State-by-state assignment of the bending spectrum of acetylene at 15 000 cm−1: A case study of quantum-classical correspondence

Jacobson, Matthew P.; Jung, Christof; Taylor, Howard S.; Field, Robert W.

doi:10.1063/1.479341

Cited by 101 publications

(74 citation statements)

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“…If successful, a dressed basis fit of the entire spectrum should be useful in conjunction with the diabatic correlation technique in illuminating the complete spectral pattern, as well as connections with concurrent bifurcation analysis of the spectroscopic Hamiltonian. Steps toward bifurcation analysis for various subsystems of acetylene have been taken by several authors [41][42][43]. The bifurcation analysis of the full threedimension stretch-bend acetylene system is clearly feasible along the analytical lines developed previously [34,[38][39][40].…”

Section: Discussionmentioning

confidence: 99%

Spectral patterns and ultrafast dynamics in planar acetylene

Kellman

Rose

Tyng

2001

The European Physical Journal D

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Abstract.A diabatic correlation diagram procedure is used to classify energy and intensity patterns in a planar model for coupled stretches and bends of acetylene using an effective spectroscopic fitting Hamiltonian. Analysis with polyad phase spheres accounts for the observed patterns in terms of classical phase space structure and bifurcations of the normal modes.PACS. 31.15.-p Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)

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Section: Discussionmentioning

confidence: 99%

Spectral patterns and ultrafast dynamics in planar acetylene

Kellman

Rose

Tyng

2001

The European Physical Journal D

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“…We want to understand how the excitation of the vibrational angular momentum and/or excitation of the rotation of the polyatomic molecule interacts with the bending excitation along the isomerization 22 (for a comparison of the [H,C,N] molecular system to the other two major model molecules acetylene [23][24][25][26][27][28][29] and HCP [30][31][32] studied so far a) Electronic mail: georg@mellau.de. URL: http://www.georg.mellau.de.…”

Section: Introductionmentioning

confidence: 99%

Complete experimental rovibrational eigenenergies of HCN up to 6880 cm−1 above the ground state

Mellau

2011

The Journal of Chemical Physics

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The [H,C,N] molecular system is a very important model system to many fields of chemical physics and the experimental characterization of highly excited vibrational states of this molecular system is of special interest. This paper reports the experimental characterization of all 3822 eigenenergies up to 6880 cm −1 relative to the ground state in the HCN part of the potential surface using high temperature hot gas emission spectroscopy. The spectroscopic constants for the first 71 vibrational states including highly excited bending vibrations up to v 2 = 10 are reported. The perturbed eigenenergies for all 20 rotational perturbations in the reported eigenenergy range have been determined. The 11 070 eigenenergies up to J = 90 for the first 123 vibrational substates are included as supplement to this paper. We show that a complete ab initio rovibrational analysis for a polyatomic molecule is possible. Using such an analysis we can understand the molecular physics behind the Schrödinger equation for problems for which perturbation theoretical calculations are no more valid. We show that the vibrational structure of the linear HCN molecule persists approximately up to the isomerization barrier and only above the barrier the accommodation of the vibrational states to the double well structure of the potential takes place.

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“…The quantum Hamiltonian acts on a Hilbert space of dimension n + 1, which is the number of ways we can distribute the n bosons in the two single-particle levels. Formally, this corresponds to the so-called "polyads" for algebraic Hamiltonians in molecular systems [19]. The reduced Hamiltonian is obtained by performing the canonical transformation defined by the generating function W = Kφ 1 + J(φ 2 − φ 1 ).…”

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“…(1) are introduced in order to have exactly a GOE or GUE Hamiltonian for n = k, where n is the number of bosons [1, 2]. For the two-level system, the dimension of Hilbert space is N = n + 1.The classical Hamiltonian is obtained as follows [6,19]: H is symmetrized with respect to the ordering of the creation and annihilation operators. This permits a correct assignment of the zero-point energy and therefore a oneto-one classical-quantum energy comparison.…”

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Wigner-Dyson statistics for a class of integrable models

Benet

Leyvraz²,

Seligman³

2003

Phys. Rev. E

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We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the boson number, and thus are integrable. To construct this ensemble we use some "reverse engineering" starting from the fact that n-bosons in a two-level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an n-body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.PACS numbers: 05.45. Mt, 05.30.Jp, 31.15.Gy Recently, there has been considerable interest in spinless n-boson systems with k-body random interactions [1,2], both for degenerate [3] and nondegenerate [4, 5] single-particle levels. In particular, anomalous statistics for the two-level system have been understood from the fact that these systems are integrable [6]. The two-level ensemble corresponds to a time-independent two degrees of freedom system, in the sense that creation and annihilation operators for the two single-particle levels are canonical operators for the system. The second integral of motion corresponds to the conservation of the number of bosons. The Hamiltonian is a function of the creation and annihilation operators, whose precise form depends on the question whether we have two-body interactions or more complicated manybody interactions. The number of (random) coefficients in this model increases quadratically with the rank k of the interaction. A classical Hamiltonian can formally be written for any number of particles but in fact only for large particle number the quantum problem reaches the classical limit [7,8]. Thus the boson number plays the role of an action. For fixed particle number, the model can be reduced to a Hamiltonian of one degree of freedom with the number of bosons appearing as parameter.In this paper we shall consider a different large-n limit for the two-level system. Our model consists in choosing the rank of the interaction equal to the particle number, k = n. Hence the Hamiltonian changes for different values of the particle number. This choice, by definition of the ensemble, directly leads to a GOE or GUE matrix [9]. We then consider the limit of large particle number. Clearly, we will have an ensemble of systems which have GOE or GUE statistics with probability one [10], while being integrable in a well-defined limit of large actions. This represents an important caveat concerning the idea that Wigner-Dyson statistics are characteristic of classical chaotic systems. Note that this has no bearing on the fairly-well established quantum chaos conjecture [11,12,13,14,15,16,17], which establishes that classical chaos implies typically Wigner-Dyson statistics.In a similar vein, Wu et al. [18] have performed the following calculation: after having chosen an unfolded fixed spectrum of given length ...

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State-by-state assignment of the bending spectrum of acetylene at 15 000 cm−1: A case study of quantum-classical correspondence

Cited by 101 publications

References 40 publications

Spectral patterns and ultrafast dynamics in planar acetylene

Spectral patterns and ultrafast dynamics in planar acetylene

Complete experimental rovibrational eigenenergies of HCN up to 6880 cm−1 above the ground state

Wigner-Dyson statistics for a class of integrable models

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