Search

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 (yS). 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 yS value, while it takes the negative maximum at a large yS value, followed by a decrease in γ amplitude, and subsequently, γ changes to positive values with a drastic increase for larger yS values. For example, in DTDA3+, the negative/positive γ values, −69 × 105/700 × 105 au at yS = 0.75/0.87, exhibit significant enhancements in amplitude, 2.4/24 times as large as that (−29 × 105 au) at intermediate yS = 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.

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.

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.

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.

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.

From the viewpoint of ‘‘diradical character,’’ referred to as ‘‘diradicalology,’’ we investigate the second hyperpolarizability c—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 c 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 c 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). V C 2012 Wiley Periodicals, Inc.

The long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method has been employed to unravel the relationship between the hole (referred to as "antidot") structure of hexagonal graphene nanoflakes (HGNFs) and their properties, including their multiradical characters y [the occupation number of the lowest unoccupied natural orbital (LUNO)+i (i = 0, 1,...)], aromaticity, and the second hyperpolarizabilities (γ), which is the third-order nonlinear optical (NLO) response at the molecular level. These systems exhibit a wide range of open-shell/multiradical character, which shows an oscillatory behavior as a function of increasing the size of the antidot. This structural dependence is shown to originate from the oscillatory variations in the HOMO-LUMO energy gap, which result from the fact that the bonding and antibonding interactions between the central antidot-shape HGNFs and the surroundings alternate in both the HOMO and the LUMO as going from the center of the molecule to the peripheral region. Moreover, the multiradical character of these structures is strongly correlated with the variations of magnetic criteria of aromaticity, the nucleus-independent chemical shift (NICS) and the out-of-plane diagonal component of the magnetic shielding tensor (-σ ), as well as with the γ. So, systems with larger multiradical characters tend to exhibit larger NICS and - σ values, i.e., less aromaticity. Although the number of π electrons of the antidot HGNFs is smaller than that of the corresponding perfect C H HGNF, their γ value can be larger as evidenced by the antidot C H HGNF, which has intermediate multiradical characters (y0 = y1 = 0.658) and displays a γvalue 1.7 times larger than that of the perfect HGNF. These strong impacts of the antidot structure on the third-order NLO properties indicate that the antidot HGNFs are promising building blocks for a new class of multiradical NLO materials, the properties of which can be controlled by adjusting the antidot size.

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 (c) 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 c values; the c 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 c. V C 2012 Wiley Periodicals, Inc.

) and third-order nonlinear opticalproperties of linear/cyclic [N]acenes and [N]phenylenes in theirground states, where N is the number of benzene rings in eachlinear and cyclic configuration. It has been found that linear andcyclic acenes with N ¼ 5–10 show singlet diradical characters,while linear and cyclic phenylenes with equivalent number ofbenzene rings have closed-shell configurations. The amplitudesof third-order nonlinear optical polarizability ( c

We investigate the second hyperpolarizabilities (γ) of singlet diradical s-indacene and its radical anion. It is found that the neutral s-indacene, which has an intermediate diradical character, exibits a positive γ value, while its radical anion does a negative γ value. Moreover, the magnitude of the γ value of s-indacene radical anion turns out to be significantly larger than that of neutral s-indacene. We also examine several singlet diradical 1,3-dipoles and their radical cations. On the basis of these results, we discuss the charging effects on γ in singlet diradical systems.

We study the (hyper)polarizabilities of a singlet diradical molecule (2-borapropane-1,3-diyl) which contains a boron atom. For the purpose to control the (hyper)polarizabilities by tuning the diradical character of the boron compound, we employ water solvent as an electron donor to the boron atom. A series of quantum chemical calculations reveal that the electron donation from the lone pair of electrons in a water molecule to the vacant p orbital of boron atom gives rise to the increase of the diradical character, leading to the large variation of the polarizability of the molecule. We also investigate the solvation effects of the bulk water by utilizing the polarizable continuum model (PCM). It is shown that the PCM environment significantly increases the degree of enhancement of the second hyperpolarizability in the intermediate diradical regime of the compound. These results suggest that a singlet diradical boron compound immersed in an electron donor solvent can exhibit efficient third-order nonlinear optical properties, which can be tuned by designing the solute-solvent interactions. We examine the reliability of the PCM results by performing the additional QM/MM simulations. It is found that the QM/MM solvation effects slightly decrease the polarizability in contrast to the PCM calculation, which implies the possibility that PCM tends to overestimate the polarizability due to the lack of the ability to represent the solvation structures.

We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i. e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.

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.

Switching on an external electric field (F) along the electron correlation direction produces a giant enhancement of the second hyperpolarizability γ in a polyaromatic diradicaloid having intermediate diradical character. This has been evidenced by carrying out spin-unrestricted density functional theory calculations with the LC-UBLYP long-range corrected exchange-correlation functional for the s-indaceno[1,2,3-cd;5,6,7-c′d′]diphenalene (IDPL) diradical compound in comparison to a closed-shell analogue of similar size composed of two pyrene moieties (PY2). For IDPL, the field-induced enhancement ratio is estimated to reach 4 orders of magnitude for an electric field of 0.0077 a.u., whereas it is less than a factor of 2 for PY2. Moreover, an enhancement is also observed by substituting both-end phenalenyl rings of IDPL with donor (NH2)/acceptor (NO2) groups, but this enhancement is limited to about 2 orders of magnitude. These enhancements are associated with a reduction of the diradical character (and therefore an improved thermal stability) as well as with the appearance of substantial type-I contributions to γ.

To demonstrate the performance of a novel approximate spin-projected (ASP) spin-unrestricted density functional theory (UDFT) method, we examine the diradical character dependences of the static polarizability (α) and second hyperpolarizability (γ) of a model open-shell singlet molecule, p-quinodimethane (PQM), using several hybrid and long-range corrected (LC) exchange–correlation functionals. The ASP-LC-UBLYP method with a range-separating parameter μ = 0.47 is found to reproduce semi-quantitatively the diradical character dependences of α and γ of the PQM model calculated using the strongly-correlated UCCSD(T) method.

The long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method has been used to determine the second hyperpolarizabilities ( γ ) of open-shell singlet π-conjugated diradical compounds, i.e., p -quinodimethane, 1,4-bis-(imidazole-2-ylidene)-cyclohexa-2,5-diene, pentalene and s -indacene. Analysis of the dependence of γ on the range separating parameter ( μ ) was carried out along with comparison to spin-unrestricted coupled cluster singles, doubles and perturbative triples [UCCSD(T)] calculations. Our investigation shows that the LC-UBLYP method with μ = 0.3–0.5 is adequate for calculating γ values for conjugated diradical systems and does not suffer from the catastrophic behavior found in conventional exchange–correlation functionals.

Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, γ, of rectangular graphene nanoflakes of different sizes have been investigated for their singlet ground state in conjunction with their open-shell character. It is shown that their multiradical nature leads to a unique dependence of the γ component along the armchair edges and that this behavior can be rationalized not only in terms of the diradical character (y0) derived from the HOMO and LUMO occupation numbers, but also in terms of the one (y1) derived from the HOMO-1 and LUMO+1 ones: the γ components are enhanced when the systems take intermediate y1 values in addition to intermediate y0 values.

Exciton recurrence motions in double-ring molecular aggregates are investigated using the quantum master equation approach. The rotatory and oscillatory recurrence behaviors are found to be controlled by changing the relative direction of the circular polarization of an incident two-mode laser field. These dynamics are understood by the relative phases among off-diagonal exciton density matrices, the feature of which is determined by the interaction between the circular-polarized field and the degenerate states of the double-ring structure. The results of exciton relaxation effects caused by the exciton−phonon coupling and static disorder also demonstrate the robustness of the exciton recurrence motions in double-ring molecular aggregates.

In order to investigate the time evolutions of electron and hole distributions in weakly and strongly coupled H 2 dimer models, we employ a novel dynamic exciton expression derived from the exciton density matrices calculated by the quantum master equation combined with the ab initio molecular orbital (MO)–configuration interaction (CI) method. The oscillation of exciton distribution over the monomers is observed in case of small inter-monomer distance, where the coupled dipole approximation is invalid. The result originates in the covalent character of inter-monomer interaction in the first excited state, i.e., delocalized character of LUMO distribution.

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 (MO-CI) 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.

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.

We investigate a singlet diradical molecule (2-borapropane-1,3-diyl) involving a B atom in an electron donor solvent, i.e., water, from the viewpoint of controlling the (hyper)polarizability through tuning the diradical character. The quantum chemical calculations for a model system reveal that a donation from the O lone pair electrons of a water molecule to the vacant p orbital of the B atom increases the diradical character, leading to a large variation in the (hyper)polarizability of the B-containing compound. The effect of the bulk solvent determined within the PCM scheme is also shown to increase the degree of enhancement of the second hyperpolarizability in the intermediate diradical regime of the B-containing compound.

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.

The coherent exciton dynamics in molecular complexes composed of ring-shaped aggregates induced by linear- and circular-polarized laser fields has been investigated by using the quantum master equation (QME) approach. As shown in previous studies, near-degenerate states create the superposition states after irradiation of linear-polarized laser fields and thus cause the oscillatory exciton recurrence motion. In contrast, the rotatory exciton recurrence motion is found to be induced by circular-polarized laser field in a C3-symmetry complex composed of identical three ring-shaped aggregates. This exciton dynamics is predicted to originate in the superposition states between the two pairs of degenerate states, which are coherently excited by a circular-polarized laser field. The rotatory exciton recurrence motion induced by a two-mode laser field with mutually opposite circular polarizations also has been examined in the complex composed of two different-sized groups of ring-shaped aggregates. It turns out ...

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.

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.

We propose a novel dynamic exciton expression based on the quantum master equation approach using the ab initio molecular orbital (MO) singly excited configuration interaction (CI) method developed in our previous paper [M. Nakano, M. Takahata, S. Yamada, R. Kishi, T. Nitta, K. Yamaguchi, J. Chem. Phys. 120 (2004) 2359]. This expression is derived from the partition of polarization density in the configuration basis into the electron and hole contributions, and can describe both the coherent and incoherent dynamics of electron and hole density distributions, e.g., dynamic electric polarization, exciton recurrence and exciton migration.

For the emission gas concentration measurement of sublimable gas phase boron compounds, the optimal collector material applied to the inside stack sampler (the type-I stack sampler developed in our previous article) was examined. The collection efficiency of alkali impregnated filter paper of K2CO3, Na2CO3, LiOH and Ba(OH)2 was investigated by using artificial stack.It was revealed that K2CO3 and Na2CO3 filter papers have a high collection efficiency and fully applicable to the type-I stack sampler. However, LiOH and Ba(OH)2 filter papers have a restricted range of applicable condition.

We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

Using density functional theory, the central role of the odd electron density for designing open-shell singlet compounds with enhanced second hyperpolarizabilities [third-order nonlinear optical (NLO) properties at the molecular level] is evidenced. Its amplitude, corresponding to the diradical character, gives the potential of enhancement, whereas its spatial distribution indicates where the donor and acceptor substituents should be placed to further increase this third-order NLO response. This is illustrated by comparing hexacenes, open-shell singlet graphene nanoflakes with intermediate diradical character, with reference closed-shell terrylenes. Enhancements up to 2 and 3 orders of magnitude are achieved when the OH/CN and NH2/NO2 substituents are placed in the middle of the zigzag edge region, which corresponds to the largest odd electron density amplitude.

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 (β(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 β(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 β(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 β(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.

One- and two-photon absorption cross sections of symmetric open-shell singlet molecular systems are investigated using a valence configuration interaction scheme. It is found for one-photon absorption (OPA) that the peak intensity decreases and the peak position moves to the low energy region as increasing the diradical character of the system. In contrast, a significant enhancement of two-photon absorption (TPA) peak is predicted for open-shell singlet systems with intermediate diradical character as compared to the 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 depends on the ratio between damping factors of the excited states.

Exciton recurrence motions in double-ring molecular aggregates have been investigated using the quantum master equation (QME) approach. In this study, the exciton recurrence motion is induced by the superposition of twopairs of degenerate states, which are created by the irradiation of a two-mode circular-polarized laser field. The rotatory and oscillatory exciton recurrence motions are found to be controlled by changing the combination of the relative direction of the two circular polarizations of the field. These unique exciton recurrences are found to be explained by the relative phases of the off-diagonal density matrices using exciton basis. We discuss a controllability of such exciton recurrence motions in general double-ring molecular aggregates.

Spin polarization and third-order nonlinear optical properties, second hyperpoalrizabilities (γ), of open-shell singlet graphene nanoflakes (GNFs) with hexagonal, rhombic and bow-tie shapes are investigated using a hybrid density functional theory method. The spatial spin polarization exhibits a strong structural dependence, i.e., edge shape effect, and the diradical character is also found to depend on the structure of zigzag-edged nanoflakes. These structural dependences of diradical characters of graphene nanoflakes are expected to provide a novel control scheme of the γ values.

Recently, we have developed a novel computational approach treating exciton dynamics of supermolecular systems based on the quantum master equation combined with the ab initio molecular orbital - configuration interaction method (MOQME). The MOQME method demonstrates the advantage of describing both coherent and incoherent exciton dynamics in supermolecular systems. In this study, we extend our method to be applicable to the open-shell systems by using broken-symmetry (BS) MO method, referred to as BS-MOQME method. In this formalism, the time evolution of not only the polarization density but also the spin density can be represented based on the MO spatial distributions. A model open-shell system, i.e., H2 dissociation process, is examined to clarify the applicability of the present scheme.

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.

The exciton dynamics in a ring‐shaped aggregate complex model induced by circular‐polarized laser field has been investigated using the quantum master equation (QME) approach. We observe the recurrence motion of exiton after the irradiation of a circular‐polarized laser field. It is found that the circular‐polarized laser field makes it possible to shift the oscillation phase of the exciton recurrence and thus to cause the out‐of‐phase recurrence motion, while such unique recurrence dynamics disappears in the case of the irradiation of the linear‐polarized laser field. It also turns out that the direction of phase‐shift in exciton recurrence oscillation can be controlled by the rotation direction of the circular‐polarized laser field.

We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i.e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.

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 alpha-, beta-, and gamma-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., Article, PLOS ONE. 6(8):e24213 (2011)

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 (N9) 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.

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.