Dynamic stark effect in strongly coupled microcavity exciton polaritons

We present experimental observations of a nonresonant dynamic Stark shift in strongly coupled microcavity quantum well exciton polaritons-a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10?K by femtosecond pump-probe measurements, with the blueshift approaching the meV scale for a pump fluence of 2 mJ?cm^{-2} and 50?meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi?doublet remains unaffected by the blueshift. The demonstrated effect should allow generation of ultrafast density-independent potentials and imprinting well-defined phase profiles on polariton condensates, providing a powerful tool for manipulation of these condensates, similar to dipole potentials in cold-atom systems.     

Comparisons of measured rate constants with spectroscopically determined electron-transfer parameters

This work involves comparison of rate constants measured for an intervalence (IV) compound with electron-transfer parameters derived from its optical absorption spectrum. The temperature-dependent rate constants for the radical cation having 3-tert-butyl-2,3-diazabicyclo[2.2.2]oct-2-yl (hydrazine) charge-bearing units attached para to a tetramethylbenzene bridge (1+) were previously measured. In this study, resonance Raman is used to calculate the magnitudes of the distortions of normal modes of vibration caused by excitation into the intervalence absorption band. These data produce a vibrational reorganization energy lambdavsym of 9250 cm(-1), and averaged single-mode omegav for use in the Golden Rule equation of 697 cm(-1). Zhu-Nakamura theory has been used to calculate preexponential factors for analysis of the previously measured variable temperature optical spectra using quartic-enhanced intervalence bands to extract the total reorganization energy and the intramolecular electron-transfer rate constants for intramolecular electron transfer using electron spin resonance. In contrast to using the Golden Rule equation, separation of lambda into solvent and vibrational components is not significant for these data. The Zhu-Nakamura theory calculations produce ln(k/T) versus 1/T slopes that are consistent with the experimental data for electronic couplings that are somewhat larger than the values obtained from the optical spectra using Hush's method.     

Best-possible bounds on the set of copulas with given degree of non-exchangeability

We establish best-possible bounds on the set of quasi-copulas with given degree of non-exchangeability. These bounds are shown to be best-possible bounds as well for the set of copulas with given degree of non-exchangeability, and, consequently, also on the set of bivariate distribution functions of continuous random variables with given margins and given degree of non-exchangeability. Non-exchangeability of a (quasi-)copula is measured in the sense of Nelsen, i.e.?proportional to the maximal absolute difference between this (quasi-)copula and its transpose.     

"Almost delocalized" intervalence compounds

Interest is high in +M-bridge-M systems that have very low barriers to intramolecular electron transfer giving M-bridge-M+ ("almost delocalized" systems). Hush showed how to evaluate the electronic coupling across the bridge (H) from the M-to-M charge-transfer optical absorption band, but did not point out that his classical model causes the extinction coefficient to suddenly drop to zero at a photon energy of 2 H. Ignoring this band cutoff leads to a low estimation of H.     

Synthesis and ligand exchange reactions of P2Pd(II) and P2Pt(II) salicylaldimates

Reaction of (dppe)MCl(2)(dppe = 1,2-bis(diphenylphosphino)ethane) with 2-(N-phenyliminomethyl)phenol leads to air-stable (dppe)M(N,O) chelates (M = Pd, 1a; M = Pt, 1b). The N-4-methylphenyl derivative of 1a has been characterized by X-ray analysis. The N,O ligands are kinetically labile and exchange occurs in solution in the presence of other salicylaldimines. In the presence of anilines, a metal-mediated imine exchange process occurs. Hammett analysis reveals that the platinum complexes are sensitive to the electronics at N but not at O. Electron donating groups on the N-aryl ring stabilize the metal complex.     

Ionized bicyclo[2.2.2]oct-2-ene: a twisted olefinic radical cation showing vibronic coupling

The bicyclo[2.2.2]oct-2-ene radical cation (1(.+)) exhibits matrix ESR spectra that have two very different types of gamma-exo hydrogens (those hydrogens formally in a W-plan with the alkene pi bond), a(2H) about 16.9 G and a(2H) about 1.9 G, instead of the four equivalent hydrogens as would be the case in an untwisted C(2v) structure. Moreover, deuterium substitution showed that the vinyl ESR splitting is not resolved (and under about 3.5 G); this is also a result of the twist. Enantiomerization of the C(2) structures is rapid on the ESR timescale above 110 K (barrier estimated at 2.0 kcalmol(-1)). Density functional theory calculations estimate the twist angle at the double bond to be 11-12 degrees and the barrier as 1.2-2.0 kcalmol(-1). Single-configuration restricted Hartree-Fock (RHF) calculations at all levels that were tried give untwisted C(2v) structures for 1(.+), while RHF calculations that include configuration interactions (CI) demonstrate that this system undergoes twisting because of a pseudo Jahn-Teller effect (PJTE). Significantly, twisting does not occur until the sigma-orbital of the predicted symmetry is included in the CI active space. UHF calculations at all levels that include electron correlation (even semiempirical) predict twisting at the alkene pi bond because they allow the filled alpha and the beta hole of the SOMO to have different geometries. The 2,3-dimethylbicyclo[2.2.2]oct-2-ene radical cation (2(.+)) is twisted significantly less than 1(.+), but has a similar temperature for maximum line broadening. Neither the 2,3-dioxabicyclo[2.2.2]octane radical cation (3(.+)) nor its 2,3-dimethyl-2,3-diaza analogue (5(.+)) shows any evidence of twisting. Calculations show that the orbital energy gap between the SOMO and PJTE-active orbitals for 3(.+) is too large for significant PJTE stabilization to occur.     

Pseudo-para-dinitro[2.2]paracyclophane radical anion, a mixed-valence system poised on the Class II/Class III borderline

Analysis of optical spectra of a pseudo-para-dinitro[2.2]paracyclophane radical anion using Marcus-Hush theory reveals that its off diagonal coupling element, H(ab), is large enough, relative to its reorganization energy, to change it from a localized class II compound to a delocalized class III compound by changing solvents. The optical spectra, along with frontier orbital analysis, show that the assumption that E(op) = 2H(ab) for class III compounds is not true in this case.     

Tuning aryl, hydrazine radical cation electronic interactions using substituent effects

Absorption spectra for 2,3-diaryl-2,3-diazabicyclo[2.2.2]octane radical cations (2(X)(*+)) and for their monoaryl analogues 2-tert-butyl-3-aryl-2,3-diazabicyclo[2.2.2]octane radical cations (1(X)(*+)) having para chloro, bromo, iodo, cyano, phenyl, and nitro substituents are reported and compared with those for the previously reported 1- and 2(H)(*+) and 1- and 2(OMe)(*+). The calculated geometries and optical absorption spectra for 2(Cl)(*+) demonstrate that p-C6H4Cl lies between p-C6H4OMe and C6H5 in its ability to stabilize the lowest energy optical transition of the radical cation, which involves electron donation from the aryl groups toward the pi*(NN)(+)-centered singly occupied molecular orbital of 2(X)(*+). Resonance Raman spectral determination of the reorganization energy for their lowest energy transitions (lambda(v)(sym)) increase in the same order, having values of 1420, 5300, and 6000 cm(-1) for X = H, Cl, and OMe, respectively. A neighboring orbital analysis using Koopmans-based calculations of relative orbital energies indicates that the diabatic aryl pi-centered molecular orbital that interacts with the dinitrogen pi system lies closest in energy to the bonding pi(NN)-centered orbital and has an electronic coupling with it of about 9200 +/- 600 cm(-1), which does not vary regularly with electron donating power of the X substituent.     

Kinetics of the reactions of chlorine atoms with CH3ONO and CH3ONO2

The kinetics of the reactions of Cl atoms with CH₃ONO and CH₃ONO₂ have been studied using relative rate techniques. In 700 Torr of nitrogen diluent at 295 ± 2K, k(Cl + CH₃ONO) = (2.1 ± 0.2) × 10⁻¹² and k(Cl + CH₃ONO₂) = (2.4 ± 0.2) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹. The result for k(Cl + CH₃ONO₂) is in good agreement with the literature data. The result for k(Cl + CH₃ONO) is a factor of 4.5 lower than that reported previously. It seems likely that in the previous study most of the loss of CH₃ONO which was attributed to reaction with Cl atoms was actually caused by photolysis leading to an overestimate of k(Cl + CH₃ONO). © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 357–359, 1999     

The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas

In this Note we show that the set of quasi-copulas is a complete lattice, which is order-isomorphic to the Dedekind–MacNeille completion of the set of copulas. Consequently, any set of copulas sharing a particular statistical property is guaranteed to have pointwise best-possible bounds within the set of quasi-copulas. To cite this article: R.B. Nelsen, M. Úbeda Flores, C. R. Acad. Sci. Paris, Ser. I 341 (2005).