FORCE CONSTANTS FOR THE CYCLOPROPENYL CATION

$^{1}$N. C. Craig, J. Pranata, J. R. Sprague, and P. S. Stevens, J. Am. Chem. Soc., 106, 7637 (1984) $^{2}$P. Pulay, G. Fogarasi, and J. E. Boggs, J. Chem. Phys., 74, 3399 (1981)Author Institution: Department of Chemistry, Oberlin College; Department of Chemistry, Oberlin College; Department of Chemistry, Oberlin College; Department of Chemistry, Oberlin CollegeKey force constants among the seven that were fitted to the vibrational assignments for the in-plane modes of $C_{3}H_{3}{^{+}}, C_{3}D_{3}{^{+}}$ and $C_{3}H_{2}D{^{+}}$ were larger than the corresponding ones for $benzene.^{1}$ To offset the considerable strain in the sigma bonds in the $C_{3}$ ring system, the $\pi$ -bonding in $C_{3}H_{3}{^{+}}$ must be exceptionally strong, indeed ``superaromatic.” Infrared and Raman spectra of the new species, $C_{3}D_{2}H{^{+}}$ give as assignments (in $cm^{-1}$) $(a_{1})$, 3154, 2423, 1535, 1268, 675; $(a_{2})$; $(b_{1})$ 2353, 1256, 973, 767; $(b_{2})$, 603. Using these new frequencies along with the ones previously assigned for the other three isotopomers, we have fitted a full set of ten general valence force constants to the inplane modes of the cyclopropenyl cation. The force constants are (in mdyn {\AA}$^{-1}$ for stretch-stretch, mdyn {\AA} $rad^{-2}$ for bend-bend, and mdyn $rad^{-1}$ for stretch-bend) CC str, 7.890(056); CH str, 5.280(009); CH bd, 0.598(008); CC str/CC str, -0.424(029); CH str/CH str, 0.031 (006); CH bd/CH bd, -0.043(004); CC str/CH str (same C), -0.236(016); CC str/CH str (different C), 0.378(034); CC str/CH bd, 0.212(023); CH str/CH bd, 0.225(041). For benzene some comparative force constants are 6.578 for CC stretching, 5.176 for CH stretching, and 0.514 for CH in-plane $bending.^{2}