Introductory Group Theory

Ferraro, John R.; Ziomek, Joseph S.

doi:10.1007/978-1-4899-6471-7

Cited by 5 publications

(8 citation statements)

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“…Note that this symmetry is maintained even if the carbons rehybridize from sp 2 to sp 3 as long as the carbon−carbon bonds remains parallel to the surface. In this case, the gas-phase A g and B 1u irreducible representations in D 2 d correlate with A 1 in C 2 v symmetry . The gas-phase frequencies for these modes are at 949.2, 1342.4, 1623.3, and 3019.3 cm -1 .…”

Section: Discussionmentioning

confidence: 78%

“…In this case, the gas-phase A g and B 1u irreducible representations in D 2d correlate with A 1 in C 2V symmetry. 24 The gas-phase frequencies for these modes are at 949.2, 1342.4, 1623.3, and 3019.3 cm -1 . 21 The B 2g and B 3u representations correlate with B 1 , and the corresponding gas-phase frequencies are at 943, 1443.5 and 2989.5 cm -1 .…”

Section: Discussionmentioning

confidence: 95%

“…24 In this case, modes of A′ symmetry transform as x and y, vectors oriented in the symmetry plane of ethyl iodide, and modes of A′′ symmetry transform as z, oriented perpendicularly to this plane. 24 The surface selection rule for RAIRS indicates that only modes that transform as a vector oriented perpendicularly to the surface are infrared active 25 and can be used to indicate adsorbate orientations. In the case of ethyl iodide adsorbed at low exposures at 80 K, the methyl bending mode of A′′ symmetry is the most intense while the mode of A′ symmetry is relatively weak (Figure 4; Table 2).…”

Section: Discussionmentioning

confidence: 98%

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An Investigation of the Reaction Pathway for Ethylene Hydrogenation on Pd(111)

et al. 2001

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The hydrogenation of ethylene on Pd(111) is probed using a combination of temperature-programmed desorption (TPD) and reflection-absorption infrared spectroscopy (RAIRS). Ethylene adsorbs on clean Pd(111) in a di-σ configuration but converts to π-bonded species when the surface is presaturated by hydrogen. Ethane is formed with an activation energy of 3.0 ( 0.3 kcal/mol only when Pd(111) is pre-covered by hydrogen and not when ethylene and hydrogen are co-dosed, indicating that ethylene blocks hydrogen adsorption. Experiments performed by grafting ethyl species onto the surface by reaction with ethyl iodide indicate that ethyl species hydrogenate much more rapidly than the overall rate of ethylene hydrogenation, demonstrating that the addition of the first hydrogen atom to adsorbed ethylene to form an ethyl species is the rate-limiting step in the hydrogenation reaction. The adsorption geometry of ethyl iodide is found to depend on dosing conditions. When adsorbed at low exposures at 80 K, the mirror symmetry plane of ethyl iodide is oriented close to parallel to the surface. At higher exposures, it adopts a geometry in which the symmetry plane is closer to perpendicular to the surface.

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Section: Discussionmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 98%

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An Investigation of the Reaction Pathway for Ethylene Hydrogenation on Pd(111)

et al. 2001

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“…(A1C1 4 )~ has four independent vibrational frequencies [29], corresponding to normal modes whose main character may be described as (i) stretching of an Al-Cl bond as a precursor to break-up into A1C1 3 + CI -(a mode conventionally denoted by u 3 ),…”

Section: Vibrational Frequenciesmentioning

confidence: 99%

A Refined Ionic Model for Clusters Relevant to Molten Chloroaluminates

Akdeniz

Tosi

1999

Zeitschrift Für Naturforschung A

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A model of ionic interactions in neutral and ionized aluminium trichloride clusters, which accounts for ionic deformability through (i) effective valences and (ii) electrostatic and overlap polarizabilities, is evaluated for applications to classical simulation studies of the pure melt and of molten alkali chloroaluminates. The disposable parameters in the model are determined from the measured values of the bond length in the (A1C1 4 )~ molecular ion and of an Al-Cl bond length and a vibrational frequency in the A1 2 C1 6 molecular dimer. The model is tested against the remaining available data from experiment and from quantum chemical calculations on molecular bond lengths, bond angles and vibrational frequencies for A1 2 C1 6 , (A1C1 4 )~ and (A1 2 C1 7 )~ clusters. Structural and dynamical properties are also evaluated for the (A1 2 C1 5 ) + , A1C1 3 and (A1C1 2 ) + clusters. The results for the energetics of dissociation, ion transfer and isomer excitation reactions are compared with as yet unpublished data obtained by P. Ballone in first-principles calculations by a density functional method. The overall quality of the tests supports the approximate validity and transferability of the model.

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“…3I-(Z) has to be read: the operation I applied to the Z axis. 4 The trace of a matrix is the sum of the diagonal elements of the matrix.…”

Section: Group Theorymentioning

confidence: 99%