Kyohei Yoneda

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.

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.

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.

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.

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 (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.

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.

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.

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.

One- and two-photon absorptions in open-shell singlet systems

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.