The Definition of the Molecular Symmetry Group

Bunker, P. R.

doi:10.1016/b978-0-12-141350-7.50015-x

Cited by 109 publications

(163 citation statements)

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“…The first four equivalent oscillators describe the fundamental stretching modes (A 1 ⊕ F 2 ), and the other six equivalent ones describe the fundamental bending modes. As is well known [9], there are only five degrees of freedom for the bending vibrations (E ⊕ F 2 ), so that the six bending oscillators must contain a spurious one. The spurious states related to the spurious degree of freedom should be ruled out in the later calculation.…”

Section: Hamiltonianmentioning

confidence: 99%

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Boson-realization model for the vibrational spectra of tetrahedral molecules

Hou

Xie

1996

Phys. Rev. A

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An algebraic model of Boson realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with T d symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-meansquare deviation 11.61 cm −1 . The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provides a five-parameter fit with a root-mean-square deviation 12.42 cm −1 . * email address: MAZQ@BEPC3.IHEP.AC.CN

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Section: Hamiltonianmentioning

confidence: 99%

“…In the traditional approach, the higher excited states are calculated by symmetrizing the products of the fundamental vibrational states [9]. However, it may be more easy to use the irreducible bases, subtracting the spurious states, for calculating the excited states.…”

Section: Irreducible Basesmentioning

confidence: 99%

Boson-realization model for the vibrational spectra of tetrahedral molecules

Hou

Xie

1996

Phys. Rev. A

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“…18,19 The power normalized FE spectrum of jet cooled 1MPI in the spectral region of the first excited state is shown in Fig. 5͑a͒.…”

Section: -Methyl-2"1h…pyridinimine "1mpi…mentioning

confidence: 99%

Spectroscopic studies on methyl torsional behavior in 1-methyl-2(1H)-pyridone, 1-methyl-2(1H)-pyridinimine, and 3-methyl-2(1H)-pyridone. I. Excited state

Sinha

Pradhan

Wategaonkar

et al. 2007

The Journal of Chemical Physics

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The laser induced fluorescence excitation and dispersed fluorescence spectra of three nitrogen heterocyclic molecules 1-methyl-2͑1H͒pyridone ͑1MPY͒, 1-methyl-2͑1H͒pyridinimine ͑1MPI͒, and 3-methyl-2͑1H͒pyridone ͑3MPY͒ have been studied under supersonic jet cooled condition. The methyl torsional and some low frequency vibrational transitions in the fluorescence excitation spectrum were assigned for 1MPY. These new assignments modify the potential parameters to the methyl torsion reported earlier. Some striking similarities exist between the torsional and vibrational transitions in the fluorescence excitation spectra of 1MPY and 1MPI. Apart from pure torsional transitions, a progression of vibration-torsion combination bands was observed for both these molecules. The excitation spectrum of 3MPY resembles the spectrum of its parent molecule, 2-pyridone. The barrier height of the methyl torsion in the excited state of 3MPY is highest amongst all these molecules, whereas the barrier in 1MPI is higher than that of 1MPY. To get an insight into the methyl torsional barrier for these molecules, results of the ab initio calculations were compared with the experimental results. It was found that the conformation of the methyl group undergoes a 60°rotation in the excited state in all these molecules with respect to their ground state conformation. This phase shift of the excited state potential is attributed to the * -* hyperconjugation between the out-of-plane hydrogen of the methyl group and the molecular frame. It has been inferred that the change in lowest unoccupied molecular orbital energy plays the dominant role in the excited state barrier formation.

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“…The permutation-inversion groups developed by Longuet-Higgins 15 and Bunker 16 are useful in describing such type of motion. The molecular states of ortho-and meta-substituted toluenes are classified according to irreducible representations of the G 6 molecular symmetry group and para-substituted toluenes which have a twofold symmetry in the molecular frame described by the G 12 symmetry group.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Origin of threefold symmetric torsional potential of methyl group in 4-methylstyrene

Sinha

Pradhan

Singh

et al. 2006

The Journal of Chemical Physics

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To understand the effect of the para position vinyl group substitution in toluene on methyl torsion, we investigated 4-methylstyrene, a benchmark molecule with an extended conjugation. The assignment for a 33 cm −1 band in the excitation spectrum to the 3a 2 torsional transition, in addition to the assignments suggested previously for the other bands in the excitation spectrum, leads to the model potentials for the ground as well as excited states with V 3 Љ= 19.6 cm −1 , V 6 Љ= −16.4 cm −1 and V 3 Ј= 25.6 cm −1 , V 6 Ј= −30.1 cm −1 , respectively. These potentials reveal that both in ground and excited states, the methyl group conformations are staggered with a 60°phase shift between them. MP2 ab initio calculations support the ground state conformations determined from experiments, whereas Hartree-Fock calculations fail to do so. The origin of the modified ground state potential has been investigated by partitioning the barrier energy using the natural bond orbital ͑NBO͒ theoretical framework. The NBO analysis shows that the local delocalization ͑bond-antibond hyperconjugation͒ interactions of the methyl group with the parent molecule is sixfold symmetric. The threefold symmetric potential, on the other hand, stems from the interaction of the vinyl group and the adjacent ring bond. The threefold symmetric structural energy arising predominantly from the electron contribution is the barrier forming term that overwhelms the antibarrier contribution of the delocalization energy. The observed 60°phase shift of the excited state potential is attributed to the * -* hyperconjugation between out of plane hydrogens of the methyl group and the benzene ring.

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The Definition of the Molecular Symmetry Group

Cited by 109 publications

References 0 publications

Boson-realization model for the vibrational spectra of tetrahedral molecules

Boson-realization model for the vibrational spectra of tetrahedral molecules

Spectroscopic studies on methyl torsional behavior in 1-methyl-2(1H)-pyridone, 1-methyl-2(1H)-pyridinimine, and 3-methyl-2(1H)-pyridone. I. Excited state

Origin of threefold symmetric torsional potential of methyl group in 4-methylstyrene

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