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Quantum studies of the vibrations in and
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Image of FIG. 1.
FIG. 1.

The structures of the four lowest-energy stationary points on the HBB potential (see Ref. 14) (a) the potential minimum, (b) the saddle point, (c) the trans saddle point, and (d) the cis saddle point. The coordinates that will be used to describe the excited states are indicated in panel (a).

Image of FIG. 2.
FIG. 2.

The normal-mode vectors at the saddle point in . The numbers in each panel indicate the corresponding harmonic frequency. For clarity totally symmetric modes are given in the left column, and modes that have symmetry are in the right column.

Image of FIG. 3.
FIG. 3.

Plot of the dependence of five harmonic frequencies along the torsion path used to define the Hamiltonian used for the VCI calculations for (a) and (b) . Using the notation in Fig. 2, the solid line shows the OO stretch frequency, the dotted- and short-dashed lines give the wag and rock frequencies, while the dot-dot-dashed and long-dashed lines give the frequencies of and . In the frequencies of the OO stretch and wag flip their energy ordering over this range of angles and we plotted both frequencies with thick solid lines. To illustrate the underlying, uncoupled (diabatic) frequencies, we have sketched them with thin lines.

Image of FIG. 4.
FIG. 4.

Plot of the energies of the OO stretch fundamental as a function of the position of the node, obtained from a DMC simulation (gray curves), as well as fifth-order fits to the raw data (black curves). The point where the two black curves cross provides the position of the node and the energy of the state, relative to the global minimum of the potential.

Image of FIG. 5.
FIG. 5.

Plot of the projection of the wave functions for the ground state onto (a) the hydrogen transfer mode and (b) the torsion coordinate . In both plots, the results for are shown with a solid line; the dashed line provides the results for . The arrows show the values of these coordinates at the minimum-energy configuration of .

Image of FIG. 6.
FIG. 6.

Slice through the VCI states at (a) 532 and (b) plotted as functions of the two normal modes that correlate to the wag and OO stretch in Fig. 2. For these plots all other normal modes are set equal to zero and .

Image of FIG. 7.
FIG. 7.

Projections of excited states for the rock [(a)–(c)], [(d)–(f)], and [(g)–(i)] fundamentals. In the left column, the probability amplitudes are projected onto the (solid lines), (dashed lines), and displacements (dotted lines) of the bridging hydrogen atom. In cases where the distributions obtained from the parts of the wave function with positive and negative amplitudes differ, the separate distributions are plotted with thin lines. The plots in the central column show projections of the probability amplitudes onto one of the OOH bends with a thick solid black line. The contributions to this distribution from the parts of the wave function with positive and negative amplitudes are plotted with thin lines. In the right column, projections of the probability amplitudes onto are plotted.


Generic image for table
Table I.

Average values and widths of projections of the ground-state wave functions for and onto the internal coordinates defined in Fig. 1.

Generic image for table
Table II.

Energies of the fundamentals of and obtained from DMC and VCI calculations. (The details of the VCI calculations are given in the text.)


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum studies of the vibrations in H3O2− and D3O2−