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Visualizing the zero order basis of the spectroscopic Hamiltonian
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View: Figures


Image of FIG. 1.
FIG. 1.

Plot of the model potential energy surface with contours representing 2000 cm−1equipotential lines. The O–O bond is fixed to the equilibrium length. The oxygen atoms are symmetrically placed on the x-axis about zero.

Image of FIG. 2.
FIG. 2.

The effective bend potentials for OH stretching states n s = 0–5. Obtaining the symmetric bending wavefunctions from these potentials yields the adiabatic basis of the potential.

Image of FIG. 3.
FIG. 3.

The squared amplitude of the |4 0〉0 and |5 0〉0 spectroscopic Hamiltonian ZOB functions in panels (a) and (b), respectively. |4 0〉0 illustrates a “conventional” basis function, while |5 0〉0 illustrates an “unconventional” basis function (see text for the meaning of these terms).

Image of FIG. 4.
FIG. 4.

The squared amplitude of |0 9〉0, |0 10〉0, and |0 11〉0 spectroscopic Hamiltonian ZOB functions, in panels (a)-(c), respectively. The first illustrates a “conventional” basis function, the second is between “conventional” and “unconventional,” and the last illustrates an “unconventional” basis function.

Image of FIG. 5.
FIG. 5.

Two snapshots of the time evolution of the squared amplitude of the |5 0〉0 spectroscopic ZOB function as propagated on the potential surface. These snapshots are at t = 0.765 ps and t = 0.830 ps for panels (a) and (b), respectively. These plots show that although the ZOB at t = 0 appears unconventional, in truth it contains a linear combination of a conventional form and a form understandable in terms of a “horseshoe” shape periodic orbit.

Image of FIG. 6.
FIG. 6.

The squared amplitude of the ZOB for the 2:1, N = 9 polyad, starting at the top with |4 1〉0 and proceeding downward through |3 3〉0 , |2 5〉0, |1 7〉0, and |0 9〉0. The left hand column displays the ZOB at time zero, while the right hand column shows the ZOB at a specific time that highlights the “conventional” nature of the basis function.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Visualizing the zero order basis of the spectroscopic Hamiltonian