Theoretical Study on the Relationship between Diradical Character and Second Hyperpolarizabilities of Four‐Membered‐Ring Diradicals Involving Heavy Main‐Group Elements

Abstract

By using spin-unrestricted density functional theory methods, the relationship between the diradical character y and the second hyperpolarizability γ (the third-order nonlinear optical (NLO) properties at the molecular scale) for four-membered-ring diradical compounds, that is, cyclobutane-1,3-diyl, Niecke-type diradicals, and Bertrand-type diradicals, were investigated by focusing on the substitution effects of heavy main-group elements as well as of donor/acceptor groups on the y and γ values. It has been found that i) γ is enhanced in the intermediate y region for these four-membered-ring diradicals, ii) Niecke-type diradicals with intermediate y values, which are realized by tuning the combination of the main-group elements involved, exhibit larger γ values than Bertrand-type diradicals, and iii) the y value and thus γ value can be controlled by modifying the both-end donor/acceptor substituents attached to carbon atoms in Nicke-type C2 P2 diradicals. These results demonstrate that four-membered-ring diradicals involving heavy main-group elements exhibit high controllability of the y and γ, which indicates the potential applications of four-membered-ring diradicals as a building block of highly efficient open-shell NLO materials.

Open-Shell-Character-Based Molecular Design Principles: Applications to Nonlinear Optics and Singlet Fission

“…Although these compounds are usually unstable, recent synthetic developments have enabled the realization of thermally stable molecular systems involving such main‐group elements, which is expected to open a way to constructing novel design guidelines for highly efficient NLO systems. For example, Matsui and I observed a similar y –γ correlation of four‐membered‐ring diradical compounds, i. e., cyclobutane‐1,3‐diyl, Niecke‐type diradicals, and Bertrand‐type diradicals, and found that (i) Niecke‐type diradicals with intermediate y values exhibit larger γ values than Bertrand‐type diradicals, and (ii) the y value and thus γ value can be controlled by modifying the donor/acceptor substituents attached to the carbon atoms of Niecke‐type C 2 P 2 diradicals . These results demonstrated that four‐membered‐ring diradicals with heavy main‐group elements exhibit high controllability of the diradical character and thus of γ.…”

Nonlinear optical properties in open‐shell molecular systems

“…In this article, we introduce the diradical character dependence of the third‐order NLO properties, e.g., the second hyperpolarizability γ at the molecular scale, for a two‐site model based on the perturbative formula including excitation energies and transition moments. From this theoretical result, we describe the correlation between y and γ , referred to as ‘ y–γ correlation,’ and state the following NLO‐design principle : ‘ γ values of systems with the intermediate diradical character ( y ~ 0.5) are enhanced as compared to those of closed‐shell ( y = 0) and pure open‐shell ( y = 1) singlet systems.’ Then, we summarize theoretical investigations on a wide variety of model and real molecular systems with intermediate diradical characters that lead to control schemes of the diradical character through chemical modification and physical perturbation . We also introduce extensions of the y–γ correlation, e.g., for multiradical systems going beyond diradicals, dynamic (frequency‐dependent) hyperpolarizabilities, asymmetric open‐shell singlet systems, and spin state dependence .…”

Third-Order Nonlinear Optical Properties of Asymmetric Non-Alternant Open-Shell Condensed-Ring Hydrocarbons: Effects of Diradical Character, Asymmetricity, and Exchange Interaction

“…Over the past few years, lots of experimental and theoretical studies have been performed to clarify the relationships between the unique electronic structures and physicochemical properties of open-shell singlet molecules. − Their electronic structures are characterized by the diradical character ( y ) − a quantum-chemical index of the open-shell nature, 0 (closed-shell) ≤ y ≤ 1 (pure diradical), and of the effective bond order, 1 – y . Among these properties, quantum chemistry calculations have revealed that their nonlinear optical (NLO) responses are strongly correlated to y . − From the analysis of a symmetric two-site diradical model using the valence configuration interaction (VCI) method, ,− we have described the diradical character dependences of the excitation energies and transition properties as well as of the second hyperpolarizabilities γ (the molecular third-order NLO properties), referred to as “ y –γ correlation”: symmetric open-shell singlet systems with intermediate diradical character exhibit larger γ values than the closed-shell and pure diradical analogues. , This prediction has been substantiated by ab initio molecular orbital (MO) and density functional theory (DFT) calculations on model and real symmetric open-shell singlet molecules, e.g., stretched hydrogen molecular model, p -quinodimethane model, diphenalenyl diradicaloids, graphene nanoflakes, , acenes and dicyclopenta-fused acenes, transition-metal–metal bonded systems, main-group compounds, quinoidal oligothiophenes, and open-shell aggregates …”