Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality

Linear fractional composition operators on H2

If ? is an analytic function mapping the unit diskD into itself, the composition operatorC _? is the operator onH ² given byC _?f=fo?. The structure of the composition operatorC _? is usually complex, even if the function ? is fairly simple. In this paper, we consider composition operators whose symbol ? is a linear fractional transformation mapping the disk into itself. That is, we will assume throughout that $$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$ for some complex numbersa, b, c, d such that ? maps the unit diskD into itself. For this restricted class of examples, we address some of the basic questions of interest to operator theorists, including the computation of the adjoint.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Iodine fluorosulfate reactions with fluorocarbons

Iodine monofluorosulfate has been found to react with fluoroolefins in the absence of a solvent to give the corresponding iodo alkyl fluorosulfates by addition of ?l and ?OSO₂F across the double bond. The observed products were ICF₂CF₂SO₃F, CF₃CFlCF₂SO₃F, and the isomer mixture ICF₂CFClSO₃F and ICFClCF₂SO₃F. Perfluorocyclobutene was unreactive. The iodine fluorosulfate used for this study was synthesized from the reactions of either I₂ or R_fI with ClSO₃F, with both reactions being new routes to this compound. These iodo fluorocarbon fluorosulfates are novel compounds and were characterized by spectroscopy and by formation of the derivatives CF₃CFICFO and ICF₂CFO.     

Charge donation to and dearomatization of benzene attending complexation: DFT estimates of binding energies of TpMXO(L) with benzene, for Tp = hydridotris(pyrazolyl) borate, MXO = MoNO, ReCO, and WNO, and L = ammonia, N-methylimidazole, pyridine, phosphine, methyl isocyanide, and carbon monoxide

By density functional methods we characterize the bonding and charge distribution in complexes of benzene with dearomatizing agents tpReCO(L), tpMoNO(L), and tpWNO(L), where tp = hydrido Tris (pyrazolyl)borate), for a range of ligands L. Our LSDA and B3LYP density functional calculations use the Spartan LACVP+ basis and pseudopotential on Re, Mo, and W and 6-31G* on light atoms. The binding energy is strongly dependent on the nature of the ligand L, being greatest for L = ammonia and N-methylimidazole and weakest for CH3NC and CO. We find a correlation between strength of binding and electron transfer from the dearomatizing agents toward benzene. For the most strongly bound systems we find substantial (up to 500 millielectrons) charge transfer towards benzene, while for the most weakly bound systems charge is withdrawn from benzene. Structural details illustrate the ability of Re, Mo, and W species to dearomatize complexed benzene, which is extensive for all but the most weakly bound species with L = MeNC and CO. Re and W dearomatizing agents, which are computed and observed to form stable complexes with benzene, may be economic alternatives to osmium dearomatizing agents.     

Bond additivity corrections for G3B3 and G3MP2B3 quantum chemistry methods

We have developed bond additivity correction (BAC) procedures for the G3-based quantum chemistry methods, G3B3 and G3MP2B3. We denote these procedures as BAC-G3B3 and BAC-G3MP2B3. We apply the procedures to compounds containing atoms from the first three rows of the periodic table including H, B, C, N, O, F, Al, Si, P, S, and Cl atoms. The BAC procedure applies atomic, molecular, and pairwise bond corrections to theoretical heats of formation of molecules. The BAC-G3B3 and BAC-G3MP2B3 procedures require parameters for each atom type but not for each bond type. These parameters have been obtained by minimizing the error between the BAC-G3B3 and BAC-G3MP2B3 predictions and the experimental heats of formation for a 155 molecule reference set, containing open and closed shell molecules representing various functional groups, multireference configurations, isomers, and degrees of saturation. As compared to former BAC-MP4, BAC-G2, and BAC-hybrid methods, BAC-G3B3 provides better agreement with experiment for a wider range of chemical moieties, including highly oxidized species involving SOx s, NOx s, POx s, and halogens. The BAC-G3B3 and BAC-G3MP2B3 procedures are applied to an extended test suite involving 273 compounds. We assess the overall quality of BAC-G3B3 with experiments and other theoretical approaches. For the reference set, the average error for the BAC-G3B3 results is 0.44 kcal/mol as compared to 0.82 kcal/mol for the raw G3B3. For the extended test set, the average error for the BAC-G3B3 results is 0.91 kcal/mol as compared to 1.38 kcal/mol for the raw G3B3. As compared to the other BAC procedures, the improved predictive capability of BAC-G3B3 and BAC-G3MP2B3 procedures is, to a large extent, due to the improved quality of G3-based methods resulting in much smaller BAC correction terms.