Introductory Group Theory and Its Application to Molecular Structure

Ferraro, John R.; Ziomek, Joseph S.

doi:10.1007/978-1-4684-8795-4

Cited by 28 publications

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“…Unlike the H 2 PO 4 − ion, two water molecules occupy general position in the crystal [39]. The band of water vibrations are illustrated in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…A pair of H 2 PO 4 − ions is related to each other by a center of symmetry. The four fundamental modes of the free phosphate ion undergo factor group splitting [39]. The O-H stretching of the H 2 PO 4 − ion gives rise to a complex feature (the A, B, C trio) of which only the two former components are clearly visible, the third component (C) possibly contributing to the breath of the bands in the water bending region (1850-1495 cm −1 ) and/or the multiple bands in this region [38].…”

Section: Resultsmentioning

confidence: 99%

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Nanocrystalline manganese dihydrogen phosphate dihydrate Mn(H2PO4)2·2H2O and its decomposition product (Mn2P4O12) obtained by simple precipitation route

Danvirutai

Boonchom

Youngme

2008

Journal of Alloys and Compounds

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“…Unlike the H 2 PO 4 − ion, two water molecules occupy general position in the crystal [39]. The band of water vibrations are illustrated in Fig.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Nanocrystalline manganese dihydrogen phosphate dihydrate Mn(H2PO4)2·2H2O and its decomposition product (Mn2P4O12) obtained by simple precipitation route

Danvirutai

Boonchom

Youngme

2008

Journal of Alloys and Compounds

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“…Group theory is discussed in specialized undergraduate textbooks, and we will review here only the basic elements relevant to vibrational spectroscopy [12,15,16]. Group theory is discussed in specialized undergraduate textbooks, and we will review here only the basic elements relevant to vibrational spectroscopy [12,15,16].…”

Section: Symmetry Of Normal Modes and Vibrational Statesmentioning

confidence: 99%

Theory of Molecular Vibrations. The Origin of Infrared and Raman Spectra

Aroca

2006

Surface‐Enhanced Vibrational Spectroscopy

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In classical mechanics, a molecule can be seen as a collection of M nuclei and N electrons. Therefore, the system of M + N particles has 3(N + M) degrees of freedom to describe its motions. First, one can fix in space the location of the heavy nuclei (fixed nuclei approximation). The symmetry of this spatial distribution of nuclei can be associated with a 'molecular point group', which is a symmetry group corresponding to a fixed point [the center of mass (CM)]. The 3N degrees of freedom describe the motion of the electrons around the frozen frame, and the corresponding energy of motion is the electronic energy E e . We can regroup the nuclei and electrons into 3M effective atoms, and fix the origin of the system of coordinates in the CM of the molecule. The motion of this point in space is described by three degrees of freedom, and gives the translational energy of the molecule that is directly related to thermal energy. According to the equipartition principle, the energy is 3/2kT, where k is the Boltzmann constant. For 1 mol of molecules, we multiply by Avogadro's number, N A , and k is simply replaced by N A k = R, the gas constant,

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“…The Wyckoff positions of individual atoms in sodalite for the two structures are given in table I [10]. Also are listed the site symmetries of these atoms as obtained from the subgroup tables for these space groups [13]. The details for the irreducible representations of T~ spanned by the set of site coordinates for each atomic species are presented in table II.…”

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confidence: 99%

“…The details for the irreducible representations of T~ spanned by the set of site coordinates for each atomic species are presented in table II. Here, the correlation tables [13] for the space group are utilized along with the site symmetries for the determination of the number of site representation for each atomic species. The number of vibrational modes Nr v at k = 0 is obtained by the direct product of T2 with the site representations N~ for each atomic species, where T2 is the …”

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confidence: 99%

Raman scattering studies of sodalite for crystal structure and coloration mechanism

1991

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(ricevuto fl 12 Luglio 1989; manoscritto revisionato ricevuto il 4 Gennaio 1990)Summary. --Group-theoretical study of the vibrational modes of chlorosodalite [Na4A13(Si04)312 has been carried out for the T~ space group. The Raman-active modes are evaluated and comparison is made with the experimental results on sodalite. It is shown that the experimental Raman spectrum does not support the structure of sodalite to be T~ but confirms it to be T~. Raman scattering studies were performed on X-ray irradiated As-grown single crystal of chloro-sodalite to identify the coloration mechanism. Enhancement of oxygen twisting and stretching mode intensities on X-ray irradiation indicates the formation of neutral sodium colloidal aggregate during the coloration process.PACS 78.30 -Infrared and Raman spectra and scattering.

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Introductory Group Theory and Its Application to Molecular Structure

Cited by 28 publications

References 0 publications

Nanocrystalline manganese dihydrogen phosphate dihydrate Mn(H2PO4)2·2H2O and its decomposition product (Mn2P4O12) obtained by simple precipitation route

Nanocrystalline manganese dihydrogen phosphate dihydrate Mn(H2PO4)2·2H2O and its decomposition product (Mn2P4O12) obtained by simple precipitation route

Theory of Molecular Vibrations. The Origin of Infrared and Raman Spectra

Raman scattering studies of sodalite for crystal structure and coloration mechanism

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