GEOMETRY , REACTIVITY, AND SPECTRUM OF CYCLOPROPANE in the case of adsorbed oxygen. Thus we conclude that different types of oxygen are involved even if, as in the first case, we cannot postulate any reasonable model. Our conclusions introduce into the chemistry of catalytic oxidation of GO on semic0,nductoroxides (we recall the analysis contained in the review of Stone3) the concept of “precursors.11 They are most likely GO molecules reversibly linked to surface metal ions, and play a determinant role in the formation of oxygenated complexes. The process GO,,, -+ CO,d, which is considered, in the usual mechanism] as the preliminary
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step is in our opinion suitably characterized by means of ir spectroscopy. The generic definition of CO,d, can thus be identified with the GO reversibly linked to metal ions through a weak u bond. Finally, we think that the oxygenated complexes might be identified with carboxylate structures, even if the complexity of our spectra do not exclude the possibility of the presence of other species on the surface. Acknowledgment. This research was supported by the Italian Consiglio Nazionale delle Ricerche.
Theoretical Study of the Geometry, Reactivity, and Spectrum of Cyclopropane by Robert J. Buenker Department of Chemistry, University of Nebraska, Lincoln, Nebraska
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and Sigrid D. Peyerimhoff Institut f u r Theoretische Physik, Justus Liebig-Universitut, 63 Giessen, Lahn, West Germany
Ab initio SCF-MO and CI calculations have been carried out for the cyclopropane molecule CsHs for a series of CCC internuclear angles in order to study the geometry of this molecule in its ground and excited states; from this treatment a n equilibrium CCC angle of 65’ is indicated. A basic similarity between cyclopropane and the series of symmetric AB2 molecules (and others) is pointed out; all possess CzVsymmetry throughout their respective bending processes and their angular correlation diagrams show a general agreement between shapes of corresponding orbital energy curves. The great disparity in the geometries of cyclopropane and its isoelectronic AB2 and HABz counterparts ozone and formate ion is thereupon related to the fact that these systems possess different ground-state electronic configurations; in turn it is shown that this distinction is caused by the ability of hydrogen AO’s to selectively alter the stability of the orbitals of a parent AB2 molecule, Development of this concept also allows a consistent explanation for the unusual reactivity of cyclopropane. C I calculations are employed to study the electronic spectrum of C& and they indicate t h a t the majority of the known ultraviolet absorptions of this system cannot reasonably be assigned to vertical transitions; instead 0-0 excitations involving upper states with wide-angle equilibrium geometries are suggested.
I. Introduction The cyclopropane molecule C3H6 is well known to exhibit anomalous behavior among organic systems with regard to binding and reactivity. According to the simplest valence bond description the molecule possesses pure CC single bonds (experimental bond 1ength’J 1.51 A) and yet its CCC angles are all approximately 60°, much smaller than the tetrahedral angle characteristic of other saturated organic molecules. Furthermore, cyclopropane undergoes certain addition reactions such as hydrogenation in the presence of a catalyst and bromination in carbon tetrachloride, also in definite contrast to the behavior generally observed for singly bonded hydrocarbons. Several explanations have previously been offered
for the unusual properties and reactivity of cyclopropanels perhaps the most celebrated of which are due to Walsh4 and Coulson and Moffitt.6 It is the purpose of the present paper to discuss these matters in considerably more quantitative detail, by means of ab initio LCAO-MO SCF calculations, than has been possible previously ; a simple qualitative theory is sought to explain the anomalous characteristics of cyclopropane in a manner which is still clearly coil(1) 0. Bastiansen, B. N. Fritsch, and K. Hedberg, Acta CTyst., 17, 538 (1963). (2) L. C. Snyder and 8. Meiboom, J. Chem. Phys., 47, 1480 (1967). (3) W. A. Benett, J . Chem. Educ., 44, 17 (1967), and references therein. (4) A. D.Walsh, Trans. Faraday SOC.,4 5 , 179 (1949). (5) 0.A. Coulson and W. E. MofBtt, Phil. Mag., 40, 1 (1949). Volume 73, Number 6 May 186#
1300 sistent with previous results concerning related systems. In particular, it is interesting to consider cyclopropane in light of a former study dealing with systems isoelectronic with it, namely ozone 0 3 and formate ion6 HCOO-; from this it has been concluded that a t least the geometrical behavior of H,AB2 molecules in ground and excited states can be understood in the same terms as that of simple triatomic systems. I n order to conduct such a study, SCF wave functions are determined for cyclopropane as a function of its internuclear CCC angle; configuration interaction calculations based on the initial SCF treatment are also helpful in this connection, in addition to enabling detailed consideration of the molecular spectrum of this compound.
11. Calculations In order to be consistent with previous work dealing with6J 0 3 and HCOO- a basis set of fixed group gaussian lobe functionss has been employed throughout this investigation. The A 0 basis set consists of 25 gaussian AO's on each of the three carbons, ten of s and 15 of p type (with the two lobes representing a p function being counted as one AO) and five additional s-type gaussians on each of the six hydrogen atoms. These functions are grouped in fixed linear combinations so that only 24 linear coefficients are left free to be determined by the SCF procedure, for three s and three p group functions on each carbon and for one s group on each hydrogen. Exact values for the exponents, lobe separations, and fixed coefficients within the various group functions have been given elsewheresrg (hydrogen scale factor of 1.414). The coordinate system employed for the 60'
