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Diphenylhexatriene and its ring-substituted derivatives act as emitters and show blue-green to green upconverted emission under photoexcitation of 640 nm when mixed with a sensitiser molecule (a palladium complex) in solution in a nitrogen atmosphere.

This perspective article provides a comprehensive but organized tutorial introduction of the kinetics related to photon upconversion (UC) by triplet-triplet annihilation (TTA) (TTA-UC). The field of TTA-UC is multi-disciplinary and rapidly growing with the involvement of researchers from diverse backgrounds. TTA-UC consists of a series of tangled photophysical processes, so a solid understanding of the kinetic features and consequences is important to develop and evaluate materials for TTA-UC. This tutorial starts with an introduction of the standard model of TTA-UC along with the assumptions used in the model. The essential concept of the spin statistics for TTA and how this concept is related to the singlet branching ratio, which directly affects the efficiency of UC, are then explained through step-by-step analyses. Using these foundations, solutions for the steady-state behaviors are derived, featuring the universal curve that describes the excitation intensity dependence of the UC quantum yield for any sample type. Various useful functions for analyzing experimental data are also introduced and summarized. The transient behaviors of TTA-UC are then discussed along with their equations, and the usefulness for analyzing transient experimental data is explained using examples. In this article, self-consistent derivations and relevant references are provided for an easy understanding of the advanced discussion and analyses.

The fluorescence and other photophysical parameters of highly polarized, quadrupolar bis-coumarins possessing an electron-rich pyrrolo[3,2-b]pyrrole bridging unit are highly dependent on the linking position between both chromophores. Delocalization of the LUMO on the entire pi-system results in intense emission and strong two-photon absorption.

We report the triplet–triplet annihilation (TTA) upconversion (UC) through triplet energy transfer (TET) from a sensitiser fixed on a solid surface to free emitters dissolved in solution. A carboxylic-acid derivative of Pt–porphyrin was used as the sensitiser fixed on an amino-treated surface of continuous nanoporous glass without aggregation. UC emission was observed under photoexcitation of 532 nm for porphyrin-fixed glass immersed in an emitter solution of 9,10-diphenylanthracene (DPA), showing that TET occurs through the solid–liquid interface. The dynamics of TET was analysed through both phosphorescence decay of the sensitiser and UC emission rise from the emitter. Two TET components with different rate constants were found, slower than diffusion-controlled reactions in solution by 1–2 orders of magnitude. Nevertheless, the solid surface TET rates were fast enough to obtain a high quantum yield over the solid–liquid interface. By melting DPA and soaking it into sensitiser-fixed porous glass, we fabricated an all-solid system enabling TTA-UC through the bulk interface.

Fluorescent organic molecules have received great attention due to their largest applications, for example, in DNA and RNA spectroscopies studies, development of new photoluminescence bioprobes, an...

It has been hypothesized that alkyl chains are inactive for electron transport processes through the chains. However, our theoretical study unveiled that loop-like alkyl chains can accelerate the e...

Although the oxidative coupling of disilenides, i.e., the disilicon analogues of vinyl anions, represents a promising route to extend the conjugation between Si═Si double bonds, previously reported synthetic routes to disilenides involve strongly reducing conditions. Herein, we report a novel synthetic route to disilenides from stable disilenes via the selective cleavage of Si(sp2)–Si(sp3) bonds under milder reaction conditions. Using this method, a 1,4-bis(trimethylsilyl)tetrasila-1,3-diene (5) was synthesized from the corresponding silyl-substituted disilene. Moreover, Et3Si-substituted tetrasila-1,3-diene 7 was synthesized via tetrasila-1,3-dien-1-ide 6, which is the first example of a functionalized tetrasila-1,3-diene.

Off-resonant excitation of the closed-ring isomer of a photochromic diarylethene derivative at 730 nm induced the efficient cycloreversion reaction with a yield of ∼20%, while the reaction yield was only 2% under one-photon excitation at 365 nm. Excitation wavelength dependence of the one-photon cycloreversion reaction yield under steady-state irradiation in a wide wavelength range showed that the specific electronic state leading to the large cycloreversion reaction yield, which is originally forbidden in the optical transition but partially allowed owing to the low symmetry of the molecule, is spectrally overlapped with the electronic state accessible by the allowed one-photon optical transition in the UV region. Femtosecond transient absorption spectroscopy also revealed that the off-resonant two-photon excitation preferentially pumped the molecule into the specific state, leading to the 10-fold enhancement of the cycloreversion reaction.

Heteroatomic derivatives of Chichibabin's hydrocarbon are explored theoretically to highlight the relationship between the electronic structure and nonlinear optical (NLO) properties. The results show that the systems are divided into two classes: one that has intermediate electronic structure between two main contributing resonance structures, and a second with an electronic structure that is approximated by only one resonance structure. It is found that the former class of derivatives exhibits approximately one-order larger static second hyperpolarizability (γ) than the latter class, because of either their intermediate diradical or charge-transfer (CT) characteristics. The asymmetric systems are further scrutinized by using the static electric field model, which shows that the intermediate CT character is essential for the very large enhancement of γ in the asymmetric systems. These results not only clarify the structure–property relationships of open-shell singlet NLO compounds with redox switching properties, but also shed light on a new and unexplored class of closed-shell NLO systems generated by the introduction of intermediate CT nature into open-shell singlet systems.

In condensed solids, triplet exciton migration and succeeding triplet–triplet annihilation (TTA) are major bottleneck processes for efficient photon upconversion (UC) using sunlight excitation. We theoretically investigated the reaction times of TTA and the triplet–triplet energy transfer (TTET) as the elementary processes of triplet exciton migration in organic crystals of two molecular species: 9,10-diphenylanthracene (DPA) and its double-strapped alkyl derivative (C7-sDPA) as the models of a recently reported crystalline system of TTA-UC by Kamada et al. The reaction times calculated based on Marcus theory clarified that the dimensionality of TTET and synergetic effects of TTA and TTET are responsible for the high UC quantum yield as well as their triplet lifetimes.

The room-temperature phosphorescence chromophore, Pt(II) coproporphyrin I (PtCP), was fixed on the surface of a 3D-network of nanoscale pores of porous glass through ion-exchange reaction. The absorption and phosphorescence spectra indicated that PtCP can be loaded while maintaining monomeric dispersion at concentrations well beyond solubility limits of PtCP in solution. The phosphorescence quantum yield of PtCP fixed on the surface was also found to have double the enhancement of solution. The extended lifetime of phosphorescence of PtCP bonded on the surface compared to that in solution clearly indicated that suppression of nonradiative deactivation plays a key role in high quantum yield and long triplet lifetime. This hybridization with nano-porous glass provides opportunities for various potential applications.

The rare-earth complex Eu(hfa)3(phen) is dispersed in the self-assembled organogel of p-chlorophenol and surfactant AOT. The time profiles of the emission intensity observed from the complex–organogel system suggest the possible generation of amplified stimulated emission when excited with a strong excitation pulse. As the host material, the organogel can support eight times as much of the complex along with better emission quantum yield. A theoretical estimation of the laser gain factor of the complex–organogel also suggested that this system might have application in laser systems.

Three boron diketonate chromophores with extended π-conjugated backbone were prepared and their spectroscopic features were investigated through a combined theoretical/experimental study. It was shown that these complexes, which undergo very large electronic reorganization upon photoexcitation, combine large two-photon absorption cross section with an emission energy and quantum efficiency in solution that is strongly dependent on solvent polarity. The strong positive influence of boron complexation on the magnitude of the two-photon absorption was clearly established, and it was shown that the two-photon absorption properties were dominated by the quadrupolar term. For one of the synthesized compounds, intense one- and two-photon-induced solid-state emission (fluorescence quantum yield of 0.65 with maximum wavelength of 610 nm) was obtained as a result of antiparallel J-aggregate crystal packing.

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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.

We systematically investigated enhancement of the molecular two-photon absorption (TPA) cross sections (σ(2)) of organic dyes confined in the interlayer space of clay films. Several possible mechanisms have been proposed to explain the enhanced TPA of dyes in the interlayer spaces of clays. The present study comprehensively investigates two of these mechanisms, namely, (1) enhanced molecular planarity and the consequent extension of the π-electron system and (2) enhanced molecular orientation. We fabricated transparent dye–clay films consisting of a synthetic saponite clay and four cationic dyes. Two of these dyes are expected to have enhanced planarity when they are hybridized with a clay mineral. The other two dyes are considered to retain the planarity of their conjugated π-electron systems when they are in solution or in the interlayer space of a clay. We experimentally measured the σ(2) of these dyes in a clay film and in solution and found that the σ(2) of all four dyes is enhanced in a clay film bu...

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.

Using the spin-unrestricted hybrid density functional theory method, we have investigated the intermolecular interaction effects on the longitudinal static second hyperpolarizability (γ) of open-shell singlet slipped-stack dimers composed of singlet diradical square planar nickel complexes involving o-semiquinonato type ligands, Ni(o-C6H4X2) 2 (where X = O, NH, S, Se, PH). For comparison, we have also examined the γ values of a closed-shell singlet slipped-stack dimer composed of closed-shell monomers Ni[o-C6H4S(NH2)] 2. It is found that for interplanar distance ranging between 3.0 and 5.0 Å the slipped-stack dimers with intermediate monomer diradical characters exhibit larger γ values per monomer (αdimer/2) than those with large monomer diradical characters or than the closed-shell dimer. These results extend the domain of validity of the relationship found between γ and the diradical character for individual molecules. It also turns out that the ratio R = (γdimer/2) /γmonomer increases upon decreasing the interplanar distance and that this increase is larger for intermediate diradical character than for the other cases. These phenomena have been analyzed by considering the γ density distributions of the dimers, demonstrating a significant field-induced third-order charge transfer between the monomers in the case of intermediate diradical character. The present results indicate that open-shell singlet slipped-stack aggregates composed of monomers with intermediate diradical characters constitute another mean for achieving highly efficient and tunable third-order nonlinear optical materials.

The synthesis and detailed photophysical studies of a series of 2,6-asymmetrically functionalized dithieno[3,2-b:2',3'-d]phospholes are reported. One-photon spectroscopy revealed that the materials show similar significant Stokes shifts supporting very polar excited intramolecular charge-transfer (ICT) states. Investigation of their two-photon absorption (TPA) behavior indicated that the materials are also valuable TPA chromophores with reasonable cross-sections between 285-385 GM in the biologically relevant wavelength range 800-1100 nm. Moreover, the nonlinear optical features of the phosphole derivatives reported herein were found to remain almost unaltered after modification of the phosphorus center, either by oxidation and/or complexation.

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.

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.

Two-photon absorption (TPA) properties of a series of cationic, linear π-conjugated systems with donor(D)/acceptor(A) substitution have been examined systematically in terms of the type and length of the π-conjugation core and symmetric and asymmetric D/A-arrangement. The TPA spectra of the chromophores measured by the femtosecond open-aperture Z-scan method reveal that the double-bond core results in much more intense TPA than the triple-bond one, with a significant red shift of the TPA peak while the TPA becomes more intense as the chain is extended for the triple-bond core compounds with a little red shift. It is also found that the difference in the D/A-arrangement gives a small difference in the amplitude of the TPA spectrum although the spectral shapes differ considerably.

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.

Hybrid density functional theory method is applied for investigating the diradical character dependence of the second hyperpolarizability (γ) of square planar nickel complexes involving several types of bidentate ligands [o-C6H4XY, where X = Y = O, NH, S, Se, and PH as well as (X, Y) = (NH, NH2) and (S, NH2)]. It is found that, as a function of the donor atoms, the diradical character of these complexes varies from 0.0 to 0.884 and is associated with substantial variations of γ ranging from 14 × 103 to 819 × 103 au. In particular, the largest γ values are associated with intermediate diradical characters in good agreement with the structure-property relationship obtained for pure hydrocarbon systems. Increasing the electronegativity of the X and Y donor groups of the ligands leads to larger diradical characters as a result of the enhancement of the double bond nature of the C=X(Y) bonds, which further stabilizes the diradicals on both-end benzene rings. This demonstrates that the electronegativities of the donor atoms of the ligands become a tuning parameter of the diradical character and then of the γ values of these complexes.

Two-photon absorption (TPA) properties of newly synthesized conjugated ketone derivatives that include nonalternant azulenyl moieties in the pi-conjugation system, alpha,alpha'-bis(1-azulenylidene)cyclopentanone (1Az), alpha,alpha'-bis(2-azulenylidene)cyclopentanone (2Az), and alpha,alpha'-bis(6-azulenylidene)cyclopentanone (6Az) are reported. TPA spectra of these azulenyl compounds were measured using the open-aperture Z-scan method with a femtosecond laser. The TPA cross section at the peak position (sigma(2)peak) of 1Az was found to be the largest among the three azulenyl compounds, which is almost 7 times larger than that of the alpha,alpha'-bis(1-naphthylidene)cyclopentanone (1Nph), an alternant isomer of 1Az with the same number of pi-electrons. The small detuning energies of the azulenyl compounds compared to those of 1Nph were responsible for the large TPA cross sections. We report that a compound having an azulenyl moiety can be a promising TPA material.

We investigate the longitudinal static second hyperpolarizability (γ) of open-shell singlet diphenalenyl radical dimer using the spin-unrestricted density functional theory method. This dimer is known to be a model unit of a slipped stacked linear chain with an unusually short average π–π distance of 3.137 A. The longitudinal γ per monomer for this dimer is found to be significantly (about twice) enhanced as compared to that of monomer. This originates in the field-induced intermolecular virtual charge transfer between both-end phenalenyl rings through the strong covalent interaction between the unpaired electrons of the cofacial phenalenyl rings.

The longitudinal static second hyperpolarizability ( γ ) has been investigated for models ( H 3 + and H 5 + ) open-shell singlet one-dimensional systems bearing a charged defect. Using various ab initio molecular orbital and density functional theory methods, the γ values of these cationic symmetric hydrogen chain models having different bond-length alternations (BLAs) are analyzed as a function of the average diradical character as well as by adopting the summation-over-states scheme. These systems exhibit negative γ values, of which the amplitudes increase nonlinearly with the average diradical character while the chain-length dependence is enhanced by increasing the BLAs. This dependence of γ with the diradical character is mostly dictated by the strong decrease of the excitation energies.

Two-photon absorption (TPA) properties of two trefoil-shaped compounds with different edge linkages--tris(hexadehydrotribenzo[12]annulene) and tris(tetradehydrotribenzo[12]annulene)--and three asterisk-shaped compounds having no edge-linkage--hexakis(phenylethynyl)benzenes--are investigated experimentally by the open-aperture Z-scan and TPA-induced fluorescence methods with wavelength tuneable femtosecond pulses. The compound with ethynylene edge-linkage exhibits the most intense TPA (the maximal TPA cross section is 1300+/-170 GM at 572 nm where 1 GM=10(-50) cm(4) s molecule(-1) photon(-1)). The TPA activity of the compounds is primarily explained in terms of the planarity of the molecules in relation with the type of edge-linkage.

Adopting density functional theory and a hybrid exchange-correlation functional, the relationship between the second hyperpolarizability (γ) and the diradical character has been investigated for diphenalenyl-based compounds containing different heterocyclic five-membered central rings (C 4H4X, where X = NH, PH, O, S, CH2, SiH 2, BH, GaH, C=O, C=S, and C=Se) or substituted by donor (NH 2)/acceptor(NO2) groups. It turns out that these structural modifications can tune the diradical character from 0.0 to 0.968 and lead to variations of γ over more than 1 order of magnitude, demonstrating the controllability of γ in this family of compounds. In particular, when the central ring is strongly aromatic, the diradical character is larger than 0.7, which is associated with pretty large γ values except for almost the pure diradical case (γ ≈ 1). On the other hand, when the aromaticity decreases-or the antiaromaticity increases-the diradical character and the second hyperpolarizability get smaller. These relationships are correlated to structural (bond length alternation) and charge distribution (charge transfer between the phenalenyl rings and the central ring) properties, which account for the relative importance of the resonance diradical, zwitterionic, and quinoid forms. Therefore, the diradical character and the second hyperpolarizability can be controlled by the aromaticity of the ring while the paradigm of the enhancement of γ for intermediate diradical character is globally verified. Then, upon introducing donor groups, the zwitterionic character increases, leading to closed-shell species and small second hyperpolarizabilities. In the case of substitution by acceptor groups, the charge transfer is reduced but the diradical character and the second hyperpolarizability hardly changes.

Ab initio spin-flip configuration interaction (SF-CI) methods with the finite-field (FF) scheme are applied to the calculation of static second hyperpolarizabilities (γ) of several singlet diradical systems, i.e., the model H2 molecule under dissociation, p-quinodimethane, o-quinoid five-membered ring, and 1,4-bis(imidazole-2-ylidene)cyclohexa-2,5-diene (BI2Y) models. The SF-CI method using the UHF reference wave function provides the qualitatively correct diradical character (γ) dependence of γ in a wide range of a diradical character region for H2 under dissociation ahd p-quinodimethane as well as o-quinoid five-membered ring models. For BI2Y, which is a real diradical system, a non-negligible spin contamination is found in the spin-unrestricted Hartree-Fock (UHF) triplet state, which results in overestimations (SF-CIS) or underestimations (SF-CIS(D)) of γ. Such deficiencies are significantly reduced when using the pure spin state, i.e., the restricted open-shell HF (ROHF) triplet wave function as the reference wave function. These results indicate the applicability of the FF-SF-CI method starting with a pure or a nearly pure high-spin state to provide qualitative or semiquantitative γ for large-size diradical systems. For selected systems, these SF-CI results are also compared to the SF equation of motion coupled cluster singles and doubles (SF-EOM-CCSD) and to SF time-dependent density functional theory (SF-TDDFT) schemes. In particular, large amounts of Hartree-Fock exchange in the functional are required to obtain qualitatively correct dependence of γ on y in the case of p-quinodimethane.

Using hybrid density functional theory methods, the static first ( β ) and second ( γ ) hyperpolarizabilities of a donor–acceptor disubstituted singlet diradical system built from phenalenyl radicals linked by an acetylene π-conjugated bridge, DA-BPLE, is investigated and compared to an analogous closed-shell system, DA-BPRY, built from pyrene rings. DA-BPLE presents an intermediate diradical character and exhibits β and γ values about 14 and 7 times larger than those of DA-BPRY having a similar π-conjugation length, respectively. These results suggest the applicability of the structure-property relation in γ of symmetric diradical systems to β and γ of asymmetric diradical systems.

We investigate the longitudinal static second hyperpolarizabilities ( γ ) of open-shell singlet one-dimensional systems. The intersite interaction effects on the average diradical character and size dependences of γ are examined using hydrogen chain models (H 2 n ) with different chain lengths and bond-length alternations (BLA) by the ab initio MO full-CI and coupled cluster methods. These systems exhibit significant enhancement of γ / n in the small average diradical character region compared to diradical H 2 . The BLA is found to reduce the maximum γ / n and to move the diradical character giving the maximum γ / n to intermediate region. These systems also show remarkable chain-length dependences of γ / n (comparable to those of closed-shell systems) in the small average diradical character region.

We have investigated the structural dependence of static second hyperpolarizabilities (γ) of polycyclic diphenalenyl radicals, i.e., IDPL, as-IDPL and TDPL, using the hybrid density functional theory method. It turns out that the diradical character of as-IDPL (0.923) is larger than that of IDPL (0.770) and is close to 1 (pure diradical state), which supports the fact that the γ of as-IDPL (472 × 103 a.u.) is smaller than that of IDPL (2284 × 103 a.u.). The replacement of a central benzene ring (as-IDPL) by a thiophene ring (TDPL) increases the γ (1375 × 103 a.u.). This is predicted to be caused by the reduction of aromaticity of the central ring and by the hypervalency of the sulfur atom of the thiophene.

The static second hyperpolarizability (γ) of a singlet diradical system involving phenalenyl radicals linked with acetylene π-conjugated bridge, BPLE, is investigated as well as reference closed-shell systems, BPRY1 and BPRY2, by the hybrid density functional theory method. The γ value of BPLE with intermediate diradical character is shown to be about four times as large as that of BPRY1 with similar π-conjugation length and to be about twice as large as that of BPRY2 with longer π-conjugation length. This feature is in agreement with our prediction that the molecules with intermediate diradical characters enhance γ values compared to the closed-shell molecules.

Supramolecular porphyrin self-assemblies have been prepared from butadiyne-linked bis(imidazolylporphyrin) by complementary coordination of imidazole to zinc, and their two-photon absorption (2PA) and higher-order nonlinear absorption properties were investigated over femtosecond time scales using an open-aperture Z-scan method. The self-assembled porphyrin dimer of the conjugated monozinc bisporphyrin 7D was shown to have a large 2PA cross section (7.6 x 10(3) GM, where 1 GM = 10(-50) cm(4) s molecule(-1) photon(-1)) at 887 nm. By comparison of this result with that for a meso-meso-linked porphyrin array without the butadiyne connection (3.7 x 10(2) GM at 964 nm), it was demonstrated that the predominant factor in this significant enhancement of the cross section was the expansion of porphyrin-porphyrin pi-conjugation. Self-coordination and monozinc metalation were also found to be contributing factors. Furthermore, a novel self-assembled porphyrin polymer 8P consisting of a biszinc complex with a mean molecular weight of M(n) = 1.5 x 10(5) Da was shown to exhibit an extraordinarily large two-photon absorption cross section (4.4 x 10(5) GM at 873 nm). Nanosecond Z-scan experiments for 7D and 8P were also undertaken and resulted in the measurement of large effective 2PA cross sections, including the excited-state absorption (2.1 x 10(5) GM for 7D and 2.2 x 10(7) GM for 8P, respectively). Finally, three-photon absorption was observed by femtosecond Z-scan experiments at 1188 nm (7.1 x 10(-89) m(6) s(2)) and 1282 nm (1.8 x 10(-89) m(6) s(2)), an observation which is the first of its kind in porphyrin chemistry.

The dependence of the second hyperpolarizability (gamma) on the diradical character (y) for singlet diradical systems is investigated using a model compound, the p-quinodimethane (PQM) molecule with different both-end carbon-carbon (C-C) bond lengths, by several ab initio molecular orbital and density functional theory methods. The diradical character based on UHF calculations indicates that at equilibrium geometry PQM is in a singlet ground state and primarily exhibits a quinoid structure, whereas the diradical character increases when increasing both-end C-C bond lengths. At the highest level of approximation, that is, using the UCCSD(T) method with the 6-31G+diffuse p (zeta = 0.0523) basis set, the longitudinal static gamma of PQM presents a maximum value for intermediate diradical character (y approximately 0.5) while the gamma values are larger for intermediate and large diradical character (y approximately 0.5-0.7) than for small diradical character (y0.2). This feature suggests that the gamma values of singlet diradical systems in the intermediate and somewhat strong correlation regimes are significantly enhanced as compared to those in the weak correlation regime. These results are substantiated by a complementary study of the variation in gamma upon twisted ethylene.

Third-order nonlinear optical properties of multinuclear organometallic complexes consisting of metal–metal multiple bonds previously studied by picosecond degenerate four-wave mixing (DFWM) are reexamined by femtosecond optical heterodyned optical Kerr effect (OHD-OKE) and femtosecond Z-scan techniques. The real part of off-resonant second hyperpolarizabilities are obtained at a wavelength of 1280 nm to be +3.0 ± 10−33 esu for a Pt–Mo–Mo–Pt tetranuclear complex and less than 10−33 esu for a Mo–Mo dinuclear complex. The present results clarify that the previously reported values are not off-resonant values and the off-resonant property of the tetranuclear complex is superior to that of the dinuclear one.

The effect of introducing charges on the two-photon absorption (TPA) is examined using the models involving the dicationic styrylpyridine units linked with a diphenyl diacetylene bridge. It turns out that the introduction of charges causes the red shift and drastic enhancement of TPA cross-section as compared to that in the neutral molecule. This is primarily ascribed to be the enhancement of transition moment between the first and second excited states, the feature of which is associated with the decrease of orbital interaction among the LUMOs of both-end dicationic styrylpyridines and the HOMO and LUMO of the central diphenyl diacetylene bridge.

Two-photon absorption (TPA) spectra are presented for newly synthesized bis(pyridylstyryl)-substituted diacetylene and related methyl triflate derivatives. The TPA cross section of a derivative (MPPBT) was found to increase drastically with decreasing the incident wavelength below 650 nm and to reach (2.42±0.46)×10 −47 cm 4 s molecule −1 photon −1 at 571 nm, in addition to the weaker, lowest energy TPA peak centered at 764 nm. A four-state model was needed to account for the observed spectral shape, suggesting that the drastic enhancement is due to one-photon resonance enhancement not only of the lowest energy TPA transition but also of a higher energy two-photon transition.

The two-photon absorption (2PA) properties of a series of dyes containing donor and acceptor groups connected via a π-electronic bridge were studied by using a femtosecond Z-scan technique. It was found that the nature of the π-electronic bridge does not substantially affect the measured 2PA intensities. In the case of the substituted azobenzenes the decrease of the strength of the donor and/or acceptor groups leads to decrease of the 2PA intensity, the effect of the acceptor strength being greater.

The electronic second hyperpolarizability γ of the carbon tetrachloride molecule is calculated by the ab initio molecular orbital method considering electron correlation with large basis sets. The static electronic γ value with the CCSD(T) method is 1.65 times the Hartree-Fock value, indicating a considerable electron correlation effect. Taking account of the frequency dispersion and vibrational effects, we estimate the most probable theoretical γ value at 800 nm to be around 17900au (9.0 × 10−36 esu). On the other hand, the experimental value recently observed by optical Kerr effect method is 10.6 × 10−36 esu at 800nm. It is concluded that the major part of the experimental χ(3) value of carbon tetrachloride can account for the static electronic hyperpolarizability.

Static molecular second hyperpolarizabilities γ of several donor-π-acceptor molecules have been examined using an ab initio molecular orbital (MO) method to evaluate the effects of substituents and molecular distortion on γ. It was found that γ values of the donor-π-acceptor compounds are affected by the degree of π electron delocalization more than the donor or acceptor strength of the substituents. Also it was found that contributions from higher order excitation process are not negligible for γ values of the donor-π-acceptor molecules.

The nonlinear refractive index, as well as the two-photon absorption (TPA), has been investigated by the femtosecond Z-scan method for push–pull molecules, in which a primary donor group is weakened by conversion into a pyrrole or related heterocycle. The results at the fast response time show that, contrary to what had been expected from a previous work, there is a little decrease in the nonlinear refractive index change by introduction of the weaker donor groups. Although the measured TPA spectra showed that the observed nonlinear refractive index change was regarded to be off-resonant; difference in the frequency dispersion among the molecules considerably contributes to the decrease, in addition to difference in the intrinsic static nonlinearity. This shows that there is some future in the development of these non-resonant materials.