Simple and effective descriptor for measuring the nonlinear optical responses of atomic clusters

Atomic clusters, a form of matter that is intermediate between atomic and condensed states, feature tremendous geometrical and chemical-compositional flexibilities. Unlike inorganic crystals and organic molecules, atomic clusters escape the well-established physical model developed decades ago for predicting nonlinear optical properties, which presents opportunities for achieving currently unattainable nonlinear optical performances. However, clear conceptual guidelines for designing specific geometries with maximal nonlinear optical responses are lacking. Herein, a simple and efficient length descriptor for determining the optical responses of atomic-cluster isomers is reported. The response charge, a newly introduced concept, reveals that the length tunes the optical performance by controlling electron delocalization in atomic-cluster isomers, with the one-dimensional geometry providing optimal optical performance. Finally, the optical behaviors of one-dimensional geometries are quantitatively rationalized by the response charge, providing a clear physical picture. The intuitive rule developed herein is expected to powerfully accelerate the rational design of novel nonlinear optical materials.