4242 Electronic States of Trimethy1enemethanela James H. Davidb and William A. Goddard III* Contribution No. 5423 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91 125. Received August 31, 1976 Abstract: Ab initio generalized valence bond (GVB) and configuration ,interaction (CI) calculations were carried out on the planar and bisected forms of trimethylenemethane. The results indicate that the ground state is the planar triplet with the pla- nar singlet state 26 kcal/mol higher. The rotational barrier for the triplet state is 18 kcal/mol, while one component of the pla- nar singlet prefers the bisected geometry by 7 kcal/mol. We predict the transitions for the chemically interesting states as fol- lows: planar triplet, zyxwvutsr k,,, 266 nm withf zyxwvutsr = 0.002; bisected singlet, zyxwvu A , 359 zyxwv nm withf= 0.0008; and planar singlet, A , 289 nm withf = 0.10. The vertical ionization potential is calculated as 8.3 eV. I. Introduction Trimethylenemethane (1) has been a subject of much the- oretical discussion since the work of Moffitt.2 Only recently, however, has the molecule become a subject of serious exper- imental and theoretical work. In 1966, Dowd3 reported the first preparation of 1 from the pyrolysis of the pyrazoline system 2. The early work of Dowd has been summarized in a review N-N -,A, 1 2 article4 and will not be discussed. In 1971, Berson5 prepared the trimethylenemethane diyl analogue 3 from the diazo compound 4, and extensive research has been conducted since \/ 4 then. Early ESR experiments showed 3 to have a triplet ground state, and CIDNP studies showed that dimerization of 3 must include at least one triplet reactive species. Additional stud- ies6-9 have shown that at least two distinct electronic states are involved in the pyrolysis of the diazo precursor 4. Berson has postulated that the two reactive species are a bisected singlet 5 and a planar triplet zyxwvutsrq 6. 5 6 Previous theoretical studies on trimethylenemethane di- radical 1 have led to contradictory results. Most workers agree that for the planar geometry the lowest state is a triplet state; however, calculations of the lowest planar singlet state lead to energies of 21,1° 68,1° and 7011 kcal/mol from ab initio Har- tree-Fock (HF) wave functions and 35 and 57 kcal/mol12 from semiempirical Hartree-Fock wave functions. Part of the problem here is a special difficulty with spatial symmetry for the Hartree-Fock wave function of the lowest singlet state.13 We report here the results of ab initio configuration inter- action (CI) calculations based on generalized valence bondI4 (GVB) wave functions of both the planar (1) and the bisected (7) geometries of trimethylenemethane, which eliminate the above difficulties and provide a description of the other excited A B A B 1 7 states, including the transition oscillator strengths. A summary of these results was communicated earlier.I5 11. Calculational Details For all calculations, a contracted Gaussian basis set equiv- alent to a double [ (DZ) basis was used. For carbon, Dunning’s contraction16 (3s, 2p) of Huzinaga’s (Ss, 5p) basis set was utilized, while for hydrogen a comparable (4s/2s) contraction was used,’(’ with each Gaussian exponent multiplied by a scale factor of 1.44, corresponding to a Slater exponent of { = 1.2. Our objective in these studies was to establish the overall character of the states of planar and bisected trimethylene- methane. Hence we have used a geometry of each form roughly appropriate for the ground state: C-C bond lengths of 1.40 A, CH bond lengths of 1.086 A, and bond angles of 1 20°. Since these geometries are roughly appropriate for the ground state, we obtain vertical excitation energies and ionization potentials. Geometry optimization would be particularly important for the rotation barriers. In the GVB calculations the a bond pair of the triplet state was correlated with all orbitals described as symmetry func- tions (for the appropriate symmetry group). For the planar configuration this led to four occupied a orbitals. In the con- figuration interaction (CI) calculations for the planar case, a full CI was carried out over these four orbitals plus the four remaining (virtual) a orbitals of the DZ basis. Thus the ground-state u orbitals were used for all excited and ion states. This is adequate for the valence excited states and reasonably adequate for the lower ion states. For the bisected configuration this GVB calculation leads to four non-closed-shell orbitals, three a and one 0. For the CI this was supplemented with three additional a and one addi- tional u (virtual) functions obtained by starting with the most diffue a function on each of the three unrotated carbons plus the corresponding u-like orbital in the rotated carbon and orthogonalizing to all original orbitals. From additional CI calculations including single excitations from the a combina- tion of C H orbitals on the rotated carbon, we concluded that such excitations are unimportant. All HF and GVB calculations were carried out with Bo- browicz-Wadt-Goddard program” using the fully self-con- Journal of the American Chemical Society / 99:13 / June 22, 1977