Almost One Bit Violation for the Additivity of the Minimum Output Entropy

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_k,t. We also showed that the set K_k,t is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of \({\ell^p}\) norms on the set K_k,t and prove that the maximum is attained on a vector of shape (a, b, . . . , b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show that for any \({\varepsilon > 0}\), it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183, and that for appropriate choice of parameters, the violation can be as large as \({\log 2 -\varepsilon}\). Conversely, our result implies that, with probability one in the limit, one does not obtain a violation of additivity using conjugate random quantum channels and the Bell state, in dimension 182 and less.     

Synthetic,Optical and Theoretical Study of Alternating Ethylenedioxythiophene–Pyridine Oligomers: Evolution from Planar Conjugated to Helicoidal Structure towards a Chiral Configuration

A series of alternating 3,4‐ethylenedioxythiophene–alkynylpyridine oligomers (DA)_n with increased solubility are synthesized and their photophysical properties and nonlinear optical properties are investigated. Their quadratic polarizabilities are determined from hyper‐Rayleigh scattering experiments to obtain information on their conformations in solution. These chromophores, based on the alternation of electron‐rich (D) and electron‐deficient (A) moieties, exhibit optical properties that arise from the combination of dipolar and helicoidal features in the (DA)_n homologue series where n=1–4. The transition from dipolar conjugated planar structures (n=1, 2) to helicoidal structures (n=3, 4) is clearly evidenced by results from symmetry‐sensitive second‐order nonlinear optical experiments. This suggests an approach towards highly efficient chiral chromophores for second‐order nonlinear optics. Interestingly, this structural evolution also has significant impact on the photophysical properties: both absorption and fluorescence emission show bathochromic and hyperchromic shifts with increasing number of repeating units in the dipolar planar derivatives (n=1–2) but show saturation effects in the helicoidal structures (n=2–4). In addition, the helicoidal structures show sizeable two‐photon absorption at 700–750 nm (40–100 GM) for compounds lacking either electron‐donating or electron‐withdrawing substituents.     

Copolymerization of 2,3,4,5,6‐Pentafluorostyrene and Methacrylic Acid by Nitroxide‐Mediated Polymerization: The Importance of Reactivity Ratios

Amphiphilic block copolymers of 2,3,4,5,6‐pentafluorostyrene (PFS) and methacrylic acid (MAA) are synthesized via nitroxide‐mediated polymerization (NMP). It is established that to obtain a controlled copolymerization a minimum of 40 mol% of PFS is required, which is significantly greater than other copolymerization systems such as using 4.5–8 mol% styrene or 1 mol% of 9‐(4‐vinylbenzyl)‐9H‐carbazole to control the copolymerization of methacrylates. It is surmised that this lack of control is due to the reactivity ratios that favor the addition of MAA rather than PFS (r_PFS = 0.14, r_MAA = 6.97). However this reactivity ratio pair suggests that a one‐shot delayed injection approach can be utilized to synthesize almost pure block copolymers in one pot. Therefore, poly(PFS)‐b‐(PFS‐ran‐MAA) block copolymers are synthesized by a one‐shot delayed addition of MAA. While the concentration of irreversibly terminated chains is evident these results suggest a promising route to the synthesis of fluorinated amphiphilic block copolymers by NMP.

     

Redox-driven intramolecular anion translocation between a metal centre and a hydrogen-bond-donating compartment

Dicationic ligands incorporating two 2,2'-bipyridine units and two imidazolium moieties, [1](2+) and [2](2+), form stable chelate complexes with Cu(II) and Cu(I) in acetonitrile solution. Each Cu(II) complex binds two X(-) ions according to two stepwise equilibria, the first involving the Cu(II) centre and the second involving the bis-imidazolium compartment. Cu(I) complexes are able to host only one NO(3)(-) ion in the bis-imidazolium cavity, while other anions induce demetallation. Thus, in the presence of one equivalent of NO(3)(-), the Cu(II)/Cu(I) redox change makes the anion translocate quickly and reversibly from one binding site to the other within the [Cu(II,I)(1)](4+/3+) system, as demonstrated by cyclic voltammetry and controlled-potential electrolysis experiments.     

Aminoborylene complexes of group 6 elements and iron: a synthetic, structural, and quantum chemical study

Transition-metal-borylene complexes of the type [(OC)(5)M=BR] {M=Cr, Mo, W; R=N(SiMe(3))(2), 1a-3a, Si(SiMe(3))(3), 4a} and [(OC)(4)Fe=B=N(SiMe(3))(2)] (8) were prepared by salt elimination reactions. Synthesis of the latter complex was accompanied by the formation of substantial amounts of an unusual dinuclear iron complex [Fe(2){mu-C(2)O(2)(BN(SiMe(3))(2))}(2)(CO)(6)] (9). The aminoborylene complexes of Group 6 metals were converted to trans-[(Cy(3)P)(CO)(4)M=B=N(SiMe(3))(2)] (5a-7a) by irradiation in the presence of PCy(3). Structural and spectroscopic parameters were discussed with respect to the trans-effect of the borylene ligand and the degree of M-B d(pi)-p(pi)-backbonding. Computational studies were performed on Group 6-borylene complexes. The population and topological analyses as well as the molecular orbital composition are consistent with the presence of both sigma-and pi-type interactions. There are, however, indications that the d(pi)-p(pi)-backbonding in the silylborylene complex is significantly more pronounced than in the aminoborylene complexes.     

Assessment of time-dependent density functional schemes for computing the oscillator strengths of benzene, phenol, aniline, and fluorobenzene

In present study the relevance of using the time-dependent density functional theory (DFT) within the adiabatic approximation for computing oscillator strengths (f) is assessed using different LDA, GGA, and hybrid exchange-correlation (XC) functionals. In particular, we focus on the lowest-energy valence excitations, dominating the UV/visible absorption spectra and originating from benzenelike HOMO(pi)-->LUMO(pi(*)) transitions, of several aromatic molecules: benzene, phenol, aniline, and fluorobenzene. The TDDFT values are compared to both experimental results obtained from gas phase measurements and to results determined using several ab initio schemes: random phase approximation (RPA), configuration interaction single (CIS), and a series of linear response coupled-cluster calculations, CCS, CC2, and CCSD. In particular, the effect of the amount of Hartree-Fock (HF) exchange in the functional is highlighted, whereas a basis set investigation demonstrates the need of including diffuse functions. So, the hybrid XC functionals--and particularly BHandHLYP--provide f values in good agreement with the highly correlated CCSD scheme while these can be strongly underestimated using pure DFT functionals. These results also display systematic behaviors: (i) larger f and squares of the transition dipole moments (mid R:mumid R:(2)) are associated with larger excitation energies (DeltaE); (ii) these relationships present generally a linear character with R>0.9 in least-squares fit procedures; (iii) larger amounts of HF exchange in the XC functional lead to larger f, R:mumid R:(2), as well as DeltaE values; (iv) these increases in f, mid R:mumid R:(2), and DeltaE are related to increased HOMO-LUMO character; and (v) these relationships are, however, not universal since the linear regression parameters (the slopes and the intercepts at the origin) depend on the system under investigation as well as on the nature of the excited state.     

An analytical derivative procedure for the calculation of vibrational Raman optical activity spectra

We present an analytical time-dependent Hartree-Fock algorithm for the calculation of the derivatives of the electric dipole-magnetic dipole polarizability with respect to atomic Cartesian coordinates. Combined with analogous procedures to determine the derivatives of the electric dipole-electric dipole and electric dipole-electric quadrupole polarizabilities, it enables a fully analytical evaluation of the three frequency-dependent vibrational Raman optical activity (VROA) invariants within the harmonic approximation. The procedure employs traditional non-London atomic orbitals, and the gauge-origin dependence of the VROA intensities has, therefore, been assessed for the commonly used aug-cc-pVDZ and rDPS:3-21G basis sets.     

Chemical end-grafting of homogeneous polystyrene monolayers on mica and silica surfaces

Homogeneous polystyrene monolayers covalently end-attached on mica and silica surfaces were obtained using a "graft to" methodology. The grafting was achieved via nucleophilic substitution between silanol groups (Si-OH) containing surface and monochlorosilyl terminated polystyrene (PS). Different parameters, such as surface activation, grafting reaction time, polymer concentration, nature of solvent, and presence of catalyst, were investigated to determine the optimal conditions for creating very homogeneous and stable polymer monolayers. Ellipsometry, atomic force microscopy (AFM), surface forces apparatus (SFA), and contact angle measurements were used to characterize the polymer-grafted layers. An efficient plasma activation procedure was established to create a maximum number of silanol groups on mica surfaces without increasing the surface roughness. Surface reactivity was investigated by grafting trimethylchlorosilane (TMS) on OH-activated mica and silica. The maximum TMS surface coverage on activated mica is similar to that observed for silica. The stability of covalently attached TMS and PS layers in toluene and water were investigated. Both grafted layers (TMS and PS) partially detached from the mica and silica surfaces when immersed in water. Hydrolysis of the siloxane bond between the monochlorosilyl groups and the surface is the most probable cause of layer degrafting. The degrafting was much slower with the long PS polymer chains, compared to the small TMS molecules, which may act as a protective layer against hydrolysis.