Erratum: Spectral patterns and dynamical bifurcation analysis of highly excited vibrational spectra [J. Chem. Phys. <b>102</b>, 4340 (1995)]

Svitak, John; Li, Zhiming; Rose, John P.; Kellman, Michael E.

doi:10.1063/1.470735

Cited by 23 publications

(63 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamics induced by these two generic resonances has been studied in detail by Kellman and co-workers in a long series of articles, 7,8,[109][110][111][112][113] where the connection with mathematical tools such as the catastrophe map and the theory of elementary bifurcations is nicely discussed and illustrated, and more recently by Joyeux. 114-117 A nonexhaustive list of the molecules for which the 1:1 Darling-Dennison coupling plays a fundamental role includes water, 66 ozone, 67 the CH stretches of acetylene, 7 hydrogen sulfide, 68 DCO,28,29 and SO 2 .…”

Section: Discussionmentioning

confidence: 99%

“…As shown in ref 116, the reason for this is that a strong Fermi resonance leads to a period-doubling bifurcation at low energies, whereas a weaker resonance leads to a SN bifurcation only at higher energies. Since the older studies 7,8,[109][110][111][112][113][114][115][116][117] were based on model Hamiltonians fitted to a relatively small number of experimentally observed transitions, it is not surprising that systems with a strong, and therefore easy to detect, resonance were focused on. Our ability to clearly identify SN bifurcations in the vibrational dynamics of HCP, HOCl, and HOBr, for which the Fermi resonance is much weaker than for CO 2 , CS 2 , and the substituted methanes, relies on the fact that we were able to compute and investigate very large sets of quantum states, up to extremely high energies.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Joyeux

Farantos

Schinke³

2002

J. Phys. Chem. A

View full text Add to dashboard Cite

The vibrational motion of highly excited molecules is discussed in terms of exact quantum and classical mechanics calculations, employing global potential energy surfaces, as well as in terms of a spectroscopic Hamiltonian and its semiclassical limit. The main focus is saddle-node bifurcations and their influence on the spectrum. The general features are illustrated by three examples, which despite their quite different intramolecular motions have several aspects in common: HCP, HOCl, and HOBr. In all three cases a 1:2 Fermi resonance is the ultimate cause of the complications observed in the spectra.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Joyeux

Farantos

Schinke³

2002

J. Phys. Chem. A

View full text Add to dashboard Cite

show abstract

“…Zones I-IV of the two maps have the same structure with regard to their fixed points, as well as the patterns of their quantum spectra. 7 We will abbreviate their discussion, but there are some new twists in the 3:2 system which deserve attention.…”

Section: Application To Individual Resonance Hamiltoniansmentioning

confidence: 99%

“…This is done using tools of nonlinear dynamics including bifurcation and catastrophe map analysis. [4][5][6] Observable patterns in the spectra that reflect the changes in the dynamics have been predicted, 7 and these patterns have been exploited in analysis of spectra of isomerizing systems, 8 highly excited spectra of CS 2 , 9 and spectra of chaotic bending dynamics of acetylene. 10,11 In this paper, our previous analyses of the 2:2 and 2:1 resonance systems is generalized to higher-order resonance Hamiltonians with m:n ) m:2 and m:4.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian^†

2002

Self Cite

View full text Add to dashboard Cite

The classical phase space structure of a spectroscopic Hamiltonian for two coupled vibrational modes is analyzed using bifurcation theory, classified on catastrophe maps, for a variety of higher order resonances (3:2, 4:2, 5:2, 6:2 and 4:4, 5:4, 6:4), cases not considered in previous work. A type of bifurcation not encountered for lower resonance orders, based on oVerlap of separatrices rather than change in behavior of fixed points, is analyzed, and a procedure is developed to augment the catastrophe map. Energy level patterns are associated with the new resonances, in analogy with the patterns of adjacent level spacings considered earlier for the 2:1 resonance.

show abstract

“…26 In region I, there is no true separatrix and there are two elliptic points on the polyad sphere, of which both are located on the longitude, ) 0. One of them corresponds to the elliptic point e 1 shown in Figure 4 and is located away from the poles.…”

Section: N 2 O With Only the 1 S :2 B Fermi Resonancementioning

confidence: 99%

Semiclassical Assignment of the Vibrational Spectrum of N₂O

2002

View full text Add to dashboard Cite

The vibrational spectrum of N 2 O as given by an effective spectroscopic Hamiltonian based on the existence of a superpolyad number is analyzed and assigned in terms of classical motions. The effective Hamiltonian includes a large number of resonances of which only one is dominant for low and intermediate superpolyad numbers. In this energy range, the corresponding classical system is quasi-integrable and can be described in terms of a system with only one nontrivial degree of freedom. This integrable system can be analyzed by considering the so-called "quantizing trajectories" on a "polyad sphere". This method is no longer applicable when the superpolyad number is further increased and classical chaos comes into play. We then turn to a powerful universal method based on the graphical representation of semiclassical wave functions on a naturally appearing toroidal configuration space. These wave functions are obtained using the already known transformation matrix used in fitting the effective Hamiltonian. Experience with the interpretation of the resulting figures allows one to draw conclusions on the classical internal motions and therefore on the assignment of the quantum states without any further calculation. As such, the method is of particular interest to nontheorists and to nonspecialists in the fields of nonlinear dynamics and quantum calculation. For higher superpolyad numbers, the chaos remains mainly concentrated about the direct neighborhood of a separatrix of the former integrable system so that a great part of the vibrational spectrum can still be assigned in terms of the EBK quantum numbers of quantized tori.

show abstract

Erratum: Spectral patterns and dynamical bifurcation analysis of highly excited vibrational spectra [J. Chem. Phys. 102, 4340 (1995)]

Cited by 23 publications

References 0 publications

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian^†

Semiclassical Assignment of the Vibrational Spectrum of N₂O

Contact Info

Product

Resources

About

Erratum: Spectral patterns and dynamical bifurcation analysis of highly excited vibrational spectra [J. Chem. Phys. 102, 4340 (1995)]

Cited by 23 publications

References 0 publications

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian†

Semiclassical Assignment of the Vibrational Spectrum of N2O

Contact Info

Product

Resources

About

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian^†

Semiclassical Assignment of the Vibrational Spectrum of N₂O