Normal Coordinate Calculations of the Vibrations of Methylene Cyclopropane-h6 and -d6

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Abstract
Normal coordinate calculations for methylene cyclopropane-h6 and -d6 have been carried out using two models. In the first model 31 internal coordinates were used, and in the second model 25 internal coordinates were used. The force constants were, in each case, refined to the 40 frequencies observed for the two molecules. Using the first model 26 force constants, of which four were constrained, fitted the frequencies with an average error of 1.2% for C4H6 and 2.8% for C4D6. Using the second model 24 force constants, of which two were constrained, fitted the frequencies with an average error of 1.4% for C4H6 and 2.8% for C4D6.The very low isotopic shift of the C=C stretching mode can be explained by an interaction with the ethylenic CH2 deformation, which is best assigned at 1047 m−1, rather than at 1139 cm−1, in C4D6. The calculations indicate that the experimental assignment for the A1 ring breathing mode and the A1 methylenic wag in C4H6 should probably be reversed. For the A1and the B1 modes with frequencies between 500 and 1300 cm−1, the normal coordinates change considerably on deuteration. The symmetry coordinates are mixed in the normal modes of C4D6 to a much greater extent than in those of C4H6.

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