The Rotation-Vibration Spectrum of C2H6 and the Question of Free Internal Rotation

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Abstract
If there were free internal rotation in C2H6 the rotational structure of certain perpendicular type infrared bands would be very different from that for the customary symmetrical top molecule without internal rotation. To account for the fact that this difference is not observed it is necessary to assume that there is a potential difference of at least 2000 cal. (700 cm—1) between the two symmetrical forms of C2H6 differing by an internal rotation of 2π/6. A potential of this magnitude corresponds to an internal torsion vibration of 230 cm—1. The above conclusion is based upon a dynamical treatment of C2H6 in which it is assumed that vibration, over‐all rotation, and internal rotation subject to a restricting potential may occur simultaneously. An approximate form of the Hamiltonian expression obtained is H = 1 2 {( P x − p x ) 2 /A+( P y − p y ) 2 /A+( P z − p z ) 2 /C+( P γ − p γ ) 2 /C+ ∑ p k 2 }+V , where γ represents the angle of internal rotation. The rotational selection rules are determined and it is found that under ordinary circumstances the internal rotation when free is inactive in the infrared rotation‐vibration spectrum. However, when there is accidental degeneracy of certain pairs of twofold degenerate vibrational levels, the internal rotation becomes active in the infrared bands for these vibrations. In such a case of accidental vibrational degeneracy, which is approximated to by at least two sets of vibrations in C2H6, the rotation‐vibration frequency for the infrared bands involves the quantity (h/4π 2 )[(K±K ′ )(1−ζ)/C–K/A] if the internal rotation is free; K and K′ are the quantum numbers of over‐all and internal rotation about the threefold symmetry axis and ζ is a quantity depending on the angular momentum of vibration. The observed rotational spacing, however, is well reproduced by a frequency containing instead the quantity (h/4π 2 )K[(1−ζ)/C−1/A] , which is to be expected if C2H6 is an ordinary symmetrical top molecule without internal rotation.

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