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The origin of the diradical character dependence of the second hyperpolarizability (γ) of neutral singlet diradical systems is clarified based on the perturbation formula of γ using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of γ 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 γ values can be controlled by the diradical character in addition to the conjugation length. [ABSTRACT FROM AUTHOR]

Abstract: Tunability of the open‐shell character, charge asymmetry, and third‐order nonlinear optical (NLO) properties of covalently linked (hetero)phenalenyl dimers are investigated by using the density functional theory method. By changing the molecular species X and substitution position (i, j) for the linker part, a variety of intermonomer distances R and relative alignments between the phenalenyl dimers can be realized from the geometry optimizations, resulting in a wide‐range tuning of diradical character y and charge asymmetry. It is found that the static second hyperpolarizabilities along the stacking direction, γyyyy, are one‐order enhanced for phenalenyl dimer systems exhibiting intermediate y, a feature that is in good agreement with the “y–γ correlation”. By replacing the central carbon atoms of the phenalenyl rings with a boron or a nitrogen, we have also designed covalently linked heterophenalenyl dimers. The introduction of such a charge asymmetry to the open‐shell systems, which leads to closed‐shell ionic ground states, is found to further enhance the γyyyy values of the systems having longer intermonomer distance R with intermediate ionic character, that is, charge asymmetry. The present results demonstrate a promising potential of covalently linked NLO dimers with intermediate open‐shell/ionic characters as a new building block of highly efficient NLO systems. [ABSTRACT FROM AUTHOR]

The diradical characters ( y) and third-order nonlinear optical (NLO) properties of open-shell quinoidal oligothiophene derivatives with phenoxyl groups, and the corresponding reduced (hydrogenated)-state oligomers, are investigated by using the broken-symmetry density functional theory method. The oxidized (dehydrogenated) states are predicted to have an open-shell singlet ground state and their y values increase with the number of units. Static second hyperpolarizabilities ( γ) of the open-shell oligomers with intermediate y are shown to be enhanced significantly compared with those of the closed-shell analogues. Furthermore, owing to the effective diradical distances, the γ values of open-shell oligomers are found to exceed that of s-indaceno[1,2,3- cd;5,6,7- c′ d′]diphenalene, which is known as an organic molecule with the largest two-photon absorption cross-section in this size of the pure hydrocarbons. This feature extends the range of efficient open-shell third-order NLO materials to a novel class of one-dimensional conjugated oligomers with redox-based high tunability of third-order NLO properties. [ABSTRACT FROM AUTHOR]

Open-shell singlet nature, aromaticity, and second hyperpolarizabilities of two kinds of curved π-conjugated fragments of C60 fullerene, called C60 flakes, together with their corresponding planar analogues are theoretically investigated. It is found that one curved system, A-1, exhibits open-shell singlet nature, while the other structure, B-1, and the two corresponding planar systems possess a closed-shell ground state. The variation of the open-shell singlet nature is explained by the number of Clar's sextets in the resonance structures, which is associated with the local aromaticity, as quantified by the NICS0 values. The calculated orientationally averaged second hyperpolarizabilities show that the open-shell singlet system A-1 exhibits the best performance, and that the other curved system B-1 is the worst among the four C60 flakes, whereas all systems exhibit better performance than the original spherical C60 system. This tendency suggests that a lower dimensionality in the π-conjugated structure is beneficial to the construction of efficient nonlinear optical molecules. The present results not only show that the open-shell singlet system A-1 is a performant nonlinear optical molecule, but they also contribute to a deeper understanding of the electronic structure of curved π-conjugated molecules. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We report a novel type of organic–inorganic hybrid material with rare two-dimensional nonlinear optical (NLO) properties. The density functional theory (DFT) calculations combined with the finite-field (FF) method show that the designed molecules (6,9 organo-derivatives of B10H14) could carry the characteristic NLO properties of both organic and inorganic materials. Interestingly, due to their unique V-shaped structures, they have large off-diagonal first hyperpolarizability tensors or nonlinear anisotropy, which is an advantage in their practical applications over conventional donor–π-acceptor (D–π-A) NLO-phores. The systematic substitutions of terminal donor/acceptor groups as well as the extension of π-conjugation along the V-shape in these derivatives have been evaluated to guide a purpose-oriented synthesis of NLO material. All the systems in the present study have been categorized into Set-I and Set-II with D–π-A–π-D and A–π-D–π-A configurations, respectively. These designed derivatives show large amplitudes of βz values. For example, systems 3N (6,9-[(N=C=Ph–NO2)2]-B10H12) and 4N (6,9-[((N=C=Ph)2-NO2)2]-B10H12) have βz amplitudes as large as 34.16 and 276.91 × 103 a.u. which are 380 and 3000 times larger than those of a typical NLO molecule of urea, respectively. Remarkably, the substitution of nitrogen atoms with 6,9 hydrogen atoms in decaborane is shown to cause a lone pair back donation to vacant p orbitals of 6,9 boron atoms of the decaborane basket. This p orbital overlapping verticalizes the V-arms of the decaborane derivatives and boosts their nonlinear anisotropies due to their larger off-diagonal tensor components. The nonlinear anisotropy values are significantly larger, ranging from 1 (minimum in system 1) to 31.90 (maximum in system 3A) due to their unique V-shape. Comparison of their efficiencies with standard molecules demonstrates that our designed organic–inorganic hybrid molecules have significant potential as excellent candidates for NLO applications. [ABSTRACT FROM AUTHOR]

From the viewpoint of 'diradical character,' referred to as 'diradicalology,' we investigate the second hyperpolarizability γ-the molecular third-order nonlinear optical (NLO) property-of one-dimensional supermolecular systems composed of acetylene-linked phenalenyl/pyrene rings using long-range corrected spin-unrestricted density functional theory. It turns out that the pyrene-based superpolyenes (Py- n) behave like closed-shell systems, whereas phenalenyl-based superpolyenes (Ph1- n and Ph2- n) have different diradical characters depending on the linked form, that is, Ph1- n and Ph2- n have intermediate and pure diradical characters, respectively. In comparison with Py- n and Ph2- n, the longitudinal γ of Ph1- n is significantly larger, and it displays larger enhancement as a function of system size. Substitutions to the terminal rings by donor (NH2) and acceptor (NO2) groups further enhance γ in Ph1- n, more than in Ph2- n and Py- n. These results are in agreement with the structure-property relationships derived for open-shell NLO systems with symmetric and asymmetric charge distributions (Nakano et al., J. Chem. Phys. 2010, 133, 154302). © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Using the long-range corrected spin-unrestricted density functional theory method, the impact of antidot structure on the open-shell character and the second hyperpolarizability (γ) of graphene nanoflakes (GNFs) has been investigated for rectangular GNFs with and without antidot structure, referred to as antidot and perfect GNFs, respectively. It is found that the two GNFs exhibit different multiradical characters; the antidot GNF shows intermediate open-shell character in contrast to the perfect GNF presenting nearly pure tetraradical character. This antidot structure dependence of open-shell character can be explained in terms of their natural orbital distributions. Such difference in open-shell characters affects their γ values; the γ of the antidot GNF is about 1.7 times larger than that of the perfect GNF, the feature of which is in agreement with our previous results on the diradical character dependence of γ. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

A long-range corrected spin-unrestricted density functional theory (LC-UDFT) approach has been used to investigate the diradical character ( y i) and third-order nonlinear optical properties of linear/cyclic [ N]acenes and [ N]phenylenes in their ground states, where N is the number of benzene rings in each linear and cyclic configuration. It has been found that linear and cyclic acenes with N = 5-10 show singlet diradical characters, while linear and cyclic phenylenes with equivalent number of benzene rings have closed-shell configurations. The amplitudes of third-order nonlinear optical polarizability (γ zzzz) for open-shell linear/cyclic acenes are larger especially in intermediate range of diradical character than those of closed-shell phenylene counterparts. For example, the γ zzzz values of [5]cyclic acene ( y0 = y1 = 0.320) is 4.89 × 103 a.u. which is about 6 times larger than those of 0.80 × 103 a.u. for closed-shell [5]cyclophenylene. Similarly, γ zzzz value of [5]linear acene is also about 9 times larger than its closed-shell [5]linear phenylene counterpart. Our results show interesting insights into the relationship among the architectures, diradical characters and γ zzzz values of different acenes and phenylenes. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

To reveal new structure-property relationships in the nonlinear optical (NLO) properties of fullerenes that are associated with their open-shell character, we investigated the interplay between the diradical character ( yi) and second hyperpolarizability (longitudinal component, γzzzz) in several fullerenes, including C20, C26, C30, C36, C40, C42, C48, C60, and C70, by using the broken-symmetry density functional theory (DFT; LC-UBLYP ( μ=0.33)/6-31G*//UB3LYP/6-31G*). We found that the large differences between the geometry and topology of fullerenes have a significant effect on the diradical character of each fullerene. On the basis of their different diradical character, these fullerenes were categorized into three groups, that is, closed-shell ( yi=0), intermediate open-shell (0< yi<1), and almost pure open-shell compounds ( yi≅1), which originated from their diverse topological features, as explained by odd-electron-density and spin-density diagrams. For example, we found that closed-shell fullerenes include C20, C60, and C70, whereas fullerenes C26 and C36 and C30, C40, C42, and C48 are pure and intermediate open-shell compounds, respectively. Interestingly, the γzzzz enhancement ratios between C30/ C36 and C40/ C60 are 4.42 and 11.75, respectively, regardless of the smaller π-conjugation size in C30 and C40 than in C36 and C60. Larger γzzzz values were obtained for other fullerenes that had intermediate diradical character, in accordance with our previous valence configuration interaction (VCI) results for the two-site diradical model. The γzzzz density analysis shows that the large positive contributions originate from the large γzzzz density distributions on the right- and left-extended edges of the fullerenes, between which significant spin polarizations (related to their intermediate diradical character) appear within the spin-unrestricted DFT level of theory. [ABSTRACT FROM AUTHOR]

We develop novel calculation and analysis methods forthe dynamicfirst hyperpolarizabilities β [the second-order nonlinear optical(NLO) properties at the molecular level] in the second-harmonic generationbased on the quantum master equation method combined with the ab initiomolecular orbital (MO) configuration interaction method. As examples,we have evaluated off-resonant dynamic β values of donor (NH2)- and/or acceptor (NO2)-substituted benzenes usingthese methods, which are shown to reproduce those by the conventionalsummation-over-states method well. The spatial contributions of electronsto the dynamic β of these systems are also analyzed using thedynamic β density and its partition into the MO contributions.The present results demonstrate the advantage of these methods inunraveling the mechanism of dynamic NLO properties and in buildingthe structure–dynamic NLO property relationships of real molecules. [ABSTRACT FROM AUTHOR]

This contribution firstly elucidates a structure–property relationship in third-order nonlinear optical molecular systems with singlet diradical characters. It turns out that the second hyperpolarizabilities (γ) of the singlet open-shell molecules with intermediate diradical characters are significantly enhanced as compared with those of closed-shell and pure diradical molecules. The hybrid density functional theory method, i.e. UBHandHLYP, is applied to the calculations of γ of dimer models composed of singlet diradical diphenalenyl molecules, which show a remarkable enhancement of γ per monomer as decreasing the intermolecular distance. The second contribution is concerned with a development of ab initio molecular orbital configuration-interaction-based quantum master equation (QME) approach. This is found to provide both coherent processes, e.g. dynamic polarization and exciton (electron–hole pair) recurrence motion, and incoherent processes, e.g. exciton migration, in molecular systems. Using this approach, the electron/hole dynamics for dynamic polarizabilities α(ω) are examined for several π-conjugated linear chain systems, and the structural dependences of α(ω) are elucidated. [ABSTRACT FROM AUTHOR]

In a previous paper we found that the cofacial intermolecular π–π orbital interaction in stacking dimers significantly changes the longitudinal second hyperpolarizability (γ) of the isolated monomer. On the basis of this result, we investigate the longitudinal γ values of π‐conjugated main chains (CnHn+2, 6 ≤ n ≤ 16) interacting in both‐end regions with two small‐size cationic perturbing π‐conjugated molecules, that is, allyl cations (C3H+5). These interacting model systems exhibit remarkable enhancement of γ values as compared with those of isolated main chains in the whole chain‐length region. The γ density analysis reveals that this enhancement is described by the virtual charge transfer between both‐end perturbing molecules via the main chain. The analysis of orbital correlation diagram between the perturbing molecules and main chain molecule also clarifies that such feature of γ density distribution originates in the “weak intermolecular antibondinglike coupling” between the (lowest unoccupied molecular orbital [LUMO], LUMO+1) of cationic perturbing molecules and (highest unoccupied molecular orbital [HOMO], HOMO−1) of main chain molecule. The current result suggests the possibility of novel nano‐size control of nonlinear optical (NLO) properties by adjusting the intermolecular orbital interactions between the main molecule and perturbing molecules. A possible control scheme of longitudinal γ for novel intermolecular interacting NLO systems using modified DNA wires is also proposed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [ABSTRACT FROM AUTHOR]

The Inside Cover picture shows the drastic change in the third ‐ order nonlinear optical properties of a quinoidal oligothiophENe derivative through the redox reactions in which its electronic structure switches betweEN the closed ‐ shell (lower side) and opEN ‐ shell (upper side) states. More details can be found in the Full Paper by R. Kishi, M. Nakano and co ‐ workers on page   506 in Issue 6, 2017 (DOI: 10.1002/opEN.201700083). [ABSTRACT FROM AUTHOR]

Abstract: Using broken-symmetry hybrid density functional theory, we investigate the relationship between the diradical character and the second hyperpolarizabilities, γ, for a trigonal graphene nanoflake (trigonal GNF) and two types of GNFs with rhombic and bow-tie structures composed of two trigonal GNFs. It is shown that the GNF architecture has a large impact on the diradical character and subsequently on γ. In particular, γ of rhombic GNF with intermediate diradical character is found to be more than twice as large as that of bow-tie GNF with nearly pure diradical character. Then, switching from the singlet to triplet state rhombic GNF exhibits a significant reduction of γ. [Copyright &y& Elsevier]

Quantum molecular engineering has been performed to determinethesecond-order nonlinear optical (NLO) properties in different halocomplexes of decaborane (B10H14) and their derivativesusing the density functional theory (DFT) method. These decaboranehalo complexes of X–@B10H14(X = F, Cl, Br, and I) are found to possess noncovalent charge transferinteractions. The static polarizability (α0) andfirst hyperpolarizability (β0) among these complexesincrease by moving down the group from F to I, partly due to the increasein size of their anionic radii and the decrease in their electronaffinities. A two-level approximation has been employed to investigatethe origin of β0values in these halo complexes,which show very consistent results with those by the finite-fieldmethod. Furthermore, in the same line, two experimentally existingcomplexes, I–@B10H14and I–@2,4-I2B10H12, arefound to have considerably large β0values of 2859and 3092 a.u., respectively, which are about three times larger thana prototypical second-order NLO molecule of p-nitroaniline,as reported by Soscun et al. [Int. J. Quantum Chem.2006, 106, 1130–1137]. Besidesthis, the special effects of solvent, counterion, and bottom substitutionshave also been investigated. Interestingly, 2,4-alkali metal-substituteddecaborane iodide complexes show remarkably large second-order NLOresponse with β0amplitude as large as 62436 a.u.for I–@2,4-K2B10H12complex, which are explained in terms of their transition energies,frontier molecular orbitals and electron density difference plots.Thus, the present investigation provides several new comparative insightsinto the second-order NLO properties of halo complexes of decaborane,which possess not only large first hyperpolarizabilities, but alsohigh tunability to get a robustly large second-order NLO responseby alkali metal substitution effects. [ABSTRACT FROM AUTHOR]

Abstract: Using hybrid density functional theory methods, we investigate the second hyperpolarizabilities (γ) of hexagonal shaped finite graphene fragments, which are referred to as hexagonal graphene nanoflakes (HGNFs), with two types of edge shapes: zigzag (Z) and armchair (A) edges. It is found that Z-HGNF, which gives intermediate diradical characters (y), exhibits about 3.3 times larger orthogonal components of γ (γxxxx = γyyyy in this case) than A-HGNF, which gives zero y value (closed-shell system). The γ density analysis reveals that this enhancement originates in the significant contribution of γ densities on edge regions in Z-HGNF. These observations strongly indicate that Z-HGNF is a promising candidate of open-shell singlet NLO systems. [Copyright &y& Elsevier]

Abstract: Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, γ, of square nanographenes presenting different diradical characters are investigated from the viewpoint of open-shell singlet nonlinear optical systems. For nanographenes with intermediate diradical character, the γ component along the armchair edges is enhanced and amounts to about four times the γ component along the zigzag edges, whereas these γ components are of similar amplitudes when the system displays nearly pure diradical character. These observations are in conformity with the diradical character dependence of γ predicted in our previous studies. [Copyright &y& Elsevier]