Geometry-Modulated Linear and Third-Order Nonlinear Optical Responses in Atomic Clusters

Atomic clusters are promising candidates for nonlinear optical (NLO) materials owing to their diverse geometric configurations and tunable electronic structures. With the development of preparation techniques, various atomic clusters, particularly carbon clusters, have been experimentally synthesized. However, understanding how cluster geometries relate to NLO response remains limited, largely because their geometric and electronic complexity prevents direct transfer of insights from traditional molecular systems. In this work, the linear and third-order NLO responses were investigated using carbon clusters as model systems, revealing that geometric evolution─from cage and planar-porous to cyclic to linear structures─continuously enhances both responses, driven by increased electron delocalization along less confined directions. Consequently, linear structures represent the optimal geometry to maximize these responses in carbon clusters. Additionally, unlike the strong dependence between optical response and the HOMO-LUMO gap that exists in traditional organic systems, predicting the linear and third-order NLO responses in carbon clusters via the HOMO-LUMO gap is infeasible owing to the absence of crucial excited states in generic geometric systems. These insights are further confirmed in multielement boron nitride cluster systems. This study provides deep insights into the linear and third-order NLO behaviors of atomic clusters and a clear design guideline for developing these materials.