The enthalpy of formation of 2II CH

The standard enthalpy of formation, δ_fH^o, of² II CH has been determined at converged levels of ab initio electronic structure theory, including high order coupled cluster and full configuration interaction benchmarks. The atomic Gaussian basis sets employed include the (aug)-cc-p(C)VXZ family with X = 3, 4, 5 and 6. Extrapolations to the complete one-particle basis set and the full configuration interaction limits, where appropriate, have been performed to reduce remaining computational errors. Additional improvements in the enthalpy of formation of ²II CH were achieved by appending the valence-only treatment with core-valence correlation, relativistic effects including spin-orbit correlation, and the diagonal Born-Oppenheimer correction. The recommended values for δfH^o ₀ and δA_f H _o ²⁹⁸ of ²II CH are 592.48^+0.47 _?0.56 kJ mol_?1 and 595.93 ^+0.47 _?0.56 kJ mol_?1, respectively.     

A combinatorial setting for questions in Kazhdan — Lusztig theory

Let(W, S) be a Coxeter group. Let s ₁ ... s _k be a reduced expression for an element y in W. A combinatorial setting involving subexpressions of this reduced expression is developed. This leads to the notion of good elements. It is proved that all elements in a group where the coefficients of Kazhdan — Lusztig polynomials are non-negative are good. If y is good then an algorithm is developed to compute these polynomials in a very efficient way. It is further proved that in these cases, the coefficients of these polynomials can be identified as sizes of certain subsets of subexpressions thereby providing an explicit setting for various questions regarding these polynomials and related topics. Similar results are obtained for the so-called parabolic case.Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthdayPartially supported by NSF grant No. DMS 8502310.     

New screening doublets in x-ray satellite spectra

Recent scrutiny of the relevant data available at present on x-ray satellite spectra in theK, L andM regions revealed the existence of two new satellite pairsα″α′ andα″α′ ₃ ′ in theKα satellite group, three pairsα′ ₂ α″,α′ ₂ α^VI andα? α ^IV in theLα satellite group, twoLβ ₂ satellite groups; viz.,β ₂ ^(b) (β ₂ ^I ,β ₂ ^II β ₂ ^(c) ) andβ ₂ ^(c) (β ₂ ^I β ₂ ^II ), two pairsγ′₁ γ′₂ andγ′₁ γ′_2′ in theLγ satellite group and also a pairβ _II β _III in theMβ satellites, which are all found to be governed by the screening doublet relationship,Δ(v/R)^1/2=constant.     

Behaviour of some faintK β for elements As(33) to Ru(44)

1. 1.
   It has been shown that the semi-Moseley graphs for theβ ₈,β ₇,β ₆,β ₅,β ₄,β ^?,β ₁₁ ^? andβ ₀ in theK-series for elements over the rangeZ=33 toZ=44 reported byHulubei, Cauchois andManescu become remarkably regular when referred toα ₁ instead ofβ ₁ as the parent line.     

Monomer volume fraction profiles in pH responsive planar polyelectrolyte brushes

Spatial dependencies of monomer volume fraction profiles of pH responsive polyelectrolyte brushes were investigated using field theories and neutron reflectivity experiments. In particular, planar polyelectrolyte brushes in good solvent were studied and direct comparisons between predictions of the theories and experimental measurements are presented. The comparisons between the theories and the experimental data reveal that solvent entropy and ion‐pairs resulting from adsorption of counterions from the added salt play key roles in affecting the monomer distribution and must be taken into account in modeling polyelectrolyte brushes. Furthermore, the utility of this physics‐based approach based on these theories for the prediction and interpretation of neutron reflectivity profiles in the context of pH responsive planar polyelectrolyte brushes such as polybasic poly(2‐(dimethylamino)ethyl methacrylate) (PDMAEMA) and polyacidic poly(methacrylic acid) (PMAA) brushes is demonstrated. The approach provides a quantitative way of estimating molecular weights of the polymers polymerized using surface‐initiated atom transfer radical polymerization. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 956–964     

A Statistic on Involutions

We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I(n) denote the set of all involutions on [n](={1,2,..., n}) and let F(2n) denote the set of all fixed point free involutions on [2n]. For an involution , let || denote the number of 2-cycles in . Let[ n] _q =1+q++q^n-1 and let denote the q-binomial coefficient. There is a statistic wt on I(n) such that the following results are true.(i) We have the expansion