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 open-shell electronic structure and third-order nonlinear optical (NLO) properties of one-dimensional (1D) stacked chains of π-radicals. By employing the finite N-mer models consisting of methyl or phenalenyl radicals with different stacking distances, we evaluated the average and standard deviation of diradical characters yi for N-mer models of π-radicals (yav and ySD). Then, we estimated these diradical characters at the limit N → ∞. These y-based indices were helpful in discussing the correlation between the open-shell electronic structures and the second hyperpolarizability per dimer at the limit N → ∞, γ∞, for the 1D chains with stacking distance alternation (SDA). The calculated γ∞ values and the polymer/dimer ratio γ∞/γ(N = 2) were enhanced significantly when both the stacking distance and the 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 reproduced well the trend of γ∞ of this type of 1D chains 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.