Theoretical study on the second hyperpolarizabilities of phenalenyl radical systems involving acetylene and vinylene linkers: diradical character and spin multiplicity dependences

We have investigated the static second hyperpolarizabilities (gamma) of the singlet diradical systems with intermediate diradical character involving phenalenyl radicals connected by acetylene and vinylene pi-conjugated linkers, 1 and 2, using the hybrid density functional theory. For comparison, we have also examined the gamma values of the closed-shell and pure diradical systems with almost the same molecular size as 1 and 2. In agreement with our previous prediction of the diradical character dependence of gamma, it turns out that the gamma values of 1 and 2 are significantly enhanced compared to those of the closed-shell and pure diradical systems. In the present case, distinct differences in gamma values are not observed between the two pi-conjugated linkers, though the diradical character is found to depend on the kind of linker. Furthermore, we have investigated the spin multiplicity effect on gamma. Changing from the singlet to the triplet state, the gamma values of the systems with intermediate diradical character in the singlet state are quite reduced, though those of the pure diradical systems are hardly changed. Such spin multiplicity dependence of gamma is understood by considering the difference of diradical character between their singlet states together with the Pauli principle. The present results provide a possibility of a novel control scheme of gamma for phenalenyl radical systems involving pi-conjugated linkers by adjusting the diradical character through the change of the linked position of pi-conjugated linkers and the spin multiplicity.     

Oligoacenes: theoretical prediction of open-shell singlet diradical ground states

A series of oligoacenes from benzene to decacene were studied computationally with DFT and CASSCF methods. In contrast to the common view that acenes are closed-shell systems or may have a triplet ground state, these results offer the first theoretical predictions for the singlet ground state and diradical character for oligoacenes. The nature of the ground states of these molecules arises from the disjoint nature of the NBMOs that are singly occupied in the diradical.     

Enhancement of second hyperpolarizabilities in open-shell singlet slipped-stack dimers composed of square planar nickel complexes involving o-semiquinonato type ligands

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-C(6)H(4)X(2))(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-C(6)H(4)S(NH(2))](2). It is found that for interplanar distance ranging between 3.0 and 5.0 ? the slipped-stack dimers with intermediate monomer diradical characters exhibit larger γ values per monomer (γ(dimer)/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 = (γ(dimer)/2)/γ(monomer) 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.     

Phenyloxenium ions: more like phenylnitrenium ions than isoelectronic phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.     

Nucleus-independent chemical shifts (NICS): distance dependence and revised criteria for aromaticity and antiaromaticity

Nucleus-independent chemical shifts (NICS) have been used extensively for the identification of aromaticity properties of molecules, ions, intermediates, and transition states since their introduction in 1996 by Schleyer et al. Initially, probes (bq's) were placed at the centers of systems (NICS(0)) and later, 1A above the molecular planes (NICS(1)). However, contradicting assignments of aromaticity by NICS and other methods were found for some systems. In this article, an alternative NICS-based method is introduced. The method is based on scanning NICS values over a distance and separating them into in-plane and out-of plane contributions. The shapes of the plots of the chemical shifts and their components as a function of the distance of the NICS probe (bq) from the molecular plane give a clear indication of diamagnetic and paramagnetic ring currents. This method is applied to several (4n + 2)- and 4n pi-electron systems (molecules and ions) in the singlet and triplet electronic states, including some of the problematic systems mentioned above. It is also shown that relative aromaticities of rings in polycyclic systems (local aromaticities) cannot be estimated by comparing NICS or NICS-scan values.     

Second hyperpolarizability of phenalenyl radical system involving acetylene π-conjugated bridge

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.     

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.     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.     

Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory

Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.     

Giant electric field effect on the second hyperpolarizability of symmetric singlet diradical molecules

This contribution reveals the effects of a static electric field on the static second hyperpolarizability γ of symmetric singlet diradical molecules using the valence configuration interaction scheme. It is found that under the effect of a field, the component of γ along the axis joining the two radical sites can be gigantically (approximately two to three orders) enhanced for symmetric diradicals having intermediate diradical characters with respect to those of closed-shell and pure diradical molecules in the absence of a field. Moreover, this electric field enhancement of γ increases as a function of the diradical character. These results and their analysis propose therefore a new strategy to design materials with exceptional nonlinear optical responses.     

Towards Magnetic Carbo‐meric Molecular Materials

Numerous studies have underlined the putative diradical character of π‐conjugated molecules that can be described by closed‐shell Lewis structures, for instance, p‐dimethylene p–n phenylenes, or long polyacenes. In the latter compounds, the only way to save the aromaticity of the six‐membered rings is to give up the Lewis electron pairing in the singlet biradical ground state. The present work considers the possibility of doing the same by using the basic C₂ units of carbo‐meric architectures. A series of acyclic and cyclic carbo‐meric architectures is studied by using UB3LYP DFT broken‐symmetry calculations, including spin decontaminations and subsequent geometry optimization of the singlet diradical. The C₂ units are shown to stabilize the singlet biradical by spin delocalization, two of them playing approximately the same role as one radical‐insulating 1,4 phenylene moiety. The results are generalized to the investigation of open‐shell polyradical singlet states of rigid hydrocarbon structures, the symmetry and rigidity of which can assist cooperativity and self spin polarization effect. Several synthesis targets with challenging magnetic/spin properties are suggested in the carbo‐mer series.     

Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character

The origin of the diradical character dependence of the second hyperpolarizability (gamma) of neutral singlet diradical systems is clarified based on the perturbation formula of gamma using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of gamma in the intermediate diradical character region turns out to originate from the increasing magnitude of the transition moment between the first and second excited states and the decrease of that between the ground and first excited states, respectively, with the increase in diradical character. This feature confirms that open-shell singlet conjugated molecules with intermediate diradical characters constitute a new class of third-order nonlinear optical systems, whose gamma values can be controlled by the diradical character in addition to the conjugation length.     

S-shaped para-Quinodimethane-Embedded Double [6]Helicene and Its Charged Species Showing Open-Shell Diradical Character

Helicenes and extended helical π-conjugated compounds have been widely studied, but most of the systems contain only aromatic benzene or heterocyclic rings, showing local aromatic character. Herein, new S-shaped double [6]helicene 1 , which has two embedded para-quinodimethane (p-QDM) units, is reported. Due to the existence of a proaromatic quinoidal substructure, it has open-shell diradical character. Its model compound, C-shaped single [6]helicene 2 containing one p-QDM unit, was also synthesized and compared. Their ground-state structures and electronic properties were systematically studied by a combination of various experimental methods assisted by theoretical calculations. Compound 1 has a double-helical structure in the crystal, with the two terminal [6]helicene units bent in opposite directions (i.e., anti form). However, an anti/syn isomerization process with a moderate interconversion energy barrier was observed on the NMR timescale. Compound 1 shows amphoteric redox behavior. It also exhibits open-shell diradical character (y₀=12.1 %) and a small singlet–triplet gap. On the other hand, compound 2 has a typical closed-shell nature. The dication and dianion of 1 also show open-shell diradical character. The dianion of 2 and the tetraanion of 1 exhibit similar electronic structures to their respective isoelectronic structures, that is, [6]helicene and a double [6]helicene. This work provides some insights into the design and synthesis of stable helical π systems with open-shell diradical character and magnetic activity.     

A DFT study of the ground state multiplicities of linear vs angular polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.     

Intramolecular singlet and triplet excimers of triply bridged [3.3.N](3,6,9)carbazolophanes

Intermoiety electronic interactions in the singlet and triplet excimer states of triply bridged [3.3.n](3,6,9)carbazolophanes ([3.3.n]Cz, n=3-6) were studied by emission and transient absorption measurements. In these [3.3.n]Cz molecules, the dihedral angle and the separation distance r between fully overlapped two carbazole rings change systematically from nearly parallel (n=3, r=3.35 A) to oblique (n=6, r=4.03 A). In rigid glass at 77 K, [3.3.n]Cz (n=3, 4) (r<4 A) exhibited red-shifted and structureless excimer fluorescence and phosphorescence while [3.3.n]Cz (n=5, 6) (r>4 A) exhibited monomer-like vibrational fluorescence and phosphorescence. In solution at 130 K, all [3.3.n]Cz molecules exhibited an excimeric fluorescence band while [3.3.5]Cz still exhibited monomer-like phosphorescence. Transient absorption spectra measured at 294 K exhibited local excitation and charge-transfer bands for all [3.3.n]Cz molecules in the excited singlet and triplet states, suggesting that not only singlet but also triplet excimers of carbazole are formed at room temperature. Furthermore, the singlet-triplet energy gap decreased with the decrease in n, suggesting that electrons are effectively delocalized over the two carbazole moieties. These findings showed that both singlet and triplet excimers of carbazole are formed with a separation distance shorter than about 4 A and are most stable in the parallel-sandwich structure and that the configurational mixing between exciton resonance and charge resonance states plays an essential role in the formation of singlet and triplet excimers of carbazole.     

The Electronic Properties of Diradicals

A review of the various possible definitions of diradicals leads the authors to describe these systems as having two odd electrons in degenerate or nearly-degenerate molecular orbitals. A study of the wave-function for the two odd electrons shows that its form depends entirely on whether the diradical is homo- or heterosymmetric. Energy schemes are given in these two cases, as well as in the intermediate “non-symmetric” case. The extent of zwitterionic character in diradical states is also investigated. This is followed by a discussion of intersystem crossing between singlet and triplet diradical states via spin-orbit coupling and other mechanisms. The electronic matrix elements for spin-orbit coupling are calculated and evaluated numerically for various model cases. It is then possible to establish general rules for favorable (electronic) intersystem crossing. In 1,3 or 1,4 diradicals its efficiency is estimated to be comparable with that in aromatics. The role of the electron-nuclear hyperfine interaction in mixing singlet and triplet states, particularly in CIDNP, is explained. Finally the question of whether diradicals actually occur as secondary minima on potential energy surfaces is examined. Recent quantum-mechanical calculations, in contradiction to some thermochemical and kinetic evidence, lead to flat singlet surfaces without significant minima.     

The diradical character of polyacenequinododimethides

Abstract  

An electronic structure study of singlet and triplet states of two series of polyacenequinododimethides was performed using the B3LYP method. It was found that the ground state of all examined polyacenequinododimethides is a singlet with significant diradical character. The diradical character of the compounds under investigation was estimated using the unrestricted symmetry-broken and complete active space methods. It was shown that polyacene-2,3-quinododimethides have more pronounced diradical character than polyacene-2,x-quinododimethides. The diradical character of polyacene-2,x-quinododimethides monotonically increases with their increasing molecular size. Within the series of polyacene-2,3-quinododimethides the diradical character is not a monotonic function of the number of hexagons. It was found that pentacene-2,3-quinododimethide has the most pronounced diradical character in this series. It can be predicted on the basis of the singlet–triplet gap values that even higher polyacenequinododimethides will be singlet, but not triplet molecules.     

Reversible Self-Assembling of Boryl Radical Anions to Their Diradicals with Tunable Singlet Ground States

Two novel boron-centered diradicals based on dimesitylpyridine borane ( 1 ) were synthesized by the self-assembling of the corresponding radical sodium and potassium salts, respectively. The sodium diradical was obtained by re-dissolving the crystals of the radical salt 1Na in toluene, while the potassium diradical was directly obtained by the reduction of 1 with potassium in THF. The diradicals could be converted back to their radical anions in THF solution, forming a reversible process. EPR spectroscopy and SQUID measurements, together with theoretical calculations, show that the diradicals have singlet ground states with excited triplet states. Their singlet–triplet energy gaps are tunable with metals.     

Photoinduced Metallonitrene Formation by N2 Elimination from Azide Diradical Ligands

Transition-metal nitrides/nitrenes are highly promising reagents for catalytic nitrogen-atom-transfer reactivity. They are typically prepared in situ upon optically induced N₂ elimination from azido precursors. A full exploitation of their catalytic potential, however, requires in-depth knowledge of the primary photo-induced processes and the structural/electronic factors mediating the N₂ loss with birth of the terminal metal-nitrogen core. Using femtosecond infrared spectroscopy, we elucidate here the primary molecular-level mechanisms responsible for the formation of a unique platinum(II) nitrene with a triplet ground state from a closed-shell platinum(II) azide precursor. The spectroscopic data in combination with quantum-chemical calculations provide compelling evidence that product formation requires the initial occupation of a singlet excited state with an anionic azide diradical ligand that is bound to a low-spin d⁸-configured Pt^II ion. Subsequent intersystem crossing generates the Pt-bound triplet azide diradical, which smoothly evolves into the triplet nitrene via N₂ loss in a near barrierless adiabatic dissociation. Our data highlight the importance of the productive, N₂-releasing state possessing azide ππ* character as a design principle for accessing efficient N-atom-transfer catalysts.     

A triplet mechanism for the formation of cyclobutane pyrimidine dimers in UV-irradiated DNA

The reaction pathways for the photochemical formation of cyclobutane thymine dimers in DNA are explored using hybrid density functional theory techniques. It is concluded that the thymine-thymine [2 + 2] cycloaddition displays favorable energy barriers and reaction energies in both the triplet and the singlet excited states. The stepwise cycloaddition in the triplet excited state involves the initial formation of a diradical followed by ring closure via singlet-triplet interaction. The triplet mechanism is thus completely different from the concerted singlet state cycloaddition processes. The key geometric features and electron spin densities are also discussed. Bulk solvation has a major effect by reducing the barriers and increasing the diradical stabilities. The present results provide a rationale for the faster cycloreaction observed in the singlet excited states than in the triplet excited states.