Edith Botek

Synthesis and Characterization of Teranthene: A Singlet Biradical Polycyclic Aromatic Hydrocarbon Having Kekulé Structures

A teranthene derivative has been successfully isolated in a crystalline form for the first time. Geometrical considerations and physical property investigations indicate that the molecule possesses prominent biradical character in the ground state.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Møller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

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.

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.

Theoretical study of the second-order nonlinear optical properties of [N]helicenes and [N]phenylenes.

The second-order nonlinear optical properties of helicenes and phenylenes have been theoretically investigated at the time-dependent Hartree-Fock level using the Austin model 1 semiempirical Hamiltonian. Both the antisymmetric isotropic component of the first hyperpolarizability (beta) and its projection on the dipole moment (beta(parallel)) have been determined for increasingly large helical systems as well as for their analogs substituted by donor/acceptor pairs. It is found that (i) in nonsubstituted helicenes and phenylenes, beta increases monotonically with the size of the system and slightly depends on the nature of the helix; (ii) the corresponding beta(parallel) is mostly determined by the radial component of the first hyperpolarizability vector; (iii) in helicenes, beta(parallel) is positive and presents quasiperiodic oscillations with the helix; (iv) in phenylenes, beta(parallel) depends upon the size of the helix and it can be either positive or negative as a result of the differences in evolution with N of the radial components of the dipole moment and first hyperpolarizability. Substituting the helicenes and phenylenes by the prototypical NH2/NO2 donor/acceptor pair provides a diversity of effects on beta and beta(parallel) that encompasses decrease, increase, and change in sign.

Second Hyperpolarizability of Zethrenes

We report a study on the static second hyperpolarizabilities (γ) of zethrenes using the UBHandHLYP hybrid density functional theory method. Though zethrenes were originally considered as closed-shell systems, the values of their diradical characters, calculated from the occupation numbers of spin-unrestricted Hartree-Fock natural orbitals (UNOs), demonstrate an open-shell diradical nature, which increases with the size of the middle ring region because of the recovery of the aromaticity in that region. As references, we examine also the γ values of tetrabenzopolyacenes, which are regarded as the corresponding closed-shell systems due to their negligible diradical characters. It is found that the longitudinal γ values for zethrenes are much larger than those of the corresponding reference closed-shell systems, whereas their ratio, γ(zethrene)/γ(reference), is reduced when increasing the length of middle ring regions, i.e., when increasing the diradical character.

Second-Harmonic Generation in GFP-like Proteins

The second-order nonlinear optical properties of green fluorescent proteins (GFPs), such as the photoswitchable Dronpa and enhanced GFP (EGFP), have been studied at both the theoretical and experimental levels. In the case of Dronpa, both approaches are consistent in showing the rather counterintuitive result of a larger second-order nonlinear polarizability (or first hyperpolarizability, beta) for the protonated state, which has a higher transition energy, than for the deprotonated, fluorescent state with its absorption at lower energy. Moreover, the value of beta for the protonated form of Dronpa is among the highest reported for proteins. In addition to the pH dependence, we have found a wavelength dependence in the beta values. These properties are essential for the practical use of Dronpa or other GFP-like fluorescent proteins as second-order nonlinear fluorophores for symmetry-sensitive nonlinear microscopy imaging and as nonlinear optical sensors for electrophysiological processes. An accurate value of the first hyperpolarizability is also essential for any qualitative analysis of the nonlinear images.

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.

Theoretical Study on Second Hyperpolarizabilities of Singlet Diradical Square Planar Nickel Complexes Involving o-Semiquinonato Type Ligands

Hybrid density functional theory method is applied for investigating the diradical character dependence of the second hyperpolarizability (gamma) 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 gamma ranging from 14 x 10(3) to 819 x 10(3) au. In particular, the largest gamma 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 gamma values of these complexes.