance. However, a clear conceptual guideline for designing specific geometries with maximal nonlinear optical responses is lacking. Herein, a length descriptor that can simply and effectively determine the third-order nonlinear optical response of atomic-cluster isomers is reported. Response charge, a newly introduced concept, reveals that the length tunes linear and third-order nonlinear optical performances by controlling electron delocalization in atomic-cluster isomers, with one-dimensional (1D) geometry offering optimal optical performances. Finally, the optical behaviors of 1D geometries are quantitatively rationalized by response charge, providing a clear physical picture. This study deepens the understanding of the linear and third-order nonlinear optical behaviors of atomic clusters and is expected to strongly accelerate the rational design of third-order nonlinear optical materials.