The electronic states of carbon monofluoride: Rydberg states

Hartree-Fock and multiconfiguration Hartree-Fock calculations are reported on some low-lying Rydberg states of CF and the ground state of CF⁺. For the CF⁺ ground state, ¹Σ⁺, the calculations give a bond length of 1.55 Å, a fundamental frequency of 1821 cm^?1, and a dissociation energy of 6.9 eV. Many interactions between the valence and Rydberg state manifolds are revealed. Also a strong mixing of the 3dσ and 4sσ components due to an accidental degeneracy is described.     

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.     

Computational investigation into the fluorescence of luciferin analogues

Luciferin analogues that display bioluminescence at specific wavelengths can broaden the scope of imaging and biological assays, but the need to design and synthesize many new analogues can be time-consuming. Employing a collection of previously synthesized and characterized aminoluciferin analogues, we demonstrate that computational TD-DFT methods can accurately reproduce and further explain the experimentally measured fluorescence wavelengths. The best computational approach yields a correlation with experiment of r = 0.98, which we expect to guide and accelerate the further development of luciferin analogues. © 2018 Wiley Periodicals, Inc.     

Probing noise in flux qubits via macroscopic resonant tunneling

Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than the target well. The rms amplitude of the noise, which is proportional to the dephasing rate 1/tauphi, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.     

Comparison between algebraic and topological K-theory of locally convex algebras

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product , and that the obstruction for the comparison map to be an isomorphism is (absolute) algebraic cyclic homology. We prove the existence of an exact sequence (Theorem 6.2.1)We show that cyclic homology vanishes in the case when J is the ideal of compact operators and L is a Fréchet algebra whose topology is generated by a countable family of sub-multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family (Theorem 8.3.3). This proves the generalized version of Karoubi's conjecture due to Mariusz Wodzicki and announced in his paper [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].We also consider stabilization with respect to a wider class of operator ideals, called sub-harmonic. Every Fréchet ideal is sub-harmonic, but not conversely; for example the Schatten ideal Lp is sub-harmonic for all p>0 but is Fréchet only if p?1. We prove a variant of the exact sequence above which essentially says that if A is a C-algebra and J is sub-harmonic, then the obstruction for the periodicity of K_∗(AC_⊗J) is again cyclic homology (Theorem 7.1.1). This generalizes to all algebras a result of Wodzicki for H-unital algebras announced in [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].The main technical tools we use are the diffeotopy invariance theorem of Cuntz and the second author (which we generalize in Theorem 6.1.6), and the excision theorem for infinitesimal K-theory, due to the first author.     

Humidity effects on the stability of a sandpile

Humidity is well-known to significantly affect the mechanical properties, static as well as dynamic, of granular materials. We present the method of humidification of granular media from an under-saturated vapor that we designed in order to experimentally quantify such moisture-induced effects under accurately-controlled humidity conditions. We report the quantitative measurements of the maximum angle of stability of a pile made of small glass beads, as a function of the relative vapor pressure, up to close to saturation. The results obtained with liquids differing in their wetting properties on glass, namely water and heptane, are presented. It is shown that the wetting properties of the liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. Received 26 October 1998 and Received in final form 30 March 1999     

Computer simulation of proton channelling in silicon

The channelling of 3 MeV protons in the 〈110〉 direction of silicon has been simulated using Vineyard model taking into account thermally vibrating nuclei and energy loss due to ion-electron interactions. A beam made up of constant energy particles but with spatial divergence has been simulated for the purpose. The values of the minimum scattering yield and half width of the channelling dip are shown to be depth sensitive and agree well with the measured values. The dependence of yield on the angle of incidence has been found to give information of all three types of channelling. The critical angles for the three types of channelling and wavelength of planar oscillations are consistent with the previous calculations.     

Some geometric properties of metric ultraproducts of finite simple groups

In this article we prove some previously announced results about metric ultraproducts of finite simple groups. We show that any non-discrete metric ultraproduct of alternating or special linear groups is a geodesic metric space. For more general non-discrete metric ultraproducts of finite simple groups, we are able to establish path-connectedness. As expected, these global properties reflect asymptotic properties of various families of finite simple groups.     

Transition-metal-free intramolecular N-arylations

N-Substituted phenoxazines and related aza analogs have been prepared from N-acetylated aryloxy anilides by transition-metal-free, base-catalyzed cyclization reactions. In the presence of a mixture of 10 mol % of N,N'-dimethylethylenediamine (DMEDA) and 2 equiv of K(2)CO(3) in toluene at 135 °C the products are obtained in high yields.     

Polynomials with and without determinantal representations

The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov [9] have proved that any real zero polynomial in two variables has a determinantal representation. Brändén [2] has shown that the result does not extend to arbitrary numbers of variables, disproving the generalized Lax conjecture. We prove that in fact almost no real zero polynomial admits a determinantal representation; there are dimensional differences between the two sets. The result follows from a general upper bound on the size of linear matrix polynomials. We then provide a large class of surprisingly simple explicit real zero polynomials that do not have a determinantal representation. We finally characterize polynomials of which some power has a determinantal representation, in terms of an algebra with involution having a finite dimensional representation. We use the characterization to prove that any quadratic real zero polynomial has a determinantal representation, after taking a high enough power. Taking powers is thereby really necessary in general. The representations emerge explicitly, and we characterize them up to unitary equivalence.