Introductory Group Theory

Ferraro, John R.; Ziomek, Joseph S.

doi:10.1007/978-1-4615-4821-8

Cited by 16 publications

(9 citation statements)

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“…This symmetry is maintained even if the carbons rehybridize from sp 2 to sp 3 , as long as the carbon-carbon bond remains parallel to the surface. Gas-phase A g and B 1u irreducible representations in D 2h correlate with A 1 in C 2v symmetry [28]. Only modes of A 1 symmetry are active in RAIRS [29] so that, in principle, ethylene adsorbed with C 2v symmetry should exhibit four peaks.…”

Section: Discussionmentioning

confidence: 95%

Ethylene adsorption on Pd( 111 ) studied using infrared reflection–absorption spectroscopy

2002

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The adsorption of ethylene has been studied on clean and hydrogen-covered Pd(1 1 1) using reflection-absorption infrared spectroscopy and molecular beam methods. Using a correlation diagram, in which vibrational frequencies are plotted versus a rp parameter proposed by Stuve and Madix, shows that ethylene is substantially rehybridized on Pd(1 1 1) having a rp parameter intermediate between those of ethylene on Ni(1 1 1) and Ru(0 0 1). In contrast, when ethylene adsorbs on hydrogen-covered Pd(1 1 1), only p-bonded species are detected. An additional species appears exhibiting a characteristic frequency of 957 cm À1 when Pd(1 1 1) is cooled to $80 K and the system pressurized with $10 À5 Torr of ethylene. This species also appears on a CO-saturated Pd(1 1 1) surface. Molecular beam measurements show that its coverage reaches $1.3 ML indicating that it is due to ethylene adsorbed in the second and subsequent layers. Ó

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Section: Discussionmentioning

confidence: 95%

Ethylene adsorption on Pd( 111 ) studied using infrared reflection–absorption spectroscopy

2002

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“…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%

“…17 The gas-phase point group of ethyl iodide is C s where the x-y plane is the symmetry plane of the molecule. 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.…”

Section: Discussionmentioning

confidence: 98%

“…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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“…As an example, Group Theory has been used to characterize many molecules' bonding and non-bonding molecular orbitals, which has led to descriptions of allowed and disallowed electronic transitions between molecular orbitals within those molecules that have been subsequently confirmed by spectroscopic experiments. Beyond its application in Chemistry, it has been used to classify functions according to how the structures behave when the symmetry operations of a point group are performed upon them [17]. The symmetry of a structure can be described in terms of the complete collection of symmetry operations it possesses.…”

Section: Group Theorymentioning

confidence: 99%

Group Theory Based Design of Isotropic Negative Refractive Index Metamaterials

Wongkasem¹,

Akyurtlu²,

Marx³

2006

PIER

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Abstract-Novel isotropic planar and three-dimensional negative refractive index (NRI) metamaterial (MTM) designs consisting of periodically arranged cross structures are developed in the terahertz (THz) frequency regime using group theory. The novel designs not only avoid magnetoelectric coupling but also enable a simplified fabrication process. Using Finite-difference Time-Domain (FDTD) simulations, the design exhibits an NRI passband which is in good agreement with the S-parameters obtained from Fresnels equation. Cross-polarized fields are used to characterize the magnetoelectric coupling mechanism and determination of material properties of the medium via group theory aid in the characterization of the isotropy of the structure. Numerical simulations of a wedge composed of the proposed metamaterials prove the negative refractive index of the models.

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Introductory Group Theory

Cited by 16 publications

References 0 publications

Ethylene adsorption on Pd( 111 ) studied using infrared reflection–absorption spectroscopy

Ethylene adsorption on Pd( 111 ) studied using infrared reflection–absorption spectroscopy

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

Group Theory Based Design of Isotropic Negative Refractive Index Metamaterials

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