Normal Vibrations, Potential Constants, and Vibration—Rotation Interaction Constants in Cyclobutane and Cyclobutane-d8

Abstract

From the fundamental frequencies of cyclobutane and cyclobutane-d8 as observed in infrared and Raman spectra, the potential constants and eigenvectors of the normal vibrations have been calculated for an assumed structure of D4h symmetry. When the available frequencies were too few in number to evaluate the constants of a given species in the general D4h potential system, appropriate nondiagonal constants were set equal to zero. From the potential constants the zeta constants of vibration—rotation interaction were computed for D4h species Eg and Eu. The Eg constants were found to be correct in magnitude but of opposite sign to the zetas suggested by the infrared band contours. The sign change is that to be expected if the actual structure is D2d (puckered ring), as was shown by Mills and Duncan for the D2d structure of allene. The zeta constants and frequencies were therefore recalculated for species E of D2d. The calculated zetas agree well with the values expected from the band contours, and explain the unusual shapes of the bands at 749 cm—1 in cyclobutane and 556 cm—1 in cyclobutane-d8.