Extraction of the Vibrational Dynamics from Spectra of Highly Excited Polyatomics:  DCO

Abstract

The effective spectroscopic Hamiltonian fitted to experiment by Troellsch and Temps (Z. Phys. Chem. 2001, 215, 207) and describing high vibrational excitation to bound and resonant states is used in conjunction with methods of nonlinear classical dynamics and semiclassical mechanics to extract, for all of the observed highly excited resonance levels in polyad 8, the molecular motions upon which they are quantized. Two types of interlaced dynamically distinct ladders of states are revealed. The rungs of these ladders intersperse, making the spectra complex. The resonant 2:2:1 frequency ratio of the DC and CO stretches and the bend, respectively, is what causes the complexity and is what caused past attempts at interpretation to be at best incomplete. All states are assigned with physically meaningful quantum numbers corresponding to quasiconserved quantities. Most interestingly, it is pointed out that much of the information and assignment can be done without any calculations at all, using only the qualitative ideas from nonlinear, semiclassical, and quantum mechanics, along with the information supplied by the experimentalist.

The Fock space method of vibrational analysis

“…The states clearly have the same resonances, same p value, and same reference state and therefore are on one subladder and belong to a class called B in Ref. 6. More states of class B with p Ͼ 0 can be found as can another class of states.…”

Intramolecular vibrational energy redistribution in DCO (X̃2A′): Classical-quantum correspondence, dynamical assignments of highly excited states, and phase space transport

“…This explains the observed lower than maximum velocity of the state 3 6 . This quantum mixing, seen in earlier studies 21,30 , is clearly 2-state and it is possible to demix the states yielding states |α(β) = |3 6 ± |3 7 and analyze the velocities. On demixing it is found thatẋ mbb (α) = 2.2 which is closer to the maximum value expected for an mbb state in polyad P = 3.…”

“…The new action-angle variables are related to the old ones, J m = I m , J n = I n , P c = 2(I m + I n ) + I b , and 20,21 . In what follows we will show the resonance template as a guideline and the local frequency analysis of the dynamics establishes the significant deviations from the zeroth order picture due to strong couplings.…”

“…However there are strong reasons 26 to believe that powerful insights into IVR can be gained by approaches based on classical-quantum correspondence. For example, Jung et al have provided dynamical assignments of the highly excited states of DCO based on certain key periodic orbits in phase space 21 . A key to the success of the many classical-quantum correspondence studies 26,27,28,29,30,31,32,33,34,35,36 is that the understanding of IVR is firmly rooted in the invariant structures inhabiting the underlying phase space.…”

Evaluation of an algebraic model for the vibrations of water, effects of a discrete symmetry

“…During recent years we have developed methods to evaluate algebraic models ('spectroscopic Hamiltonians') for the vibrations of molecules and could give a complete assignment for various examples [1][2][3][4][5]. The central idea always was to study the skeleton of the classical dynamics and to interpret the quantum states as excitations of the motion corresponding to an appropriate classical guiding centre.…”