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- W4248546706 abstract "The bending motion of a linear triatomic molecule has two unique characteristics: the bending mode is doubly degenerate and only positive values of the bending angle, expressed by the bond angle supplement ρ¯, can be observed. The double degeneracy requires the wavefunction to be described as a two-dimensional oscillator. In the present work, we first review the conventional expressions based on two, symmetrically equivalent normal coordinates. Then we discuss an alternative expression for the bending wavefunction in terms of two geometrical coordinates, the bond angle supplement ρ¯ (=π-τ⩾0, where τ is the bond angle) and the rotation angle χ (0⩽χ<2π) describing rotation of the molecule around the molecular axis. In this formalism, defined for the (ρ¯,χ) polar-coordinate space with volume element ρ¯dρ¯dχ, the one-dimensional wavefunction resulted through re-normalization for χ has zero amplitude at ρ¯=0, and the ro-vibrational average of the bending angle, i.e., the expectation value 〈ρ¯〉, attains a non-zero, positive value for any ro-vibrational state including the vibrational ground state. This conclusion appears to cause some controversy since much conventional spectroscopic wisdom insists on 〈ρ¯〉 having the value zero." @default.
- W4248546706 created "2022-05-12" @default.
- W4248546706 date "1993-05-01" @default.
- W4248546706 modified "2023-09-30" @default.
- W4248546706 title "Program index to volume 75" @default.
- W4248546706 doi "https://doi.org/10.1016/0010-4655(93)90054-g" @default.
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