Simulated MCTDH spectrum in the range of . Excitation in the direction (top), perpendicular to the O–H–O axis (middle) and total spectrum, i.e., perpendicular (bottom). Note the different scale of intensities in the perpendicular-component plot. Autocorrelation time . Absorption is given in absolute scale in Mb .
Comparison between the MCTDH spectrum (top) and the spectrum of Ref. 5 (bottom). The intensity of the experimental spectrum is adjusted in each spectral region (800–2000 and ) using the most intense peak of the MCTDH spectrum as a reference. Absorption for the MCTDH spectrum is given in absolute scale in Mb .
Reduced probability density on the internal rotation for (a) the ground state and the first three excited states: (b) , (c) , and (d) . The dotted lines correspond to an enlarged scale . The +/− symbols are intended to clarify the symmetry properties of each state. They indicate the sign of the underlying wavefunction based on a 1D computation for coordinate and do not refer directly to the multidimensional wavefunctions from which densities are given.
Reduced probability density on the wagging coordinates and of (a) the ground vibrational state and (b) the first-excited wagging-mode states.
Reduced probability density on the wagging coordinates and of the excited states , , and , characterized by two quanta of excitation (compare with Table I).
Schematic representation of the two most important coupled motions responsible for the doublet peak at .
Vibrational-excited states as identified in the MCTDH calculations. Comparison is given to harmonic-analysis (HO) results in the same surface, the MM/VCI results, and the experimental results on the cation. In the MCTDH column, the subscript indicates that the state was obtained by improved relaxation and the subscript indicates that the state was identified by Fourier analysis. In the column, refers to for states and to (or ) for states. In the assignment column, in parentheses, a number followed by a letter indicates the quanta of excitation in that coordinate. Other states are named after their definition in the text. As a remainder, we note that , , , and refer to wagging, rocking, bending, and stretching. When meaningful, a ket description of the state is given. In the ket description of the OH stretchings, indicate symmetric/asymmetric stretching-motion within each monomer, respectively. The last column shows the irreducible representation of the permutation-inversion group to which the vibrational state belongs. The irreducible representations of the more familiar point group , which is a subgroup of , are obtained by simply dropping the upper (+/−) index.
Overlaps , where are test states and are eigenstates.
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