Open‐Shell Characters and Second Hyperpolarizabilities of One‐Dimensional Graphene Nanoflakes Composed of Trigonal Graphene Units

The impact of topology on the open‐shell characters and the second hyperpolarizabilities (γ) has been addressed for one‐dimensional graphene nanoflakes (GNFs) composed of the smallest trigonal graphene (phenalenyl) units. The main results are: 1) These GNFs show not only diradical but also multiradical characters when increasing the number of linked units. 2) GNFs composed of an equivalent number of units can exhibit a wide range of open‐shell characters—from nearly closed‐shell to pure multiradical characters—depending on the linking pattern of the trigonal units. 3) This wide variation in open‐shell characters is explained by their resonance structures and/or by their (HOMO?i)?(LUMO+i) gaps deduced from the orbital correlations. 4) The change in the linking structure of the units can effectively control their open‐shell characters as well as their γ values, of which the longitudinal components are significantly enhanced for the singlet GNFs having intermediate open‐shell characters. 5) Singlet alternately linked (AL) systems present intermediate multiradical characters even in the case of a large number of units, which creates a significant enhancement of γ with increasing the size, whereas nonalternately linked (NAL) systems, which present pure multiradical characters, possess much smaller γ values. Finally 6) by switching from the singlet to the highest spin states, the γ values of NAL systems hardly change, whereas those of AL systems exhibit large reductions. These fascinating structure–property relationships between the topology of the GNFs, their open‐shell characters, and their γ values not only deepen the understanding of open‐shell characters of GNFs but aim also at stimulating further design studies to achieve giant NLO responses based on open‐shell graphene‐like materials.