The use of complex wiggle-beat patterns for the estimation of small splittings in NMR spectra

The analysis of the ‘wiggle-beat’ patterns produced by rapid passage through simple NMR multiplets is modified and extended to permit analysis of beats from multiplets where adjacent signals are not equally separated and where the intensities are not necessarily in the ratio of the appropriate binomial coefficients. The simple example of mono-silane-d₁ (SiH₃D) is illustrated: J _HD = 0·427 ± 0·003 c/s. Allowance is also made for the finite time of passage through the signal and the usefulness of this demonstrated by analysing the beat pattern from the asymmetric spectrum of a mixture of SiH₃D and SiH₄. In this way the SiH₄-SiH₃D chemical shift is estimated to be 0·0080 ± 0·0005 p.p.m., the SiH₄ resonance being to low field.     

Zeeman spectroscopy of the 4 Eu → 2 B 1g phosphorescence of copper porphin in an n-alkane single crystal

The phosphorescence spectrum of the metastable ⁴ E_u state of copper porphin in single crystals of n-octane (C₈) and n-decane (C₁₀) has been studied between 2·3 and 35 K, with and without a magnetic field B. The crystal field splitting between the orbital components observed at 35 K is δ = 30·3 ± 0·3 (C₈), 13·8 ± 0·2 cm^-1 (C₁₀). From the Zeeman shifts we derive the effective orbital angular momentum Λ′ = 0·8 ± 0·2 (C₁₀), the spin-orbit coupling parameter |Z′| = 1·5 ± 1·0 cm^-1 (C₁₀), the spin-spin dipolar interaction parameters D = -0·1 ± 0·2 cm^-1 (C₈, C₁₀) and |E| = 0·31 ± 0·03 cm^-1 (C₈, C₁₀), and the g-factors g _∥ = 2·14 ± 0·04 (C₈, C₁₀) and g _⊥ = 2·00 ± 0·03 (C₈, C₁₀).     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

Electron spin resonance study of oxygen-17 enriched N,N-dimethyl-4-nitroaniline radical anion

N,N-Dimethyl-d₆-4-nitroaniline enriched to approximately 11 atom. per cent in oxygen-17 has been prepared and the oxygen-17 isotropic hyperfine interaction in the corresponding radical anion has been examined. In dry dimethylformamide solution we find a _O = -8·85 ± 0·02 and a _N = 11·39 ± 0·10 gauss, while in moist acetonitrile solution a _O = -8·82 ± 0·07 and a _N = 12·23 ± 0·11 gauss. These results substantiate the recent suggestion that the isotropic oxygen-17 splittings in π-radicals may be described by a single parameter equation analogous to McConnell's relation for aromatic proton splittings, i.e. a _O = Q _OρO ^π, where Q _O = -41 ± 3 gauss.     

Formulae which relate pressure,activity and potentials of mean force to sums of integrals over Ursell-Mayer correlation functions of the distribution functions

The pure rotational spectrum in the far-infrared between 30 and 170 cm^-1 and its absolute intensity has been measured for CH₂D₂ in the vibrational ground state by high-resolution interferometric Fourier transform techniques. The analysis of the integrated cross-sections in the essentially water-free spectrum results in an accurate value for the permanent, vibrationally induced ground state electric dipole moment of CH₂D₂|μ₀| = (6·40±0·33) x 10^-3D.The influence of centrifugal effects on intensities and on the determination of the permanent dipole moment was investigated. Although centrifugal effects are important for the explanation of single band profiles, they appear to be of little relevance for the resulting permanent dipole moment. A new, more general 9- dimensional dipole moment function for methane is derived from ab initio calculations and experimental band strength information of CHD₃. Quantum Monte Carlo calculations using this function and a new, more general 9- dimensional analytical, anharmonic potential function for methane yield a semi-theoretical estimate μ₀ ^z = – (7·8±0·5)x10^-3D for CH₂D₂.     

Hydrogen bond studies

The deuteron magnetic resonance spectra from partially deuterated single crystals of NaHC₂O₄. H₂O have been studied. The quadrupole coupling tensors for stationary deuterons are determined at about 25°C. The quadrupole coupling constants and the assymmetry parameters η of the tensors for the two deuterons in the water molecule are, 235·2 ± 1·9 and 228·5 ± 1·6 kHz, and 0·09 ± 0·01 and 0·13 ± 0·01, respectively. The principal axes corresponding to the largest components both deviate by 0·9 ± 0·5° from their respective O-H directions. For one of the tensors this angular displacement is in the plane of the H₂O molecule and towards the other O-H direction. The displacement for the other tensor is out of the plane of the H₂O molecule.     

Isotope effects on the degree of order and the deuterium quadrupole coupling constants,as measured by N.M.R. of oriented benzene-d 1, 1,4-benzene-d 2 and 1,3,5-benzene-d 3

Proton and deuteron magnetic resonance spectra of benzene-d ₁, 1,4-benzene-d ₂ and 1,3,5-benzene-d ₃, oriented in various liquid crystal solvents have been analysed. Isotope effects on the degree of order have been measured. The ratios of S-values in the benzene plane are found to be S_xx/S_zz =1·0201 ± 0·0009 in benzene-d ₁ and 1·0389 ± 0·0004 in 1,4-benzene-d ₂ with the deuterons substituted on the z-axis. Deuteron quadrupole coupling constants of 190·4 ± 1·2 kHz and 192·4 ± 1·2 kHz have been obtained for 1,4-benzene-d ₂ and 1,3,5-benzene-d ₃.     

Microwave cyclotron resonance of hot electrons in p-type GaSb

A microwave photocreated cyclotron resonance signal is observed in p-type GaSb in the temperature range 1–30 K. Circular polarization and other measurements identify the carriers as electrons in the (000) conduction band. The problem of a surface effect on the measured peak position, reported for the first time is avoided by bulk carrier creation. An exponential loss of signal intensity at 27 K is explained by the theory of background plasma effects. The measured ωτ of 1·5–4 yields an electron collision time of τ ～ 10^?11 sec. The scattering mechanism at liquid helium temperatures is identified as being partly due to neutral defect acceptor scattering of hot electrons, with an unidentified residual scattering process. The electron polaron effective mass is measured to be (m *(polaron)/m₀) = 0·0412 ± 0·0012 for hot electrons with an average energy of ～ 14 MeV and is isotropic within 1 per cent. When corrections for conduction-band non-parabolicity and hot polaron effects are applied, the band-edge free electron mass is calculated to be (m₀*(free)/m₀) = 0·0396 ± 0·0021 (±5·2 per cent).     

19F double resonance in the presence of chemical exchange

The ¹⁹F N.M.R. spectra of CF₂BrCClBr₂ in CS₂ from 20°c to -80°c are reported. Computer-fitting of the experimental spectra using the density matrix formalism of Alexander yields the chemical exchange correlation times and produces a computed internal rotation barrier for trans →gauche of 39·7 ± 0·5 kJ mol^-1 (9·5±0·1 kcal/mole). Results of double resonance studies on the -80°c spectrum upon irradiation of the various peaks with a strong r.f. field are presented. The density matrix equations in the presence of chemical exchange and several relaxation mechanisms were solved to obtain theoretical changes in peak intensities on irradiation. The indirect spin saturation data and their relation to the rate of internal rotation and the relaxation mechanism are discussed. Random field relaxation is shown to be the important relaxation mechanism in the system. The strong irradiation of one component of a strongly coupled spin multiplet with intramolecular exchange causes indirect saturation of the transitions connecting energy levels that have the same m _I values as the one being irradiated whereas the intensities of other transitions are only slightly affected. It appears therefore to be an important complement to the spin-tickling technique in determining energy level diagrams and relative signs of coupling constants.     

Amorphous germanium III. Optical properties

The optical properties of thick sputtered films (～30μ) of amorphous Ge, grown with different substrate temperatures (0ˇ-T _sˇ-350°C), were obtained between 0·05 and 4·5 eV by a combination of reflectance, transmittance and ellipsometric measurements. The refractive index at 0·15 eV decreases monotonically with increasing T _s, or equivalently, with increasing density, and is 4·13±0·05 eV in the highest density films. The absorption edge is approximately exponential (10²?α?10⁴ cm^?1) but shifts monotonically to higher energy and increases in slope with increasing T _s. Similarly, the peak in ε₂ grows by about 10% and shifts by about 0·15 eV to higher energies, reaching a maximum of about 23 at 2·90±0·05 eV in the high density films. The peak in the transition strength ω²ε₂ occurs at 4·2±0·2 eV in all films, but increases in magnitude with increasing T _s. The sum rules for n _eff(ω) and ε_0,eff(ω) are evaluated for ▄ω?5 eV and vary monotonically with T _s. These trends are neither compatible with Galeener's void resonance theory nor with changes in the oxygen content of the films, determined by the examination of absorption peaks at 0·053 eV and 0·09 eV. An explanation, suggested here and expanded in I, is based on the observed changes in the structure of the network and voids.     

Electromagnetic properties of low lying levels in75As

Theg-factors of the 265 and 280 keV levels have been measured to be 0.61±0·16 and 0·30±0·05 respectively. The PAC technique was used for the measurements. In addition, the half-life of the 280 keV level has been remeasured to beT _1/2=0·32±0·02 ns using γ-γ delayed coincidences. Electromagnetic properties of the various levels calculated on the core-particle coupling model agree with the experimental results. The results are compared with other existing theoretical calculations.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

On the calculation of the orientational correlation parameter g 2

The g ₂ factor for a model of liquid carbon disulphide has been calculated by molecular dynamics simulation. The values of g ₂ for the model at three points along the orthobaric curve are: 1·17 ± 0·04 (298 K), 1·27 ± 0·03 (245 K), 1·39 ± 0·06 (193 K). These values are in good agreement with available experimental values. By calculating g ₂ in shells of cubic symmetry it is found that the value of g ₂ is determined by the orientational correlation of a molecule with neighbours within a few (two to three) molecular diameters. Spurious orientational correlations are introduced by the periodic boundary conditions and the calculation of collective correlation functions by averaging over the whole cube is shown to be unreliable. A theoretical calculation of g ₂ using RISM + SSA fails to reproduce the state dependence of the g ₂ values calculated from the simulation. This failure is not due to the small differences between the simulation and RISM g _αβ(r) for r < 4·5 Å but to inaccuracies in the SSA in the intermediate region r ～ 6 Å.     

Mass-spectroscopic study of the diffusion and solubility of helium in submicrocrystalline palladium

By the method of helium thermal desorption from submicrocrystalline palladium presaturated in the gaseous phase, the diffusion coefficient D _eff and solubility coefficient C _eff of helium are measured in the range P=0–3 MPa and T=293–508 K. The pressure dependence of C _eff flattens at high pressures. At low saturation pressures, the temperature dependences of the diffusion and solubility coefficients may be divided into (1) high-temperature (400–508 K) and (2) low-temperature (293–400 K) ranges described by the exponentials D _{1, 2}=D ₀exp (−E _{1, 2} ^D /kT) and C _{1, 2}=C ₀exp (−E _{1, 2} ^S /kT). The energies of diffusion activation are E ₂ ^D =0.0036±0.0015 eV and E ₁ ^D =0.33±0.03 eV, and the solution energies are E ₂ ^S =−0.025±0.008 eV and E ₁ ^S =0.086±0.008 eV in the low-and high-temperature ranges, respectively. Mechanisms behind the diffusion and solution of helium are discussed.     

Determination of A 0 for CH3F from ground-state combination differences

The direct determination of the ground-state rotational constants A ₀ and D ₀ ^K of methyl fluoride has been accomplished through ground-state combination differences including perturbation-allowed transitions. The values found are A ₀ = 5·182009 ± 0·000012 and D ₀ ^K = (70·33 ± 0·25) × 10^-6 cm^-1. The ‘ normal ’ GSCD have also been used, in conjunction with microwave transitions, to yield improved values for the other rotational constants, including values for H ₀ ^{J K} and H ₀ ^KJ .     

Elastische und unelastische Streuung von Elektronen an Gasen

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10^?4≦?≦4·10^?2. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for?>7·10^?3 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2¹ P and 3¹ P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2¹ P differential cross section in the angular range 3·10^?3<?<1·10^?2 only. The oscillator strength of these two transitions has been determined from the scattering measurements:f ₂₁=0·312±0·04 andf ₃₁=0·0898±0·006.     

Magneto-acoustic attenuation in AuSb2

Quantum oscillations in the ultrasonic attenuation in AuSb₂ were studied as a function of temperature, magnetic field and crystal orientation. The effective masses of the carriers associated with the F₅ and F₆ oscillations were measured in a (110) plane. For the F₅ oscillations, the Dingle temperature and apparent magnetic breakdown field appear to depend strongly upon orientation. For the F₆ oscillations, however, there were no signs of magnetic breakdown up to the highest magnetic fields available (70 kOe) and the Dingle temperature was roughly independent of orientation. From the acoustic velocities, the elastic constants were determined at 77 K: C₁₁ = (14·7 ± 0·9) × 10¹¹ dyne/cm², C₁₂ = (6·0 ± 0·9) × 10¹¹ dyne/cm², and C₄₄ = (2·59 ± 0·06) × 10¹¹ dyne/cm². These elastic constants give an adiabatic compressibility K_s = (1·13 ± 0·12) × 10^?12 cm²/dyne and a Debye temperature ?_D = (203 ± 15) K.     

Femtosecond ionization of magnesium clusters grown in ultracold helium droplets

Magnesium clusters grown in helium droplets and ionized with femtosecond laser pulses have been studied by high resolution mass spectrometry. For moderate laser intensities the abundance spectra show characteristic features indicating electronic shell effects. Compared to clusters of s¹-electron metals additional shell closures appear resulting from an electron rearrangement. Irradiation with higher laser intensities leads to a decomposition of the magnesium clusters into atomic ions. Due to charge exchange with the surrounding helium matrix mainly singly and doubly charged magnesium ions remain. In addition, the occurrence of MgHe_N ⁺-complexes is observed. Their abundance depends on the shape of the laser field, i.e. the laser width and the optical delay when applying the pump-probe technique. Received 2 January 2001