Relativistic virial theorem for diatomic molecules. Application to H 2 +

Summary The virial theorem for a molecule in the relativistic clamped-nuclei approximation is derived. The individual energy contributionsA (momentum energy),B (mass energy),T=A+B (kinetic energy) andV (potential energy) are expressed in terms ofE, E/R (derivate w.r.t. the nuclear coordinates) and the relativistic correction E/² (derivative w.r.t. Sommerfield's fine-structure constant ). IfE and E/R are known as functions of , then all individual energy terms are also known as functions of . As an example, numerical results for H ₂ ⁺ are presented. The relativistic and nonrelativistic potential energy curves and the paradoxical behavior of their different contributions are analyzed and interpreted in both the largeR and shortR ranges.Dedicated to Professor W. Kutzelnigg on the occasion of his 60th birthday     

The vibrational spectra and normal coordinate analysis of tetracyclopropyllead

All the fundamental frequencies observed in IR and Raman spectra have been assigned to the normal modes of the molecule (C₃H₅)₄Pb (C₃H₅ = cyclopropyl). The calculated force field is compared to that of (C₃H₅)₂Hg and the Cmetal stretching force constants are discussed along with those of Me₄Pb and Me₂Hg; The similarity of the spectra of cyclopropyllead and cyclopropyl-mercury proves that the vibrations of cyclopropyl structural units are isolated in both molecules.     

Relativistic perturbation theory of molecular structure

Summary The recently developed relativistic double perturbation theory is extended to handle relativistic changes of molecular structure more easily. This is achieved by simple coordinate scalings. Accurate higher order mixed perturbation energies for H ₂ ⁺ are calculated. The relativistic changes of bond energy,DE, of bond length,R _e , and especially of force constant,k, and of anharmonicity,a, are large, up to 100%·(Z/c)². The dominant contributions tok anda are due to the indirect change of the nonrelativistick anda connected with the relativistic change of bond length. Accordingly the relativistic changes obey Badger's and Gordy's rules (–RDEk).Dedicated to Prof. Klaus Ruedenberg in appreciation of his fundamental contributions to both formal theory and physical explanations in quantum chemistry     

Photochemical syn-anti isomerization reactions in N2-hydroxyisocytosines--an experimental matrix isolation and theoretical study

N2-hydroxyisocytosine and 1-methyl-N2-hydroxyisocytosine were studied using a matrix isolation technique combined with infrared absorption spectroscopy. For N2-hydroxyisocytosine isolated in an Ar matrix (at 10 K), two imino-oxo isomers, one with the hydroxyimino =N-OH group directed toward the N1-H group (the form called further anti) and the second with the =N-OH group directed toward N3-H (syn), were observed in the ratio 1.4:1. The syn isomer is converted totally to the anti form after UV (lambda > 295 nm) irradiation of the matrix. A small amount of the N(3)H-hydroxy-amino tautomer of N2-hydroxyisocytosine was also detected in the matrix. This form did not react photochemically. For 1-methyl-N2-hydroxyisocytosine, only the syn form of the imino-oxo tautomer was observed after deposition of the matrix. UV (lambda > 295 nm) irradiation induced a photoreaction converting this isomer into the anti form. After 15% of the starting material had been converted into the product, a photostationary state was achieved, and no further progress of the reaction was observed. Subsequent UV irradiation (lambda > 335 nm) caused a back reaction, leading to a disappearance of the anti form and to the recovery of the initial syn isomer. All isomers were identified by comparing their experimental IR spectra with the spectra theoretically calculated at the DFT(B3LYP)/6-31G(d,p) level, where DFT is the density functional theory. Good agreement between the observed and predicted patterns of the spectral lines allowed for reliable identification. The experimental IR spectra were interpreted and discussed. The relative energies of the 12 isomers of N2-hydroxyisocytosine were calculated at the MP2/6-31G(d,p) and MP4//MP2/6-31G(d,p) levels. For six isomers of 1-methyl-N2-hydroxyisocytosine, the calculations were carried out at the MP2/6-31G(d,p) level. The anti form of the imino-oxo tautomer of N-hydroxyisocytosine and the syn form of the imino-oxo tautomer of 1-methyl-N2-hydroxyisocytosine were predicted to be the most stable.     

Thermodynamic properties of the NdBr3–MBr binary systems (M = Na,K)

Thixoforming involves heating different types of alloys to the semisolid state at high heating rates and forming in die-casting machines or conventional presses. At temperatures higher than the solidus and lower than the liquidus, the mush metal behaves like a high-viscosity thixotropic material. Therefore, determining the thermodynamic behavior of the solid-to-liquid transition is paramount to control thixoforming processes. This article describes a simple, novel experimental setup based on differential thermal analysis (DTA) for analyzing the phase transitions in an alloy heated using high heating rates typical of industrial applications. A365 alloy was chosen to demonstrate the effectiveness of the method as the phase transformations for this alloy in semisolid materials (SSM) processing are well understood. Samples were heated to 750 °C using constant linear heating rates of 5, 10, 15, 20, 25, 50, 75, 100 and 125 °C min in a Norax 25 kW 8 kHz induction furnace with an Omron E5CK temperature controller. AISI 316 austenitic stainless steel was used as the inert reference. Comparison of the results of DTA using the proposed method and the results of simulation with Thermo-Calc^® indicates that the proposed in situ DTA device and its method is suitable for analyzing phase transitions when high heating rates are used.     

Tunable dual-band liquid crystal based near-infrared perfect metamaterial absorber with high-loss metal

ABSTRACT

In this work, a tunable dual-band near-infrared perfect metamaterial absorber formed by combining a highly birefringent nematic liquid crystal with a nanoscale metamaterial cavity arranged in mirror symmetry is designed and numerically investigated. Electromagnetic simulations indicate that the absorbance greater than 99.4% may be achieved at 328 THz and 364 THz. Perfect absorbance results both form the use of highly lossy metal and the optimization of the metamaterial structure. In addition, absorbance of the metamaterial device can be substantially tuned both in terms of its magnitude and wavelength with the spectral tunability up to 8 THz by switching of liquid crystal alignment. The soft-matter-based metamaterial absorbers may pave a crucial role towards various active multifunctional systems working in the near-infrared range.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

Chimera Spectrum Diagnostics for Peptides Using Two-Dimensional Partial Covariance Mass Spectrometry

The rate of successful identification of peptide sequences by tandem mass spectrometry (MS/MS) is adversely affected by the common occurrence of co-isolation and co-fragmentation of two or more isobaric or isomeric parent ions. This results in so-called `chimera spectra’, which feature peaks of the fragment ions from more than a single precursor ion. The totality of the fragment ion peaks in chimera spectra cannot be assigned to a single peptide sequence, which contradicts a fundamental assumption of the standard automated MS/MS spectra analysis tools, such as protein database search engines. This calls for a diagnostic method able to identify chimera spectra to single out the cases where this assumption is not valid. Here, we demonstrate that, within the recently developed two-dimensional partial covariance mass spectrometry (2D-PC-MS), it is possible to reliably identify chimera spectra directly from the two-dimensional fragment ion spectrum, irrespective of whether the co-isolated peptide ions are isobaric up to a finite mass accuracy or isomeric. We introduce ‘3-57 chimera tag’ technique for chimera spectrum diagnostics based on 2D-PC-MS and perform numerical simulations to examine its efficiency. We experimentally demonstrate the detection of a mixture of two isomeric parent ions, even under conditions when one isomeric peptide is at one five-hundredth of the molar concentration of the second isomer.