1690 CAN. J. CHEM. \ IOL. 63, 1985 proceeds without any activation energy along the asymmetric path. Here we report the results of another, higher quality ab initio molecular orbital study with limited configuration interaction on the potential energy surfaces of both the addition and insertion reactions of (2%) ground state methylidyne to ethylene (PA,). Method All the molecular geometrical parameters of ground state ethylene ('A,), CH('II), doublet cyclopropyl and allyl radicals, and the reaction intermediates involved were optimized at the SCF level by the energy gradient method (1 8, 19) with 6-3 1G basis set (for C, see ref. 20a; for H, see ref. 20b). The Restricted Hartree Fock (RHF) open shell SCF method was used for the doublet state radicals. Configuration interaction (CI) calculations include all singly and doubly excited configurations (CISD) with respect to the SCF configuration, and were done using the direct CI method (21) at the SCF level optimized geometry. Davidson's formula (22) was applied to the CI results to estimate the correction for the quadruple excitations (CISDQ). The lowest three orbitals corresponding to the core orbitals of carbon 1 s were kept doubly occupied and frozen, and the top ten virtual orbitals were also kept frozen in the CI calculations. All the computations were performed with the "MONSTERGAUSS" Program (23) on an AMDAHL 5860 computer at the University of Alberta. The optimized C-H Results bond distance of 1.117 A calculated for the 'II ground state of methylidyne is in good agreement with the experimental value of 1.120 A (24). The optimized molecular parameters for ethylene ('A,) are summarized in Table 1 and the double ground state optimized geometry for the cyclopropyl radical, the product of the addition reaction is shown in Fig. 1. These values are in close agreement with the earlier optimized geometry with minimal (17, 26) and extended (4-31G) (27) basis sets. The radical center in the cyclopropyl radical is non planar with an out-of-plane angle between CIHlo and the CCC ring, of 40.86". The corresponding planar (Cat,) structure has the optimized geometry of R(Cl-Cz) = 1.467 A, R(C2-S3) = 1.539 A, R(Cl-Hl0) = 1.060 A, R(C2-H6) = 1.076 A, LH6CzH7 113.360, LC3C2H6 = 117.860, and H6C,C3Cl out-of-plane L = 109.06", with total energies: EsCF = - 116.354881 au, EclsDo = - 116.502782 au. This transition state structure for the inversion motion of the radical center is 4.3 kcal mol-' at the SCF and 9.0 kcal mol-' at the CISDQ level higher in energy than the C, symmetry lowest energy structure. The CH insertion into the ethylene C-H bond yields an allyl radical. The SCF optimized geometries of both C, and CXP structures are depicted in Fig. 2. Electron spin resonance studies (28) have shown that the allyl radical has a C,, symmetry. Several theoretical studies on electronic structure (29, 30), doublet instability (31-34), and symmetry dilemma (35, 36) have been reported for the allyl radical. The RHF SCF geometry optimization for three center, three.rr electron systems usually overestimates the stability of structures containing one short and one long bond (C,r)(Fig. 2a) relative to the one with intermediate equal bond lengths (Czv)(Fig. 2b). This problem has been solved by inclusion of the correlation energy (32, 33). The optimized geometry of the symmetric allyl radical is similar to the one obtained from 4-31G basis set FIG. I. Doublet ground state, RHF-SCF optimized geometry of the cyclopropyl radical. Bond distances are in A and bond angles in degree. TABLE I. SCF-optimized molecular parameters of ethylene (?'A,) with 6-31G basis set Molecular parameters Calculated Experimental" R(C-C) (4) 1.322 R(C--H) (A) 1.074 LHCH (deg) 116.14 "Reference 25. calculations (29). As expected, at the SCF level the C, symmetry radical is more stable - by 1.8 kcal mol-' - than the C2v structure but the inclusion of the correlation energy has the effect of lowering the energy of the C2,. structure below the Cs symmetry structure by 1.2 kcal mol-'. The addition reaction path Two reaction paths for the addition of CH(lII) to ethylene ('A,) have been studied; in both cases CH is approaching at the center of the C=C bond, from the plane perpendicular to the ethylene, Fig. 3. Total energies as a function of the XI-C, distance (d, Fig. 3) have been calculated for the SCF level optimized geometry and CI calculations were then done on the SCF optimized geometry. In the first reaction path, C4H9 and XI are in the plane perpendicular to the C,C3C4 plane.the single electron on the C, atom remains in thep, orbital until the XI-C, distance reaches 1.85 A, and Localized Molecular Orbital (LMO) analysis sh9ws ethylene and methylidyne as separate entities. At 1.85 A distance partial bond formation between C4-C2 and C4-C3 takes place. Below this distance the single electron moves from the p, orbital to the p, orbital on C,. This transition complex has a small energy barrier of 3 kcal mol-' at the SCF level, Fig. 4, which disappears in the CISDQ potential energy surface, Fig. 5. In the second reaction path, where the CH approach is in the plane of C2C3C4H9, the single electron remains always in the p,, orbital of C,. LMO analysis of the reaction intermediates shows that CH and ethylene remain as separate entities until the XI-C, distance again reaches 1.85 A, at which point partial bond formation between C4-C2 and C4-C3 takes place. The
GOSAVI ET AL. (a) I H Frc. 2. Doubl~t ground state, RHF-SCF optimized geometry of the allyl radical. (a) C, symmetry ('A"); (b) C?,. symmetry ('A>). Bond distances are in A and bond angles in degree. Frc. 3. Addition and insertion reaction path C,XlC4 angle at this distance is 104.5" and the XlC4H, angle is 95.2". The C2X1C4 angle in the first reaction path remains at 90, whereas in the second reaction path this angle is greatfr than 100" until the XI-C, distance reaches a value of 1.60 A. For this in-plane approach both the SCF and CI calculations predict no activation energy (Figs. 4 and 5). The insertion reaction path In the insertion reaction path CH is approaching in the plane of the ethylene molecule. The total energy of the 2A" state as a function of the XI-C4 distance (d) has been calculated with optimizing all the rest of the molecular parameters, Fig. 6. The C2XlC4 angle at large distances is small (e.g. at d = 5 A, LC2XIC4 = 42.6") and increases as the distance decreases reaching a maximum of 99" at 2.5 A. Then again it starts decreasing as d decreases to the final product of the allyl radical. LMO analysis shows that methylidyne and ethylen: remain as separate entities until d reaches a value of 2.325 A corresponding to the transition complex, Fig. 7, where C2-C4 bond formation starts to take place. At this transition state the C, atom is right above the C1 carbon, i.e. LC,C2C4 = 9?" and H, is still bound to the C? atom. Below d = 2.325 A the H, migrates from C2 to C,. The energy barrier at the SCF level is 29 kcal mol-i. The configuration interaction studies on the potential energy surface with the SCF optimized geometries, Fig. 6, for the insertion reaction predicts an activation energy of - 15 kcal mol-i. (b) FIG. 4. Potential energy surface of lowest doublet state addition of CH + CzH4 reaction path at the SCF level. 0, perpendicular approach; 0, planar approach of CH. Discussion The first addition reaction path studied, where the CH is approaching in the plane perpendicular to the CCC plane is similar to the symmetric path we reported earlier (17). At the RHF open shell SCF level with 6-31G basis set, the energy barrier, 3 kcal mol-i, is smaller than the minimal STO-4G UHF value of 7.7 kcal mol-i. On inclusion of the correlation energy by configuration interaction computation, the energy barrier disappears completely (Fig. 5). The second reaction path, the in-plane approach, where C-H is approaching in the CCC plane, is close to the asymmetric approach reported earlier (17) where the reaction coordinate was the C2X,C, angle while in the present study we choose the XI-C, distance as the reaction coordinate. This asymmetric approach, both at minimal STO- 4G basis (UHF-SCF) and 6-31G basis (with RHF-SCF), predicts no energy barrier for the addition reaction even at the SCF level. On inclusion of correlation energy by the CI calculations, the energy along the addition reaction path decreases monotonically and again without any energy barrier (Fig. 5). The LMO analysis at the critical level of 0.07 for bond identification shows partial bond formati~n~between C4-C2 and C,-C, at an XI-C, distance of 1.85 A in both reaction paths. Bond formation probably takes place by the p: electrons
1692 CAN. J. CHEM. VOL. 63, 1985 FIG. 5. Potential energy surface of lowest doublet state addition of CH + C,H, reaction path at CISDQ level. 0, perpendicular approach; 0, planar approach of CH. -11635 I I I I 1-11620 FIG. 6. Potential energy surface for CH insertion into ethylene. --- SCF; --- CISDQ level. of the ethylene (C2C3) moving to the p, in-plane empty orbital of methylidyne C4 in both cases but back donation occurs from the lone pair of the p, orbital of C4 in path two and in path one the single p, electron forms a partial bond withoa carbon atom of ethylene. In the latter case, below d = 1.85 A, one electron from the lone pair in the p, orbital of methylidyne moves to the in-plane p, orbital to complete the bond formation with ethylene. This electron rearrangement could perhaps be the reason why the asymmetric approach, reaction path twc initially has a lower energy until d reaches a value of - 1.75 A below which the symmetric path lies lower in energy leading to the cyclopropyl radical structure (Figs. 4 and 5). In either case the addition appears to be a one-step, concerted process, in agreement with the experimental stereospecific addition results obtained for the carbethoxymethylldyne. These potential energy surface calculations suggest that the addition of ()?'n) ground state methylidyne to ethylene ('A,) follows the asymmetric path two in the early stages of the reactions untll d = 1.75 A, then crosses over to the symmetric path one, without any energy barrier. This asymmetric approach 1s in line with the predic- ESCF = - 116.209395 a u ECISDO = -1 16.361519 a u FIG. 7. RHF-SCF optimized geometry of the transition complex of CH insertion into ethylene. Bond distance in A and bond angles in degree. tions of the molecular orbital studies of the reaction path for the addition of singlet ('A,) methylene to ethylene (37, 38) favoring the asymmetric approach without any activation energy. Asymmetric reaction paths were also predicted for several singlet ('A,) substituted carbene cycloaddition reactions with some activation energy (37, 39). The present computational results' prediction of a zero activation energy for the addition reaction of CH(~'II) to c2h4(x1~,) compares well with the experimental value of -0.35 kcal mol-i recently reported by Berman, Fleming, Harvey, and Lin (2). The knowledge of the geometry of the activated complex makes it also possible to estimate a value for the preexponential factor of the reaction on the basis of transition state theory. The preexponential factor of the reaction has been reported to be 1.34 X 10" M-' s-' (2). Assuming that the preexponential factor for the insertion reaction into the C-H bonds of ethylene is the same as the one measured for methane (3), 0.30 x 10'' M-' s-', we correct the experimental value for the ethylene reaction by subtracting the experimental value for methane 1.34 X 10" - 0.30 x 10" = 1.04 X 10" M-' s'. From the above experimental A factor the entropy of activation at 300 K and AS,* = AS,* - An R In (RT) = -18.47 eu The standard entropy for the activated complex is obtained from the equation AS,' = S~(AC) - so,(ch) - so,(c~h~) Taking S;(CH) = 43.7 eu and Si(c2H4) = 52.4 eu (40) the entropy of activation calculated from the experimental A factor yields the value S~(AC) = 77.63 eu for the standard entropy of the activated complex. Based on the similarity between the cyclopropyl radical and the optimized structure computed for the activated complex of
GOSAVI ET AL. 1693 the CH + C2H, addition, the standard entropy for the activated complex, s~(ac), can be estimated using Benson's method (40). Starting out with the standard entropy for the cyclopropyl radical, S; = 60.4 eu (40), the longer C(H)-C(H?) bonds will give 1 eu additional rotational and 3-4 eu additional vibrational contributions for the entropy of the activated complex. The vibrational contribution is compensated somewhat by the increased frquencies of the CH? groups due to the shorter H,C-CH2 bond. Thus, the standard entropy for the activated complex is estimated to be about S:(AC) = 65 + 2 eu, in serious disagreement with the value derived from the experimental A factor. The A factor derived from the estimated S:(AC) value lies in the range of 6.5 X lo7-4.9 x 10XM-' s-' which is over two orders of magnitude lower than the reported experimental value. We are not able at present to rationalize this discrepancy. Turning to tbe insertion reaction, the transition state complex at d = 2.325 A still resembles the reactant state (Fig 7), with the methylidyne carbon C4 being close to C, at an angle C3C2C4 = 93", and the Cz-C, distance being similar to ethylene. At d = 2.30 A the H6 hydrogen migrates from C2 to C4 and C2-C4 bond f?rmation begins to take place with C2-C4 distance of 1.735 A. The energy barrier is 15 kcal mol-' which is higher than the measured activation energies for insertion into the C-H bonds which are all negative and have values in the order of 0.4-0.06 kcal mol-' (3). The computed energy barrier is sensitive to the correlation energy and geometry optimization at the CI level would very likely have a significant decreasing effect on it. The computed energy barrier, 4 kcal mol-', for the insertion of CH()?'II) into the hydrogen molecule (16) is also probably somewhat larger than the experimental value. 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