Resonance-induced spectral tuning

Yang, Shuangbo; Kellman, Michael E.

doi:10.1103/physreva.81.062512

Cited by 4 publications

(6 citation statements)

References 34 publications

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“…One can think of these momentary appearances of regularity as reflecting simple quantizing structures, such as cantori [29][30][31] (the chaotic remnants of tori) and quantizing periodic orbits. 32,33 The chaotic nature of the phase space, however, causes these brief interludes of regularity to quickly dissolve once again into the chaotic sea. The ability of the effective Hamiltonian to tune automatically the basis depending on the underlying complexity of phase space is the reason that it can reproduce vibrational states that sample more than one stationary point.…”

Section: Discussionmentioning

confidence: 98%

Visualizing the zero order basis of the spectroscopic Hamiltonian

Barnes

Kellman

2012

The Journal of Chemical Physics

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Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.

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Section: Discussionmentioning

confidence: 98%

Visualizing the zero order basis of the spectroscopic Hamiltonian

Barnes

Kellman

2012

The Journal of Chemical Physics

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“…The avoidance of a barrier by what seemingly should be the natural reaction modes has been seen in other systems. 26,34,35 As noted in Sec. III A, the |1 m series does reach the barrier and the |1 8 state is the first to have significant TS amplitude.…”

Section: Qualitative Models For Spectral and Wave Function Patternsmentioning

confidence: 93%

Detailed analysis of polyad-breaking spectroscopic Hamiltonians for multiple minima with above barrier motion: Isomerization in HO2

Barnes

Kellman

2011

The Journal of Chemical Physics

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We present a two-dimensional model for isomerization in the hydroperoxyl radical (HO(2)). We then show that spectroscopic fitting Hamiltonians are capable of reproducing large scale vibrational structure above isomerization barriers. Two resonances, the 2:1 and 3:1, are necessary to describe the pertinent physical features of the system and, hence, a polyad-breaking Hamiltonian is required. We further illustrate, through the use of approximate wave functions, that inclusion of additional coupling terms yields physically unrealistic results despite an improved agreement with the exact energy levels. Instead, the use of a single diagonal term, rather than "extra" couplings, yields good fits with realistic results. Insight into the dynamical nature of isomerization is also gained through classical trajectories. Contrary to physical intuition the bend mode is not the initial "reaction mode," but rather isomerization requires excitation in both the stretch and bend modes. The dynamics reveals a Farey tree formed between the 2:1 and 3:1 resonances with the prominent 5:2 (2:1 + 3:1) feature effectively dividing the tree into portions. The 3:1 portion is associated with isomerization, while the 2:1 portion leads to "localization" and perhaps dissociation at higher energies than those considered in this work. Simple single resonance models analyzed on polyad phase spheres are able to account in a qualitative way for the spectral, periodic orbit, and wave function patterns that we observe.

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“…3(a) a zoom of the three levels is shown. Although at first sight crossing of levels appears, a more detailed analysis shows that they are avoided crossings [29,30].…”

Section: Intmentioning

confidence: 95%

Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomenon

Bermúdez-Montaña¹,

Lemus²,

Castaños³

2016

EPL

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-In search of a region where a local mode model stop being adequate to estimate the local force constants, the correlation diagram of the vibrational energy spectra associated with the stretching modes of triatomic molecules such as CO2 and H2O is analyzed by means of two interacting Morse oscillators. By considering a linear dependence of the structure and force constants, it is shown that the fidelity, entropy and Poincaré sections detect the polyad breaking process manifested in the transition from local to normal mode behaviors. Additionally Poincaré sections show a transition to chaos where the local polyad cannot be defined.

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Resonance-induced spectral tuning

Cited by 4 publications

References 34 publications

Visualizing the zero order basis of the spectroscopic Hamiltonian

Visualizing the zero order basis of the spectroscopic Hamiltonian

Detailed analysis of polyad-breaking spectroscopic Hamiltonians for multiple minima with above barrier motion: Isomerization in HO2

Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomenon

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