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Selection rules for catalysis in symmetry-forbidden reactions
Vo!ume 41, number 2
SELECTION RTcartio
CHEMICAL PHYSKS
RULES
FOR
CATALYSIS
15 July 1976
LETTERS
IN SYMMETRY-FORBIDDEN
REACTION§*
FERREXU
Departamento
de Fi&a,
Univenidade Federal de Pernambuco. Recife, Penzambuco.
Brasil
Received 19 March 1976
Selection rules for catalytic activity in symmetry-forbidden reactions are derived from perturbation theory. In the framework of the frontier orbital approximation the catalyst perturbation potential for bimolecular processes must contain the direct product of the representations of the HO&l0 of reagent Q and of the LUMO of reagent g_ In the case of unimolecular processes the catalyst perturbation potential must contain the direct product of the representations of (HO_MO),, (LUMO)P and Q, where Q is the distortion coordinate. In all cases the point group should be that of the transition state.
interpretations of chemical kinetics in terms of orbital symmetry considerations are now more than one-decade old [l-8]. That catalytic centers act as a perturbation on pertinent substrate orbitals was proposed by Mango [9], Caldow and MacGregor [lo], and more recently by Klopman [I I]. These ideas have been generalized by Houk and Strozier 1121, Fujimoto and Hoffmann [ 13 ] and especially by Imamura and Hirano [14] and Fukui and Inagaki [I 51, the main point being that catalysts act by a perturbation effect on the frontier orbit& of the reacting species. In this communication we formulate general selection rules for catalytic activity in symmetry-forbidden reactions. Of the many approaches to the problems of chemical activity in terms of orbital symmetry we choose to
consider changes in the orbit& as e whole [1,7&S]. These may be canonical molecular orbitals or symmetryequivalent bond orbitals [16] _The approach is based on the perturbation theory of chemica1 reactions, fiistly proposed by Dewar [17] and Fukui [IS] and later developed by Klopman and Hudson [5,6,19], Imamura [20], Salem (73, and Hoffmann [21]. We will use the frontier orbital approximation of Fukui 14,221, in which interest centers in the flow of electrons from the highest occupied molecular orbitals (HOMO’s) to the lowest unoccupied molecular orbitals (LUMO’s). The separation between these frontier orbitals and * Work supported in part by CNFq and BNDE (Brazilian Agencies).
370
other orbitals has been justified by Fukui and Fujimoto [23] _ Within these approximations the transition moment for a bimolecular reaction may be written as ($ 5%‘po),where #? is the interaction hamiltonian, kz represents the HOMO of one of the reactants and 2; represents the LIJMO of the other reactant. Also, if e is a bonding orbital then lf is an antibonding one, so that bonds are broken and new ones formed. The hamiltonian symmetric
5% always
representation
transforms
like the totally
of the point group of the transition state; hence a bimolecular reaction is symmetry-allowed ((kz & Z$ + 0) if the direct product rk; @ lY’@contains the identity or scaIar representation of the point group [S J . For unimolecular processes the transition moment is Uct (&?I/?@) lz ), where kz and 1: are the HOMO and the LUMO of the reacting species Q, and (&Y/&J) is the derivative of the potential energy with respect to the normal mode of vibration (distortion coordinate) Q. The derivative (aU/aQ) has the same transformation properties of Q. A unimolecular reaction will be symmetry-allowed (Xk! (&Y,,aQ) 1: > f 0) if the direct product I?,$ @ I’$ contains the representation of e [I .8] _ Catalytic effects may occur in processes which are not symmetry-forbidden in the absence of the catalyst. Thus, the Diels-Alder reaction of acrolein with a diene is a (4s f 2s) allowed reaction [2,24]_ Lewis acid catalysts such as the HC ion produces orbital mixing with considerable changes in the orbital energy levels
CHEMICAL PHYSICS LE’lXZRS
Volume 41, number 2
and in the electron densities of the various atoms, and these effects explain the increased reaction rates and regiosclectivity [ 12,14]_ The cycloaddition of ethyIene to give cyclobutane, on the other hand, is a (2~ + 2s) *
forbidden reaction [2,24] in the absence of a catalyst. In these cases, as discussed in the present note, the orbital mixing due to the catalyst must lead to changes in the symmetry of the frontier orbitals. Suppose then that for a bimolecular reaction in the absence of a catalyst the direct product rkg @ G does not contain the identity representation oft I?e pertinent point group, the reaction being therefore forbidden. In the presence of a catalyst kz (or $) may be expanded in the usual way. To first order:
where Pk, = (kt & ‘nE)/( &$g - &&)_ The transition moment for the perturbed system (reactants f catalyst) is: (2) This will be different from zero if G # 0 and, at the same time, there is at least one nz which transforms as Zf_ However, for Cgn to be different from zero the catalyst perturbation potential &must contain the representation of the product r,g @ I&. Since rtz must transform like Z$if the reaction is to be symmetry-allowed, we conclude that the catalyst perturbation potential must contain the representation of the direct product r(HOMO), @ I’ (LUMO$Consider now a unimolecular process for which the direct product l?,~ @ rQ @I l$ does not contain the identity representation of the pertinent point group, the process being therefore forbidden. In the presence of a catalyst the transition moment is: “‘p = @
+ ,lTk C, n:)
WPQ)
@,
(3)
where G = (kz &‘n~>/(&j& - &f!). Again, if C& is to differ from zero the perturbation hamiltonian @’ due to the catalyst must contain the representation of the direct product rko 09 I&. But the transition moment given by (3) WI-8 vanish unless there is at least one nz such that l?,$ @ I$ transforms like Q. We conclude that unimolecular processes wiil be symmetryallowed if the cata&st perturbation potential contains
15 July 1976
the representation of the direct product I’,$ ~3 Fe Cg reApplication of these rules depends on detailed information about the reaction path. Also, other factors besides orbital symmetry, such as the orbital energies, affect the feasibility of a catalytic pathway. The predictability of the rules per se may therefore be small. On the other hand, a mechanism which violates these rules should be considered with suspicion_ As an example, we may consider the cycloaddition of two ethylene molecules in the presence of certain d [S] complexes, which we will assume to be a concerted reaction * . Assuming a Ch symmetry for the process it is seen that the ethylene HOMO is an a1 orbital and the ethylene LUMO is a b, orbital. Since A, @ B1 =BI, the reaction is symmetry forbidden. However, the d,, orbital of a transition metal ion lying below the ethylene carbon atoms is also b L_This doubly occupied orbital will mix the LUMO with some aI character (BI @J 81 = Al) and the catalyzed reaction will be allowed, as proposed by Caldow and MacGregor [lo]. One specific difficulty in applying these rules is the choice of what constitutes the cata!yst potential. In their perturbation theory of catalysis Imamura and Hirano 1141 distinguish between a “static orbital mixing” and a “dynamic orbital mixing”. The two cases correspond rather closely with Klopman’s “charge controlled” and “frontier controlled” (uncatalyzed) processes [6], and represent only limiting situations. In the case of ‘-dynamic orbital mixing” the potential has the symmetry of the catalyst orbital, or orbitals, involved. If a monocentric interaction between substrate and catalyst is assumed, the “static orbital mixing” corresponds to assign to the perturbation potential the symmetry of the atomic orbital to which the catalytic species is bonded. In the cases of multicentric interactions, which may be important in enzymatic catalysis, the symmetry of the perturbation potential is that of the resulting electrostatic potential. Finally, in all cases the symmetry properties should always refer to the point group of the transition state.
* Recent data on similar oIefin methatesis reactions throw some doubts on the validity of this mechznism; see refs. 125-271. On the other hand, the thermal dimerization of 1,3_butadiene follows largely a concerted forbidden (4s+2a) path [28).
371
Volume 41 t numb& 2
CHEMICALPHYSICS LETrERS
References
111 R.F.W. Bader,Can. J. Chem. 40 (1962) 1164.~ PI R-B. Woodward and R. Hoffmarm, J. Am- Chem-SOL.
87 (1965) 395, a.1 1; R. Hoffmann and R.B. Woodward, J. Am. Chem. Sot. 87 (1965) 2046.4389. r31 H.C. Longuet-Higgins and E.W. Abrahamson, J. Am. Chem. Sot. 57 (1965) 2045. t41 K. Fukui, BuiI. Chem. Sot. Japan 39 (1966) 49% K. Fukui and h-. Fujimoto, Bull. Chem. Sot Japan 39 (1966) 2116. . G. Klopman and R.F. Hudson, Theoret. Chim. Arta 8 (1967) 165; R.F. Hudson and G. Klopman, Tetrahedron Letters (1967) 1103. PI G. Klopman, 3. Am. Chem. Sot. 90 (1968) 223. 171L. Salem, J. Am. Chem. Sot. 90 (1968) 543,553; A. Devaguet and L. Salem, J. Am_ Chem. Sot. 91(1969) 3793. R.G. Pearson, J. ATT. Chem. Sot. 91 (1969) 1252,4947;
Theoret. Chim. Acta 16 (1970) 107; J. Am. Chem. Sot. 94 (1972) 8287F.D. Mango and J.H. Schachschneider, J. Am. Chem. Sot. 89 (1967) 2484; 91<1969) 1030; F.D. Mango?Tetrahedron Letters (1969) 4813; (1971) SOS_
G.L. Caldow and R.A. MacGregor, Inorg. Nucl. Chem. Letters 6 (1969) 645; J. Chem. Sot. A (1971) 1654. [ 111 G. Klopman, ed. in: Reactivity and reaction paths (Wiley, New York, 1974) pp. 139, 161.
372
I5 July 1976
[12] KN. Houk and R.W.‘Strozier. J. Am. Chem- Sot. 95 (1973) 4094. [13] H. Fjimoto and R,Hoffmann, J. Phys. Chem. 78 (1974) 1874. 1141 A. I-mum and T. Hirano, J. Am. Cbem. Sot. 97 (1975) 4192. [ 151 K. Fukui and S. Inagaki, J. Am. Chem. Sot. 97 (197i)
4445. (161 H-B. Thompson, Inorg. Chem. 7 (1968) 604. [17] M.J.S. Dewar. J. Am. Chem. Sot. 74 (1952) 3341, et seq. [iSI K. Fukui. T. Yoneaawa and H. Shingu, J. Chem. Phys. 20 (1952) 722; 22 (1954) 1433; K. Fukui, Accounts Chem. Res 4 (1971) 57. [19] R.F. Hudson, Angew. Chem. Intern. Ed. 12 (1973) 36. [20] A. Imamura, Mol. Phys. 15 (1968) 225. [21] L. Libit and R. Hoffmann, J. Am. Chem- Sot. 96 (1974) 1370; H. Fujimoto and R. Hoffmann, J. Phys. Chem. 78 (1974) 1167.
WI
K. Fukui, Theory of orientation and s?ereoselection
(Springer, Berlin, 1970); Accounts Chem. Res. 4 (1971) 57. [231 K. Fukui and H. Fujimoto, Bull. Chem. Sot Japan 41 (1968) 1989. [241 ND_ Epiotis, J. Am. Chem. Sot. 94 (1972) 1924. 75. [251 R.C. Pearson, Topics Current Chem. 41(1973) 1261 T.J. Katz and J. McGinnis, J. Am. Chem. Sot. 97 (1975) 1592. 1271 R.H. Grubbs, P-L. Burk and D.D. Carr, J. Am. Chem. Sot. 97 (1975) 3265. 1281 L.M. Stephenson, R.V. Gemmer and S. Current, J. Am. Chem. Sot. 97 (1975) 5909.
SELECTION RTcartio
CHEMICAL PHYSKS
RULES
FOR
CATALYSIS
15 July 1976
LETTERS
IN SYMMETRY-FORBIDDEN
REACTION§*
FERREXU
Departamento
de Fi&a,
Univenidade Federal de Pernambuco. Recife, Penzambuco.
Brasil
Received 19 March 1976
Selection rules for catalytic activity in symmetry-forbidden reactions are derived from perturbation theory. In the framework of the frontier orbital approximation the catalyst perturbation potential for bimolecular processes must contain the direct product of the representations of the HO&l0 of reagent Q and of the LUMO of reagent g_ In the case of unimolecular processes the catalyst perturbation potential must contain the direct product of the representations of (HO_MO),, (LUMO)P and Q, where Q is the distortion coordinate. In all cases the point group should be that of the transition state.
interpretations of chemical kinetics in terms of orbital symmetry considerations are now more than one-decade old [l-8]. That catalytic centers act as a perturbation on pertinent substrate orbitals was proposed by Mango [9], Caldow and MacGregor [lo], and more recently by Klopman [I I]. These ideas have been generalized by Houk and Strozier 1121, Fujimoto and Hoffmann [ 13 ] and especially by Imamura and Hirano [14] and Fukui and Inagaki [I 51, the main point being that catalysts act by a perturbation effect on the frontier orbit& of the reacting species. In this communication we formulate general selection rules for catalytic activity in symmetry-forbidden reactions. Of the many approaches to the problems of chemical activity in terms of orbital symmetry we choose to
consider changes in the orbit& as e whole [1,7&S]. These may be canonical molecular orbitals or symmetryequivalent bond orbitals [16] _The approach is based on the perturbation theory of chemica1 reactions, fiistly proposed by Dewar [17] and Fukui [IS] and later developed by Klopman and Hudson [5,6,19], Imamura [20], Salem (73, and Hoffmann [21]. We will use the frontier orbital approximation of Fukui 14,221, in which interest centers in the flow of electrons from the highest occupied molecular orbitals (HOMO’s) to the lowest unoccupied molecular orbitals (LUMO’s). The separation between these frontier orbitals and * Work supported in part by CNFq and BNDE (Brazilian Agencies).
370
other orbitals has been justified by Fukui and Fujimoto [23] _ Within these approximations the transition moment for a bimolecular reaction may be written as ($ 5%‘po),where #? is the interaction hamiltonian, kz represents the HOMO of one of the reactants and 2; represents the LIJMO of the other reactant. Also, if e is a bonding orbital then lf is an antibonding one, so that bonds are broken and new ones formed. The hamiltonian symmetric
5% always
representation
transforms
like the totally
of the point group of the transition state; hence a bimolecular reaction is symmetry-allowed ((kz & Z$ + 0) if the direct product rk; @ lY’@contains the identity or scaIar representation of the point group [S J . For unimolecular processes the transition moment is Uct (&?I/?@) lz ), where kz and 1: are the HOMO and the LUMO of the reacting species Q, and (&Y/&J) is the derivative of the potential energy with respect to the normal mode of vibration (distortion coordinate) Q. The derivative (aU/aQ) has the same transformation properties of Q. A unimolecular reaction will be symmetry-allowed (Xk! (&Y,,aQ) 1: > f 0) if the direct product I?,$ @ I’$ contains the representation of e [I .8] _ Catalytic effects may occur in processes which are not symmetry-forbidden in the absence of the catalyst. Thus, the Diels-Alder reaction of acrolein with a diene is a (4s f 2s) allowed reaction [2,24]_ Lewis acid catalysts such as the HC ion produces orbital mixing with considerable changes in the orbital energy levels
CHEMICAL PHYSICS LE’lXZRS
Volume 41, number 2
and in the electron densities of the various atoms, and these effects explain the increased reaction rates and regiosclectivity [ 12,14]_ The cycloaddition of ethyIene to give cyclobutane, on the other hand, is a (2~ + 2s) *
forbidden reaction [2,24] in the absence of a catalyst. In these cases, as discussed in the present note, the orbital mixing due to the catalyst must lead to changes in the symmetry of the frontier orbitals. Suppose then that for a bimolecular reaction in the absence of a catalyst the direct product rkg @ G does not contain the identity representation oft I?e pertinent point group, the reaction being therefore forbidden. In the presence of a catalyst kz (or $) may be expanded in the usual way. To first order:
where Pk, = (kt & ‘nE)/( &$g - &&)_ The transition moment for the perturbed system (reactants f catalyst) is: (2) This will be different from zero if G # 0 and, at the same time, there is at least one nz which transforms as Zf_ However, for Cgn to be different from zero the catalyst perturbation potential &must contain the representation of the product r,g @ I&. Since rtz must transform like Z$if the reaction is to be symmetry-allowed, we conclude that the catalyst perturbation potential must contain the representation of the direct product r(HOMO), @ I’ (LUMO$Consider now a unimolecular process for which the direct product l?,~ @ rQ @I l$ does not contain the identity representation of the pertinent point group, the process being therefore forbidden. In the presence of a catalyst the transition moment is: “‘p = @
+ ,lTk C, n:)
WPQ)
@,
(3)
where G = (kz &‘n~>/(&j& - &f!). Again, if C& is to differ from zero the perturbation hamiltonian @’ due to the catalyst must contain the representation of the direct product rko 09 I&. But the transition moment given by (3) WI-8 vanish unless there is at least one nz such that l?,$ @ I$ transforms like Q. We conclude that unimolecular processes wiil be symmetryallowed if the cata&st perturbation potential contains
15 July 1976
the representation of the direct product I’,$ ~3 Fe Cg reApplication of these rules depends on detailed information about the reaction path. Also, other factors besides orbital symmetry, such as the orbital energies, affect the feasibility of a catalytic pathway. The predictability of the rules per se may therefore be small. On the other hand, a mechanism which violates these rules should be considered with suspicion_ As an example, we may consider the cycloaddition of two ethylene molecules in the presence of certain d [S] complexes, which we will assume to be a concerted reaction * . Assuming a Ch symmetry for the process it is seen that the ethylene HOMO is an a1 orbital and the ethylene LUMO is a b, orbital. Since A, @ B1 =BI, the reaction is symmetry forbidden. However, the d,, orbital of a transition metal ion lying below the ethylene carbon atoms is also b L_This doubly occupied orbital will mix the LUMO with some aI character (BI @J 81 = Al) and the catalyzed reaction will be allowed, as proposed by Caldow and MacGregor [lo]. One specific difficulty in applying these rules is the choice of what constitutes the cata!yst potential. In their perturbation theory of catalysis Imamura and Hirano 1141 distinguish between a “static orbital mixing” and a “dynamic orbital mixing”. The two cases correspond rather closely with Klopman’s “charge controlled” and “frontier controlled” (uncatalyzed) processes [6], and represent only limiting situations. In the case of ‘-dynamic orbital mixing” the potential has the symmetry of the catalyst orbital, or orbitals, involved. If a monocentric interaction between substrate and catalyst is assumed, the “static orbital mixing” corresponds to assign to the perturbation potential the symmetry of the atomic orbital to which the catalytic species is bonded. In the cases of multicentric interactions, which may be important in enzymatic catalysis, the symmetry of the perturbation potential is that of the resulting electrostatic potential. Finally, in all cases the symmetry properties should always refer to the point group of the transition state.
* Recent data on similar oIefin methatesis reactions throw some doubts on the validity of this mechznism; see refs. 125-271. On the other hand, the thermal dimerization of 1,3_butadiene follows largely a concerted forbidden (4s+2a) path [28).
371
Volume 41 t numb& 2
CHEMICALPHYSICS LETrERS
References
111 R.F.W. Bader,Can. J. Chem. 40 (1962) 1164.~ PI R-B. Woodward and R. Hoffmarm, J. Am- Chem-SOL.
87 (1965) 395, a.1 1; R. Hoffmann and R.B. Woodward, J. Am. Chem. Sot. 87 (1965) 2046.4389. r31 H.C. Longuet-Higgins and E.W. Abrahamson, J. Am. Chem. Sot. 57 (1965) 2045. t41 K. Fukui, BuiI. Chem. Sot. Japan 39 (1966) 49% K. Fukui and h-. Fujimoto, Bull. Chem. Sot Japan 39 (1966) 2116. . G. Klopman and R.F. Hudson, Theoret. Chim. Arta 8 (1967) 165; R.F. Hudson and G. Klopman, Tetrahedron Letters (1967) 1103. PI G. Klopman, 3. Am. Chem. Sot. 90 (1968) 223. 171L. Salem, J. Am. Chem. Sot. 90 (1968) 543,553; A. Devaguet and L. Salem, J. Am_ Chem. Sot. 91(1969) 3793. R.G. Pearson, J. ATT. Chem. Sot. 91 (1969) 1252,4947;
Theoret. Chim. Acta 16 (1970) 107; J. Am. Chem. Sot. 94 (1972) 8287F.D. Mango and J.H. Schachschneider, J. Am. Chem. Sot. 89 (1967) 2484; 91<1969) 1030; F.D. Mango?Tetrahedron Letters (1969) 4813; (1971) SOS_
G.L. Caldow and R.A. MacGregor, Inorg. Nucl. Chem. Letters 6 (1969) 645; J. Chem. Sot. A (1971) 1654. [ 111 G. Klopman, ed. in: Reactivity and reaction paths (Wiley, New York, 1974) pp. 139, 161.
372
I5 July 1976
[12] KN. Houk and R.W.‘Strozier. J. Am. Chem- Sot. 95 (1973) 4094. [13] H. Fjimoto and R,Hoffmann, J. Phys. Chem. 78 (1974) 1874. 1141 A. I-mum and T. Hirano, J. Am. Cbem. Sot. 97 (1975) 4192. [ 151 K. Fukui and S. Inagaki, J. Am. Chem. Sot. 97 (197i)
4445. (161 H-B. Thompson, Inorg. Chem. 7 (1968) 604. [17] M.J.S. Dewar. J. Am. Chem. Sot. 74 (1952) 3341, et seq. [iSI K. Fukui. T. Yoneaawa and H. Shingu, J. Chem. Phys. 20 (1952) 722; 22 (1954) 1433; K. Fukui, Accounts Chem. Res 4 (1971) 57. [19] R.F. Hudson, Angew. Chem. Intern. Ed. 12 (1973) 36. [20] A. Imamura, Mol. Phys. 15 (1968) 225. [21] L. Libit and R. Hoffmann, J. Am. Chem- Sot. 96 (1974) 1370; H. Fujimoto and R. Hoffmann, J. Phys. Chem. 78 (1974) 1167.
WI
K. Fukui, Theory of orientation and s?ereoselection
(Springer, Berlin, 1970); Accounts Chem. Res. 4 (1971) 57. [231 K. Fukui and H. Fujimoto, Bull. Chem. Sot Japan 41 (1968) 1989. [241 ND_ Epiotis, J. Am. Chem. Sot. 94 (1972) 1924. 75. [251 R.C. Pearson, Topics Current Chem. 41(1973) 1261 T.J. Katz and J. McGinnis, J. Am. Chem. Sot. 97 (1975) 1592. 1271 R.H. Grubbs, P-L. Burk and D.D. Carr, J. Am. Chem. Sot. 97 (1975) 3265. 1281 L.M. Stephenson, R.V. Gemmer and S. Current, J. Am. Chem. Sot. 97 (1975) 5909.