vibrational quantum number

vibrational quantum number

[vī′brā·shən·əl ′kwän·təm ‚nəm·bər]
(physical chemistry)
A quantum number v characterizing the vibrational motion of nuclei in a molecule; in the approximation that the molecule behaves as a quantum-mechanical harmonic oscillator, the vibrational energy is h (v + ½)ƒ, where h is Planck's constant and ƒ is the vibration frequency.
References in periodicals archive ?
In accordance with current standard notation in spectral analysis, here we use exclusively symbols J for rotational quantum number and v for vibrational quantum number, regardless of the symbols employed in the original sources.
621) actually applied [(J + 1/2).sup.2] rather than J (J + 1), consistent with previous experimental work in which he had proved the necessity of half-integer vibrational quantum numbers (Mulliken, 1924).
where v is the ground state vibrational quantum number, [E.sub.0] is the excited-state zero-phonon energy, [omega] is the ground-state harmonic vibration frequency (in [cm.sup.-1]units) and [chi] is the anharmonicity constant.
Here, we assign the vibrational quantum number n to a diatom if its energy is closest to the one of the n-th state of the corresponding quantum oscillator [28].
Eventually note that the vibrational quantum number n appears to be here the number of quantum states allowed to the oscillator.
In addition, it is labeled with the vibrational quantum number v and rotational quantum number J', where J' = F' - I and I is the total nuclear spin angular momentum quantum number (13).
The [beta] values are expected to be independent of the vibrational quantum numbers of the ionic state.

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