Ring Orbitals Research Articles

THE ORBITS OF THE URANIAN SATELLITES AND RINGS, THE GRAVITY FIELD OF THE URANIAN SYSTEM, AND THE ORIENTATION OF THE POLE OF URANUS

French et al. determined the orbits of the Uranian rings, the orientation of the pole of Uranus, and the gravity harmonics of Uranus from Earth-based and Voyager ring occultations. Jacobson et al. determined the orbits of the Uranian satellites and the masses of Uranus and its satellites from Earth-based astrometry and observations acquired with the Voyager 2 spacecraft; they used the gravity harmonics and pole from French et al. Jacobson & Rush reconstructed the Voyager 2 trajectory and redetermined the Uranian system gravity parameters, satellite orbits, and ring orbits in a combined analysis of the data used previously augmented with additional Earth-based astrometry. Here we report on an extension of that work that incorporates additional astrometry and ring occultations together with improved data processing techniques.

Electrostatic injection kicker for the KEK digital accelerator

An electrostatic injection kicker (ES-Kicker) has been developed and installed in the KEK digital accelerator, which is a synchrotron aimed at accelerating all ion species. The ES-Kicker kicks an injected ion beam horizontally into the ring orbit and consists of two main electrodes for electric field generation and three intermediate electrodes to correct field homogeneity. In our single-turn injection scheme, the circulating beam and the injected beam both pass through the electrode aperture of the kicker, so the kicker field must be turned off before arrival of the first circulating beam. The ES-Kicker is therefore operated in a pulse mode. This means that the excitation circuit for the ES-Kicker must be carefully designed, since the falling edge of the electric field is strongly affected by parasitic capacitance of this circuit, and any remaining field may disturb the circulating beam. This paper describes performance of the ES-Kicker on the basis of simulations and measurement results.

LOCAL VARIABILITY IN THE ORBIT OF SATURN'S F RING

We present an analysis of the orbit of Saturn's F ring using images recorded by the Imaging Science Subsystem of the Cassini spacecraft. A total of 9805 observations have been made from 10 image sequences obtained between 2006 November 23 and 2009 July 28. Each sequence of up to 240 images spans a single orbit of the F ring, allowing 10 independent high-precision estimates of the ring orbit to be made over this ∼3 year period. The ring has been modeled as an inclined uniformly precessing ellipse. The results show a variability in the orbital elements with, for example, the semi-major axis scattered between 140211.2 ± 0.1 km and 140232.9 ± 0.4 km and the fitted periapses locked to the value obtained from a combined fit using the entire three-year span of observations. We show that the observed scatter between the individual estimates of the ring orbit reflect the differing past histories of the particular segments of ring being fitted and that the values are scattered within the limits expected from a single gravitational encounter with the nearby moon, Prometheus. In the combined fit, the scatter averages out to reveal a small systematic bias with respect to the results ofmore » Bosh et al. and Albers et al. We believe this is a consequence of the proximity of Prometheus to the ring in the image sequences chosen for this analysis. Finally, we note a close empirical commensurability between the apsidal precession rate, ϖ-dot , of the F ring and the synodic period between Prometheus and the F ring, such that n {sub Prom} – n {sub Fring} ≈ 2 ϖ-dot {sub Fring}, where n {sub Prom} and n {sub Fring} are the mean motions, and discuss its implications.« less

Electronic effects of the functional groups in ortho-Nitrobenzenesulfonic acids on the results of NBO analysis

An NBO analysis of electronic density distribution is performed for gaseous benzenesulfonic acid and its mono- and trinitro-substituted molecules (B3LYP, MP2, HF /cc-pVTZ). The energy of orbital inter-actions of nitro and sulfonic groups with benzene ring orbitals is calculated for the most stable acid conformers, and the contributions of inductive and resonance effects of substituents are determined. The dependences of these contributions on the positions and number of nitro groups in an aromatic ring and the possibility of intramolecular hydrogen bond formation are revealed. The nitro group in nitrobenzene exhibits a stronger electron-acceptor effect than the sulfonic group in benzenesulfonic acid. Under the influence of the strong electron-acceptor properties of the nitrogroups, the sulfonic group has a donating effect in ortho-nitrosubstituted benzenesulfonic acids.

Kinetic Study and NBO Analysis of the Dehydrogenation Mechanism of Five‐membered Ring Heterocyclic 2,5‐Dihydro‐[furan, thiophene, selenophene

AbstractThe theoretical study of the dehydrogenation of 2,5‐dihydro‐[furan (1), thiophene (2), and selenophene (3)] was carried out using ab initio molecular orbital (MO) and density functional theory (DFT) methods at the B3LYP/6‐311G**//B3LYP/6‐311G** and MP2/6‐311G**//B3LYP/6‐311G** levels of theory. Among the used methods in this study, the obtained results show that B3LYP/6‐311G** method is in good agreement with the available experimental values. Based on the optimized ground state geometries using B3LYP/6‐311G** method, the natural bond orbital (NBO) analysis of donor‐acceptor (bond‐antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from non‐bonding lone‐pair orbitals [LP(e)X3] to δ*C(1)H(2) antibonding orbital, decrease from compounds 1 to 3. The LP(e)X3→δ*C(1)H(2) resonance energies for compounds 1–3 are 23.37, 16.05 and 12.46 kJ/mol, respectively. Also, the LP(e)X3→δ*C(1)H(2) delocalizations could fairly explain the decrease of occupancies of LP(e)X3 non‐bonding orbitals in ring of compounds 1–3 (3>2>1). The electronic delocalization from LP(e)X3 non‐bonding orbitals to δ*C(1)H(2) antibonding orbital increases the ground state structure stability, Therefore, the decrease of LP(e)X3→δ*C(1)H(2) delocalizations could fairly explain the kinetic of the dehydrogenation reactions of compounds 1–3 (k1>k2>k3). Also, the donor‐acceptor interactions, as obtained from NBO analysis, revealed that the (C(4)C(7)→δ*C(1)H(2) resonance energies decrease from compounds 1 to 3. Further, the results showed that the energy gaps between (C(4)C(7) bonding and δ*C(1)H(2) antibonding orbitals decrease from compounds 1 to 3. The results suggest also that in compounds 1–3, the hydrogen eliminations are controlled by LP(e)→δ* resonance energies. Analysis of bond order, natural bond orbital charges, bond indexes, synchronicity parameters, and IRC calculations indicate that these reactions are occurring through a concerted and synchronous six‐membered cyclic transition state type of mechanism.

Theoretical study on effects of hydrogen bonding on the ring stretching modes of pyridine

Pyridine generally acts as the proton acceptors in the hydrogen bonding interaction by using its lone pair n(N) or pi-electrons. Some previous research indicated that for the N-type H-bond, the ring breathing mode v(1), the N-para-C stretching mode v(6a) and the meta-CC stretching mode v(8a) of pyridine showed a frequency blueshift but the triangle mode v(12) had no change in frequency. Both electrostatic interaction and charge transfer caused by intermolecular hyperconjugation n(N)-->sigma( *)(HX) have contributions to the frequency blue shifts, while charge transfer is predominant at equilibrium intermolecular distance. An intramolecular hyperconjugation between the lone pair n(N) and the two sigma( *)(meta-CC) orbitals in the pyridine ring provides a reasonable interpretation for the effect of charge transfer on the ring stretching modes upon formation of the N-type H-bonding.

RING EDGE WAVES AND THE MASSES OF NEARBY SATELLITES

Moons embedded in gaps within Saturn’s main rings generate waves on the gap edges due to their gravitational disturbances. These edge waves can serve as diagnostics for the masses and, in some cases, orbital characteristics of the embedded moons. Although N-body simulations of the edges are far better in inferring masses from edge morphology, the long run-times of this technique often make it impractical. In this paper, we describe a faster approach to narrow the range of masses to explore with N-body simulations, to explore the multidimensional parameter space of edge/moon interactions, and to guide the planning of spacecraft observations. Using numerical, test-particle models and neglecting particle–particle interactions, we demonstrate that the simple analytic theory of the edge waves applies well to Pan in the Encke Gap but breaks down for smaller moons/ gaps like Daphnis in the Keeler Gap. Fitting an analytic model to our simulation results allows us to suggest an improved relationship between moon-mass and edge wave amplitude. Numerical methods also grant freedom to explore a wider range of moon and ring orbits than the circular, coplanar case considered by analytic theory. We examine how pre-encounter inclinations and eccentricities affect the properties of the edge waves. In the case where the moon or ring-edge particle orbits initially have eccentric radial variations that are large compared to the gap width, there is considerable variation in edge wave amplitude depending on the orbital phase of the encounter. Inclined moons also affect the edge wave amplitude, potentially significantly, as well as generate vertical waves on the gap-edges. Recent Cassini images acquired as Saturn approaches equinox and the Sun’s elevation on the ringplane is extremely low have revealed long shadows associated with the Keeler gap edge waves created by the embedded moon Daphnis. We interpret these as being cast by ∼1 km high vertical structure in the waves created by Daphnis’ out-of-plane perturbations on the ring particles.

The Torque at a Lindblad Vertical Resonance

A fairly uniform, rapidly and differentially rotating disk of rarely colliding particles (when the frequency of interparticle collisions is much smaller than the local orbital frequency) in a planet-moon system is considered. A moon causes a number of orbital resonant effects in this continuous, viscous (through ordinary collisions) disk. In the frame of hydrodynamical theory, the gravitational torques exerted by an exterior moon on particles at an inner Lindblad horizontal resonance and corresponding vertical resonance are estimated. It is shown that the torques are negative at these resonances, so gaps in the disk near each resonance may be created. The latter result can be used to provide a viable clue to solving the puzzle of narrow, dense, and widely separated rings of Uranus. The model advocated suggests that the Uranian ring orbits have a close connection with the small moons of the planet that are interior to the orbit of Miranda, from Cordelia to Mab, discovered by Voyager 2 imaging observations in 1986.

Effect of fluorination: Conformation of 2,6-difluoroanisole

The geometric structure and conformation of 2,6-difluoroanisole, 2,6-C 6H 3F 2OCH 3, has been determined with gas electron diffraction (GED) and quantum chemical calculations (MP2 and B3LYP with 6-311++G(2df,pd) basis sets). The GED intensities have been analyzed with a static as well as with a dynamic model. The static model resulted in a structure with near-perpendicular orientation of the O–CH 3 bond with a thermal average dihedral angle τ(C2C1–OC) = 70 ± 3°. With the dynamic model a perpendicular equilibrium structure and a potential function for internal rotation around the C–O bond with a very flat minimum at τ(C2C1–OC) = 90° and with a barrier of 1.8 ± 0.6 kcal/mol at τ(C2C1–OC) = 0° was derived. Quantum chemical calculations predict double-minimum potential functions for the electronic energies, which become single-minimum potentials upon addition of zero-point vibrational energies. The change of conformation from planar in anisole to perpendicular in 2,6-difluoroanisole has been rationalized by orbital interactions between the oxygen electron lone pairs and benzene ring orbitals and by steric repulsion.

Condensed Two- and Three-Dimensional Aromatic Systems: A Theoretical Study on the Relative Stabilities of Isomers of CB19H16+, B20H15Cl, and B20H14Cl2 and Comparison to B12H10Cl22-, C6H4Cl2, C10H7Cl, and C10H6Cl2

DFT studies (B3LYP/6-31G) on mono- and dichloro derivatives of benzene, naphthalene, B12H12(2-), four-atom-sharing condensed systems B20H16, and monocarborane isomers of B20H16 are used to compare the variation of relative stability and aromaticity between condensed aromatics. The trends in the variation of the relative energies and aromaticity in these two- and three-dimensional systems are similar. Aromaticity, estimated by NICS values, does not change considerably with condensation or substitution. The minor variation in the relative energies of the isomers of chloro derivatives is explained by the topological charge stabilization rule of Gimarc. The compatibility of the cap and ring orbitals decides the relative stability of CB19H16+.

Di([5]trovacenyl)ethyne, Di([5]trovacenyl)butadiyne, and Di-1,4-([5]trovacenylethynyl)benzene: Electrocommunication and Magnetocommunication Mediated by C⋮C, C⋮CC⋮C and C⋮CC6H4C⋮C Spacers

The synthesis of dinuclear derivatives of trovacene (eta7-C7H7)V(eta5-C5H5) (1.) is reported, in which ethynyl (6..), butadiynyl (7..), and 1,4-di(ethynyl)phenyl (8..) groups serve as spacers between paramagnetic (S = 1/2) [5]trovacenyl units. The mononuclear precursors [5]trovacenylcarbaldehyde (2.) and [5]trovacenylacetylene (4.) are also described. Structural characterization by X-ray diffraction has been performed for 4., 6.., 7.., and 8.. Electronic communication as gleaned from cyclic voltammetry only manifests itself in the reduction processes where redox splitting deltaE1/2(0/ 1-, 1-/2-) is resolved for 6.. (deltaE1/2 = 150 mV) and indicated for 7.. (deltaE1/2 < or approximately 80 mV). Magnetocommunication leads to exchange coupling of the two electron spins which reside in vanadium centered orbitals. The values JEPR(6..) = (-)0.92, JEPR(7..) = (-)0.56, and JEPR(8..) = (-)0.005 cm(-1) are derived from the 51V hyperfine patterns. Accordingly, attenuation of exchange interaction by oligoalkyne spacers is weak, corresponding to a factor of 0.6 only per added --C triple bond C-- unit. In the determination of very weak long distance exchange interactions, EPR excels because of the range 5 x 10(-4) < or approximately J < or approximately 1.5 cm(-1) accessible in the case of 51V as a reporting magnetic nucleus and because competing intermolecular exchange is quenched in dilute fluid solution. This is demonstrated by the value Jchi(7..) = -3.84 cm(-1) obtained from a magnetic susceptibility study, which exceeds JEPR(7..) by a factor of 7. The small magnitude of spin exchange interaction between trovacene units reflects the fact that the spin bearing V3dz2 orbital is virtually orthogonal to the pi-perimeter ligand orbitals and weakly overlapping only with the a1g(sigma) ring orbitals, creating two bottlenecks for spin-exchange in the spacer-containing ditrovacenes.

Electronically Excited States of Methylenecycloalkanes

The vacuum UV spectra of methylenecyclopropane, methylenecyclobutane, methylenecyclopentane, and methylenecyclohexane have been obtained from 45 000 to 70 000 cm-1. The transitions for methylenecyclopropane have been calculated at the EOM-CCSD/6-311(2+,2+)G** level. Using the equilibrium CC bond lengths, the calculated transition energies are uniformly larger than observed, but increasing the bond length a small amount led to quite good agreement. Here, the transitions are found to originate from the two higher energy occupied cyclopropane ring orbitals in addition to the π orbital. The transitions for methylenecyclohexane are found to be linearly related to those for isobutene. CIS calculations for all of the methylenecycloalkanes using somewhat lengthened CC bonds reproduced the lower energy transition energies fairly well.

Alkyl Substituent Effects on the Conductivity of Polyaniline

AbstractThe oxidative polymerization of aniline hydrochloride derivatives in water at low temperature is studied without lithium chloride. The resulting polymers have high molecular weight but the conductivity of the acid‐doped films is strongly dependent on the alkyl‐substituted chain at the 2‐positions. The root cause of the alkyl‐substitution effects is thoroughly investigated using density functional theory (DFT) methods (B3LYP using 6–1G(d,p) and 6‐311++G(2d,2p) basis sets). Internal structural changes observed on substitution appear to be more significant than a variety of electronic parameters measured using the natural bond orbital (NBO) method. Interplanar angles steadily increase on substitution, whereas ring orbital properties and the amount of ring delocalization remain fairly constant. An investigation into the extent to which lone pair–σ‐orbital overlap is affected by substitution indicates that increasing the steric bulk of the substituent reduces the ability of the lone pair to delocalize into the ring orbitals. However, the amount of overlap between the two is not adversely affected until the dihedral between them is &gt; 30°, a situation that only occurs in i‐propyl and s‐butyl substitution. This finding is completely reflected in the experimental conductivity measurements.

The barrier to internal rotation and electronic effects in para-halogenophenols: theoretical study

The OH rotational barrier height in phenol and para-halogenophenols systematically decreases in the series Br, Cl and F, while the changes in the CO bond length and CO bond strength do not follow this order. On the basis of the NBO analysis it is suggested that lowering of the barrier height in p-halogenophenols is caused by the decrease of electron density in the sigma antibonding orbital, σ *(CO), and a weak occupancy of this orbital is due to the electron delocalization from the σ(CC) ring orbitals. This effect can be either reinforced or reduced, depending on the extent of conjugation between the p z -type lone electron pair on the oxygen atom and the π *(CC) acceptor orbitals in the aromatic ring.

Elucidation of a Sc(I) complex by DFT calculations and reactivity studies.

Sc(BrMgL)(2)Br (L = (R(2)NCH(2)CH(2)NCMe)(2)CH, R = H) was studied by DFT methods leading to the conclusion that this diamagnetic formal scandium(I) system enjoys stabilization of its Sc-based filled d(yz)() orbital by a delta-acceptor linear combination of BrMgL ring orbitals. Investigation of the reactivity of Sc(BrMgL)(2)Br (L = (R(2)NCH(2)CH(2)NCMe)(2)CH, R = Et) with H(2)O.B(C(6)F(5))(3) and (HOCH(2))(2)CMe(2), respectively, led to decomposition, with LMgBr being isolated in the latter case.

The electronic states of 2-furanmethanol (furfuryl alcohol) studied by photon absorption and electron impact spectroscopies

The photoelectron spectrum of 2-furanmethanol (furfuryl alcohol) has been measured for ionization energies between 8 and 11.2 eV and the first three ionization bands assigned to π3, π2, and no ionizations in order of increasing binding energy. The photoabsorption spectrum has been recorded in the gas phase using both a synchrotron radiation source (5–9.91 eV, 248–125 nm) and electron energy-loss spectroscopy under electric-dipole conditions (5–10.9 eV, 248–90 nm). The (UV) absorption spectrum has also been recorded in solution (4.2–6.36 eV, 292–195 nm). The electronic excitation spectrum appears to be dominated by transitions between π and π* orbitals in the aromatic ring, leading to the conclusion that the frontier molecular orbitals of furan are affected only slightly on replacement of a H atom by the –CH2OH group. Additional experiments investigating electron impact at near-threshold energies have revealed two low-lying triplet states and at least one electron/molecule shape resonance. Dissociative electron attachment also shows to be widespread in furfuryl alcohol.

Theoretical Studies on the Stabilities of Metallabenzynes

Theoretical calculations at the B3LYP level of density functional theory have been carried out to study the stability of osmabenzyne complexes. Isodesmic reactions have been designed to analyze the ring strain and conjugation energies of the complexes. The ring strain energy was found to be small, primarily because of the relatively small angle of bending at the carbyne carbon. The conjugation energy is comparable to those of benzene and osmabenzene. The effect of substituents at the ring carbons on the stabilities has also been examined. Through molecular orbital analyses, we found that the effect of substituents on the energies of π orbitals in the six-membered ring play important roles in determining the relative stabilities.

Saturn's F Ring: Kinematics and Particle Sizes from Stellar Occultation Studies

The occultation of GSC5249-01240 by Saturn's rings was observed in a spectrally resolved mode using the Faint Object Spectrograph on the Hubble Space Telescope. By combining these data with other occultation data, we have determined the inclination of the F ring to be 0.0065±0.0014 deg. Our inclined F ring orbit model explains an abrupt decrease in flux at the west ansa of the ring that was observed during the November 1995 ring-plane crossing as well as the nondetection of 1995 S5 during one set of observations in November 1995. The F ring's equivalent depth is found to have no significant dependence on wavelength between 0.27 and 0.74 μm, indicating the presence of a population of ring particles larger in size than ∼10 μm. This contrasts with the results from a previous analysis of Voyager images at various phase angles, in which the particles were determined to be predominantly submicron in size. The difference may be due to temporal or longitudinal variability within the ring.

Control of stability through overlap matching: closo-carborynes and closo-silaborynes.

The matching of ring and cap orbitals for overlap is used to arrive at the best carborynes among the many possibilities. Accordingly, 1,2-carboranes, 1,2-silaboranes (C2BnHn+2, and Si2BnHn+2, n = 4, 5, 8, and 10), and their dehydrogeno derivatives were studied with use of the Density Functional Theory (B3LYP/6-311+G*). The dehydrogenation of 2,3-C2B5H7 (6a) to 2,3-C2B5H5 (13a) is estimated to be even less endothermic than those of benzene and 1,2- C2B10H12 (1a) to benzyne and 1,2-C2B10H10 (8a) by more than 21 kcal/mol. This is due to the extra stabilization gained through better overlap of the C2B3H3 ring with the 2 BH caps. The relatively larger size of the Si atom leads to overlap requirements in silaboranes that are different from those in carboranes. The lower Si-Si single bond energy and the preference of Si for lower coordination result in unusual structures in dehydrogenosilaboranes. One of the Si atoms moves away from the surface in Si2B10H10 (15), Si2B8H8 (16, 17, and 18), and 1,2-Si2B5H5 (19). One Si atom forms a bridge to a trigonal surface in 2,3-Si2B5H5 (20) and 1,2-Si2B4H4 (21). Estimates of three-dimensional aromaticity with NICS calculations show that the exohedral double bond does not influence three-dimensional aromaticity.

An experimental and theoretical study of the valence shell photoelectron spectrum of the chlorobenzene molecule

The photoelectron spectrum of the chlorobenzene molecule has been studied using both monochromated synchrotron radiation with photon energies between 15 and 120 eV and HeI radiation at 21.22 eV. Photoelectron angular distributions and branching ratios have been determined over the entire energy range studied. Theoretical investigations have been performed using ab initio SCF and many-body Green’s function methods to evaluate wave functions, binding energies and relative intensities. The ADC(3) calculations of binding energies and pole strengths were particularly important for the interpretation of the inner valence spectrum where electron correlation effects are found to be important. The main part of the photoelectron spectrum is similar to that of benzene but some of the bands are characteristic of the chlorine atom. The Cooper minimum of the Cl 3p orbital is clearly reflected in some of the bands and is used to assess the mixing between ring orbitals and chlorine atomic orbitals. The HeI-excited spectra show extensive vibrational structure in the X̃ 2B 1, Ã 2A 2, B̃ 2B 2, C̃ 2B 1 and K̃ 2A 1 photoelectron bands. The vibrational structure is analysed in detail and compared to results obtained from multiphoton ionisation photoelectron spectroscopy.