LUMINESCENT AND NONLINEAR OPTICAL PROPERTIES OF ORGANOMETALLIC COMPLEXES

Organometallic chromophores with both luminescent and second-order nonlinear optical properties are of growing interest as new molecular multifunctional materials, since they offer additional flexibility compared to organic chromophores by introducing active electronic charge-transfer transitions between the metal and the ligand, which are tunable by virtue of the nature, oxidation state and coordination sphere of the metal centre. This is the main reason why our interest was brought in this specific research area. My PhD thesis is divided in two main parts: 1) Luminescent properties of cyclometallated metal complexes. 2) Second-order NLO properties of organometallic complexes and third-order NLO activity of organic \u3c0-conjugated and coordination compounds. The first section is dedicated to the preparation and study of the luminescence properties of some novel platinum(dipyridylbenzene) complexes. These organometallic compounds, known for being extremely bright emissive and having long lifetimes, are of particular interest for applications in electroluminescent devices. My aim was to achieve mono- and dinuclear complexes possessing emission properties that can be tuned with external factors. The two dinuclear platinum(II) complexes that I synthesized alternate monomer-like and eximeric emission, depending on the temperature, the solvent and the presence of metal cations in solution. The mononuclear platinum(II) complexes that I studied, instead, bear a photochromic unit linked with different tethers to the metal moiety: this allows the modulation of their switching ability and the study of the effect of the linker. These complexes were prepared in Rennes, France, during my stay in the group of Dr. V. Guerchais. The second section is dedicated to the second-order nonlinear optical properties of mononuclear platinum(dipyridylbenzene) complexes. In the first place, we will discuss how the second-order NLO properties of such compounds can be modified by virtue of the presence of different \u3c0-conjugated pendants linked to the central metal unit with different bridges: this will allow a fine tuning of the NLO properties. Secondly, we will study related photochromic platinum(II) complexes and see that their second-order NLO properties are switchable, too. The two-photon absorption (TPA) ability of different organic \u3c0-conjugated and organometallic complexes will be discussed. At first, the outstanding TPA properties of some 3,4,9,10-perylenetetracarboxylic diimide derivatives will be presented. These purely organic compounds will be used as springboard to achieve new multinuclear ruthenium(II) complexes with a highly \u3c0-conjugated ligand. Afterwards, the TPA activity of some ruthenium(II) \u3c3-acetylide and iridium(III) tris-(phenylpyridine) complexes will be discussed. The two-photon absorption measurements were performed in the laboratory of Dr. K. Kamada, in Ikeda, Japan, during my stay there. Throughout this dissertation, the luminescent, second- and third-order nonlinear optical properties of a new multifunctional cationic iridium(III) complex will also be presented

Asymptotic corrections to the eigenvalue density of the GUE and LUE

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density, to which we apply the saddle point method. The main correction to the bulk density is oscillatory in N and depends on the distribution function of the limiting density, while the corrections to the Airy kernel at the soft edge are again expressed in terms of the Airy function and its first derivative. We demonstrate numerically that these expansions are very accurate. A matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk.Comment: 14 pages, 4 figure

Perylenetetracarboxy-3,4:9,10-diimide derivatives with large two-photon absorption activity

Three new perylenetetracarboxy-3,4:9,10-diimides, bearing 2,6-diisopropylphenyl groups at the imide positions and 4-(R-ethynyl)phenoxy moieties (R = 4,7-di(2-thienyl)benzo[c][1,2,5]thiadiazole (P2), pyrene (P3) or pyrene-CH2OCH2 (P4)) at the four bay positions, were prepared, along with the known related derivative (R = phenyl (P1)), and well characterized. They have large two-photon absorption (TPA) cross-sections (sigma(2)), as determined by the Z-scan technique, the highest values being reached with P2 which bears a planar -delocalized donor moiety. P3 is characterized by higher sigma(2) values than both P1, as expected for the higher -conjugation of the donor pyrene moiety with respect to phenyl, and P4, due to the presence of the flexible and non-conjugated CH2OCH2 bridge between the pyrene and the ethynyl fragment in the latter compound. The molecular geometry of P1-P4 has been optimized by DFT modeling, showing that in P2 and P3 the bay substituents are stacked due to the - interactions of both pyrene and thiophene groups. The LUMO of P1-P4 lies at the same energy and is essentially delocalized on the perylene core whereas the HOMO and HOMO-1 of both P2 and P3 are degenerate and do not show contribution from the perylene core contrarily to that of P1 and P4. The HOMO-LUMO gap is therefore essentially influenced by the HOMO which reflects the electronic charge delocalization on the bay substituents, the lower gaps being observed for P2 and P3, which are characterized by the best TPA properties

Finite one dimensional impenetrable Bose systems: Occupation numbers

Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupations $\lambda_i$ of effective single particle states $\phi_i$, in the theoretical 1d impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The $\lambda_i$ and $\phi_i$ are the eigenvalues and eigenfunctions respectively of the one body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed $i$ the occupations $\lambda_i$ are asymptotically proportional to $\sqrt{N}$ in both the circular and harmonically trapped cases.Comment: 22 pages, 8 figures (.eps), uses REVTeX

Moments of the Position of the Maximum for GUE Characteristic Polynomials and for Log-Correlated Gaussian Processes

We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional Brownian motion with Hurst index $H \to 0$ (fBM0). In previous collaborations we obtained the probability distribution function (PDF) of the value of the global minimum (equivalently maximum) for the first two processes, using the {\it freezing-duality conjecture} (FDC). Here we study the PDF of the position of the maximum $x_m$ through its moments. Using replica, this requires calculating moments of the density of eigenvalues in the $\beta$-Jacobi ensemble. Using Jack polynomials we obtain an exact and explicit expression for both positive and negative integer moments for arbitrary $\beta >0$ and positive integer $n$ in terms of sums over partitions. For positive moments, this expression agrees with a very recent independent derivation by Mezzadri and Reynolds. We check our results against a contour integral formula derived recently by Borodin and Gorin (presented in the Appendix A from these authors). The duality necessary for the FDC to work is proved, and on our expressions, found to correspond to exchange of partitions with their dual. Performing the limit $n \to 0$ and to negative Dyson index $\beta \to -2$, we obtain the moments of $x_m$ and give explicit expressions for the lowest ones. Numerical checks for the GUE polynomials, performed independently by N. Simm, indicate encouraging agreement. Some results are also obtained for moments in Laguerre, Hermite-Gaussian, as well as circular and related ensembles. The correlations of the position and the value of the field at the minimum are also analyzed.Comment: 64 page, 5 figures, with Appendix A written by Alexei Borodin and Vadim Gorin; The appendix H in the ArXiv version is absent in the published versio

Measuring social synchrony and stress in the handler-dog dyad during animal assisted activities : a pilot study

Synchrony\u2014the coordination of behavior between interacting partners\u2014is a complex phenomenon requiring the perception and integration of multimodal communicative signals. Originally conceptualized by developmental psychologists to study the human-human relationship, it could also apply to cross-species interactions. Here, we examined synchrony patterns as a potentially important mechanism to evaluate human-dog interactions during animal-assisted activities. Four dog handler-dog dyads were videotaped before (T0), during (T1), and after (T2) 45-minute sessions of animal-assisted activities and coded for the following synchrony patterns: gaze synchrony, joint attention, and touch synchrony. Both partners' salivary cortisol and heart rate and dogs' behaviors were measured to identify any signs of stress that would lower levels of synchrony. All dyads showed synchronous behaviors in T0 and T1, whereas these were absent in T2. On average, the highest frequency was recorded in T1 (P < 0.05), particularly with regard to joint attention. All dogs fulfilled most of their handler's cues (74%; P < 0.05) while working with a patient, showing appropriate levels of cooperation. No stress-related signs were detected in either the dogs or their human handlers. These findings highlight the human-dog bonding as one prototypical context for studying the biologic basis of cross-species social synchrony. This may also generate evidence-based knowledge that can help strengthen the scientific foundation of current canine-assisted intervention practices

Symbol-Based Analysis of Finite Element and Isogeometric B-Spline Discretizations of Eigenvalue Problems: Exposition and Review

We present an example-based exposition and review of recent advances in symbol-based spectral analysis. We consider constant- and variable-coefficient, second-order eigenvalue problems discretized through the (isogeometric) Galerkin method based on B-splines of degree p and smoothness C k , 0 64 k 64 p- 1. For each discretized problem, we compute the so-called symbol, which is a function describing the asymptotic singular value and eigenvalue distribution of the associated discretization matrices. Using the symbol, we are able to formulate analytical predictions for the eigenvalue errors occurring when the exact eigenvalues are approximated by the numerical eigenvalues. In this way, we recover and extend previous analytical spectral results. We are also able to predict the existence of p- k spectral branches, one \u201cacoustical\u201d and p- k- 1 \u201coptical\u201d, when discretizing the one-dimensional Laplacian eigenvalue problem. We provide explicit and implicit analytical expressions for these branches, and we quantify the divergence to infinity with respect to p of the largest optical branch in the case of C smoothness (the case of classical finite element analysis)

Tuning the dipolar second-order nonlinear optical properties of 5-π-delocalized-donor-1,3-di(2-pyridyl) benzenes, related cyclometallated platinum(II) complexes and methylated salts

The synthesis and characterization of three 5-π-delocalized-donor-1,3-di(2-pyridyl)benzenes is reported along with that of their related cyclometallated platinum(II) complexes and N,N-dimethylated iodide salts. The second-order nonlinear optical (NLO) properties of all the compounds have been determined by the Electric Field Induced Second Harmonic generation technique, showing how the μβEFISH absolute value of 1,3-di(2-pyridyl)benzenes can be tuned by the nature of the substituent on position 5 of the central benzene ring, and greatly increased by cyclometallation to Pt or by N-methylation