Third-order nonlinear optical properties of open-shell supermolecular systems composed of acetylene linked phenalenyl radicals

The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, γ, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger γ values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of γ and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 ?), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to γ. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.     

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.     

Enhancement of the third-order nonlinear optical properties in open-shell singlet transition-metal dinuclear systems: effects of the group, of the period, and of the charge of the metal atom

Metal-metal multiply bonded complexes in their singlet state have been predicted to form a novel class of "σ-dominant" third-order nonlinear optical compounds based on the results of dichromium(II) and dimolybdenum(II) systems (H. Fukui et al. J. Phys. Chem. Lett.2011, 2, 2063) whose second hyperpolarizabilities (γ) are enhanced by the contribution of the dσ electrons with an intermediate diradical character. In this study, using the spin-unrestricted coupled-cluster method with singles and doubles as well as with perturbative triples, we investigate the dependences of γ on the group and on the period of the transition metals as well as on their atomic charges in several open-shell singlet dimetallic systems. A significant enhancement of γ is observed in those dimetallic systems composed of (i) transition metals with a small group number, (ii) transition metals with a large periodic number, and (iii) transition metals with a small positive charge. From the decomposition of the γ values into the contributions of dσ, dπ, and dδ electrons, the γ enhancements are shown to originate from the dσ contribution, because it corresponds to the intermediate diradical character region. Furthermore, the amplitude of dσ contribution turns out to be related to the size of the d(z(2)) atomic orbital of the transition metal, which accounts for the dependence of γ on the group, on the period, and on the charge of the metal atoms. These dependences provide a guideline for an effective molecular design of highly efficient third-order nonlinear optical (NLO) systems based on the metal-metal bonded systems.     

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.     

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.     

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.     

Second hyperpolarizability of phenalenyl radical system involving acetylene π-conjugated bridge

The static second hyperpolarizability (γ) of a singlet diradical system involving phenalenyl radicals linked with acetylene π-conjugated bridge, BPLE, is investigated as well as reference closed-shell systems, BPRY1 and BPRY2, by the hybrid density functional theory method. The γ value of BPLE with intermediate diradical character is shown to be about four times as large as that of BPRY1 with similar π-conjugation length and to be about twice as large as that of BPRY2 with longer π-conjugation length. This feature is in agreement with our prediction that the molecules with intermediate diradical characters enhance γ values compared to the closed-shell molecules.     

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.     

Phenyloxenium ions: more like phenylnitrenium ions than isoelectronic phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.     

Matrix isolation and density functional theory study of bis(trifluoromethyl)dioxodiazine: a photodimer of trifluoronitrosomethane

Trifluoronitrosomethane (CF3NO) was trapped in rare gas matrixes and irradiated at 633 and 670 nm. The infrared spectra of the postirradiation samples exhibit features consistent with cis and trans conformers of bis(trifluoromethyl)dioxodiazine, a previously uncharacterized species. The concentration dependence of the formation of the dimer is consistent with a mechanism in which monomers trapped in adjacent sites undergo excitation and subsequent reaction. The dimers reversibly form the monomer when irradiated with ultraviolet light. Density functional theory was used to determine the structure of the dimers and predict their infrared and Raman spectra. The predicted vibrational frequencies are in agreement with those observed. A third (skewed) conformation was predicted to have a triplet ground state, but no evidence of this species was observed. All three dimers exhibit significant diradical character, as evidenced by comparatively low N-N and high N-O stretching frequencies. Transition-state calculations predict the dimerization barrier to range from 17.1 (cis) to 35.0 (trans) kJ mol(-1) for the singlet dimers and to be 62.1 kJ mol(-1) for the triplet dimer. This is an example of nitroso dimerization that requires electronic excitation to proceed.     

S-shaped para-Quinodimethane-Embedded Double [6]Helicene and Its Charged Species Showing Open-Shell Diradical Character

Helicenes and extended helical π-conjugated compounds have been widely studied, but most of the systems contain only aromatic benzene or heterocyclic rings, showing local aromatic character. Herein, new S-shaped double [6]helicene 1 , which has two embedded para-quinodimethane (p-QDM) units, is reported. Due to the existence of a proaromatic quinoidal substructure, it has open-shell diradical character. Its model compound, C-shaped single [6]helicene 2 containing one p-QDM unit, was also synthesized and compared. Their ground-state structures and electronic properties were systematically studied by a combination of various experimental methods assisted by theoretical calculations. Compound 1 has a double-helical structure in the crystal, with the two terminal [6]helicene units bent in opposite directions (i.e., anti form). However, an anti/syn isomerization process with a moderate interconversion energy barrier was observed on the NMR timescale. Compound 1 shows amphoteric redox behavior. It also exhibits open-shell diradical character (y₀=12.1 %) and a small singlet–triplet gap. On the other hand, compound 2 has a typical closed-shell nature. The dication and dianion of 1 also show open-shell diradical character. The dianion of 2 and the tetraanion of 1 exhibit similar electronic structures to their respective isoelectronic structures, that is, [6]helicene and a double [6]helicene. This work provides some insights into the design and synthesis of stable helical π systems with open-shell diradical character and magnetic activity.     

Open-shell singlet character of stable derivatives of nonacene, hexacene and teranthene

The electronic ground states of the recently synthesized stable nonacene derivatives (J. Am. Chem. Soc. 2010, 132, 1261) are open-shell singlets with a polyradical nature instead of closed-shell singlets as originally assumed, according to the unrestricted broken spin-symmetry density functional theory (UBS-DFT) computations (at B3LYP/6-31G*). It is the bulky protecting groups, not the transfer from the open-shell singlet to closed-shell singlet ground state, that stabilizes these longest characterized acenes. Similar analyses also confirmed the open-shell singlet character of the hexacene and teranthene derivatives.     

Diradical Character Tuning for the Third‐Order Nonlinear Optical Properties of Quinoidal Oligothiophenes by Introducing Thiophene‐S,S‐dioxide Rings

To create a design guideline for efficient third‐order nonlinear optical (NLO) molecules, the chain‐length (n) dependences of the diradical character y and the longitudinal second hyperpolarizability γ of quinoidal oligothiophenes (QTs), from monomers to octamers, involving thiophene‐S,S‐dioxide rings are investigated by using the density functional theory method. It turns out that the diradical character of the modified QTs is reduced as compared to those of the pristine QTs. By introducing an appropriate number of oxidized rings into the QT framework, intermediate y values can be achieved even in the systems with large values of n, in which the pristine QTs are predicted to have pure diradical character. Such intermediate diradical oligomers are shown to exhibit enhanced γ values as compared to the pristine QTs with the same value for n. From the calculation results, the introduction of the optimal number of thiophene‐S,S‐dioxide rings is predicted to be an efficient chemical modification for optimizing the third‐order NLO properties of open‐shell QTs through tuning the diradical characters.     

Local aromaticity of the lowest-lying singlet States of [N]acenes (N = 6-9)

The local aromaticities of the six-membered rings in the two lowest-lying singlet states of [n]acenes (n = 6-9) have been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. Important differences between the local aromaticities of the closed-shell and diradical singlet electronic states are found. Thus, while the inner rings have the largest aromatic character in the closed-shell singlet states, the outer rings become the most aromatic for the diradical singlet states.     

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.     

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.     

A Highly Stable Organic Luminescent Diradical

It is very challenging to obtain stable room-temperature luminescent open-shell singlet diradicals. Herein we report the first stable Müller's hydrocarbon TTM-PhTTM with luminescent properties. Variable-temperature electron paramagnetic resonance spectroscopy measurements and theoretical calculations show that TTM-PhTTM has an open-shell singlet ground state with a diradical character of 90 %. Because of a small singlet-triplet energy gap, the open-shell singlet ground state can be thermally excited to a triplet state. TTM-PhTTM shows room-temperature deep-red emission in various solutions. Unusually high stability of TTM-PhTTM was also observed owing to effective steric hindrance and spin delocalization. Our results are beneficial to the rational design and discovery of more stable luminescent diradical materials.     

Carbazolyl nitrenium ion: electron configuration and antiaromaticity assessed by laser flash photolysis, trapping rate constants, product analysis, and computational studies

Laser flash photolysis of 1-(carbazol-9-yl)-2,4,6-trimethylpyridinium tetrafluoroborate generates the carbazolyl nitrenium ion (tau = 333 ns, kobs = 3.0 x 106 M-1s-1) having absorption bands at 570 and 620 nm in CH3CN. The nitrenium ion is found to have reactivity comparable to structurally similar closed-shell diarylnitrenium ions, but spectroscopic evidence favors an open-shell singlet diradical assignment for the observed nitrenium ion. The carbazolyl nitrenium ion is also more reactive than diarylnitrenium ions as a likely result of antiaromatic character. Ab initio and hybrid DFT calculations were performed to address the degree of antiaromaticity in this and similar nitrenium ions through analysis of optimized geometries, nucleus independent chemical shifts, and isodesmic reactions.     

双咪唑苯和双三唑苯及其衍生物非线性光学性质的密度泛函研究

采用密度泛函理论(DFT)的UB3LYP(B3LYP)/6-31+G**方法对双咪唑苯和双三咪唑苯双自由基及其衍生物几何结构进行优化,并结合有限场(FF)方法计算这些体系的非线性光学(NLO)系数.结果表明,引入给、受体取代基都能使体系的极化率α和二阶超极化率γ增大.在双自由基体系中,引入给体NH2的α和γ值大于引入受体NO2的值,与闭壳层体系中结果相反.分析自由基成分和电荷对体系的二阶超极化率γ影响的结果表明,处于中间双自由基成分的分子比相似共轭性的闭壳层分子有更大的二阶超极化率γ;带电荷的双自由基体系引入给、受体之后,与中性自由基体系相比具有更大的二阶超极化率γ.     

Definitive evidence for the contribution of biradical character in a closed-shell molecule, derivative of 1,4-bis-(4,5-diphenylimidazol-2-ylidene)cyclohexa-2,5-diene

This study provides conclusive proof that the thermally excited open-shell state with biradical character is contributing to the ground state of a closed-shell molecule, tF-BDPI-2Y, where four hydrogen atoms at the central phenylene ring are substituted with four fluorine atoms of 1,4-bis-(4,5-diphenylimidazol-2-ylidene)cyclohexa-2,5-diene (BDPI-2Y). A small increase in the population of biradical species of tF-BDPI-2Y results in the formation of the dimer form by the radical recombination reaction. Controlling the equilibrium between a closed-shell diamagnetic-quinoid state and an open-shell paramagnetic-biradical state will provide significant progress in the field of pi-conjugated delocalized biradical chemistry.