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WIREs Comput Mol Sci
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Local modes in vibration–rotation spectroscopy

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Abstract The present paper is concerned with the description of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. Local mode effects are most common in molecules with multiple equivalent H–X bonds, which give rise to equivalent H–X local mode stretching vibrations, and the theory is outlined for the simplest such case, that of an H2X molecule. In the local mode picture of molecular vibration, experimentally observed, initially unexpected near‐degeneracies of vibrational states at high vibrational excitation, and of rotation–vibration states at high rotational excitation, can be explained in a relatively straightforward manner. The local mode theory predicts relations between the conventional rotation–vibration parameters whose values are determined in least‐squares fittings to observed rotation–vibration transition frequencies or wavenumbers. It should be emphasized, however, that such relations are valid only for particular forms of the effective rotation–vibration Hamiltonian used in the spectral analysis. We illustrate the theory with examples of experimental spectroscopic work where local mode effects play an important role in the interpretation of the experimental findings. The fact that local mode vibrations not only cause clustering of highly excited vibrational energy levels, but also of highly rotationally excited rotation–vibration energy levels, has been understood fairly recently. We outline the theoretical background for this phenomenon and relate it to the existing experimental work. © 2012 John Wiley & Sons, Ltd. This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy

Schematic representation of the stretching energy level pattern for H280Se (middle column), compared with the energies obtained in the normal mode (left column) and local mode (right column) limits (see text). Levels of A1(B2) symmetry in C2v(M) are marked in blue (red). In the normal mode limit, the vibrational energy is obtained from Eq. (4), and in the local mode limit this energy is taken to be E + E with E given by Eq. (10).

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The rotational energy surface of BiH3 for J = 60. The energies are given relative to the minimum RES energy (see text).

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Term level diagram for the rotational states in the vibrational ground state of PH3. The energies are plotted relative to the highest energy in each J manifold. The symmetry labels of the states in the molecular symmetry group10, 11 C3v(M) are indicated.

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The four possibilities for molecular rotation (labeled 1R, 1L, 2R, and 2L in an obvious notation) in a fourfold near‐degenerate energy cluster of an H2X molecule.

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The probability density function P(r1, r2) for the rotational level = 00 0 in the (v1, v2, v3) = (0,0,4) [local mode label (22+, 0)] vibrational state of H280Se.

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The probability density functions P(r1, r2) for the rotational levels = 00 0 in the (a) (v1, v2, v3) = (4,0,0) [local mode label (40+, 0)] and (b) (v1, v2, v3) = (3,0,1) [local mode label (40, 0)] vibrational states of H280Se. The panels (c) and (d) show for H280Se the probability density functions for the wavefunctions given on the right‐hand sides of Eqs (25) and (26), respectively, for n1 = 4 and n2 = 0. These two wavefunctions are approximately equal to the products ψ4(r10(r2) |v2 = 0〉 and ψ0(r14(r2) |v2 = 0〉.

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Schematic representation of the HCAO energy matrix for N = 5. The horizontal lines represent the diagonal matrix elements and the off‐diagonal elements are indicated. Note that by definition, the parameter xM < 0.

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Schematic representation of the HCAO energy matrix for N = 4. The horizontal lines represent the diagonal matrix elements and the off‐diagonal elements are indicated. Note that, by definition, the parameter xM < 0.

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