Theoretical Study on the Correlation between Open-Shell Electronic Structures and Third-Order Nonlinear Optical Properties in One-Dimensional Chains of π-Radicals

This paper theoretically investigated the correlation between the open-shell electronic structure and third-order nonlinear optical (NLO) properties of one-dimensional (1D) stacked chains of π-radicals. By employing the finite <i>N</i>-mer models consisting of methyl or phenalenyl radicals with different stacking distances, we evaluated the average and standard deviation of diradical characters <i>y</i>_<i>i</i> for <i>N</i>-mer models of π-radicals (<i>y</i>_av and <i>y</i>_SD). Then, we estimated these diradical characters at the limit of <i>N</i> → ∞. These <i>y</i>-based indices were helpful in discussing the correlation between the open-shell electronic structures and the second hyperpolarizability per dimer at the limit <i>N</i> → ∞, γ_∞ for the 1D chains with stacking distance alternation (SDA). The calculated γ_∞ values and the polymer/dimer ratio γ_∞/γ(<i>N</i> = 2) were enhanced significantly when both the stacking distance and SDA are small. We also found that the spin-unrestricted long-range-corrected (LC-)UBLYP method with the range-separating parameter μ = 0.47 bohr^-1 well reproduced the trend of γ_∞ of this type of 1D chain estimated at the spin-unrestricted coupled-cluster levels. The present study is expected to contribute to establishing the design guidelines for future high-performance open-shell molecular NLO materials.