1126
Electronic Structures of Bicyclo [ 1.1.Olbutane and Bicyclo [ 1.1.1] pentane Donald R. Whitman* and Joseph F. Chiang
Contribution from the Department of Chemistry, Case Western Reserue University, Cleveland, Ohio 44106, and the State University College, Oneonta, New York 13820, Received April 2, 1971 Abstract: Mulliken population analyses of ab initio SCF calculations for bicyclo[l.l.O]butane and bicyclo[l.l.l]pentane are reported and used to clarify the nature of the bonding in these molecules. The central CC bond of bicyclobutane is found to be describable as partially olefinic, although not strictly of a character. The central carbon atoms of bicyclopentane have strongly antibonding overlap population, consistent with their small separation and the large spin-coupling constant between the bridgehead protons. The bridgehead CH bonds of bicyclobutane are found to be strongly polarized, in explanation of the marked acidity of these bridgehead protons.
B
icyclo[ 1.1.O]butane and bicyclo[ 1.1. Ilpentane have striking properties which make examination and comparison of their electronic structures of interest, The central bond of bicyclobutane exhibits both olefinic' and nonolefinicZproperties, and its bridgehead proton is distinctly acidic, with a very large 13C-H spin coupling constant (205 Hz). Bicyclopentane has the shortest nonbonded carbon-carbon distance on r e ~ o r d and ,~ a surprisingly large long-range spin coupling constant between bridgehead protons (18 Hz). The electronic structure of bicyclobutane has been the subject of several apparently conflicting investigations. To explain the olefinic properties of the central bond Pomerantz and Abrahamsonj proposed two largely qualitative models, one attributing ethylenic character and the other acetylene-like character to this bond. Wiberg6 has performed CNDO calculations on bicyclobutane with the conclusion that the central bond bas appreciable p character, and most recently Schulman and Fisanick' have reported the results of ab initio SCF calculations which indicate that the central bond is nearly pure p character. The nature of the bonding orbitals in bicyclopentane has also been the subject of speculation. Chiang and Bauer4 suggest that the bridgehead carbon-hydrogen bond involves a carbon orbital that is nearly pure p character and that substantially pure p orbitals on the methylene carbons are involved in bonding to the bridgehead carbons. The present ab initio SCF calculations with Mulliken population analyses are intended to identify the similarities and differences of the electronic structures of these two bicyclic molecules and to select among the proposed descriptions of their bonding. Ab Initio SCF Calculations. A modified form of the IBMOL programs has been used for the calculations reported here. The basis functions for the molecular (1) K. B. Wiberg, G. M. Lampman, R. P. Cuila, D. S. Connor, P. Schertler, and J. Lavanish, Tetrahedron, 21, 2749 (1965). (2) E. P. Blanchard, Jr., and A. Cairncross, J . Amer. Chem. Soc., 88, 496 (1966). (3) K. Wiithrich, S. Meiboom, and L. C. Snyder,J. Chem. Phys., 52, 230(1970). (4) J. F. Chiang and S . H . Bauer, J. Amer. Chem. SOC.,92, 1614 (1970). ( 5 ) M. Pomerantz and E. W. Abrahamson, ibid., 88, 3970 (1966). (6) K. B. Wiberg, Tetrahedron, 24, 1083 (1968). (7) J. M. Schulman and G. J. Fisaiiick, J . Amer. Chem. Soc., 92, 6653 (1970). (8) E. Clementi and D . R. Davis, J. Comput. Phys., 1,223 (1966).
Journal of the American Chemical Society
94:4
orbital expansions were atomic-optimizedg Gaussian type functions
x
= Nr' exp( - a r z )Yl"(O,+)
where the Ylm(O,+)are normalized spherical harmonics and a is the optimized orbital exponent. Such functions have proved useful and near optimal for other molecular calculations. The uncontracted bases used for carbon (3s, Ip) and hydrogen are listed in Table I. Table I. Gaussian Type Functions Optimized Orbital Exponents Exponents----
----
Atom
S
C
46.5100 6.7170 0.3117
H
1.6150 0.2521
P
0.3545
The total bases consist of 36 functions for bicyclobutane and 46 functions for bicyclopentane. While these bases are by no means sufficient to approach the Hartree-Fock limit, nevertheless they are well balanced and thus can be expected to yield reasonably reliable bonding and antibonding properties in Mulliken population analyses. l 2 The geometry of bicyclobutane determined by microwave spectroscopy l 3 and the electron diffraction geometry of bi~yclopentane~ were assumed for these calculations. The numbering and coordinate systems are identified in Figure 1. Symmetry orbitals were not predetermined in either calculation, and thus the electron (9) D. R. Whitman and C . J. Hornback, J . Chem. P h y s . , 51, 398 (1969). (10) C. J. Hornback, Ph.D. Thesis, Case Institute of Technology, 1967. (11) L. M. Sachs, M. Geller, and J. J. Kaufman, J . Chem. P h y s . , 51, 2771 (1969); L. C. Snyder, R. G.Shulman, and D. B. Neumann, ibid., 53, 256 (1970); J. F. Chiang and D. R. Whitman, Theor. Chim. Acta, 17, 155 (1970); J. R. Sabin, R. E. Harris, T. W. Archibald, P. A. I
