Theoretical Study\non the Correlation between Open-Shell\nElectronic Structures and Third-Order Nonlinear Optical Properties\nin One-Dimensional Chains of π‑Radicals

This paper theoretically investigated\nthe correlation\nbetween the\nopen-shell electronic structure and third-order nonlinear optical\n(NLO) properties of one-dimensional (1D) stacked chains of π-radicals.\nBy employing the finite <i>N</i>-mer models consisting of\nmethyl or phenalenyl radicals with different stacking distances, we\nevaluated the average and standard deviation of diradical characters <i>y</i><sub><i>i</i></sub> for <i>N</i>-mer\nmodels of π-radicals (<i>y</i><sub>av</sub> and <i>y</i><sub>SD</sub>). Then, we estimated these diradical characters\nat the limit of <i>N</i> → ∞. These <i>y</i>-based indices were helpful in discussing the correlation\nbetween the open-shell electronic structures and the second hyperpolarizability\nper dimer at the limit <i>N</i> → ∞, γ<sub>∞</sub> for the 1D chains with stacking distance alternation\n(SDA). The calculated γ<sub>∞</sub> values and the polymer/dimer\nratio γ<sub>∞</sub>/γ(<i>N</i> = 2) were\nenhanced significantly when both the stacking distance and SDA are\nsmall. We also found that the spin-unrestricted long-range-corrected\n(LC−)UBLYP method with the range-separating parameter μ\n= 0.47 bohr<sup>–1</sup> well reproduced the trend of γ<sub>∞</sub> of this type of 1D chain estimated at the spin-unrestricted\ncoupled-cluster levels. The present study is expected to contribute\nto establishing the design guidelines for future high-performance\nopen-shell molecular NLO materials.