J. Phys. Chem. 1982, 86, 3288-3292
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molecular state to the final states of the fragments, both for diatomic and for polyatomic molecules. Unfortunately, these theoretical treatments have not yet been applied to any of the ionic systems where detailed experimental data exists.
Conclusions Studies of ion photofragment spectroscopy have led to significant new knowledge of potential curves and their couplings in the region important in low-energy collisions. However, our understanding of molecules near their dissociation limits is very clearly incomplete. Future effort should be directed both toward obtaining more detailed
experimental data on molecules which are simple enough to allow comparison with accurate theoretical calculations, and to further development of the theoretical description of the dissociation process, and of the application of this knowledge to the calculation of collisional properties. Acknowledgment. I acknowledge a longstanding collaboration with Dr. P. C. Cosby and Professor Jean Durup on this subject, and to express appreciation to Professors Allan Carrington and P. J. Sarre for communication of their recent results prior to publication. My participation in the work described was supported by the National Science Foundation under Grants No. CHE-791804, AST-7918371, and INT-8010763.
ARTICLES Theory of Spin-Forbidden and Cheietropic Reactions Involving O( 3P), C3H,, and C302 Ying-Nan Chlu' and M. S. F. A. Abidi Center for Molecular Dynamics and Energy Transfer, Department of Chemistry, The Catholic University of America, Washington, D.C. 20064 (Received: July 7, 1981; In Final Form: February 1, 1982)
A self-consistenttheory is proposed to explain the spin-forbiddenreaction of O(3P)with C3H4and C302.Unique combinationsof spin-orbit and vibronic interaction, angular-momentumconservation in perpendicular a-electron systems, and concerted cheletropic dissociation of the intermediate are shown. A detailed consideration of available orbitals via quantum mechanical perturbation theory shows that the orbitals naturally lead to the correct spin inversion needed for the subsequent formation of the cyclic intermediate and to the correct normal vibrational modes for dissociation.
where the superscript t indicates slight vibrational excitation and tt strong vibrational excitation. In the second reaction all C-C bonds are broken resulting in three carbon monoxides, one of which was found to be more vibrationally excited than the other two.2 In the first reaction one new C-C bond is formed in the product ethylene. We propose here a detailed theory to explain the reason for the ready occurrence of this spin-forbidden reaction, for the vibrational excitation, and for the difference in products. We shall discuss the following points: (1)Detailed orbital considerations are necessary for intellectual understanding of the symmetry relations in these reactions. (2) The singlet-triplet conversion by spin-orbit interaction is favored by the built-in perpendicular n-electron
system, and spin-orbit interaction coincidentally "aligns" the orbitals and spin for the subsequent formation of the cyclic intermediate. (3) The two perpendicular 7r systems, C3H4and C302, are similar in their spin inversion and in the formation of cyclic intermediate, but dissimilar in dissociation. (4) A self-consistent mechanism guarantees the dissociation of C202(to two carbon monoxide molecules) but nondissociation of C2H4 (ethylene) in the product. (5) The manner in which concerted cheletropic dissociation occurs follows naturally from the mechanism of formation of the intermediate and from vibronic interaction after the orbitals involved are considered in detail. (6) We discuss also how the formation and dissociation mechanism leads to preferential vibrational excitation of only one of the product CO molecules. It has been generally accepted,'V2 as in the case of O(3P) reaction with m e t h ~ l e n e ,that ~ , ~ the oxygen atom takes a broadside approach to attack the center carbon atom in C302and C3H4. It has also been deduced2 that the intermediate forms a cyclic C3ring, which undergoes (cheletropic) decomposition, breaking two bonds in concert. Although a valence-bond theory for the reaction mechanism has been given by Havel' and by Hsu and Liq2 none
(1) P. Herbrechtsrmeier and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem., 76, 517 (1972); J. J. Havel, J. Am. Chem. Soc., 96, 530 (1974). (2) D. S. Y. Hsu and M. C. Lin, J. Chem. Phys., 68, 4347 (1980); G. Pilz and H. Gg. Wagner, 2.Phys. Chem., 92, 323 (1974).
(3) E. S. Yeung and C. B. Moore, J. Chem. Phys., 60, 2139 (1974). (4) R. G. Miller and E. K. C. Lee, Chem. Phys. Lett., 27, 475 (1974); J. Chem. Phys., 68, 4448 (1978).
Triplet oxygen O(3P)reacts readily with singlet allene' and singlet carbon suboxide,2both of which have perpendicular carbon a-electron systems. In both cases the final products are spin singlets, viz. O(3P) + C3H4('A1) COt(X'E+) + C2H4(X1Ag) (1) O(3P) + C302('Z,+) COtt(X1~+) + 2COt(X1z+) (2)
--
0022-365418212086-3288$0 1.2510 0 1982 American Chemical Society
Cheletropic Reactions Involving O(3P), C3H4,and C302
'X
w
The Journal of Physical Chemistry, Vol. 86, No. 17, 1982
3289
rotation is necessary (see below) to line up the four H atoms in ethylene to give D 2 h symmetry vs. the Dad symmetry of allene. These lone carbon electrons on p, and interp, still have parallel spin and form a triplet (3B1) mediate. For these two electrons to form a bond and to result in a triangular C3 intermediate, it is necessary (1) for the orbitals to rotate so that they are in the same plane, say both becoming carbon p, orbitals and (2) for one of the two parallel CY spins to be flipped to p to give an antiparallel singlet arrangement. These two conditions can be achieved simultaneously and coincidentally by the proper choice of the magnetic spin-orbit interaction operator. The probability amplitude for this happening can be expressed as a first-order spin-orbit mixing coefficient, viz.
I
0
1
PX"(2)P,b(l)+ P,b(l)P,W - PXb(2)P,"(l))W2 Flgure 1. Reaction of q36,)with C302forming a cyclic intermediate.
of the three orbital states of O(3P)has been mentioned specifically, no detailed orbital picture and quantum mechanical perturbation theory were given, and no detailed dissociation mechanism was presented for the intermediate. Although the three degenerte orbital states, which can linearly combine, can in principle all react, we found, by delving into the detailed spin-orbit interaction, one orbitally polarized O(3B1)state can coincidentally achieve triplet-singlet conversion and simultaneously facilitate the formation of the cyclic intermediate. This we feel is unique in O(3P) reaction with perpendicular a-electron systems. By delving into the detailed vibronic interaction we found that the formation of the intermediate leads to a vibrational mode (A,) favoring the exciation of one CO over the other two. Also from vibronic interaction and from the available orbitals of the right symmetry inherent in the system there is excitation of vibrational normal modes (B,, B2,and A,) that correspond to particular cheletropic dissociation mechanisms known in physical organic chemistry. These particular mechanisms will give a self-consistent interpretation of the decomposition of the intermediate and simultaneously account for the breaking or nonbreaking of the C-C bonds in the product. For the reaction with C302,we assume the oxygen atom approaches along the z axis (which is taken to be the twofold axis for the linear symmetric C3O2 molecule) forming a C2"pyint-group symmetric system (Figure 1). Of the three orbital states of O(3P),consider O(3B1,p,py2p,) which has two mutually perpendicular lone electrons, one in the oxygen pr orbital (capable of forming a C-O u, bond with the center carbon atom) and one in the oxygen p, orbital (capable of forming a C-O a, bond with the center carbon atom). The repulsion is less than O(3A2,p,pyp,2) and O(3B2,pX2pyp,)which have more electrons situated near the occupied (a, and a,) bonding orbitals of C302. The linear C302 molecule has its figure axis lying along the y axis and has two mutually perpendicular C-C a bonds, axand a,, which react with the incoming O(3B1)electrons to form the above-mentioned a, and u, bonds (Figure 1). The initial reaction thus results in lone electrons in the atomic orbitals of the side carbon atoms a and b. It also results in single C-C bonds which may rotate freely. Such
>/ (3)
where S a b is the a-overlap integral. Here the orbital angular momentum operator belongs to the B1irreducible representation and can connect p,(B,) and p,(A,). The change of spin angular momentum is compensated by the change in orbital momentum. Thus the overall angular momentum is conserved. The theory also explains that the singlet oxygen O(lD) state will not react this way, because the spin-orbit interaction matrix element between two singlets vanishes. The two p, orbitals (r,. = nonbond) (Figure 1) on the side carbon atoms a and b now fortuitously line up, and with spin paired can via a bending vibration combine to form a covalent bond resulting in a cyclic intermediate (rab= bond = re). We believe this coincidence is the reason for the ready occurrence of this type of spin-forbidden reaction involving perpendicular a-electron systems. The bending vibration may be seen as resulting from the vibronic interaction (dH/dQ,,)Q, which converts the electronic energy ,A1' (Tab = nonbond = large) to electronic ('A, state with rab= bond = re) plus vibrational state (x,,) energy. This A, bending vibration may be the V6a in X3Y3( D 3 h ) m o l e ~ u l ewhich ,~ favors vibrational excitation of one CO over the other two. The next task is to explain the concerted decomposition of the cyclic intermediate which splits off the newly formed and vibrationally hotter2 CO leaving a transient (CO),. The latter accounts for the two colder CO's. Such concerted breaking of two bonds falls into the category of cheletropic reactiom6 The bonds may break in conrotatory or in disrotatory modes and in either linear or nonlinear cheletropic reactions. Of the various possibilities we found that the following two paths will give an antibonding a* orbital between the two carbon atoms ca and cbin the remaining transient (CO), species: (1)disrotatory motion in a linear cheletropic reaction (Figure 2); (2) conrotatory mode in a nonlinear cheletropic reaction (Figure 3). We believe this antibonding a* orbital is responsible for the subsequent decomposition of (CO), into two colder CO's. In (l), the disrotatory motion with si(5) G. Herzberg, 'Infrared and Raman Spectra of Polyatomic Molecules", Van Nostrand, New York, 1962, p 91. (6) R. B. Woodward and R. Hoffmann, "The Conservation of Orbital Symmetry", Verlag Chemie, Berlin, 1970.
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The Journal of Physical Chemistty, Vol. 86, No. 17, 1982
Figwe 2. Linear cheletropic decomposition of c303 and the correlation diagram in disrotatory mode.
Chiu and Abidi
to the reaction of O(3P) with C3H4. Here the similarity lies in the spin forbiddenness and a perpendicular ?r system. The formation of the cyclic intermediate (in this case cyclopropanone) is similar to the preceding reaction. The difference lies in the facta that (1)there is no C%but only C2 symmetry and (2) the one C-C bond between side atoms ab, instead of being broken, is preserved in CzH4. Nevertheless, we found (Figure 4) that a linear cheletropic reaction in a conrotatory mode (where coincidentally CZ, symmetry is preserved) is able to account for the products from the cyclic intermediate. Here the conrotatory motion of course requires a vibrational "rotation" (of A2 symmetry) with respect to the z axes (see above). The task is now to show that these vibrational normal modes are reasonably accessible during the reaction. By a combination of spin-orbit and vibronic perturbation we found that indeed all desired modes are achievable albeit with different degrees of difficulty from orbitally polarized O(3P)states reacting with C302as follows (the last two involve excited initial complexes). Note that the greater the change in electronic configuration, the more difficult the transformation. The orbitals that are different from the preceding step in the transformation are underlined with a wavy line
U Flgure 3. Nonlinear cheletropic decomposltbn of c303 and the correlation diagram in conrotatory mode (solid line, dotted line for disrotatory mode).
multaneous upward bending of two C-C bonds resembles the out-of-plane bending mode7 v6(bl) of formaldehyde. This latter mode is in part responsibles for dissociation of H2C0 into H2and CO. In (2) the nonlinear cheletropic decomposition with the rotation of one CO resembles the v5(b2)vibrational mode of formaldehyde which is also in part responsible for the latter's decomposition. For C303 the modes are vsb(bl)and ~7b(b2)(illustrated in Chart I). The A2 vibrational mode is locally a rotation with respect to the top CO and can also be visualized as a result of rotational electronic interadion9J0-Bd&, (see below). It is noted that L, has Az symmetry and can convert an electron in px*(BI)into ns0(B2). The J, matrix element is nonvanishing, of course, only if the motion of the complex has rotational angular momentum along z. The test of the above theory comes when it is applied (7) G.Herzberg, ref 6, p 65.
(8) D.F.Heller, M. L. Elert, and W. M. Gelbart, J. Chem. Phys., 69, 4061 (1978). (9) C . H. Tomes and A. L. Schawlow, "Microwave Spectroscopy", McGraw-Hill, New York, 1955, p 208. (10) Y. N. Chiu, J. Chem. Phys., 41,3235 (1964).
where only orbitals needed to illustrate the sequential changes are used and abbreviation of the Slater determinant is employed so that, for example, for a singlet
The Journal of Physical Chemistry, Vol. 86, No. 17, 1982
Cheietropic Reactions Involving O(3P), C,H,, and C302 TABLE I
' !f tjljZSi2
c'B lpZbt( pxabnxCot) (n, co nyoJ- )nNo $(I)
I3B2pzb'(*xCCLnxCCt)( P,
J-
'
pw0 )nyo t )
,= I
=
E"
-
3291
X
E('B,)
11B,p2bf(p,aJ.nxCot)(~xCoJ.nNo )nyo+)
E ( ' B 1 )- E('A,'x;
I
''
Chart I
P
Figure 4. Linear cheletropic decomposition of C3H,0 and the correlation diagram in conrotatory mode.
Ipozapu>lstands for 2-1/2[lpuzapo>l - puzapuzbl]. The vibrational modes are precursors to the modes of the same symmetry in the C303(D3&~ o m p l e xillustrated ,~ in Chart I. The orbital pictures of the various initial complexes are given in the Appendix, as are also the perturbation wave functions for one of these (4b). Only (4b) and (4c) correspond to the valence bond structures of Havel' and of Hsu and Lin.2 However, they did not indicate what bond (T or a) was initially formed and what reorganization of orbitals results. It would require knowledge of the rotational energy distribution to decide whether the reaction is linear or nonlinear cheletropic. We wish to point out that although symmetry analysis of the spin-orbit interaction is ~ e l l - k n o w n , ~and ~ - ' ~the (11)D.S.McClure, J. Chem. Phys., 20,682 (1952). (12)N. J. Turro and A. Devaquet, J.Am. Chem. SOC.,97,3859(1975). (13)N. J. Turro, 'Modern Molecular Photochemistry", Benjamin Cummings, Menlo Park, CA, 1978.
analysis has been reiterated until recently,'l-'' it was useful only for specification of the necessary condition. For a more complete analysis, there must also be sufficient conditions which derive from the availability of atomic or molecular orbitals of the correct symmetry and suitable energy. This is the reason for examining the availability of such orbitals from among the three degenerate orbitally polarized states (3B1,3B2,3A2). Although it is also wellknown18J9that the angular momentum operator "rotates" p orbitals by go", it has been neces~ary'~ to invoke rotations to get the perpendicular orbitals for nonvanishing spin-orbit matrix elements. However, we wish to point out that in the perpendicular s systems we are studying, the perpendicular orbitals are already built in. The rotation, by spin-orbit interaction, of an orbital to a per(14)R. M. Hochstrasser, "Molecular Aspects of Symmetry", W. A. Benjamin, New York, 1966. (15)L. Salem, Pure Appl. Chem., 33,317 (1973). (16)E.A. Halevi and C. Trindle, Isr. J. Chem., 16,283 (1977). 99,3909 (1977). (17)T. Lee, J. Am. Chem. SOC., (18)S.P. McGlynn, L. G . Vanquickenborne, M. Kinoshita, and D. G. Carroll "Introductionto Applied Quantum Chemistry",Holt, Rinehart and Winston, New York, 1972,p 347. (19)S.S.Shaik, J. Am. Chem. SOC.,101,3184 (1979).
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The Journal of Physical Chemistry, Vol. 86, No. 17, 1982
Chart 11. The dotted arrows indicate the spin flip and orbit rotation in triplet t o singlet conversion (see eq 3 )
1
3
B:
2
A' :
Chiu and Abidi
theory to similar systems, for example, the diazenes6pZ0 where N2, instead of CO, is split off in the concerted reaction. We also hope to incorporate some of the electronic vibrational and rotationa121,22 correlations we have studied in the past.
Acknowledgment. We thank Kathy Werner for typing the first draft of the manuscript, Ngoc phan Do for drawing the figures, and Mrs. Betty Pohlhaus for typing the revised manuscript. Thanks are also due Dr. Walter Shaub for reading the manuscript and suggesting improvements in presentation. Appendix Orbital pictures of the initial complexes are given in Chart 11. The dotted arrows indicate the spin flip and orbit rotation in triplet to singlet conversion (see eq 3). From degenerate perturbation theoryz3the wave function for the reaction of the three degenerate orbital states of O(3P) with C302may be written as follows: +[O(3p)+C30z(18g+)] = cp
2'
3'
pendicular position with spin inverted (that matches the other orbital in alignment and spin pairing) and hence promoting the subsequent bonding of these two orbitals to form a cyclic intermediate is a new situation and must be identified. We also mention several points which differentiate the reaction systems studied here from others: (1) oxygen O(3P)has one more pair of lone electrons than the carbene, C(3P). The repulsion of these lone-pair electrons with the perpendicular H system will make the three orbitally polarized states of O(3P) react differently, whereas the three states of carbon (X3B1,P,P,) P,P,), and (J3B2, P P,) may be more nearly equivalent in their reactions. (2) +he reaction of O(3p) as a free radical with perpendicular H system forms in a first step an cup unsaturated ketone. This is different from the better-known also spin-forbidden reaction of O(3P)with methylene CH2. The latter has only one set of two H electrons and reaction with the latter in the first step forms a saturated ketone (formaldehyde). There is little electronic parallel to the latter reaction. For example, we can compare the reaction of O(3A2,p,2p,py) which with :CH2(lA1,p,2) can give HzC0(3Az,ny7rz*),which in turn gives rise to HZCO('A1,H,'x",*) in a typical nr* to TH* conversion via 1,S, interaction, or gives rise, via lySy, to H2CO('B2,n+%*), a well-known spectroscopic state. (3) The fact that from detailed orbital considerations we have identified the spectroscopic normal modes (Chart I) as presursors for concerted cheletropic dissociation, we feel, also makes our work different from existing studies of purely electronic orbital correlations. In the case of reaction with allene, a disrotatory nonlinear cheletropic decomposition path may also be postulated (see Figure 3, dotted h e ) . We are applying the above
+
+
+(')
+ +(3) + ...
(A-1)
where the "zeroth" order is a linear combination of the three "degenerate" states: 3
CP =
C C k + k o = Cl+o[O(3Bi)+C30,(1~~)l +
k = l
C,+0[O(3Bz)+C30,(1zg+)1 + C3+o[O(3Az)+C30z(1Zg+)l (A-2) where the mixing coefficients C1> C2 > C3 in the ground state based on relative amount of repulsion (higher repulsion, smaller CJ, see Figures 1-3. Two higher energy excited states (2' 3') with correspondingly smaller coefficients ( C , C,) may also be included in 4, viz.
d=
C,,+O[ 0(3Bi)+(C302('Zg+)] +
0 ( 3 A i )+C302('2,+)] 64-3) The first-order corrections to wave functions are, for example
where Eo is the initial threefold degenerate energy, H(') is the perturbation interaction as the O(3P)approaches C302. The expressions in Table I serve to illustrate the successive perturbation mixing starting from the orbitally polarized 3B2state. Parallel to (4b) some abbreviation of orbitals in higher order wave functions is introduced. (20) R. G.Pearson, "SymmetryRules for Chemical Reactions",Wiley, New York, 1976, pp 371-2. (21) Y. N. Chiu, J. Chem. Phys., 58, 722 (1973); 64,2997 (1976). (22) A. Metropouloa and Y. N. Chiu, J. Chem. Phys., 68,5609 (1978); Chem. Phvs.. 47. 369 (1980).
(23) H.*E&ing, J. Walter', and G . F. Kimball, "Quantum Chemistry"; Wiley, New York, 1957, p 96.
