Benchmark calculations with correlated molecular wavefunctions. XIII. Potential energy curves for He2, Ne2 and Ar2 using correlation consistent basis sets through augmented sextuple zeta

The potential energy curves of the rare gas dimers He2, Ne2, and Ar2 have been computed using correlation consistent basis sets ranging from singly augmented aug-cc-pVDZ sets through triply augmented t-aug-cc-pV6Z sets, with the augmented sextuple basis sets being reported herein. Several methods for including electron correlation were investigated, namely Møller—Plesset perturbation theory (MP2, MP3 and MP4) and coupled cluster theory [CCSD and CCSD(T)]. For He2 CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 7.35 cm-1 (10.58 K), with an estimated complete basis set (CBS) limit of 7.40 cm-1 (10.65 K). The latter is smaller than the 'exact' well depth (Aziz, R. A., Janzen, A. R., and Moldover, M. R., 1995, Phys. Rev. Lett., 74, 1586) by about 0.2 cm-1 (0.35 K). The Ne2 well depth, computed with the CCSD(T)/d-aug-cc-pV6Z method, is 28.31 cm-1 and the estimated CBS limit is 28.4 cm-1, approximately 1 cm-1 smaller than the empirical potential of Aziz, R. A., and Slaman, M., J., 1989, Chem. Phys., 130, 187. Inclusion of core and core—valence correlation effects has a negligible effect on the Ne2 well depth, decreasing it by only 0.04 cm-1. For Ar2, CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 96.2 cm-1. The corresponding HFDID potential of Aziz, R. A., 1993, J. chem. Phys., 99, 4518 predicts of De of 99.7 cm-1. Inclusion of core and core-valence effects in Ar2 increases the well depth and decreases the discrepancy by approximately 1 cm-1.     

Obstructions to lifting automorphisms of free algebras

ABSTRACT

A monomial basis and a filtration of subalgebras for the universal enveloping algebra 𝔘(𝔤 _l ) of a complex simple Lie algebra 𝔤 _l of type A _l is given in this note. In particular, a new multiplicity formula for the Weyl module V(λ) of 𝔘(𝔤 _l ) is obtained in this note.     

Metal‐nanoparticle plasmonics

The rapid emergence of nanoplasmonics as a novel technology has been driven by recent progress in the fabrication, characterization, and understanding of metal‐nanoparticle systems. In this review, we highlight some of the key advances in each of these areas. We emphasize the basic physical understanding and experimental techniques that will enable a new generation of applications in nano‐optics.     

Crystallization of dense binary hard-sphere mixtures with marginal size ratio

Molecular dynamics simulations are performed for binary hard-sphere mixtures with a size ratio of gamma =0.9 and a volume fraction of phi=0.58 over a range of compositions. We show how, at this high volume fraction, crystallization depends sensitively on the composition. Evidence is presented that crystallization in these mixtures does not proceed by the standard nucleation and growth paradigm. Rather, some crystallite forms almost immediately and then an interplay between compositional fluctuations and crystal growth is able to dramatically extend the time scale on which further crystallization occurs. This can be seen as a form of geometric frustration.     

i-perfectm-cycle systems,m ≤ 19

Summary For allm 19 and each meaningful value ofi (2 i m/2), the spectrum problem fori-perfectm-cycle systems is examined.     

Polymerizable derivatives of long-chain fatty acids. IV. Vinyl esters

Contrary to some published reports, the vinyl esters of saturated fatty acids polymerize readily and rapidly. Vinyl oleate, when present in excess of 5%, and oxygen exert marked retarding effects. Techniques are described for the free-radical-initiated polymerization of the vinyl esters of caprylic, capric, lauric, myristic, palmitic, and stearic acids in bulk, dispersion, solution, and emulsion. Some data are given for polymerization in the presence of chain-transfer agents, such as carbon tetrachloride, dodecylmercaptan, and ethylbenzene. Conditions are reported for obtaining degrees of polymerization from about 2 (when chain-transfer agents are employed) to 10,000 (weight average). The weight average degree of polymerization increases markedly as the conversion increases, particularly above 80%. Even up to extremely high conversions, soluble polymers are obtained in most cases. Solubility characteristics, transition point data, molecular weights (osmometric and light-scattering), and isolation and purification techniques are also reported.     

Temporal evolution of an electron-free afterglow in the pulsed plasma polymerisation of acrylic acid

By use of time and energy-resolved mass spectrometry, negative ions with masses ranging from m/z = 1-287 amu have been observed in the afterglow of a low-pressure (10 mTorr) pulsed acrylic acid polymerizing plasma. The most intense peaks, seen at m/z = 71, 143, 215, and 287, are assigned to the dehydrogenated oligomer of the form [nM-H](-) for n = 1, 2, 3, and 4, respectively. The results strongly suggest that both m/z = 71 and 143 ions are produced in the on period of the pulse cycle (0.1 ms duration), with higher masses m/z = 215 and 287 being produced by neutral ion chemistry in the off period (up to 40 ms in duration). The increase in the intensity of the [3M-H](-) and [4M-H](-) peaks in the off period is accompanied by a rapid fall in the concentration of [M-H]- ions and electrons, the latter decreasing from approximately 10(15) m(-3) to zero within 150 micros. Deep into the afterglow, Langmuir probe measurements show that the charge species only consist of positive and negative ions, present at equal concentrations in excess of approximately 10(14) m(-3) even after 10 ms that is, the plasma is wholly electron free. To describe the growth of large negative ions a number of possible ion-neutral chemical pathways have been postulated, and a calculation of the ambipolar diffusion rates to the walls suggests that, in the off period, the positive and negative ion contribution to the deposition rate is small ( approximately 1%) compared to the net total deposition rate. However, the observations do indicate that it may be necessary to update models of film growth in the pulsed plasma polymerization of acrylic acid to account for negative ions.     

4H‐1‐Benzopyrans by a tandem SN2‐SNAr reaction

Treatment of 2‐fluoro‐5‐nitrobenzyl bromide with active methylene compounds in the presence of excess potassium carbonate in acetone leads to the formation of highly functionalized 4H‐1‐benzopyrans by a tandem S_N2‐S_NAr reaction sequence. The reaction works well with β‐keto esters, β‐keto sulfones, β‐keto phosphine oxides, β‐keto phosphonates and β‐keto nitriles. The reaction is simple to perform and affords products in 50‐92% yields.     

Estimation of the persistence length of DNA from the torsion elastic constant and supercoiling free energy: effect of ethylene glycol

Two different methods are proposed to estimate the persistence length ( P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter ( E T ) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E T for model DNAs that possess the measured alpha and selected trial values of P. Comparison of the computed E T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (kappa beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E T , alpha, kappa beta (or P), and an unknown "constant" ( B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E T via this analytical expression agree with those determined from the simulations and E T values reckoned from the input alpha and kappa beta by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing kappa beta. The original analytical expression is modified to take this apparent variation of B with kappa beta into account. By using this modified analytical relation to estimate P (from the measured alpha and E T ) or E T (from the input alpha and kappa beta), much closer agreement is obtained respectively with the values of P or E T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.