Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character

The origin of the diradical character dependence of the second hyperpolarizability (gamma) of neutral singlet diradical systems is clarified based on the perturbation formula of gamma using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of gamma in the intermediate diradical character region turns out to originate from the increasing magnitude of the transition moment between the first and second excited states and the decrease of that between the ground and first excited states, respectively, with the increase in diradical character. This feature confirms that open-shell singlet conjugated molecules with intermediate diradical characters constitute a new class of third-order nonlinear optical systems, whose gamma values can be controlled by the diradical character in addition to the conjugation length.     

Theoretical study on the second hyperpolarizabilities of phenalenyl radical systems involving acetylene and vinylene linkers: diradical character and spin multiplicity dependences

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.     

Theoretical study on second hyperpolarizabilities of singlet diradical square planar nickel complexes involving o-semiquinonato type ligands

Hybrid density functional theory method is applied for investigating the diradical character dependence of the second hyperpolarizability (gamma) of square planar nickel complexes involving several types of bidentate ligands [o-C6H4XY, where X = Y = O, NH, S, Se, and PH as well as (X, Y) = (NH, NH2) and (S, NH2)]. It is found that, as a function of the donor atoms, the diradical character of these complexes varies from 0.0 to 0.884 and is associated with substantial variations of gamma ranging from 14 x 10(3) to 819 x 10(3) au. In particular, the largest gamma values are associated with intermediate diradical characters in good agreement with the structure-property relationship obtained for pure hydrocarbon systems. Increasing the electronegativity of the X and Y donor groups of the ligands leads to larger diradical characters as a result of the enhancement of the double bond nature of the C=X(Y) bonds, which further stabilizes the diradicals on both-end benzene rings. This demonstrates that the electronegativities of the donor atoms of the ligands become a tuning parameter of the diradical character and then of the gamma values of these complexes.     

Size dependences of the diradical character and the second hyperpolarizabilities in dicyclopenta-fused acenes: relationships with their aromaticity/antiaromaticity

Using long-range corrected density functional theory, the relationships between the electronic, magnetic, and nonlinear optical properties are drawn for two families of organic compounds, the dicyclopenta-fused acenes (DPAs) and the polyacenes (PAs), containing up to N = 12 fused rings. First, the longitudinal second hyperpolarizability (γ) of singlet DPAs is significantly enhanced with increasing system size, in comparison to PAs. This behavior is associated with an increase in the longitudinal spin polarization between the terminal five-membered rings of DPAs and is consistent with previous studies where γ is maximized for intermediate diradical character. The size dependence of the diradical character is also found to cause a hump in the γ/N evolution for singlet DPAs around N = 8. In fact, in the case of singlet PAs, the diradical characters y(0) and y(1), the various magnetic properties and the γ/N values vary monotonically with N, whereas for singlet DPAs, the shielding, the magnetizability, and the γ/N values exhibit extrema near N = 8 due to the appearance of transversal spin polarization in the middle six-membered rings in addition to the longitudinal spin polarization between the terminal five-membered rings. Moreover, it is shown that for singlet DPAs the longitudinal spin polarization (characterized by y(0)) is associated with the antiaromaticity (N ≤ 3) and the slight- or non-aromaticity (N ≥ 4) of the terminal five-membered rings, whereas the appearance of transversal spin-polarization (characterized by y(1)) is associated with the decrease in the aromaticity in the inner six-membered rings as shown for large PAs. Therefore, the exceptional behaviors in singlet DPAs for small N (N < 9) are caused by the increase in diradical character y(0) correlated with the anti-aromaticity or the slight-/non-aromaticity of terminal rings and the corresponding emergence of a global aromatic character. Such a relationship between the aromaticity/antiaromaticity and the diradical character is useful for designing real open-shell NLO molecules through the control of their diradical characters.     

Second hyperpolarizabilities (gamma) of bisimidazole and bistriazole benzenes: diradical character, charged state, and spin state dependences

The second hyperpolarizabilities of bisimidazole- and bistriazole-benzene compounds have been calculated at different levels of approximation to unravel the effects of diradical character as well as of charge and spin multiplicity. The largest second hyperpolarizabilities are associated with intermediate diradical character, provided positive charging does not compensate for this effect. For the neutral diradical bisimidazole compound, the singlet diradical species possesses a second hyperpolarizability two to three times larger than the corresponding triplet, demonstrating the possibility of spin state control of the third-order NLO responses for diradical species.     

Second hyperpolarizabilities of singlet polycyclic diphenalenyl radicals: effects of the nature of the central heterocyclic ring and substitution to diphenalenyl rings

Adopting density functional theory and a hybrid exchange-correlation functional, the relationship between the second hyperpolarizability (gamma) and the diradical character has been investigated for diphenalenyl-based compounds containing different heterocyclic five-membered central rings (C(4)H(4)X, where X = NH, PH, O, S, CH(2), SiH(2), BH, GaH, C=O, C=S, and C=Se) or substituted by donor (NH(2))/acceptor(NO(2)) groups. It turns out that these structural modifications can tune the diradical character from 0.0 to 0.968 and lead to variations of gamma over more than 1 order of magnitude, demonstrating the controllability of gamma in this family of compounds. In particular, when the central ring is strongly aromatic, the diradical character is larger than 0.7, which is associated with pretty large gamma values except for almost the pure diradical case (y approximately 1). On the other hand, when the aromaticity decreases--or the antiaromaticity increases--the diradical character and the second hyperpolarizability get smaller. These relationships are correlated to structural (bond length alternation) and charge distribution (charge transfer between the phenalenyl rings and the central ring) properties, which account for the relative importance of the resonance diradical, zwitterionic, and quinoid forms. Therefore, the diradical character and the second hyperpolarizability can be controlled by the aromaticity of the ring while the paradigm of the enhancement of gamma for intermediate diradical character is globally verified. Then, upon introducing donor groups, the zwitterionic character increases, leading to closed-shell species and small second hyperpolarizabilities. In the case of substitution by acceptor groups, the charge transfer is reduced but the diradical character and the second hyperpolarizability hardly changes.     

DFT study on singlet diradical character of zethrenes

The diradical character of zethrenes was investigated using a symmetry-broken UB3LYP/6-311G(d,p) method. The number of hexagons in the investigated molecules ranges from 6 to 12. It was found that all zethrenes are singlet diradicals, whose diradical character increases with the increasing size of the molecules. A singlet diradical structure provides a possibility for an electron pair to occupy different parts of space, and allows for achieving aromatic stabilization. It can be predicted, on the basis of the singlet-triplet values, that even higher zethrenes will be singlet, but not triplet molecules.     

The diradical character of polyacenequinododimethides

Abstract  

An electronic structure study of singlet and triplet states of two series of polyacenequinododimethides was performed using the B3LYP method. It was found that the ground state of all examined polyacenequinododimethides is a singlet with significant diradical character. The diradical character of the compounds under investigation was estimated using the unrestricted symmetry-broken and complete active space methods. It was shown that polyacene-2,3-quinododimethides have more pronounced diradical character than polyacene-2,x-quinododimethides. The diradical character of polyacene-2,x-quinododimethides monotonically increases with their increasing molecular size. Within the series of polyacene-2,3-quinododimethides the diradical character is not a monotonic function of the number of hexagons. It was found that pentacene-2,3-quinododimethide has the most pronounced diradical character in this series. It can be predicted on the basis of the singlet–triplet gap values that even higher polyacenequinododimethides will be singlet, but not triplet molecules.     

Giant electric field effect on the second hyperpolarizability of symmetric singlet diradical molecules

This contribution reveals the effects of a static electric field on the static second hyperpolarizability γ of symmetric singlet diradical molecules using the valence configuration interaction scheme. It is found that under the effect of a field, the component of γ along the axis joining the two radical sites can be gigantically (approximately two to three orders) enhanced for symmetric diradicals having intermediate diradical characters with respect to those of closed-shell and pure diradical molecules in the absence of a field. Moreover, this electric field enhancement of γ increases as a function of the diradical character. These results and their analysis propose therefore a new strategy to design materials with exceptional nonlinear optical responses.     

Theoretical evidence for the singlet diradical character of square planar nickel complexes containing two o-semiquinonato type ligands

Density functional theory and complete active space self-consistent field computations are applied to elucidate the singlet diradical character of square planar, diamagnetic nickel complexes that contain two bidentate ligands derived from o-catecholates, o-phenylenediamines, o-benzodithiolates, o-aminophenolates, and o-aminothiophenolates. In the density functional framework, the singlet diradical character is discussed within the broken symmetry formalism. The singlet-triplet energy gaps, the energy gained from symmetry breaking, the spin distribution in the lowest triplet state, and the form of the magnetic orbitals are applied as indicators for the singlet diradical character. Moreover, a new index for the diradical character is proposed that is based on symmetry breaking. All symmetry breaking criteria show that the complexes obtained from o-catecholates and o-benzodithiolates have the largest and the smallest singlet diradical character, respectively. The singlet diradical character should be intermediate for the complexes derived from o-phenylenediamines, o-aminophenolates, and o-aminothiophenolates. The diradical character of all complexes suggests the presence of Ni(II) central atoms. This is also indicated by the d-populations computed by means of the natural population analysis.     

Oligoacenes: theoretical prediction of open-shell singlet diradical ground states

A series of oligoacenes from benzene to decacene were studied computationally with DFT and CASSCF methods. In contrast to the common view that acenes are closed-shell systems or may have a triplet ground state, these results offer the first theoretical predictions for the singlet ground state and diradical character for oligoacenes. The nature of the ground states of these molecules arises from the disjoint nature of the NBMOs that are singly occupied in the diradical.     

Dimerizations of nitrile oxides to furoxans are stepwise via dinitrosoalkene diradicals: a density functional theory study

Density functional theory calculations at the B3LYP/6-31G* level on the dimerization reactions of acetonitrile oxide and para-chlorobenzonitrile oxide to form furoxans indicate that these processes are stepwise involving dinitrosoalkene intermediates that have considerable diradical character. The rate-determining steps for these two reactions correspond to C-C bond formation. The retardation of dimerization in aromatic nitrile oxides arises from the interruption of conjugation between the nitrile oxide and aryl groups in the C-C bond formation step. The present study also suggests that the isomerization of single-ring furoxans occurs via a diradical intermediate mechanism.     

Enhancement of second hyperpolarizabilities in open-shell singlet slipped-stack dimers composed of square planar nickel complexes involving o-semiquinonato type ligands

Using the spin-unrestricted hybrid density functional theory method, we have investigated the intermolecular interaction effects on the longitudinal static second hyperpolarizability (γ) of open-shell singlet slipped-stack dimers composed of singlet diradical square planar nickel complexes involving o-semiquinonato type ligands, Ni(o-C(6)H(4)X(2))(2) (where X = O, NH, S, Se, PH). For comparison, we have also examined the γ values of a closed-shell singlet slipped-stack dimer composed of closed-shell monomers Ni[o-C(6)H(4)S(NH(2))](2). It is found that for interplanar distance ranging between 3.0 and 5.0 ? the slipped-stack dimers with intermediate monomer diradical characters exhibit larger γ values per monomer (γ(dimer)/2) than those with large monomer diradical characters or than the closed-shell dimer. These results extend the domain of validity of the relationship found between γ and the diradical character for individual molecules. It also turns out that the ratio R = (γ(dimer)/2)/γ(monomer) increases upon decreasing the interplanar distance and that this increase is larger for intermediate diradical character than for the other cases. These phenomena have been analyzed by considering the γ density distributions of the dimers, demonstrating a significant field-induced third-order charge transfer between the monomers in the case of intermediate diradical character. The present results indicate that open-shell singlet slipped-stack aggregates composed of monomers with intermediate diradical characters constitute another mean for achieving highly efficient and tunable third-order nonlinear optical materials.     

Triplet ground state derivative of aza-m-xylylene diradical with large singlet-triplet energy gap

Organic molecules with a strong preference for triplet ground states, in which the triplet state is below the lowest singlet state by ≥10 kcal/mol, are typically short-lived and mostly detected as reactive intermediates. We now report a triplet ground state derivative of aza-m-xylylene diradical with a large singlet-triplet energy gap (ΔE(ST)) of ～10 kcal/mol, which is comparable to ΔE(ST) for the well-known reactive intermediate m-xylylene diradical. The aminyl diradical persists in solution at room temperature on the time scale of minutes.     

Full configuration interaction calculations of the second hyperpolarizabilities of the H4 model compound: summation-over-states analysis and interplay with diradical characters

The second hyperpolarizability (γ) of the one-dimensional H(4) model compound has been calculated at the full configuration interaction level to describe its relationships with the diradical characters y(i) [the occupation numbers of the lowest unoccupied natural orbital (LUNO) + i] and the geometry. It is found that the system with intermediate y(0) ( = 0.527) and small y(1) ( = 0.178) exhibits the largest γ value [enhanced by a factor of 9 compared to that of a nearly closed-shell H(4) analog (y(0) = 0.099, y(1) = 0.029)], where both the outer H-H distances are slightly larger than the inner one. These results provide a molecular design guideline for enhancing and controlling the third-order nonlinear optical properties of singlet multiradical linear molecular systems such as multiradical organic aggregates, supermolecular systems, and extended metal atom chains.     

One-dimensional alkylate-bridged Würster's blue-based diradical dications

By using weakly coordinating anions we succeeded in the stabilization and isolation of two Würster's blue-based diradicaloid dications with saturated spacers. Their geometries and electronic structures were investigated by various experiments in conjunction with DFT calculations. Both one-dimensional alkylate-bridged dications show considerable diradical character with spacer-dependent singlet-triplet energy gaps. One of them displays a much enhanced diradical character and could basically be viewed as a pure diradical with degeneracy of singlet and triplet states.     

Mechanism of oxidation of α,β-unsaturated thiones by singlet oxygen

Photo-oxidation of α,β-unsaturated thiones yields the corresponding ketones as the only product. Studies carried out on three systems, namely thioketones, α,β-unsaturated thiones and thioketenes, have revealed that there exists a similarity in their mechanism of oxidation. It has been suggested that the thiocarbonyl chromophore is the site of attack by singlet oxygen in α,β-unsaturated thiones and that the adjacent C-C double bond is inert under these conditions. Absence of sulphine during the oxidation of α,β-unsaturated thiones is attributed to the electronic factors operating on the zwitterionic/diradical intermediate. While α,β-unsaturated ketones are poorly reactive, α,β-unsaturated thiones are highly reactive toward singlet oxygen.     

Aromaticity of four-membered-ring 6pi-electron systems: N2S2 and Li2C4H4

N(2)S(2) is a four-membered-ring system with 6pi electrons. While earlier proposals considered N(2)S(2) to be aromatic, recent electronic structure calculations claimed that N(2)S(2) is a singlet diradical. Our careful reexamination does not support this assertion. N(2)S(2) is closed shell and aromatic since it satisfies all three generally accepted criteria for aromaticity: energetic (stability), structural (planarity with equal bond lengths), and magnetic (negative nucleus-independent chemical shift due to the pi electrons). These characteristics as well as the electronic structure of N(2)S(2) are compared with those for an isoelectronic pi system, Li(2)C(4)H(4), motivated by theoretical and recent experimental investigations that confirmed its aromaticity. However, N(2)S(2) and Li(2)C(4)H(4) are both essentially 2pi-electron aromatic systems with a formal N-S (C-C) bond order of 1.25 even though they both have 6pi electrons. This is because four of the six pi electrons occupy the nonbonding pi HOMOs and only two electrons participate effectively in the aromatic stabilization. However, wave function analysis shows relatively large LUMO occupation numbers; this antibonding effect can be said to reduce the aromatic character by approximately 7% and 4% for N(2)S(2) and Li(2)C(4)H(4), respectively.     

Structure and chemistry of 1-silafluorenyl dianion, its derivatives, and an organosilicon diradical dianion.

1-Silafluorene dianion was synthesized by potassium reduction of 1,1-dichloro-1-silafluorene in refluxing THF. The X-ray structure of 1,1-dipotassio-1-silafluorene (3b) shows C-C bond length equalization in the five-membered silole ring and C-C bond length alternation in the six-membered benzene rings, indicating aromatic delocalization of electrons in the silole ring. The downfield (29)Si chemical shift at 29.0 ppm and theoretical calculations also support electron delocalization in the silole ring of 3b. Dianion salt 3b underwent nucleophilic reactions with Me(3)SiCl and EtBr to form the corresponding disubstituted products. Benzaldehyde underwent reductive coupling in the presence of 3b. Slow oxidation of 3b yielded 1,1'-dipotassio-1,1'-bis(silafluorene) (16). The X-ray structure and (29)Si chemical shift (-38.0 ppm) of 16 indicate localized negative charges at the silicon atoms and no aromatic character. Heating a DME/hexane solution of 3b in the presence of 18-crown-6 led to a novel diradical dianion salt.