Microwave spectrum and structure of methyl phosphonic difluoride

The rotational spectrum of methyl phosphonic difluoride has been reinvestigated using a pulsed-molecular-beam Fabry-Perot cavity microwave spectrometer. The enhanced resolution of the Fourier transform microwave (FTMW) spectrometer (compared to the original work done in a conventional Stark spectrometer) has allowed the measurement of small A-E splittings of many of the rotational transitions caused by the internal rotation of the methyl top. The barrier to internal rotation, V₃ = 676 (25) cm⁻¹, has been determined experimentally from the A-E splittings of the rotational transitions in the ground vibrational state. This barrier height is substantially lower than the previously determined value for the barrier, which was 1252 (14) cm⁻¹. High-level ab initio calculations at the MP2/aug-cc-pVTZ level predict a barrier to internal rotation of 638 cm⁻¹, in agreement with the experimentally determined value found here. The high sensitivity of the FTMW spectrometer has also permitted the measurement of the ¹³C and ¹⁸O isotopomers in natural abundance. The addition of these two isotopomers has allowed an improved structural determination.     

The formation and decomposition kinetics of alkylidynes on Pt(111)

The formation and decomposition kinetics of ethylidyne and propylidyne on Pt(111), were studied using static secondary ion mass spectrometry and temperature programmed desorption. For the maximum amounts of dissociatively adsorbed ethylene and propylene formed during adsorption at 200 K and subsequent temperature programmed desorption, the following activation energies (E) and pre-exponential factors (A) are determined: (a) for ethylidyne formation: E = 17±1 kcal mol⁻¹ and A = 1×10^12±1 s⁻¹; (b) ethylidyne decomposition: E = 27 ±2 kcal mole⁻¹ and A = 6×10^11±1 s⁻¹; (c) propylidyne formation: E = 17.5 ± 2 kcal mol⁻¹ and A = 7×10^12±1 s⁻¹; and (d) propylidyne decomposition: E = 22.5±2 kcal mol⁻¹ and A = 4×10^{11 ± 1} s⁻¹.     

A kinetic study of the thermal decomposition process of potassium metabisulfite: Estimation of distributed reactivity model

The thermal decomposition kinetics of potassium metabisulfite was studied by thermogravimetric (TG) and differential thermogravimetric (DTG) techniques using non-isothermal experiments. The apparent activation energy (E_a) is determined using the differential (Friedman) isoconversional method. The results of the Friedman's isoconversional analysis of the TG data suggests that the investigated decomposition process follows a single-step reaction and the observed apparent activation energy was determined as 122.4±2.1 kJ mol⁻¹. A kinetic rate equation was derived for the decomposition process of potassium metabisulfite with contracting area model, f(α)=2(1−α)^1/2, which is established using the Malek's kinetic procedure. The value of pre-exponential factor (A) is also evaluated and was found to be A=1.37×10¹² min⁻¹. By applying the Miura's procedure the distributed reactivity model (DRM) for investigated decomposition process was established. From the dependence α versus E_a, the experimental distribution curve of apparent activation energies, f(E_a), was estimated. By applying the non-linear least-squares analysis, it was found that the Gaussian distribution model (with distribution parameters E₀=121.3 kJ mol⁻¹ and σ=1.5 kJ mol⁻¹) represents the best reactivity model for describing the investigated process. Using the Miura's method, the A values were estimated at five different heating rates and the average A values are plotted against E_a. The linear relationship between the A and E_a values was established (compensation effect). Also, it was concluded that the E_a values calculated by the Friedman's method and estimated distribution curve, f(E_a), are correct even in the case when the investigated decomposition process occurs through the single-step reaction mechanism.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

Effect of the second order spin orbit and spin-spin interactions on the E (G) level of Mn in ZnS

An interpretation of the structure of the ⁶A₁ → {₁A₁, ⁴E} zero phonon and phonon assisted transitions is given. Covalency effects show that the ⁶A₁ → ⁴A₁ and ⁶A₁ → ⁴E transitions are well separated; consequently none of the experimentally observed lines can be due to the ⁶A₁ → ⁴A₁ transition. The fine structure for the ⁴E level is interpreted in terms of the spin-spin and spin-orbit interactions. The results obtained are consistent with experiments.     

The Mössbauer effect and magnetic phase transitions

The Mössbauer effect provides a direct method for identifying the spin axis in magnetic crystals and observing magnetic phase transitions. The order of the transition may be inferred from the Mössbauer spectrum. Phase changes can occur as a function of temperature (e.g. when the anisotropy fieldB _A changes sign) or as a function of applied magnetic field. In an antiferromagnet a field ?(2B _E B _A)^1/2 along the spin axis whereB _E is the exchange field causes the spin-flop transition which is normally first order (sharp) whereas the transition to the paramagnetic phase which occurs at higher fields?2B _E is second order (continuous). In quasi-one-dimensional crystals Mössbauer spectra show that the spin-flop transition is first order locally but occurs over a range of fields throughout the crystal, so that the first order character is masked in a conventional magnetization measurement. In fields applied at a finite angle>B _A/2B _E to the spin axis the transition becomes second order, i.e. a continuous rotation of the spins occurs. In canted antiferromagnets (or weak ferromagnets) the spin-flop transition is also continuous; in addition a “screw” re-orientation may be induced by fields applied perpendicular to the spin axis and arises from antisymmetric exchange. For crystals with lowT _N the hyperfine field changes when a magnetic field is applied and has a minimum at a phase transition; this may be used to map out the magnetic phase diagram.     

Euler elasticae in the plane and the Whitney-Graustein theorem

In this paper, we study normal forms of plane curves and knots. We investigate the Euler functional E (the integral of the square of the curvature along the given curve) for closed plane curves, and introduce a closely related functional A, defined for polygonal curves in the plane ?² and its modified version A _R , defined for polygonal knots in Euclidean space ?³. For closed plane curves, we find the critical points of E and, among them, distinguish the minima of E, which give us the normal forms of plane curves. The minimization of the functional A for plane curves, implemented in a computer animation, gives a very visual approximation of the process of gradient descent along the Euler functional E and, thereby, illustrates the homotopy in the proof of the classical Whitney-Graustein theorem. In ?³, the minimization of A _R (implemented in a 3D animation) shows how classical knots (or more precisely thin knotted solid tori, which model resilient closed wire curves in space) are isotoped to normal forms.     

Secondary electron emission yield behaviour of polymers

The secondary electron emission yields of highly-insulating, thin polymer foils have been measured for incident primary beam energies, 50 ? E_p ? 2500 eV. The results follow closely a ‘universal’ reduced yield curve determined by the energy loss law, dE_p/dx = -A/E_p^n-1, where n = 2 and A is a constant proportional to the density of the solid, as predicted by the elementary theory of Lye and Dekker (1957). This behaviour remains true up to high primary beam energies and, as such, is unique to these low density solids.     

Realizations of the exceptional modular invariant A(1)1 partition functions

We show that the E₆ and E₈ modular invariant combinations of A⁽¹⁾₁ characters in the classification of Cappelli, Itzykson and Zuber can be realized as partition functions of k=1 conformally invariant WZW models on the group manifolds of Sp(4) and G₂, respectively. Together with the D₄ combination, which is known to be realized by the WZW model on SU(3), these are the only such cases where the SU(2) local symmetry extends to a larger one. The E₇ combination is briefly discussed.     

Zeeman effect in the 4A22E pair states in the first nearest neighbour Cr(III) pair in ruby

The Zeeman splitting of the ⁴A⁴₂A₂ → ⁴A²₂E transitions in the first nearest neighbour Cr(III) pair in ruby is determined by excitation spectroscopy. Previous assignments are shown to be incorrect and evidence is presented for a large trigonal field.     

The average structure of 5.10-Dihydro-5.10-Diethylphenazinium-Iodide (E2P·I1.6): A new linear chain Polyiodide compound

Upon oxidation of 5.10-dihydro-5.10-diethylphenazine (E₂P) with iodine golden-green lustrous crystals of a compound with stoichiometry E₂P.I_1.6 were isolated. The compound crystallizes in the tetragonal space group D₄² with $\text{a = 12.321(2)}\text{A}\text{?}$ and $\text{c = 5.330(2)}\text{A}\text{?}$. The E₂P and I form interpenetrating incommensurate sublattices along c, with an iodine repeat distance of 9.7 Å. Static susceptibility measurements at room temperature give χ_g = + 0.994 × 10^?6g^?1 × cm³. This corresponds to one unpaired electron spin per two formular units. Single-crystal EPR indicates that the paramagnetism is associated with weakly interacting E₂P⁺ cation radicals. The 300K-d.c. conductivity of 3×10^?2Ω^?1cm^?1 and activation energy of 0.17±0.02eV for single crystals is consequently associated with the polyiodide chains, and not with the E₂P⁺ cation radicals.     

Emission and laser-excitation spectra of rotationally cooled methylcyanodiacetylene cation (A˜2EāX˜2 E) and photoelectron—photon

The A?²EāX?² E band system of rotationally cooled methylcyanodiacetylene cation has been studied by emission and excitation spectroscopies. Spectra were obtained by electron-impact ionisation of a seeded helium supersonic free jet and by Penning ionisation followed by laser excitation. These data enable the vibrational frequencies of most of the A₁ fundamentals to be inferred for the X?²E (to within ±2 cm^?1) andX?²E (to within ±4 cm?1) states. The fluorescence quantum yields and lifetimes of the cation prepared in selected levels of theA?²E andB?²A₁, excited states have been determined by photoelectron—photon coincidence measurements and yield a quantitative insight into the radiationless-decay pathways.     

Fano line shape and anti-crossing of Raman active E2g peaks in the charge density wave state of NbSe2

Low energy Raman scattering from the ab-plane of the 2H polytype single crystal NbSe₂ has been investigated in the normal (N), incommensurate charge density wave (ICDW) and superconducting (SC) phases. The temperature dependence of the polarization resolved Raman response has been obtained for the excitation wavelength of 647 nm and fitted to phenomenological models for the E_2g and A_1g symmetry channels. The A_1g response can be fitted by a simple damped oscillator peak superimposed on continuous background. The E_2g response displays an anti-resonance interference pattern between the inter-layer phonon and the CDW-induced mode such that a hybridized configuration (Fano line shape [1]) is required for modelling. The polarization specific peak maxima positions and line widths as a function of temperature, deduced in this manner, are presented. Partial suppression of the electronic continuum scattering in the Raman shift range up to 110 cm⁻¹ in the A_1g symmetry channel and beyond 300 cm⁻¹ in the E_2g symmetry channel is indicative of high energy electronic states far away from the Fermi surface participating in the ICDW formation.     

Description of charge-exchange resonances in deformed nuclei

The (p, n) and (n, p) transition strength functions with excitation of the GT resonance, other 1⁺ states, spin-dipole with λ^π=0^- andE1 charge-exchange resonances in deformed nuclei in the regions 156≦A≦168 and 236≦A≦240 are calculated in the RPA. It is shown that the GT resonance has a maximum at 18–20 MeV, and in the region of 5–6 MeV around maximum (60–70)% of strength is concentrated. The spindipole resonance with λ^π=0^-, 1^- and 2^? strength is distributed within 14–33 MeV and theE1 strength within 25–29 MeV. The latter is splitted withΔE equal to 0.6–2 MeV into two peaks withI ^π I=1^-0 and 1^?1. In the region of 4–7 MeV around maximum 73–77% ofE1 strength is concentrated. The total (n,p) transition strength is 10–200 times as small as the total (p, n) transition strength.     

Dynamical structure of peptide molecules: Fourier transform microwave spectroscopy of N-methylpropionamide

In order to clarify the dynamical aspects of the peptide structure, N-methylpropionamide (NMPA) was investigated as an example of peptide molecules: XCONHY (X=CH₃CH₂ and Y=CH₃ for NMPA), paying special attention to the internal rotation of the two methyl groups. NMPA was found to have an almost planar skeleton with an extended syn/trans conformation, as indicated by the observed value of I_aa+I_bb−I_cc, and its rotational spectra were interpreted in terms of group G₁₈ consisting of six symmetry species: A₁, A₂, E₁, E₂, E₃, and E₄. The A₁ and E₂ spectra were observed split in most of b-type transitions, yielding the internal-rotation potential barrier V₃ of 796 (21) cm⁻¹ for CH₃ in the ethyl group referred to as C-CH₃. The spectra of the three E species: E₁, E₃, and E₄ appeared several tens to thousands MHz apart from the corresponding A₁ spectra, suggesting the internal-rotation potential barrier of CH₃ bonded to the nitrogen, called N-CH₃, to be quite low. In sharp contrast with the A₁ spectra, which were well fitted to the ordinary asymmetric-rotor spectral pattern, a few higher-order terms were required to reproduce the E₁ spectra, presumably because of the low N-CH₃ barrier. The spectral analysis thus performed, in fact, led to the V₃ of 80.06487 (14) cm⁻¹, an order of magnitude lower than that of C-CH₃. The E₃ and E₄ spectra were found to form triplets with the corresponding E₁ lines at the center, and the E₃-E₁ and E₄-E₁ splittings were explained essentially by the contributions of the C-CH₃ internal rotation combined with the kinetic-energy coupling between the two methyl groups. The torsion around the C-C bond between the ethyl and carbonyl groups was suggested by an ab initio calculation to be of double minimum nature, but the observed A₁ spectra did not show any indication of such a double-minimum potential for the C-C torsion, although the possibility of a small hump being present at a planar conformation could not be entirely eliminated. The present results on NMPA along with those obtained on other peptide molecules will be of some significance in clarifying important problems of structural biology such as protein folding and signal transfer through biological systems.     

One-Shot Decoupling

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.     

Jahn-Teller effect for the 3A2-term

The first detection of the zero-phonon line (ZPL) structure in the absorption spectrum for an optical transition between the ³T₁ and ³A₂-terms (λ = 1.3–1.5 μm) is reported for CdS:Ni crystals. An analysis of the structure shows that its occurrence is due to the weak vibronic coupling of the ³A₂-state with trigonal pseudolocal vibrations of energy hω = 22 cm⁻¹, i.e. the dynamic Jahn-Teller (JT) effect is observed. The energy of the JT coupling is E_JT = 13 cm⁻¹. With E_JT < hω, a weak JT coupling takes place. Besides the ZPL, the absorption spectrum also involves other lines of vibronic nature which can be treated as dielectric local vibration modes. An axial pressure (P) is shown to lead to a change in the magnitude of E_JT: for P ∥ C(C being the optical axis of the crystal), E_JT increases, and for P ⊥ C, it decreases.     

The stabilization of unusual conformers in guest-host systems: Solid-state NMR investigations of 2-methylhexadecane in urea and thiourea

Solid-state nuclear magnetic resonance (NMR) spectroscopy is employed for the first time on urea and thiourea inclusion compounds (UICs and TICs) containing branched alkyl chains. In the present work,²H and¹³C NMR as well as X-ray diffraction studies of two selectively deuterated 2-methylhexadecanes in UIC and TIC are presented. An analysis of the derivedT ₁ data reveals significant differences between UICs and TICs, which can be attributed to differences in the motional features of the guest species. It is found that four different motional contributions have to be considered, namely, chain rotation, chain wobbling,trans-gauche isomerization and methyl group rotation. 2-Methylhexadecane in UIC exists in an almost all-trans conformation (gauche amount not more than 5%) and undergoes fast chain rotation (6-site jump process, activation energyE _A=16.7 kJ/mol). The analysis of the²H NMR spectra of 2-methylhexadecane-1,1′,2-d₇ in urea proves that the branched chain end exists in an eclipsed conformation. TheT ₁ data of 2-methylhexadecane-3-d₂ in thiourea can be reproduced by an overall rotation (E _A=9.8 kJ/mol) and atrans-gauche isomerization with torsional jumps around the C-3-C-4 bond (E _A=11.0 kJ/mol,gauche population=15%). As for the corresponding UIC, the²H NMR spectra of 2-methylhexadecane-1,1′,2-d₇ in TIC can be only explained by the existence of an eclipsed conformation at the branched chain end.     

Temperature dependence of the fine structure of the C and E absorption bands in RbMnF3 below the Néel temperature

The variation in the parameters (width, position, intensity) of the fine structure lines in the C[⁶ A _1g → ⁴ A _1g , ⁴ E _g(⁴ G)] and E[⁶ A _1g → ⁴ E _g(⁴ D)] bands in RbMnF₃ with temperature is studied in the temperature range 10–70 K. In the C band, two narrow (<6 cm^?1) lines are are distinguished at distances of 77 and 80 cm^?1 from the exciton line at T = 10 K. The other lines in the C band and all lines in the E band are more than 20 cm^?1 wide. It is demonstrated that the narrow lines become allowed because of the spin-exchange interaction within a long-range magnetic order model and originate from the excitation of exciton-magnon bound states and that the other lines are made allowed by the exchange-vibronic mechanism within a short-range magnetic order model and originate from the excitation of bound states composed of an exciton, magnon, and oddparity phonon. The vibrational replicas of the main exciton-magnon-phonon lines are due to the quadratic vibronic interaction with odd-parity vibrations. Variations of the intensities and widths of the absorption lines with temperature indicate that these parameters are affected by relaxation and delocalization of the bound states.     

Systematization of intermediate-mass fragments

We consider the power law dependence of cross-sections of formation of intermediate-mass fragments on the mass number and atomic number, σ (A _f ) ～ A _f ^?τ and σ (Z _f ) ～ Z _f ^?τ . The values of parameter τ are determined for fragments detected by the ΔE ? E and the induced activity methods. It is shown that in “liquid-gas” phase transition τ varies within the limits of 2–3. A conclusion was drawn that at high beam energies parameter τ does not depend on the detection angle of the fragment. At the increase in the energy τ passes through a minimum at E _i ～ 6–7 GeV which is typical “critical behavior” predicted by models.