Theoretical Study on the Second Hyperpolarizabilities of Phenalenyl Radical Systems Involving Acetylene and Vinylene Linkers:  Diradical Character and Spin Multiplicity Dependences

Abstract

We have investigated the static second hyperpolarizabilities (gamma) of the singlet diradical systems with intermediate diradical character involving phenalenyl radicals connected by acetylene and vinylene pi-conjugated linkers, 1 and 2, using the hybrid density functional theory. For comparison, we have also examined the gamma values of the closed-shell and pure diradical systems with almost the same molecular size as 1 and 2. In agreement with our previous prediction of the diradical character dependence of gamma, it turns out that the gamma values of 1 and 2 are significantly enhanced compared to those of the closed-shell and pure diradical systems. In the present case, distinct differences in gamma values are not observed between the two pi-conjugated linkers, though the diradical character is found to depend on the kind of linker. Furthermore, we have investigated the spin multiplicity effect on gamma. Changing from the singlet to the triplet state, the gamma values of the systems with intermediate diradical character in the singlet state are quite reduced, though those of the pure diradical systems are hardly changed. Such spin multiplicity dependence of gamma is understood by considering the difference of diradical character between their singlet states together with the Pauli principle. The present results provide a possibility of a novel control scheme of gamma for phenalenyl radical systems involving pi-conjugated linkers by adjusting the diradical character through the change of the linked position of pi-conjugated linkers and the spin multiplicity.

Unusual Interchromophoric Interactions in β,β′ Directly and Doubly Linked Corrole Dimers: Prohibited Electronic Communication and Abnormal Singlet Ground States

“…[36][37][38] To explore the NLO properties of the oxidized corrole dimers with a focus on the effect of the singlet biradical character, we employed the finite-field approach to calculate the dominant longitudinal component of static γ (γ xxxx ) value of the oxidized corrole dimers. 37,38 As a result, the γ values calculated for DH 2 CD and DZnCD are distinctly enhanced (4.540 × 10 6 and 9.217 × 10 6 au, respectively) compared with that for DH 3 CD (2.100 × 10 6 au).…”

Third-order nonlinear optical properties of trigonal, rhombic and bow-tie graphene nanoflakes with strong structural dependence of diradical character

“…For trigonal GNF, the D 3h symmetry ensures that c xxxx = c yyyy Since c strongly depends on the size of systems (i.e., in p-conjugated systems c increases nonlinearly with increasing the p-conjugation lengths until saturation is reached [44]), rhombic and bowtie GNFs have been chosen with similar dimension in the x direction, so that one could highlight the spin polarization effect on c xxxx , i.e., diradical character dependence of c xxxx .We employ the finite-field (FF) approach to calculate the static c xxxx values. This approach consists in the fourth-order differentiation of the energy or the third-order differentiation of the x-component of dipole moment with respect to different amplitudes of the applied external electric field [28,32]. The employed differentiation scheme and field amplitudes are respectively chosen so as to reduce the numerical error to within 1% of the c xxxx value.…”

“…In such molecular systems, the second hyperpolarizability (c) -the microscopic origin of the third-order NLO propertiesexhibits a remarkable dependence on the diradical character [39,40]: the systems with intermediate y value tend to exhibit a large enhancement of c as compared to the closed-shell and pure diradical systems. This dependence has been theoretically clarified by the valence configuration interaction (VCI) method for two-site diradical model [36], and has been exemplified by the spinunrestricted post Hartree-Fock (UHF) and density functional theory (DFT) calculations on various real and model systems [28][29][30][31][32][33][34][35][36][37][38] including square and hexagonal GNFs [37,38]. Experimentally, polyaromatic diphenalenyl diradicals have been found to exhibit huge two-photon absorption cross section (a typical third-order NLO property) [41], which is in agreement with our structure-property relationship of c in diradical systems.…”

“…Experimentally, polyaromatic diphenalenyl diradicals have been found to exhibit huge two-photon absorption cross section (a typical third-order NLO property) [41], which is in agreement with our structure-property relationship of c in diradical systems. Moreover, the systems with intermediate diradical character exhibit strong spin state dependence of c: a significant reduction of c amplitude by changing singlet to triplet state [32,37].…”

“…On the other hand, based on theoretical and computational studies, we have recently found a novel class of nonlinear optical (NLO) systems, i.e., open-shell singlet molecular systems, [28][29][30][31][32][33][34][35][36][37][38]. In such molecular systems, the second hyperpolarizability (c) -the microscopic origin of the third-order NLO propertiesexhibits a remarkable dependence on the diradical character [39,40]: the systems with intermediate y value tend to exhibit a large enhancement of c as compared to the closed-shell and pure diradical systems.…”