Complex molecular dynamics of (CH3NH3)5Bi2Br11 (MAPBB) protons from NMR relaxation and second moment of NMR spectrum

Molecular dynamics of a polycrystalline sample of (CH(3)NH(3))(5)Bi(2)Br(11) (MAPBB) is studied on the basis of the proton T(1) (55.2 MHz) relaxation time and the proton second moment of NMR line. The T(1) (55.2 MHz) was measured for temperatures from 20K to 330 K, while the second moment M(2) for those from 40K to 330 K. The proton spin pairs of the methyl and ammonium groups perform a complex stochastic motion being a resultant of four components characterised by the correlation times τ(3)(T), τ(3)(H), τ(2), and τ(iso), referring to the tunnelling and over the barrier jumps in a triple potential, jumps between two equilibrium sites and isotropic rotation. The theoretical expressions for the spectral densities in the cases of the complex motion considered were derived. For τ(3)(H), τ(2), and τ(iso) the Arrhenius temperature dependence was assumed, while for τ(3)(T)-the Schr?dinger one. The correlation times τ(3)(H) for CH(3) and NH(3) groups differ, which indicates the uncorrelated motion of these groups. The stochastic tunnelling jumps are not present above the temperature T(tun) at which the thermal energy is higher than the activation energy of jumps over the barrier attributed to the hindered rotation of the CH(3) and NH(3) groups. The T(tun) temperature is 54.6 K for NH(3) group and 46.5 K for CH(3) group in MAPBB crystal. The tunnelling jumps of the methyl and ammonium protons are responsible for the flattening of T(1) temperature dependence at low temperatures. The isotropic tumbling is detectable only from the M(2) temperature dependence. The isotropic tumbling reduces the second moment to 4 G(2) which is the value of the intermolecular part of the second moment. The motion characterised by the correlation time τ(2) is well detectable from both T(1) and M(2) temperature dependences. This motion causes the appearance of T(1) minimum at 130 K and reduction of the second moment to the 7.7 G(2) value. The small tunnelling splitting ω(T) of the same value for the methyl and ammonium groups was estimated as 226 MHz from the Haupt equation or 80 MHz from the corrected by us Haupt equation. These frequencies correspond to 0.93 μeV and 0.34 μeV tunnel splitting energy.     

Rotational tunnelling splitting of a chain of four coupled methyl groups

It is our goal to obtain a reliable prediction of the rotational tunnelling spectrum to be expected for a long chain of coupled one-dimensional quantum rotors. The problem is intractable by the simple methods used so far for up to three coupled methyl groups. Therefore, an efficient, nevertheless sufficiently precise method for solving the stationary Schrödinger equation of interacting methyl groups is developed first; it proves to be valid for a broad range of not too weak potential strengths. Then, three scenarios are investigated: they differ with respect to the relative strength of the single-rotor potential and the interaction potential. For each scenario, we illustrate the dependence of the energy level scheme on the number of coupled groups. For strong coupling and weak single-particle potential, the characteristic features of the energy level scheme of interacting methyls are most clearly observable: For as few as four coupled methyl groups we predict tunnelling spectra which are hardly distinguishable from single-methyl spectra. However, the collective behaviour is still important for the value of the tunnelling splitting. Therefore, the interpretation of such a spectrum in terms of single-methyl tunnelling is obvious but misleading with respect to the potential seen by a methyl group in the crystal.     

Derivation and evaluation of the fourth moment of NMR lineshape in zero-field

An expression for the fourth moment in zero-field NMR has been analytically derived and numerically evaluated for a rigid cubic lattice. Model simulations have been performed to calculate the second moment, the fourth moment, the ratio of the fourth moment to the square of the second moment, and the width of the resonance line for a crystal and a polycrystalline material in high-field as well as in zero-field NMR. The simulation results allow us to draw two conclusions: (1) zero-field NMR gives sharper and better defined spectra than the high-field NMR and (2) the ratio of the high- to zero-field resonance line-widths is 4 for a crystal, whereas it is 11 for a polycrystalline material.     

Coupling the methyl group in acetamide to phonons: a consistent view of tunnelling and lattice dynamics

Inelastic neutron spectra of acetamide-h5 and acetamide-h2 have been measured at different temperatures below 40K and with high energy resolution in the energy range up to 15 meV. A lattice dynamical model on the basis of atom-atom potentials and electric charges obtained from first principles calculations describes the spectra well if soft internal molecular modes are included. The model is used to reproduce the temperature dependence of the tunnelling transition of the methyl group. For this purpose the density of states is split into that of an isolated rotor in a static field and that of the phonon bath. The effects of the rotor-phonon coupling are evaluated in second order perturbation theory. The broadening of tunnelling lines comes out correctly when the atom atom potentials taken from literature are scaled down by 20%. To get the shift right the strength of the coupling to the lattice needed to be different for the A type symmetry state from that for the E type state. The coupling with the low frequency phonons appears to be very weak.     

Deuteron NMR spectra of NH3D+ Ions

A theory of deuteron nuclear magnetic resonance (NMR) spectra is outlined for NH₃D⁺ ions. Dipolar interactions among all five spins in the ion contribute to the shape of the deuteron spectra. Dimensions of the ammonium ion can be derived from the structure of the single-crystal spectra. The analysis of the spectra supplies ways to distinguish between cases of rigid, tunnelling or reorienting protons. Single-crystal spectra of partially deuterated ammonium perchlorate measured at 5 K provide examples of the applicability of the theory. Distances between nuclei are derived. Evidence is provided for tunnelling and reorientation of protons in NH₃D⁺ ions. Deuteron spectra indicate that NH₃D⁺ ions exhibit a diverse mobility. There exist ions with immobile deuterons which populate one position in the crystal unit cell (isotopic ordering), while the deuterons in the remaining ions reorient about C₃ axes parallel to the N-D bond orientation of the rigid ones. The contribution of the latter increases with increasing temperature.     

13C NMR of tunnelling methyl groups

The dipolar interactions between the protons and the central ¹³C nucleus of a ¹³CH₃ group are used to study rotational tunnelling and incoherent dynamics of such groups in molecular solids. Single-crystal ¹³C NMR spectra are derived for arbitrary values of the tunnel frequency ν_t. Similarities to ESR and ²H NMR are pointed out. The method is applied to three different materials. In the hydroquinone/acetonitrile clathrate, the unique features in the ¹³C NMR spectra which arise from tunnelling with a tunnel frequency that is much larger than the dipolar coupling between the methyl protons and the ¹³C nucleus are demonstrated, and the effects of incoherent dynamics are studied. The broadening of the ¹³C resonances is related to the width of the quasi-elastic line in neutron scattering. Selective magnetization transfer experiments for studying slow incoherent dynamics are proposed. For the strongly hindered methyl groups of L-alanine, an upper limit for ν_t is derived from the ¹³C NMR spectrum. In aspirin? (acetylsalicylic acid), incoherent reorientations dominate the spectra down to the lowest temperatures studied; their rate apparently increases with decreasing temperature below 25 K.     

Deuteron NMR spectra of ammonium ion isotopomers at low temperatures

Partially deuterated ammonium compounds contain ammonium ion isotopomers with relative abundances given by the binomial distribution of protons and deuterons. All isotopomers with deuterons contribute characteristic deuteron NMR spectra at 5K. Experimental NMR spectra were separated and respective contributions of isotopomers were determined. The derived contributions agree with expected values for a given deuteration in the case of ammonium hexafluorophosphate. In ammonium hexachlorotellurate both NH2D2+ and about 50% of NH3D+ ions are rigid, while the remaining NH3D+ perform limited jumps. NHD3+ and ND4+ ions undergo tunnelling rotation, NH3D+ ions perform either jumps about C2 axis or limited jumps, but some stay rigid in ammonium hexachlorostannate. NH2D2+, NHD 3+ and ND4+ undergo rotational tunnelling. In the case of ammonium perchlorate, the NH3D+ ions perform either jumps about C3 axis or limited jumps whilst some remain rigid. Very low values of activation energies were derived for all spectral components from the temperature dependence of their spectra, up to about 20K, which indicates an incoherent tunnelling nature of the observed dynamic processes. The diverse mobility of NH3D+ ions appears to be the most interesting and new feature.     

2H NMR studies for the examination of methyl group rotations between their classical and quantum mechanical limits

²H NMR spectra of copper acetate monohydrate [Cu(CD₃CO₂)₂]·H₂O, hexamethylbenzene-d₁₈ and acetone-d₆ were analyzed to characterize methyl group rotations between their classical and quantum mechanical limits. The temperature dependent spectra show the three different possible developments of the lineshapes. Hexamethylbenzene is typical of compounds with small but resolvable tunnelling frequencies. Characteristic splittings in the spectra of copper acetate monohydrate reveal the temperature dependence of tunnelling frequencies that are slightly larger than the quadrupole coupling constant. While the tunnelling frequency of acetone is already too large to be specified from²H NMR lineshape analysis at temperatures low enough that quantum effects influence the spectra, the temperature dependent spectra deviate characteristically from those found for classical rotation. Additionally to these experimental results, we outline how from an NMR point of view mixed classical and quantum rotations can be described by a single complex frequency.     

Spectral parameters for quantitative mobility contrast in NMR imaging of solid polymers

Different procedures based on parameters of the wideline NMR absorption spectrum are presented to obtain localized molecular mobility contrast for imaging of solid polymers. For this purpose a ¹H-NMR imaging technique with magic sandwich echoes is used for acquiring localized wideline spectra. With samples composed of polystyrene and high impact strength polystyrene, and polycarbonate and low density polyethylene a spatial difference in NMR absorption spectrum lineshape and linewidth is displayed. Furthermore, the spatial distribution of rigid and mobile domains in a heterogeneous polymer can be derived from the NMR spectral components. It is demonstrated that a van Vleck moment analysis can be performed from spatially resolved magic echo decays. The second (M₂) and fourth (M₄) moments of the rigid components show considerable variation with the spatial composition of the investigated samples.     

Van Vleck second moments and hydrogen diffusion in YH2.1--measurements and simulations

Proton magnetic resonance absorption spectra of yttrium dihydride (YH(2+x)), with x = 0.10, were recorded in the temperature ranges 4.2-310 K at 36.01 MHz and 150-400 K at 299.8 MHz. The evidence of proton self-diffusion follows from the changes of linewidth with temperature. The second moment of the resonance lines was determined from the experimental spectra and was compared with values calculated from the crystallographic data. The averaging effect of diffusion on the second moment was taken into account through Monte Carlo simulations of the diffusion process. The simulation was performed in a block of unit cells 5 x 5 x 5 with periodic boundary conditions. They compensated the effect of finite dimensions of the block. The calculated temperature dependence of the proton second moment values was fitted to the experimental ones. The fitting parameters were: the attempt frequency v0 and the activation energy Ea for hydrogen diffusion, assuming Arrhenius behavior of the jump frequencies vc = v0 exp(-Ea/k(B)T). In these preliminary studies, the Monte Carlo simulations were performed for tetrahedral-octahedral exchanges while direct tetrahedral-tetrahedral jumps were neglected for simplicity. Three models of hydrogen diffusion, differing in the maximum jump lengths allowed for a given model, were considered. These lengths were taken as the distances from the hydrogen attempting to jump to the first (1NN), second (2NN), and third (3NN) nearest neighbor position able to accept the jumping atom. Assuming the same attempt frequency v0 = 6.0 x 10(12)s(-1) for all three models, the activation energies giving the best fit to experimental data were 0.5, 0.54, and 0.55 eV for 1NN, 2NN, and 3NN models, respectively.     

1H NMR study of lithium D-lactate.

Polycrystalline D-lactic acid lithium salt [(R)-2-hydroxypropanoic acid lithium salt, lithium D-lactate] has been investigated by pulsed proton magnetic resonance methods between 77 and 300 K at 25 MHz. The main relaxation mechanism is methyl rotation; the motion is characterized by an activation energy Ea = 14.5 +/- 0.5 kJ/mol and time factor tau 0 = (1.5 +/- 0.5) x 10(-13) s. The activation energy is higher than the potential barrier obtained by ESR and ENDOR techniques for methyl rotation in the lactate radical. The methyl rotation is also responsible for a reduction of the dipolar second moment. Below 100 K the reduction of the dipolar second moment is ascribed to quantum-mechanical tunneling; an excitation energy of 6.1 +/- 1 kJ/mol is derived from a contribution to the spin-lattice relaxation times from the tunneling.     

Molecular dynamics of n-dodecylammonium chloride studied by nuclear magnetic resonance

The relation between molecular dynamics and phase properties of the bilayered compound C₁₂H₂₅NH₃C1 is studied by differential scanning calorimetry, proton second moment, and spin-lattice relaxation times. In the low-temperature phase I of the compound methyl and ammonium groups execute a classical threefold reorientation, while the alkylammonium chains are rigid on the nuclear magnetic resonance time scale. In the intermediate-temperature phase δ a trans-gauche isomerization of the alkyl chains is observed. In the high-temperature phase α the reorientation of the whole chains about their long axes, which are parallel to the normal to the ionic layer is evidenced. In the metastable ε phase the dynamics involves classical rotation of methyl and ammonium groups and CH₂ groups motion of the trans-gauche isomerization type.     

The symmetry group paradox for non-rigid molecules

In many situations, the energy levels for a quantum system, whose Hamiltonian is invariant under a specific symmetry group, are split when the Hamiltonian is replaced by a new one with lower symmetry. In non-rigid molecules (NRM), fast quantum tunnelling processes allow the molecule to change between different geometrical configurations related by permutations of identical nuclei (or with inversion as well), resulting in the splitting of the energy levels for the rigid molecule (RM) case where tunnelling is absent. However, for NRM, there is apparently a paradoxical situation where although the original RM energy levels are associated with a symmetry group isomorphic to the point group for the geometrical configuration, the split NRM energy levels are associated with a symmetry group consisting of all permutations and inversions related to the fast quantum tunnelling processes between configurations, and for which the point group is a subgroup. The resolution of this paradox, where energy level splitting is evidently accompanied by an enlargement of the symmetry group, is the subject of this article.     

Microwave spectrum, rs structure,dipole moment,and internal rotation of methyl fluorosilane

Microwave spectra of methyl fluorosilane and its 20 isotopic species were measured. In order to determine the most reliable r_s structure, atom coordinate values were obtained by solving the Kraitchman equations from several sets of the substituted and parent species and by averaging the solutions. For unreliable Kraitchman coordinate values, several trials were made in order to fix the values. The second difference method was also applied to the unreliable Kraitchman values. The dipole moment and its direction in the molecule were obtained by Stark-effect measurements for the normal and two deuterated species. From the A-E splittings of the observed spectra in the ground state for nine species, the barrier to internal rotation and the direction of the top axis of the methyl group were determined. It is noted that the top axes obtained from the structure and from the analysis of the A-E splittings do not coincide with each other. From the structural analysis the methyl group is found to tilt toward two hydrogen atoms on the silicon atom by about 1°45′, whereas the analysis of the A-E splittings shows the methyl group tilting toward the fluorine atom by about 37′. Comparison of the results was made among methyl fluorosilane, ethyl fluorosilane, ethyl fluoride, and methyl fluorogermane.     

Magnetization process of Fe layers in Fe/Nd multilayered films investigated by57Fe Mössbauer spectroscopy

The magnetization process of Fe and Nd layers at 5K in Fe/Nd multilayered films with strong perpendicular magnetic anisotropy is elucidated from a comparison of⁵⁷Fe Mössbauer spectra in the presence of the external field applied parallel to the film plane with total magnetization. At zero external field, the film has a magnetic multi-domain structure. The Nd layer moment is perpendicular to the film plane and the Fe layer moment points in the out-of-plane direction. The Fe layer moment monotonically rotates to the in-plane direction with increasing external field parallel to the film plane, while the Nd layer moment is oriented to the film normal direction up to the external field of 10kOe, above which the Nd layer moment gradually turns to the direction of the external field.     

用三线摆研究垂直轴定理

用三线摆对刚体薄圆盘绕不同轴转动时的转动惯量进行测量,通过实验与数据分析,验证了反映刚体转动惯量重要性质的垂直轴定理,从而实现了对刚体转动惯量实验内容的扩充.     

均质并有对称面的刚体转动惯量的一个定理

提出并证明了一个关于刚体转动惯量的新定理.该定理指出具有对称面的均质刚体,当位于与对称面垂直的某个平面上的转轴满足特定条件时,转动惯量大小与位于该平面上的转轴方向无关.     

Proton relaxation NMR study of polycrystalline progesterone.

Polycrystalline progesterone (4-pregnene-3,20-dione, C21H30O2) has been investigated by proton NMR methods between 80 and 350 K. A reduction in dipolar second moment is ascribed to methyl group reorientation. Minima in the spin-lattice relaxation time found in measurements at five frequencies from 7 to 200 MHz are attributed to reorientation of two of the three methyl groups in each molecule, characterized by activation energy Ea = 10.9 +/- 0.8 kJ/mol and tau o = (2.3 +/- 0.2) x 10(-13) s. Additional relaxation at lower temperatures is attributed to reorientation of the third methyl group with Ea approximately 3.4 kJ/mol. Measurements were also made of relaxation in the rotating frame.     

Methyl group tunnelling and torsion in 2,4-hexadiyne

The tunnelling splitting of the ground torsional level of solid 2,4-hexadiyne and transitions to excited torsional states have been measured at low temperatures using neutron inelastic scattering. At 4 K the tunnelling splitting is 1·060 μeV (0·0086 cm^-1). It decreases as the temperature is raised, to 0·834 μeV (0·0067 cm^-1) at 35 K, and to less than 0·6 μeV at 50 K. A V-2←V=0 transition in the torsional vibration has been observed at 222 cm^-1 which shifts to 160 cm^-1 in the fully deuterated compound.

The values of the torsional frequencies, tunnelling frequency, and the change of tunnelling splitting with temperature have been fitted exactly to a potential energy for rotation of a methyl group given by

with a barrier to rotation of 432 cm^-1.

Changes in the tunnelling transitions as the temperature increases are compared with existing theories of the mechanism.     

Molecular dynamics in solid anhydrous beta-estradiol studied by 1H NMR.

Proton second moment and spin-lattice relaxation times T1 and T1p in solid anhydrous beta-estradiol are measured as a function of temperature. The results show that the C3 reorientation of the single methyl group provides the mechanism dominating relaxation at low temperatures and reveal the existence of a conformational motion of the carbon skeleton dominating relaxation at high temperatures. The activation energies of the respective motions are found to be 9.3 and 37.3 kJ/mol.