Theoretical Study on Third-Order Nonlinear Optical Properties for One-Hole-Doped Diradicaloids.

We investigate the relationships between open-shell character and longitudinal static second hyperpolarizabilities γ for one-hole-doped diradicaloids using the strong-correlated ab initio molecular orbital methods and simple one-dimensional (1D) three-site two-electron (3s-2e) models. As examples of one-hole-doped diradicaloids, we examine H3 +, methyl radical trimer cation ((CH3)3 +), silyl radical trimer cation ((SiH3)3 +), and 1,2,3,5-dithiadizolyl trimer cation (DTDA3 +). For H3 +, the static γ exhibits negative values and shows a monotonic increase in amplitude with an increase in the open-shell character defined by a neighbor-site interaction (y S). On the other hand, it is found for (CH3)3 +, (SiH3)3 +, and DTDA3 + that the static γ value exhibits similar behavior to that for H3 + up to an intermediate y S value, while it takes the negative maximum at a large y S value, followed by a decrease in γ amplitude, and subsequently, γ changes to positive values with a drastic increase for larger y S values. For example, in DTDA3 +, the negative/positive γ values, -69 × 105/700 × 105 au at y S = 0.75/0.87, exhibit significant enhancements in amplitude, 2.4/24 times as large as that (-29 × 105 au) at intermediate y S = 0.59 as is often the case in DTDA2. Using the 1D 3s-2e valence-bond configuration interaction model, these sign inversions and drastic increase in the amplitude of γ are found to originate in the differences in Coulomb interactions between valence electrons, between valence and core electrons, and between valence electrons and nuclei. These results contribute to pave the way for the construction of novel control guidelines for the amplitude and sign of γ for one-hole-doped diradicaloids.

Theoretical Study on the Open-Shell Singlet Nature and the Second Hyperpolarizabilities of Corannulene Derivatives with Two Phenoxyl Radicals.

Using the spin-unrestricted density functional theory method, we investigate the interplay between the diradical character y and second hyperpolarizabilities γ (the third-order nonlinear optical (NLO) properties at the molecular scale) of corannulene derivatives with two phenoxyl radicals. This molecule in the singlet state exhibits intermediate y and thus displays a significantly larger γ value than the triplet state and the closed-shell bis-phenol analogue. We also examine the planar molecules involving a coronene moiety in place of the curved corannulene. The intermediate y and large γ values of the corannulene systems are found to originate not from their curved skeleton but from the equilibrium between benzenoid/quinoid resonance forms due to delocalization of the radical electrons of the terminal phenoxyl rings. The longitudinal γ value of the singlet state is found to be comparable to that of s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene, which is known to be one of the organic molecules with the largest two-photon absorption cross section in this size of pure hydrocarbons. The present system is thus expected to be a promising candidate for highly efficient open-shell NLO molecules.

Role of a singlet diradical character in carbon nanomaterials: a novel hot spot for efficient nonlinear optical materials.

Carbon atoms have the potential to produce a variety of fascinating all-carbon structures with amazing electronic and mechanical properties. Over the last few decades, several efforts have been made using experimental and computational techniques to functionalize graphene, carbon nanotubes and fullerenes for potential use in modern hi-tech electronic, medicinal, optical and nonlinear optical (NLO) applications. Since photons replaced electrons as a carrier of information, the field of NLO material design has drawn immense interest in contemporary materials science. There have been several reports of bridging the gap between the exciting fields of carbon nanomaterials and NLO materials by functionalizing carbon nanomaterials for potential NLO applications. In contrast to previous reports of the design of third-order NLO materials using conventional closed-shell materials, a novel strategy using open-shell diradical molecular systems has recently been proposed. Quantum chemically, diradical character is explained in terms of the instability of the chemical bonds in open-shell molecular systems. Interestingly, several carbon nanomaterials, which naturally possess open-shell singlet configurations, have recently gained momentum in the design of these classes of open-shell NLO materials with excellent NLO properties, stability and diversity. The present review establishes a systematic sequence of different studies (spanning over two decades of intense research efforts), starting from the simplest theoretical two-site diradical model, continuing to its experimental and theoretical realization in actual chemical systems, and finally applying the abovementioned model/rule to novel carbon nanomaterials to tune their NLO properties, particularly their second hyperpolarizability (γ). In the present report, we highlight several recent efforts to functionalize carbon nanomaterials by exploiting their open-shell diradical character to achieve efficient third-order NLO properties. Several issues and opportunities are discussed, including the inherited disadvantages of both experimental (the high reactivity and short life of diradical compounds) and quantum (need for multi-reference methodology) techniques when dealing with carbon nanomaterials. A comparative analysis of several quantum chemical investigations, along with contemporary experimental results, will be performed to emphasize the core issues and opportunities related to carbon nanomaterials with singlet open-shell diradical character. Thus, the present review will highlight carbon nanomaterials with diradical/biradical character for their prospective applications in the NLO field.

Diradical character and nonlinear optical properties of buckyferrocenes: focusing on the use of suitably modified fullerene fragments.

The buckyferrocenes, synthesized through face-to-face fusion of ferrocene and fullerene fragments (C60Me10), are expected to enjoy the rich scientific heritage of ferrocene and fullerene with an extensively large π-conjugation network between the two Fe atoms [Y. Matsuo, K. Tahara and E. Nakamura, J. Am. Chem. Soc., 2006, 128, 7154]. However, the addition of pentamethyl groups at each end of the fullerene fragment breaks the π-conjugation path as well as metal-metal spin correlation between the two-ferrocene faces in a buckyferrocene. We found that the unblocking of π-conjugation from different positions in fullerene fragments have substantial effects on their topologies, spin densities, diradical characters as well as nonlinear optical (NLO) properties of these buckyferrocenes. We study the topological dependence of open-shell diradical character and second hyperpolarizability (γ), the third-order NLO properties at the molecular scale, in several buckyferrocenes. On the basis of their different diradical characters (yi), which are defined by the occupation number of the lowest unoccupied natural orbital (LUNO) + i (i = 0, 1,…), these buckyferrocenes are categorized into three groups, i.e., closed-shell (yi = 0), intermediate open-shell singlet (0 < yi < 1), and almost pure open-shell singlet (yi = 1) compounds. For example, we found that buckyferrocenes including (CpFe)2η(5)C60Me10 and (CpFe)2η(5)C70Me10 have closed-shell configurations. The buckyferrocenes (CpFe)2η(5)C60, (CpFe)2η(5)C70, (CpFe)2η(5)C70Me8, (CpFe)2η(5)C70Me4 and (CpFe)2η(5)C30 are intermediate open-shell singlet, while (CpFe)2η(5)C60Me4 and (CpFe)2η(5)C60Me8 are pure open-shell singlet complexes. Interestingly, the γzzzz amplitude of (CpFe)2η(5)C60, an open-shell intermediate diradical complex, is about 41 times and 13 times as large as those of its closed-shell ((CpFe)2η(5)C60Me10) and pure diradical ((CpFe)2η(5)C60Me8) counterparts, respectively. Similarly, the γzzzz amplitudes of (CpFe)2η(5)C70, (CpFe)2η(5)C70Me4, and (CpFe)2η(5)C70Me8 with intermediate diradical character are about 36, 17, and 9 times as large as that of their closed-shell (CpFe)2η(5)C70Me10 counterpart. The fact that larger γzzzz values are obtained for buckyferrocenes with intermediate diradical characters is in line with the "y-γ correlation" obtained from the valence configuration interaction (VCI) results for a two-site diradical model [M. Nakano, et al., Phys. Rev. Lett., 2007, 99, 033001] as well as for fullerene and graphene systems. The γzzzz density analysis shows that the large positive contributions originate from the large γzzzz density distributions on the upper- and lower-extended edges of the buckyferrocenes, between which significant spin polarizations appear within the spin-unrestricted DFT level of theory. These results demonstrate that such buckyferrocenes are potential candidates for a novel class of open-shell singlet NLO systems, where γzzzz values are modulated by tuning their diradical character through the use of suitably modified fullerene fragments.

Third-order nonlinear optical properties of one-dimensional open-shell molecular aggregates composed of phenalenyl radicals.

The impact of intermolecular interactions on the third-order nonlinear optical (NLO) properties of open-shell molecular aggregates has been elucidated by considering one-dimensional aggregates of π-π stacked phenalenyl radicals with different intermolecular distances and the long-range corrected spin-unrestricted density functional theory method. In the phenalenyl dimer, which can be considered as a diradicaloid system, the diradical character strongly depends on the intermolecular distance, and the larger the intermolecular distance is, the larger the diradical character becomes. Then, around the equilibrium stacking distance that corresponds to an intermediate diradical character, its second hyperpolarizability (γ) is maximized and its value per monomer exhibits about a 30-fold enhancement with respect to the isolated phenalenyl monomer. This suggests that equilibrium is an optimal compromise between localization and delocalization of the radical electron pairs in such pancake bonding. No such effect was observed for the closed-shell coronene dimer. Moreover, when going from the dimer (diradical) to the tetramer (tetraradical), the γ-enhancement ratio increases nonlinearly with the aggregate size, whereas switching from the singlet to the highest spin (quintet) state causes a significant reduction of γ. Finally, for the tetramer, another one-order enhancement of γ is achieved for the dicationic singlet relative to its singlet neutral state. These results demonstrate the key role of intermolecular π-π stacking interactions and charge in open-shell (supra)molecular systems to achieve enhanced third-order NLO properties.

Halide ion complexes of decaborane (B10H14) and their derivatives: noncovalent charge transfer effect on second-order nonlinear optical properties.

Quantum molecular engineering has been performed to determine the second-order nonlinear optical (NLO) properties in different halo complexes of decaborane (B(10)H(14)) and their derivatives using the density functional theory (DFT) method. These decaborane halo complexes of X(-)@B(10)H(14) (X = F, Cl, Br, and I) are found to possess noncovalent charge transfer interactions. The static polarizability (α(0)) and first hyperpolarizability (ß(0)) among these complexes increase by moving down the group from F to I, partly due to the increase in size of their anionic radii and the decrease in their electron affinities. A two-level approximation has been employed to investigate the origin of ß(0) values in these halo complexes, which show very consistent results with those by the finite-field method. Furthermore, in the same line, two experimentally existing complexes, I(-)@B(10)H(14) and I(-)@2,4-I(2)B(10)H(12), are found to have considerably large ß(0) values of 2859 and 3092 a.u., respectively, which are about three times larger than a prototypical second-order NLO molecule of p-nitroaniline, as reported by Soscun et al. [Int. J. Quantum Chem.2006, 106, 1130-1137]. Besides this, the special effects of solvent, counterion, and bottom substitutions have also been investigated. Interestingly, 2,4-alkali metal-substituted decaborane iodide complexes show remarkably large second-order NLO response with ß(0) amplitude as large as 62436 a.u. for I(-)@2,4-K(2)B(10)H(12) complex, 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 insights into the second-order NLO properties of halo complexes of decaborane, which possess not only large first hyperpolarizabilities, but also high tunability to get a robustly large second-order NLO response by alkali metal substitution effects.

An FXPRLamide neuropeptide induces seasonal reproductive polyphenism underlying a life-history tradeoff in the tussock moth.

The white spotted tussock moth, Orgyia thyellina, is a typical insect that exhibits seasonal polyphenisms in morphological, physiological, and behavioral traits, including a life-history tradeoff known as oogenesis-flight syndrome. However, the developmental processes and molecular mechanisms that mediate developmental plasticity, including life-history tradeoff, remain largely unknown. To analyze the molecular mechanisms involved in reproductive polyphenism, including the diapause induction, we first cloned and characterized the diapause hormone-pheromone biosynthesis activating neuropeptide (DH-PBAN) cDNA encoding the five Phe-X-Pro-Arg-Leu-NH(2) (FXPRLa) neuropeptides: DH, PBAN, and α-, ß-, and γ-SGNPs (subesophageal ganglion neuropeptides). This gene is expressed in neurosecretory cells within the subesophageal ganglion whose axonal projections reach the neurohemal organ, the corpus cardiacum, suggesting that the DH neuroendocrine system is conserved in Lepidoptera. By injection of chemically synthetic DH and anti-FXPRLa antibody into female pupae, we revealed that not only does the Orgyia DH induce embryonic diapause, but also that this neuropeptide induces seasonal polyphenism, participating in the hypertrophy of follicles and ovaries. In addition, the other four FXPRLa also induced embryonic diapause in O. thyellina, but not in Bombyx mori. This is the first study showing that a neuropeptide has a pleiotropic effect in seasonal reproductive polyphenism to accomplish seasonal adaptation. We also show that a novel factor (i.e., the DH neuropeptide) acts as an important inducer of seasonal polyphenism underlying a life-history tradeoff. Furthermore, we speculate that there must be evolutionary conservation and diversification in the neuroendocrine systems of two lepidopteran genera, Orgyia and Bombyx, in order to facilitate the evolution of coregulated life-history traits and tradeoffs.

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.

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 Å), 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.

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.

Long-range corrected density functional theory study on static second hyperpolarizabilities of singlet diradical systems.

Within the spin-unrestricted density functional theory (DFT) the long-range correction (LC) scheme combined with the Becke-Lee-Yang-Parr exchange-correlation functional, referred to as LC-UBLYP method, has been applied to the calculation of the second hyperpolarizability (gamma) of open-shell singlet diradical systems of increasing complexity and has demonstrated good performance: (i) for the simplest H(2) dissociation model, the gamma values calculated by the LC-UBLYP method significantly overshoot the full configuration interaction result but reproduce qualitatively the evolution of gamma as a function of the diradical character, (ii) for small singlet diradical 1,3-dipole systems, the diradical character dependence of gamma determined by the UCCSD and UCCSD(T) reference methods is reproduced semiquantitatively by the LC-UBLYP method except in the small diradical character region, where the spin-unrestricted solutions coincide with spin-restricted solutions, (iii) the LC-UBLYP method also closely reproduces the UCCSD(T) results on the diradical character dependence of gamma of the p-quinodimethane model system, particularly in the intermediate and large diradical character regions, whereas it shows an abrupt change for a diradical character (y) close to 0.2 originating from the triplet instability, (iv) the reliability of LC-UBLYP to reproduce reference coupled cluster results on open-shell singlet systems with intermediate and large diradical characters has also been substantiated in the case of gamma of 1,4-bis-(imidazol-2-ylidene)-cyclohexa-2,5-diene (BI2Y), then (v), for real systems built from a pair of phenalenyl radicals separated by a conjugated linker, the LC-UBLYP results have been found to closely match the UBHandHLYP values-which, for small systems are in good agreement with those obtained using correlated molecular orbital methods-whereas the UB3LYP results can be much different. These results are not only important from the viewpoint of an efficient determination of the nonlinear optical properties of open-shell singlet systems, but also from the viewpoint of defining new challenges for elaborating improved exchange-correlation functionals.

Remarkable two-photon absorption in open-shell singlet systems.

Remarkable enhancement of two-photon absorption (TPA) peak is theoretically predicted in symmetric open-shell singlet diradical systems with intermediate diradical character as compared to closed-shell and pure diradical systems. It is revealed that the largest TPA peak intensities occur for open-shell singlet diradicals having a ferromagnetically coupled ground state and strongly depend on the ratio between damping factors of the excited states. This result confirms that open-shell singlet conjugated molecules with intermediate diradical characters have precedence over conventional closed-shell conjugated systems in resonant third-order nonlinear optical properties.

Theoretical study on exciton dynamics in dendritic systems: exciton recurrence and migration.

The optical functionalities such as exciton recurrence and migration for dendritic systems, e.g., dendrimers, are investigated using the quantum master equation (QME) approach based on the ab initio molecular orbital configuration interaction (MOCI) method, which can treat both the coherent and incoherent exciton dynamics at the first principle level. Two types of phenylacetylene dendrimers, Cayley-tree dendrimer and nanostar dendrimer with anthracene core, are examined to elucidate the features of excion recurrence and migration motions in relation to their structural dependences. It is found that the nanostar dendrimer exhibits faster exciton migration from the periphery to the core than Cayley-tree dendrimer, which alternatively exhibits exciton recurrence motion among dendron parts in case of small relaxation parameters. Such strong structural dependence of exciton dynamics demonstrates the advantage of dendritic molecular systems for future applications in nano-optical and light-harvesting devices.

Theoretical study on exciton recurrence motion in anthracene dimer using the Ab initio MO-CI based quantum master equation approach.

We apply the ab initio molecular orbital (MO)-configuration interaction (CI) based quantum master equation (MOQME) method to the investigation of ultrafast exciton dynamics in an anthracene dimer modeled after anthracenophane, which is experimentally found to exhibit an oscillatory signal of fluorescence anisotropy decay. Two low-lying near-degenerate one-photon allowed excited states with a slight energy difference (42 cm(-1)) are obtained at the CIS/6-31G** level of approximation using full valence pi-orbitals. The time evolution of reduced exciton density matrices is performed by numerically solving the quantum master equation. After the creation of a superposition state of these near-degenerate states by irradiating a near-resonant laser field, we observe two kinds of oscillatory behaviors of polarizations: field-induced polarizations with faster periods, and amplitude oscillations of x- and z-polarizations, P(x) and P(z), with a slower period, in which the amplitudes of P(x) and P(z) attain maximum alternately. The latter behavior turns out to be associated with an oscillatory exciton motion between the two monomers, i.e., exciton recurrence motion, using the dynamic exciton expression based on the polarization density. From the analysis of contribution to the exciton distributions, such exciton recurrence motion is found to be characterized by both the difference in eigenfrequencies between the two near-degenerate states excited by the laser field and the relative phases among the frontier MOs primarily contributing to the near-degenerate states.