Open‐Shell Characters and Second Hyperpolarizabilities of One‐Dimensional Graphene Nanoflakes Composed of Trigonal Graphene Units

The impact of topology on the open‐shell characters and the second hyperpolarizabilities (γ) has been addressed for one‐dimensional graphene nanoflakes (GNFs) composed of the smallest trigonal graphene (phenalenyl) units. The main results are: 1) These GNFs show not only diradical but also multiradical characters when increasing the number of linked units. 2) GNFs composed of an equivalent number of units can exhibit a wide range of open‐shell characters—from nearly closed‐shell to pure multiradical characters—depending on the linking pattern of the trigonal units. 3) This wide variation in open‐shell characters is explained by their resonance structures and/or by their (HOMO?i)?(LUMO+i) gaps deduced from the orbital correlations. 4) The change in the linking structure of the units can effectively control their open‐shell characters as well as their γ values, of which the longitudinal components are significantly enhanced for the singlet GNFs having intermediate open‐shell characters. 5) Singlet alternately linked (AL) systems present intermediate multiradical characters even in the case of a large number of units, which creates a significant enhancement of γ with increasing the size, whereas nonalternately linked (NAL) systems, which present pure multiradical characters, possess much smaller γ values. Finally 6) by switching from the singlet to the highest spin states, the γ values of NAL systems hardly change, whereas those of AL systems exhibit large reductions. These fascinating structure–property relationships between the topology of the GNFs, their open‐shell characters, and their γ values not only deepen the understanding of open‐shell characters of GNFs but aim also at stimulating further design studies to achieve giant NLO responses based on open‐shell graphene‐like materials.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 Structural Stability and Nonlinear Optical Properties of Non-conjugated Carbon and Nitrogen Diradical Molecules

The geometrical structures and stability of non-conjugated C5H10 and C3H8N2 singlet and triplet diradical molecules have been investigated at the UCCSD/6-311g** level. The effects of molecular structure, radical position, amount of Hartree Hork (HF) exchange and spin multiplicity on the nonlinear optical (NLO) coefficients have been also investigated. The reliable UCCSD results show that the triplets of all diradical molecules are more stable compared to their singlet analogues. In addition, the α s and β tot values of C5H10 and C3H8N2 triplet diradical mo-lecules have been investigated by the UBHandHLYP, UB3LYP, UBLYP, UHF and UCCSD methods. The investigation shows that the variations in α s and β tot values are closely connected to the amount of HF exchange. The increasing amount of HF exchange results in monotonic decreases in α s and β tot values, while the α s and β totvalues of singlet diradical molecules and the γ s of C5H10 and C3H8N2 singlet and triplet diradical molecules have been studied by the UBHandHLYP method. The results illustrate that the NLO coefficients for our studied non-conjugated carbon and nitrogen diradical species can be tuned by molecular structure, radical position and spin multiplicity, which are very significant for designing NLO materials.     

Elementary radical formation and conversion processes in γ-irradiated polyvinylchloride

Elementary processes of γ-irradiated polyvinylchloride (PVC) have been investigated by both electron spin resonance (ESR) and optical absorption measurements. On irradiating PVC film with γ rays at ?196°C, alkyl-type radicals are produced. When the PVC film is warmed to room temperature, the radicals convert to polyenyl type. γ Irradiation of PVC film containing biphenyl (Ph₂) or pyrene (Py) at ?196°C yields the corresponding radical cation. The relative ESR peak heights of the radicals decrease and the G values for the formation of cation radicals increase with increasing additive concentrations. These facts indicate that energy is transferred from the precursor of the radicals to the additive. In the case of PVC film containing Py, the Py cation radical decreases and the cyclohexadienyl-type radical from Py is produced by thermal annealing. A possible mechanism for radical formation and conversion is proposed.     

Theoretical study on nonlinear optical properties of metalloporphyrin using elongation method

A quantum-chemical analysis of the central metal effect on the (hyper)polarizabilities of meso-meso-linked metalloporphyrin (MP) oligomers was carried out using elongation finite-field (ELG-FF) method. It is found that meso-meso-linked MPs exhibit evident evolution of the third-order nonlinear optical (NLO) response (γ) along with an increasing number of porphyrin units N. The order of γ values is as following: γ_Mg > γ_Zn > γ_Ni. In contrast to the polarizability, the γ values of meso-meso-linked MPs are sensitive to the metals, that is, the nature of the metal can influence the third-order NLO response of MPs. However, the band structures for three MPs are similar to each other, and the differences on the band gaps of three MPs are very small. The local density of states (LDOSs) shows that the central metal gives the significant contributions for unoccupied bands in meso-meso-linked MPs.     

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.     

Pulse radiolysis studies of poly(methyl methacrylate) containing pyrene

A pulse radiolysis study of poly(methyl methacrylate) in the presence of pyrene has been carried out in the temperature range 100–295 K. The concentration of pyrene was changed from 10⁻³ to 10⁻¹ mol dm⁻³. The absorption/emission spectra and kinetics of solute excited states and solute radical ions were investigated. It was found that pyrene excited states were formed as a result of their radical ion recombination in a time scale up to seconds. The decay of solute radical ions was influenced by photobleaching and can be described by a time-dependent rate constant. The activation energy of Py ions decay was temperature dependent and was equal to 35.7 and 1.2 kJ/mol for temperatures >T_γ and <T_γ, respectively, where T_γ ∼ 175 K represented the transition temperature responsible for γ-relaxation. The reaction mechanism was proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1209–1215, 1998     

Radical cyclization of α-bromo aluminum acetals onto alkenes and alkynes (radic[Al] process): a simple access to γ-lactols and 4-methylene-γ-lactols

An efficient preparation of γ-lactols and methylene-γ-lactols is described. Highly acid-sensitive lactols are prepared in a concise manner by using a radical cyclization of aluminum acetals. The precursors for the radical reactions are readily prepared from allyl or propargyl alcohols and α-bromo acids. Functionalization of the resulting γ-lactols and methylene-γ-lactols can be achieved following isolation, leading to synthetically useful building blocks, such as 1,4-diols, 1,4-dienes, γ-lactones, and polysubstituted tetrahydrofurans.     

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

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 C₂P₂ 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.     

CASCI-DFT study of the phenalenyl radical system

We present ab initio complete-active-space configuration interaction (CASCI) density functional theory (DFT) study of the phenalenyl radical systems. Our approach employed in this study is based on the assumption that one-electron per one phenalenyl unit is responsible for magnetic properties of the phenalenyl radical dimeric compounds and that the residual correlation effects can be covered by DFT correlation potential for CASCI[2,2] wavefunction. The effective exchange integrals and lowest-lying excited energies of several phenalenyl dimeric compounds are calculated by CASCI[2,2]-DFT method. The implication of the computational results are discussed in relation with those of spin unrestricted Hartree–Fock (UHF), hybrid DFT, and pure DFT, and the experimental ones.     

Synthesis of β,γ-disubstituted-γ-lactones through a Johnson–Claisen rearrangement: a short route to xylobovide,nor-canadensolide,canadensolide, sporothriolide and santolinolide

The Johnson–Claisen rearrangement of allyl alcohols with chiral vicinal diol functionality was employed to access chiral β,γ-disubstituted-γ-lactones in high enantio- and diastereoselectivity. These were efficiently converted into nor-canadensolide, the advanced γ-(lactone–lactol) intermediate for xylobovide, canadensolide and sporothriolide and the lactone moiety of the santolinolides.