Rotational Potential Research Articles

Stereochemistry of 1,2-dichloroethane adsorbed on Pt(111)

The rotational isomerism of 1,2-dichloroethane (DCE, CH2ClCH2Cl) adsorbed on Pt(111) was studied in the temperature range of 35-100 K using high-resolution electron energy loss spectroscopy and metastable atom electron spectroscopy. In the coverage below monolayer the physisorbed and chemisorbed species coexist at 35 K in the gauche and slightly distorted trans form, respectively. Owing to the direct Pt-Cl interactions, the nonbonding Cl 3p states of the chemisorbed DCE are split off, giving rise to degradation in symmetry from the pure trans form (C2h). The physisorbed gauche conformers are arranged with the C2 axis parallel (or heavily tilted) to the substrate and converted irreversibly to the pseudo-trans form by heating at 70 K. In the multilayer, the trans and gauche conformers exist at 35 K, where the former population is increased with increasing layer thickness. Upon annealing the bilayer at 80 K, the irreversible conversion takes place to yield a higher population of the gauche conformer in the topmost layer. The conformational stabilities and mutual changes of DCE adsorbed on a metal surface are discussed in terms of intramolecular rotational potential.

Effect of Packing and Tilt on the Rotational Barriers of an Amino, Nitro-Substituted Phenylene Ethynylene Trimer

Rotational potentials are computed for heptamers and nonamers of an amino, nitro-substituted phenylene ethynylene trimer molecule. A herringbone and a parallel-slipped packing arrangement are considered. The effect of tilting the molecules with respect to the surface as well as the effect of the gold support are also taken into account. The herringbone structure with the molecules perpendicular to the surface has a low rotational barrier (2 kcal/mol). Tilting the molecules by 30 degrees increases the rotational barriers significantly (16 kcal/mol). The parallel-slipped structure has rotational barriers of 7 kcal/mol. Including the effect of the gold support increases the rotational barriers for tilted molecules but has little effect on perpendicular molecules.

Density functional calculation of conformations and potentials of internal rotation in polychlorinated biphenyls

Full geometry optimization for all 209 isomers of polychlorinated biphenyls (PCBs) and calculations of internal rotation potentials for 154 isomers have been performed by density functional method B3LYP/6-31G(d, p). Conformations and internal rotation barriers in PCBs were proved to depend on a number of chlorine atoms in ortho-positions and, less, the presence of chlorine atoms in adjacent meta-positions. Subject to the number of chlorine atoms in ortho-and adjacent meta-positions, 209 PCB isomers were classified into 18 groups, within each of them molecules having very close conformations and potentials of internal rotation. It makes possible to evaluate with high accuracy the potential functions of the last 55 PCB molecules for which potential curve calculations have not been made.

Rotational tunneling of methyl groups in low temperature phases of mesitylene: potentials and structural implications

Mesitylene can be stabilized at He temperature in three solid phases of so far unknown crystal structures. Rotational tunneling of methyl groups is based on rotational potentials and used to characterize structural aspects. In phase III found after the first fast cooling of the sample three nonequivalent methyl rotors with splittings of 2.7, 4.1 and 16.3 microeV are observed. Three other unresolved bands are identified by their librational modes. In the second phase II the metastability is emphasized by tunneling energies still changing at temperatures T< or = 12 K. Above this temperature tunneling bands at 6.6, 12.5, 15.0 and 18.3 microeV evolve in the manner characteristic of coupling to phonons. In the equilibrium phase I a single tunnel splitting of 10.2 microeV represents all methyl groups. A unit cell containing a single molecule at a site of threefold symmetry explains quantitatively this spectrum. Phases II and III most likely contain two nonequivalent molecules in the unit cell with no local symmetry in phase II and a mirror plane in phase III. The good moderator properties for neutrons are most likely not connected to the low energy tunneling bands but to a dense vibrational phonon density of states.

Adsorption sites and rotational tunneling of methyl groups in cubic I methyl fluoride water clathrate

Neutron spectroscopy in the microeV and meV regime and quasielastic scattering is applied to characterize the dynamics of methyl groups of methyl fluoride guest molecules in cubic I CH3F-water clathrate. Only above T approximately 60 K quasielastic spectra are unaffected by quantum effects. They are well described by two Lorentzians representing the CH3F species in the small and large cages of the structure. The intensities show that both cages are completely filled. The linear broadenings with temperature follow the model of rotational diffusion. Two clearly separated tunneling bands were observed at T = 4.2 K and are also assigned to the two types of water cages. Disorder of the environment (H-bonds) is reflected in the shape of the bands. For the less hindered species housing the large cages the tunneling band can be quantitatively converted into a potential distribution function within the model of single particle rotation. Transitions to excited rotational states show the dominance of a sixfold potential term V6 = 13 meV modified by a weak threefold term distributed around a characteristic value V3 = 0.9 meV. The potential distribution of V3 influences the barrier for classical reorientation only weakly in agreement with the results from quasielastic data. Adsorption sites with the guest molecules oriented towards a hydrogen bond along one of twelve local twofold axes of the cage are proposed. Such sites are consistent with the sixfold rotational potential and earlier results from methyl iodide clathrate. Rotation-translation coupling as an alternative dynamical process is excluded.

Molecular Structure and Internal Rotation in 2,3,5,6-Tetrafluoroanisole as Studied by Gas-Phase Electron Diffraction and Quantum Chemical Calculations

The geometric structure of 2,3,5,6-tetrafluoroanisole and the potential function for internal rotation around the C(sp2)-O bond were determined by gas electron diffraction (GED) and quantum chemical calculations. Analysis of the GED intensities with a static model resulted in near-perpendicular orientation of the O-CH3 bond relative to the benzene plane with a torsional angle around the C(sp2)-O bond of tau(C-O) = 67(15) degrees. With a dynamic model, a wide single-minimum potential for internal rotation around the C(sp2)-O bond with perpendicular orientation of the methoxy group [tau(C-O) = 90 degrees] and a barrier of 2.7 +/- 1.6 kcal/mol at planar orientation [tau(C-O) = 0 degrees] was derived. Calculated potential functions depend strongly on the computational method (HF, MP2, or B3LYP) and converge adequately only if large basis sets are used. The electronic energy curves show internal structure, with local minima appearing because of the interplay between electron delocalization, changes in the hybridization around the oxygen atom, and the attraction between the positively polarized hydrogen atoms in the methyl group and the fluorine atom at the ortho position. The internal structure of the electronic energy curves mostly disappears if zero-point energies and thermal corrections are added. The calculated free energy barrier at 298 K is 2.0 +/- 1.0 kcal/mol, in good agreement with the experimental determination.

Non-planarity and solvent effects on structural and polarizability properties of cytosine tautomers

We report equilibrium geometries, relative stabilities, electronic and vibrational polarizabilities of cytosine tautomers and of reference compounds phenol, aniline and pyrimidine, in the gas phase and in solution, calculated by conventional correlated ab initio (CCSD, CCSD(T) and MP2) and density functional (B97-1) methods, using a variety of basis sets. Gas phase ionization potentials, electron affinities and torsional potentials for the internal rotation of the –OH and –NH2 groups, were obtained at MP2 and B97-1 levels of theory. The results show that the structures of the tautomers are non-planar in the gas phase and become planar as the polarity of the solvent increases, in contrast with aniline where the amino group remains non-planar also in the polar CH3CN solvent, what has a correspondence in the NH2 inversion barrier and NH2 wagging vibration lower in cytosine than in aniline. To constrain NH2 to be planar does not produce important changes in the relative energies, polarizabilities, ionization potential and electron affinities of the tautomers in vacuo. Polarizabilities are consistently influenced by solvent effects. The –OH and –NH2 groups show much higher π interaction with the heterocyclic ring than with the phenyl ring, what determines barriers for internal rotation of the groups much higher in cytosine than in phenol and aniline. Hardness and polarizability profiles for the –OH and –NH2 rotation do not follow, however, the maximum hardness and the minimum polarizability principles, respectively.

Rotational dynamics of methyl groups in m-xylene

Methyl group dynamics of m-xylene was investigated by using incoherent inelastic and quasi-elastic neutron scattering. Inelastic measurements were carried out at the high flux backscattering spectrometer HFBS at the National Institute of Standards, quasi-elastic measurements at the time-of-flight spectrometer NEAT at the Hahn-Meitner-Institute. Rotational potentials are derived which describe the tunnel splittings, first librational, and activation energies of the two inequivalent CH(3) groups. Indications for coupling of the methyl rotation to low-energy phonons have been found. The finite width of one tunneling transition at He temperature is described by direct methyl-methyl coupling. The combined results of the experiments and the calculations allow a unique assignment of rotor excitations to crystallographic sites.

One-dimensional models of internal rotation in CX 3NO molecules (X = H, D, F)

Various non-empirical methods for estimating the parameters of one-dimensional internal rotation potentials and energies of torsional transitions were compared for the CX 3NO molecules (X = H, D, F) in the ground ( S 0) and lowest excited singlet ( S 1) electronic states. The potential energy surfaces were studied by the ab initio MR-AQCC/cc-pVTZ, MR-AQCC/cc-pVTZ(- f), MP2/6-311G(2 d), and MP2/6-311G( d, p) methods. The one-dimensional internal rotation problem was solved using the following models: (1) geometry optimization at a given internal rotation coordinate; (2) intrinsic reaction path; (3) gradient extremal; and (4) use of only the data on potential energy surface stationary points. Special attention was paid to the problem of calculation of kinematic coefficient. In all cases, the calculated torsional energies for CX 3NO molecules (X = H, D, F) are in agreement with experiment. The results from different methods for constructing torsional cross-sections of the potential energy surface are virtually equivalent and differ insignificantly from the results of calculations within the framework of the simplest model, hence, estimates of the barrier to internal rotation are of most importance. It was found that a change in the zero-point energy could give a correction to the internal rotation potential as large as 15% of the potential barrier. However, in the case under consideration the calculations in the harmonic approximation taking into account this correction do not improve the agreement between the calculated torsional transitions and the experimental data.

Maximal dismounts from high bar

In men's artistic gymnastics the triple straight somersault dismount from the high bar has yet to be performed in competition. The present study used a simulation model of a gymnast and the high bar apparatus (J. Appl. Biomech. 19(2003a) 119) to determine whether a gymnast could produce the required angular momentum and flight to complete a triple straight somersault dismount. Optimisations were carried out to maximise the margin for error in timing the bar release for a given number of straight somersaults in flight. The amount of rotation potential (number of straight somersaults) the model could produce whilst maintaining a realistic margin for error was determined. A simulation model of aerial movement (J. Biomech.23 (1990) 85) was used to find what would be possible with this amount of rotation potential. The model was able to produce sufficient angular momentum and time in the air to complete a triple straight somersault dismount. The margin for error when releasing the bar using the optimum technique was 28 ms, which is small when compared with the mean margin for error determined for high bar finalists at the 2000 Sydney Olympic Games (55 ms). Although the triple straight somersault dismount is theoretically possible, it would require close to maximum effort and precise timing of the release from the bar. However, when the model was required to have a realistic margin for error, it was able to produce sufficient angular momentum for a double twisting triple somersault dismount.

Dynamical model for theC5H5cycles in theC60∙2Fe(C5H5)2solvate

A model for uniaxial rotation is used in order to calculate the rotational potential for the ${\mathrm{C}}_{5}{\mathrm{H}}_{5}$ rings in the crystal. The contribution from nonbonded interactions is then compared with intra-molecular bounding forces, showing that the observed equilibrium position of the cycles is due to a combination of crystal packing forces and bonding forces within the molecule. The height of the barriers are also extracted and it confirms that there are two kinds of cycles with specific magnetic and electrical environments. The temperature evolution of the spin-lattice relaxation time is probed by $^{1}\mathrm{H}$ NMR spectroscopy over the range 54--394 K and is treated with the model proposed for the simulation. One of the two calculated activation energies is observed in the experimental curve; this indicates coupling with one kind of cycle over the studied temperature range.

Measurement of the rotational velocity in Hanbit mirror device by using the Gundestrup-emissive-triple probe system

A new probe set, called the Gundestrup-emissive-triple (GET) probe, is developed to measure the rotational velocity, plasma potential, electron temperature, and plasma density profiles simultaneously in Hanbit mirror device. The GET probe system is composed of the Gunderstrup, an emissive, and a triple probe installed in one boron nitride probe holder, which is attached on the fast scanning injection system. Rotational and parallel flow velocities are deduced from the measurement of Gundestrup probe by using fluid and kinetic theories for unmagnetized and magnetized plasmas. The E×B drift velocity is also deduced from the measurement of plasma potential by an emissive probe. Electron temperature and plasma density variations are measured by a triple probe. Applicability of various theories will be addressed.

Thermodynamic Properties of Polychlorinated Biphenyls in the Gas Phase

The molecular structures, vibrational frequencies, and internal rotational potentials of 209 polychlorinated biphenyls were computed at the B3LYP/6-31G(d,p) density functional theory level. Standard entropies, S°(T), heat capacities, and enthalpies, H°(T) − H°(0) (100 K ≤ T ≤ 1500 K), were calculated using the rigid-rotor harmonic-oscillator approximation with correction for internal rotation. Enthalpies of formation, were calculated at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d,p) level using isodesmic reactions and the recommended values for biphenyl, benzene, and polychlorinated benzenes. The uncertainties of the calculated values are estimated to be 5−10 J K-1 mol-1 for and and 5−35 kJ mol-1 for The calculated thermodynamic properties are compared with values determined earlier by the semiempirical and group additivity methods.

A molecular beam Fourier transform microwave study of 2-methylpyridine and its complex with argon: structure, methyl internal rotation and 14N nuclear quadrupole coupling

The rotational spectrum of 2-methylpyridine (α-picoline, CH3C5H4N) in the two lowest levels of methyl internal rotation (m=0, ±1) has been recorded in the frequency range from 2 to 15 GHz using a molecular beam Fourier transform microwave spectrometer. The high resolution and sensitivity of this spectroscopic technique allowed resolution of hyperfine structures due to l4N nuclear quadrupole coupling with high accuracy and detection of the spectra of the 15N- and all 13C-isotopomers. These investigations considerably extend the results from an earlier study on the normal species (Dreizler, H., Rudolph, H. D., and Mader, H., 1970, Z. Naturforsch., 25a, 25); improved rotational and centrifugal distortion constants as well as all components of the 14N quadrupole coupling tensor have been obtained. Analysis of the spectra of the isotopomers yielded the I4N quadrupole coupling constants χ cc and χ aa – χ bb (for the 13C species), the potential parameter V 3 for the barrier hindering the internal rotation of the methyl group, and, in particular, ro, rs r m (1) and r m (2) structural parameters for the molecule. In addition to the microwave studies on the monomer, we have also investigated the rotational spectrum of the weakly bound dimer of normal 2-methylpyridine with Ar. The results obtained for the quadrupole coupling constants and the hindering potential for the internal methyl rotation show that the corresponding parameters are not significantly, or only slightly, changed in the complex.

Electron–transverse acoustic phonon interaction in martensitic alloys

Based on the consideration of $\ensuremath{\nabla}\ifmmode\times\else\texttimes\fi{}{u}_{TA}\ensuremath{\ne}0$, a rotation potential model is proposed to study electron--transverse acoustic phonon interaction in the martensitic alloys. The electron or phonon self-energy correction and the scattering of electron due to the rotation potential are derived. The driving force of premartensitic transformation has been estimated to be about several meV. The phase transition can be driven by electron--TA phonon interaction and the coupling mechanism may be taken as its main nucleation mechanism. Tweed structure is suggested to originate from the ionic density fluctuation which is perpendicular to the wave vector of TA phonon. The anomalous change in electrical resistivity during phase transition results from the strong scattering of electron by the $(110){\mathrm{TA}}_{1}$ phonon at the critical temperature.

Molecular Structure and Internal Rotation Potential of Dimethylphenylphosphine, According to Gas-Phase Electron Diffraction Data and Quantum-Chemical Calculations

Geometric parameters of dimethylphenylphosphine molecule were determined by gas-phase electron diffraction using a dynamic model in which the rotation of the PMe2 group is treated as large-amplitude motion. Refinement of the structural parameters and parameters of the potential function was performed taking into account the geometry relaxation on the basis of HF/6-311++G** calculations. The internal rotation potential has a single minimum at ϕ 0° (ϕ is the angle between the bisector of the MePMe angle and the phenyl ring plane) and may be described by the function of the form V(ϕ) = 0.5V2(1 - cos2ϕ), where V2 = 0.38±0.36 kcal mol-1. The data obtained are compared with those for related molecules. Steric effects affect the geometry of the phenylphosphine molecule more significantly than does p-π interaction.

An intrinsic reaction coordinate calculation of the torsion-internal rotation potential of hydrogen peroxide and its isotopomers.

Intrinsic reaction coordinate (IRC) calculations of the internal rotation (torsional) potentials for H(2)O(2) and its isotopomers HDO(2) and D(2)O(2) were carried out at the CCSD(T)/CBS//aug-cc-pVDZ level. Two extrapolation methods were used to obtain energies in the complete basis set (CBS) limit. The full IRC potential was constructed from scans from the C(2v) (cis) and C(2h) (trans) transition states to the equilibrium C(2) (gauche) structure. The IRC potential for H(2)O(2) was fit to a five-term Fourier function; coefficients were compared with values obtained from spectroscopic data. The twofold IRC torsional potentials were used to obtain torsional eigenvalues, which yielded values of the transitions between various ntau states. These results compare favorably with Raman and near-infrared data. Our calculations provide values of the cis and trans barriers of 2495 and 364 cm(-1), respectively, which are in good agreement with both previously calculated and experimentally derived values. It appears that coupling between torsional motion and other degrees of freedom is not significant in these molecules.

Methyl rotational potentials as a probe of the cage potential surface in methyl iodide clathrate

Methyl iodide water clathrates crystallize in the cubic II structure. Methyl tunneling spectra of CH 3I identify three adsorption sites. The presence of 3 types of H-bonds in the cage surface are considered as likely origin. The barriers to rotation of methyl groups are low at all sites. Due to finite and different spin conversion times two of the three excited tunnel levels are not in thermal equilibrium. The classical methyl dynamics is almost unaffected by the weak potentials and described as rotational diffusion. A second slower quasielastic process may be interpreted as overall rotation of the molecule.

Accurate torsional potentials in conjugated systems: ab initio and density functional calculations on 1,3-butadiene and monohalogenated butadienes

Accurate calculations of the torsional potentials for rotation around the carbon–carbon single bond of all conceivable monohalogenated 1,3-butadienes C4 H 5X, (X ∈ [F, Cl, Br]), are presented. The parent compound, 1,3-butadiene, is also included as a benchmark and reference case. Large-scale ab initio calculations were performed at the second-order Møller–Plesset perturbation theory (MP2) and the coupled cluster, CCSD(T), levels. Additionally, density functional methods were applied. In all compounds considered, the anti- or s-trans-conformation is the most stable. For all three halogens, the 2-halo-1,3-butadiene is the most stable isomer, followed by the cis-1-halo-1,3-butadiene. Depending on the position and the type of halogen, the original 1,3-butadiene torsional potential is modified in a different manner. The modifications are particularly visible in the region of the syn- or s-cis and the gauche structures and in the barrier heights.

Spatiotemporal dynamics of circular flow modes in a ring array of Bose-Einstein condensates

We numerically investigate the spatiotemporal dynamics of a circular flow mode in a ring array of Bose-Einstein condensates, which consists of $M$ identical Bose-Einstein condensates that couple to the nearest-neighbor sites by tunneling. Introducing a rotational potential in the Gross-Pitaevskii equation, a series of circular flow modes is resonantly excited. For the initial conditions with uniform density and one-round phase difference of $2\ensuremath{\pi}\ensuremath{\ell}\phantom{\rule{0.3em}{0ex}}(l=0,1,\dots{},M\ensuremath{-}1)$, two circular flow modes are excited for each circulation-quantized number $l$. It is shown that these circular flow modes periodically appear in time in the presence of the rotational field and persistently survive with a constant shape even after the external potential is removed, the transitions between the circular flow modes with different quantized number $l$ can be realized by applying the phase-imprinting optical pulses, and the rotational velocity of the circular flow mode can be continuously modulated by adiabatically tuning the scattering length in a magnetic field, i.e., by use of the Feshbach resonance.