Single-particle rotations in molecular crystals

Dynamics of coupled rotors in external fields

Coupled hindered rotor model is crucial for exploring the rotational dynamics of complex molecules under different external environments. When coupled hindered rotor molecules are subjected to the combined action of static electric and laser fields, their rotational dynamics get significantly modified, leading to interesting physics. In this study, we solve the time-independent Schrödinger equation for the coupled pair of rotors in the combined action of static electric and laser fields using the nine-point finite difference method and obtain rotational energy spectra and eigenvectors. We then use the partition function approach to understand thermal behaviour by studying thermal properties like heat capacity and entropy. We also explore the impact of temperature, coupling strength, and external fields strength parameters on these properties. The orientation of the coupled rotor is strongly dependent on the coupling strength between the coupled rotors as well as the hindrance. We analyse this directional parameter under a broad range of barrier height, coupling strength, and external fields strength parameters. Our analysis may provide insight into the rich and interesting physics, which may pave the way for future experimental and theoretical studies in this area.

Spin-symmetry conversion in methyl rotors induced by tunnel resonance at low temperature

Field-cycling NMR in the solid state at low temperature (4.2 K) has been employed to measure the tunneling spectra of methyl (CH3) rotors in phenylacetone and toluene. The phenomenon of tunnel resonance reveals anomalies in (1)H magnetization from which the following tunnel frequencies have been determined: phenylacetone, νt = 6.58 ± 0.08 MHz; toluene, νt(1) = 6.45 ± 0.06 GHz and νt(2) = 7.07 ± 0.06 GHz. The tunnel frequencies in the two samples differ by three orders of magnitude, meaning different experimental approaches are required. In phenylacetone the magnetization anomalies are observed when the tunnel frequency matches one or two times the (1)H Larmor frequency. In toluene, doping with free radicals enables magnetization anomalies to be observed when the tunnel frequency is equal to the electron spin Larmor frequency. Cross-polarization processes between the tunneling and Zeeman systems are proposed and form the basis of a thermodynamic model to simulate the tunnel resonance spectra. These invoke space-spin interactions to drive the changes in nuclear spin-symmetry. The tunnel resonance lineshapes are explained, showing good quantitative agreement between experiment and simulations.

Low-temperature tunneling and rotational dynamics of the ammonium cations in (NH4)2B12H12

Low-temperature neutron scattering spectra of diammonium dodecahydro-closo-dodecaborate [(NH(4))(2)B(12)H(12)] reveal two NH(4)(+) rotational tunneling peaks (e.g., 18.5 μeV and 37 μeV at 4 K), consistent with the tetrahedral symmetry and environment of the cations. The tunneling peaks persist between 4 K and 40 K. An estimate was made for the tunnel splitting of the first NH(4)(+) librational state from a fit of the observed ground-state tunnel splitting as a function of temperature. At temperatures of 50 K-70 K, classical neutron quasi-elastic scattering appears to dominate the spectra and is attributed to NH(4)(+) cation jump reorientation about the four C(3) axes defined by the N-H bonds. A reorientational activation energy of 8.1 ± 0.6 meV (0.79 ± 0.06 kJ/mol) is determined from the behavior of the quasi-elastic linewidths in this temperature regime. This activation energy is in accord with a change in NH(4)(+) dynamical behavior above 70 K. A low-temperature inelastic neutron scattering feature at 7.8 meV is assigned to a NH(4)(+) librational mode. At increased temperatures, this feature drops in intensity, having shifted entirely to higher energies by 200 K, suggesting the onset of quasi-free NH(4)(+) rotation. This is consistent with neutron-diffraction-based model refinements, which derive very large thermal ellipsoids for the ammonium-ion hydrogen atoms at room temperature in the direction of reorientation.

Methyl group dynamics in polycrystalline and liquid ubiquinone Q(0) studied by neutron scattering

We present a quasi-elastic neutron scattering (QENS) study on the methyl group dynamics of ubiquinone Q(0) in the solid and liquid state. For solid ubiquinone Q(0), the dynamics can be described with three Lorentzian functions in the framework of a jump model among three equidistant sites on a circle. According to the known molecular structure of Q(0) in the solid state, this is consistent with three nonequivalent methyl groups in the molecule. From the temperature-dependent analysis of the QENS spectra, the activation energies were determined. The barrier heights could be evaluated from librational bands in the inelastic part of the spectra. The results from neutron spectroscopy are compared to Gaussian 03 calculations leading to an assignment of the activation energies to the different methyl groups in Q(0). The dynamics of Q(0) in the liquid state is evaluated with a scattering function taking into account three different molecular motions. It is demonstrated that the temperature dependence of the long-range diffusion and isotropic rotational diffusion exhibit an Arrhenius-like behavior, whereas the process of methyl group rotation in the liquid phase is virtually free of a barrier.

Quasielastic and inelastic neutron scattering study of methyl group rotation in solid and liquid pentafluoroanisole and pentafluorotoluene

The rotational motion of the methyl group in pentafluoroanisole (PFA) and in pentafluorotoluene (PFT), respectively, was investigated by quasielastic neutron scattering (QENS). For solid PFA, the rotation can be described by a model for uniaxial rotational jumps between three equidistant sites on a circle. Similar to the molecular structure of alpha-toluene, two nonequivalent methyl groups in the unit cell with two different rotational barriers were found for solid PFT. From the analysis of the quasielastic scattering, the activation energies were determined. The barrier heights could be evaluated from bands in the inelastic part of the spectra. The methyl group dynamics in the liquid state is evaluated for both substances using different scattering functions, which are discussed. An empirical model for the description of the contribution of methyl groups in liquids of small organic molecules to the QENS spectra is presented. It is demonstrated that the process of methyl group rotation in the liquid phase is nearly free of a barrier.

2-methylterrylene in hexadecane: do we see single rotational quantum jumps of methyl groups?

We performed comparative low temperature (2-30 K) hole-burning and single molecule experiments with 2-methylterrylene with the goal to detect single rotational tunneling jumps of methyl groups. The hole-burned spectrum with its sharply structured side features which are perfectly symmetrically arranged with respect to the central hole supports the assignment to rotational tunneling transitions. However, instead of one, three clearly distinguishable methyl groups show up in the spectrum. Based on molecular mechanics simulations we attribute them to different, nearly degenerate orientations of guest molecules in one specific site of the hexadecane lattice. The frequency distribution of spontaneous jumps of single molecules reflects the features of the hole-burned spectra, although the distribution in the single molecule experiments is significantly broader. The photoinduced frequency transformation of single molecules ("single molecule photobleaching experiments") fits to the features of the hole-burned spectra, except that, surprisingly, no significant number of spectral jumps could be generated in the frequency range where the prominent narrow antiholes are observed in the hole-burned spectra.

Quasielastic neutron scattering experiments including activation energies and mathematical modeling of methyl halide dynamics

Quasielastic neutron scattering experiments were carried out using the multichopper time-of-flight spectrometer V3 at the Hahn-Meitner Institut, Germany and the backscattering spectrometer at Forschungszentrum Julich, Germany. Activation energies for CH(3)X, X=F, Cl, Br, and I, were obtained. In combination with results from previous inelastic neutron scattering experiments the data were taken to describe the dynamics of the halides in terms of two different models, the single particle model and the coupling model. Coupled motions of methyl groups seem to explain the dynamics of the methyl fluoride and chloride; however, the coupling vanishes with the increase of the mass of the halide atom in CH(3)Br and CH(3)I.

Superposition of quantum and classical rotational motions in Sc2C2@C84 fullerite

The superposition of the quantum rotational motion (tunneling) of the encapsulated Sc(2)C(2) complex with the classical rotational motion of the surrounding C(84) molecule in a powder crystal of Sc(2)C(2)@C(84) fullerite is investigated by theory. Since the quantum rotor is dragged along by the C(84) molecule, any detection method which couples to the quantum rotor (in casu the C(2) bond of the Sc(2)C(2) complex) also probes the thermally excited classical motion (uniaxial rotational diffusion and stochastic meroaxial jumps) of the surrounding fullerene. The dynamic rotation-rotation response functions in frequency space are obtained as convolutions of quantum and classical dynamic correlation functions. The corresponding Raman scattering laws are derived, and the overall shape of the spectra and the width of the resonance lines are studied as functions of temperature. The results of the theory are confronted with experimental low-frequency Raman spectra on powder crystals of Sc(2)C(2)@C(84) [M. Krause et al., Phys. Rev. Lett. 93, 137403 (2004)]. The agreement of theory with experiment is very satisfactory in a broad temperature range.

Methane clathrate: CH4 quantum rotor state dependent rattling potential

In methane hydrate the dominant peak in the density of states above 3 meV represents a rattling mode of the guest molecule CH(4) in the large ice cages. This mode shifts from 6.7 meV at T=4.5 K to T=30 K to 7.14 meV with conversion of CH(4) guest molecules into the tunneling ground state. The less symmetric angular density distribution PsiPsi(*) in the excited rotational state compared to the ground state allows the methane to fit better in the orientation dependent cage potential surface. This leads to a larger average distance to the cage-forming molecules with a weaker potential and a reduced rattling energy. A two state single particle model with characteristic rattling energies of 5.20 meV for pure T-methane and 7.3 meV for pure A-methane weighted by the population factors can fit the data.

X-ray diffraction and inelastic neutron scattering study of 1:1 tetramethylpyrazine chloranilic acid complex: temperature, isotope, and pressure effects

The x-ray diffraction studies of the title complex were carried out at room temperature and 14 K for H/D (in hydrogen bridge) isotopomers. At 82 K a phase transition takes place leading to a doubling of unit cells and alternation of the hydrogen bond lengths linking tetramethylpyrazine (TMP) and chloranilic acid molecules. A marked H/D isotope effect on these lengths was found at room temperature. The elongation is much smaller at 14 K. The infrared isotopic ratio for O-H(D)...N bands equals to 1.33. The four tunnel splittings of methyl librational ground states of the protonated complex required by the structure are determined at a temperature T=4.2 K up to pressures P=4.7 kbars by high resolution neutron spectroscopy. The tunnel mode at 20.6 microeV at ambient pressure shifts smoothly to 12.2 microeV at P=3.4 kbars. This is attributed to an increase of the strength of the rotational potential proportional to r(-5.6). The three other tunnel peaks show no or weak shifts only. The increasing interaction with diminishing intermolecular distances is assumed to be compensated by a charge transfer between the constituents of deltae/e approximately 0.02 kbar(-1). The phase transition observed between 3.4 and 4.7 kbars leads to increased symmetry with only two more intense tunneling bands. In the isotopomer with deuterated hydrogen bonds and P=1 bar all tunnel intensities become equal in consistency with the low temperature crystal structure. The effect of charge transfer is confirmed by a weakening of rotational potentials for those methyl groups whose tunnel splittings were independent of pressure. Density functional theory calculations for the model TMP.(HF)2 complex and fully ionized molecule TMP+ point out that the intramolecular rotational potential of methyl groups is weaker in the charged species. They do not allow for the unequivocal conclusions about the role of the intermolecular charge transfer effect on the torsional frequencies.

Fullerene quantum gyroscope

We report the observation of quantized rotational states of a diatomic C2 unit in solid endohedral fullerene C(2)Sc(2)@C(84). The rotational transitions induce a periodic line pattern in the low energy Raman spectrum. The rotational constant B and the C-C distance were found to be 1.73 cm(-1) and 0.127 nm, respectively. Density functional calculations revealed an intrinsic rotational barrier of the order of only a few meV for the C2 unit. The Schrödinger equation involving the potential barrier was solved and the Raman tensor matrix elements were calculated, yielding good quantitative agreement with the experiment. To our best knowledge this is the first intrinsic rotational spectrum of a diatomic plane molecular rotor.

Molecular reorientations in liquid crystals pentyloxybenzylidine hexylanilene (PBHA) and butyloxybenzylidine octylanilene (BBOA)

Molecular reorientational motions in undeuterated pentyloxybenzylidine hexylanilene (PBHA or 5O.6) and butyloxybenzylidine octylanilene (BBOA or 4O.8) as studied by the quasielastic neutron scattering (QENS) technique in their different mesophases are reported. Models are built up in stages to account for the experimental elastic incoherent structure factor (EISF). It is found that there exist simultaneous reorientational motions of the chain group and the reorientational motions of the whole molecule around its molecular axis in the smectic- G, smectic- B, and smectic- C phases. In smectic- A and nematic phases, additional body axis fluctuations are found to exist in both 5O.6 and 4O.8 systems. The average amplitude of body axis fluctuations is found to be approximately 15 degrees and 25 degrees, respectively, in the smectic- A and nematic phases of 5O.6, and approximately 14 degrees and 29 degrees, respectively, in 4O.8.

Wave properties of a methyl group under ambient conditions

Liquid-phase NMR studies on hindered rotation of methyl group in a 9-methyltriptycene derivative are reported where the standard, classical jump model of the methyl dynamics proves inadequate. On the other hand, accurate reproduction of the observed NMR line shape effects is afforded by the use of a recent quantum mechanical model in which the relevant methyl dynamics are described in terms of two quantum rate (coherence-damping) processes, characterized by two different rate constants. For ambient temperatures, such a direct evidence of the quantum nature of a rate process generally believed to be classical seems to have no precedence in the literature.

Resonant coupling of free quantum rotors in inclusion compounds

NH3 groups in certain Hofmann clathrates form almost free one-dimensional quantum rotors with energy levels E(n) = n(2)B and angular momentum n (planck constant), where n = 0, +/-1, +/-2,.... Recent neutron scattering experiments revealed a surprising temperature dependence for the linewidths of the n = 0 <--> 1, 0 <--> 2, and 1 <--> 2 transitions. We propose a novel line broadening mechanism based on rotor-rotor coupling and obtain a simple analytic expression for the widths that depends on the rotor level occupation and on the 3-proton spin degeneracies of initial and final states. Our model provides, without adjustable parameters, a good fit both to the temperature dependence of the observed widths and to their relative magnitude.

Tracking the evolution of interatomic potentials with high resolution inelastic neutron spectroscopy

High resolution inelastic neutron scattering has been used to characterize the low temperature rotational dynamics of methane ( CH4) films on MgO(100) surfaces as a function of layer thickness. At low temperatures the films grow layer-by-layer similar to the (100) planes of bulk solid CH4. We observe a crossover in the CH4 tunneling spectrum from one characteristic of the 2D solid at monolayer coverages into one that is bulklike (i.e., 3D) when the film is six layers thick. These findings place significant constraints on the microscopic models used to describe CH4-CH4 and CH4-MgO interactions.