J. Phys. Chem. 1991, 95, 175-178
+ ePNH2+ + ePNH2+ + e-
PNH2+ TS1
115.1
TS2 122.4
'H
-
175
+H P N + H, P N + 2H
PNH
Conclusions A theoretical study of the possible products of the reaction of P+ with ammonia has been carried out. PNH+ (3A') is found to be the lowest lying triplet state on the (PNH)' surface. The isomer with a P-H bond, HPN+ (3A') was found to lie higher in energy, about 50 kcal/mol at correlated levels. In the case of the (H2NP)+ system, the PNH2+isomer was found to be the ground state, with trans-HPNH' and H2PN+ lying 44 and 93 kcal/mol, respectively, higher in energy at correlated levels. The stability order for the triplet (H3NP)+ system is PNH3+ > HPNH2+ > H2PNH+> H3PN. The PNH3+ ion-molecule complex lies more than 40 kcal/mol below HPNH2+ at correlated levels. The reaction P+ (3P) + NH3 ('Al) (HNP)' + H2 is endothermic for the production of both triplet PNH+ and HPN+. On the other hand, the process P+ ('P) + NH3 ('A,) (H2NP)+ H is exothermic for the production of PNH2+, whereas it is endothermic when HPNH+ or H2PN+ are formed. Therefore, only the formation of the most stable (H2NP)+ species, namely PNH2+,is thermodynamically favored. Furthermore, two different mechanisms for the production of PNH2+ that are barrier free have been found. The first proceeds through hydrogen abstraction from the PNH3+ ion-molecule complex, and the second involves isomerization of PNH3+ into HPNH2+ and subsequent hydrogen abstraction of the hydrogen atom bonded to phosphorus. Therefore, the reaction of P+ with ammonia is feasible under interstellar conditions, but only toward the production of PNH2+.
-
H
+
H Figure 4. Optimized geometries at the HF/6-31G** level for the relevant transition structures on the triplet (H3NP)+ potential energy surface.
barrier than bond breaking in PNH3+. A dynamical analysis should be carried out to ascertain which mechanism is favored. Therefore, reaction 2 is exothermic for the production of PNH2+ and also appears to be barrier free through two different mechanisms. Consequently, this reaction fulfills the basic requirements to be a plausible interstellar reaction and a source of phosphorus compounds in space. For instance, subsequent dissociative recombination reaction could lead to production of P N H or PN:
-
Acknowledgment. This research was partially supported by the Basque Country University (Euskal Herriko Unibertsitatea), Grant No. UPV/203.215-107/89.
Theoretical Studies of the Mechanism of the Alumination Reaction of Ethylene as a Ziegier-Natta-Type Reaction Model Shogo Sakai Department of Computer Science, Faculty of Engineering, Osaka Sangyo University, Daito 574, Japan (Received: March 22, 1990; In Final Form: July 2, 1990)
The reactions of ethylene + RA1R'2 (R = H, CH3; R' = H, CI) were treated by ab initio molecular orbital methods. A push-pull two-stage reaction mechanism via the transition state was shown by the LMO charge centroids analysis. The substituent effects per AI atom in the above reactions were also discussed.
I. Introduction The chemical reaction mechanisms with a metal catalyst have been a very active area for both experimental and theoretical studies. Especially, the Ziegler-Natta-type reaction is one of the important industrial reactions, and many experimental studies were reported.'*2 The reaction mechanisms of the Ziegler-Natta ( I ) Ziegler, K.; Holzkamp, E.;Breil, H.; Martin, H. Angew. Cfiem. 1955, 67, 541. Natta, T. Mucromol. Cfiem. 1955, 16, 213. Ivin, K. J.; Rooney, J. J.; Stewart, C. D. J . Cfiem. Soc., Cfiem. Commun. 1978, 604. Katz, T. J.; Lee, S. J. J . Am. Cfiem. Soc. 1980, 102,422. Uppal, J. S.; Johnson, D. E.; Staley, R. H. J . Am. Cfiem. SOC.1981, 103, 508. Soto, J.; Steigerwald, M. L.; Grubbs, R . H. J . Am. Cfiem. SOC.1982, 104, 4479. Clarke, T. C.; Yannoni, C. S. J . Am. Cfiem. SOC.1983, 105, 7787. Clawson, L.; Soto, J.; Buchwald, S. L.; Steigerwald, M.L.; Grubbs, R. H. J . Am. Cfiem. Soc. 1985, 107, 3377. Eisch, J. J.; Piotrowski. A. M.; Brownstein, S. K.; Gabe, E. J.; Lee, F. L. J . Am. Cfiem. SOC.1985, 107, 7219.
0022-3654/91/2095-0175$02.50/0
catalysis based on modern concepts of electronic structure and the ligand field theory were proposed by C o s ~ e eCossee' .~ s model identifies as active site an octahedrally coordinated transition metal, with the 3d orbitals hybridized with the a*-antibonding orbitals of the olefin as suggested by an orbital correlation diagram based on indirect experimental data. In theoretical studies, Cossee's model was treated with the semiempirical S C F MO (CNDO approximation) method by Armstrong and co-workers3 and by Novaro and c o - ~ o r k e r s . ~ Their results suggested that the Ziegler-Natta mechanism might be explained by a concerted motion of the olefin and the alkyl (2) Cossee, P. J . Catal. 1964, 3, 80. (3) Armstrong, D. R.;Perkins, P. G.; Stewart, J. J. P. J . Cfiem. SOC., Dalton Trans. 1972, 1972. (4) Novaro, 0.;Chow, S.; Magnouat, P. J . Catal. 1976, 41, 91.
0 1991 American Chemical Society
Sakai
176 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 TABLE I: Relative Energies for the Alumination of Ethylene from the Isolated Molecules (kcal/mol) complex transition state products AlHi + C2H4 HF/6-3 lG(d) -7.1 14.1 -21.3 MP3/6-31G(d) -10.7 5.1 -32.4 CHjAIH2 + CZH4 HF/6-31G(d) -6.4 31.9 -20.0 MP3/6-3 I G(d) -9.5 21.8 -24.5 HAIC12 C2H4 -9.0 16.4 -29.6 HF/6-3 IG(d) MP3/6-3 IG(d) -11.4 11.2 -35.0
121 6
+
group that would bring about a transition from octahedral coordination to a trigonal-bipyramidal coordination for the Ti atom. This view was also confirmed with the ab initio SCF M O method by Clementi and co-workers.' Balazs and Johnson6 demonstrated the reaction CH3TiCI4 C2H4 by using a SCF-Xa-SW M O method. Recently the interactions between C2H4 and CH3TiCI2+ and between CzH4 and HTiCI2+ were examined by using the ab initio MO method by Fujimoto and co-~orkers.~These systems were shown to resemble the electrophilic addition of BH3 to an olefin double bond via a four-centered transition state.8 The reaction mechanism is still unknown. The hydroalumination reaction is one of the simplest Ziegler-Natta-type reaction models. Okninski and Starowieyski9 studied the hydroalumination reaction of acetylene, AIH3 + HCCH, using the semiempirical C N D 0 / 2 molecular orbital method. The character of electron migration for the hydroalumination reaction was shown. In this paper we studied the polymerization reaction mechanism of the alumination of ethylene as the Ziegler-Natta-type reaction model. The following three reactions were studied: AlH3 + H2C=CH2 H2AICH2CH3 (1) H2AlCH3 + H2C=CH2 H2AlCHZCH2CH3 (2) C12AlCH2CH3 HAICl2 H2C=CH2 (3)
121.7 )=105.3
101.7
k36.0 /
15-1
COMPLEX-I
+
+
--
+
11. Methods
Ab initio molecular orbital calculations were carried out by using the G A U S S I A N ~and ~ ~ GAMEssI'programs. ~ The basis sets used were the split-valence 3-21G set*2and the split-valence plus d polarization 6-3 1G(d) set.]) All equilibrium and transition-state geometries were determined by using analytical energy gradient^'^ at the Hartree-Fock (HF) level with the 3-21G basis set. The stationary points were identified as the equilibrium or the saddle point by examining the calculated normal vibrational frequencies. The force constant matrix, and thereby the vibrational frequencies, was obtained with analytically calculated energy second derivatives. I s (5) Giunchi, G.; Clementi, E.; Ruiz-Vizcaya, M. E.; Novaro, 0. Chem. Phys. Lett. 1977, 49, 8. Novaro, 0.; Blaisten-Barojas, E.; Clementi, E.; Giunchi. G.; Ruiz-Vizcaya, M. E. J . Chem. Phys. 1978, 68, 2337. (6) Balazs. A. C.: Johnson. K. H. J . Chem. Phvs. 1982. 77. 3148. (7j Fujimoto, H . ; Yamasaki, T.; Mizutani, H.;'Koga, N. J:Am. Chem. SOC.1985, 107,6157. (8) Nagase, S.; Ray, N. K.; Morokuma, K. J . Am. Chem. SOC.1980,102, 4536. (9) Okninski, A.; Starowieyski, K. €3. J. Mol. Siruct. (THEOCHEM) 1986, 138, 249. (IO) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Ragavachari, K.; Whiteside, R. A.; Schlegel, H. 8.; Fluder, E. M.; Pople, J. A. GAUSSIANBZ, Carnegie-Mellon University, Pittsburgh, PA, 1983. ( I I ) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCCSofrware Catalog 1980, 1 . Program QGO1. Schmidt, M. W.; Boatz, J. A.; Buldridge, K. K.; Koseki. S.; Gordon, M. S.; Elbert, S. T.; Lam, B. T. QCPE 1987, I , 115. (12) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. SOC.1980, 102, 1980. Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. Ibid. 1982, 104, 2997. (13) Hariharan, P. C.; Pople. J. A.; Mol. Phys. 1974, 27, 209. Franc], M. M.; Pietro. W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M.S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (14) Komornicki, A.; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977, 45, 595. (15) Pople, J. A.; Binkley, J. S.; Seeger, R . In?.J . Quant. Chem. 1975, 9, 229. Pople, J. A.; Krishnan, R.; Schegel, H. B.; Binkley, J. S. Ibid. 1979, 513, 225.
PRODUCT [ - A
PRODUCT
1-0
Figure 1. Geometries of reactants, complex, transition state, and products of reaction 1 (bond lengths in angstrom, angles in degrees).
Additional calculations were performed, at the HF:optimized structures, with electron correlation (excluding inner shells) incorporated through the second- and third-order Maller-Plesset perturbation theoryI6 (MP2 and MP3) in order to obtain improved energy comparisons. Full geometry information in the form of Z-matrix style, the total energies, and the vibrational frequencies are available as supplementary material. A localized molecular orbital (LMO) centroids analysis of the reactions was carried out by following a method described elsewhere17in order to study the electronic reaction mechanism. The calculation of the localized orbitals was based on the Foster-Boys method,18 in which the sum over all the orbitals of the average interelectronic separation between the two electrons in a given orbital, 4:(p)Ir&~(u)), is minimized. This requirement maximizes the separation between the centroids Ri, R, of two different orbitals, where Ri = (4i(p)l+#Ji(p)) defines the position of the 4i orbital centroid. The location of the centroid, Ri, is used to represent the position of the electrons in the following discussion.
xi(
111. Results and Discussions I . AIH, H2C=CH2. The stationary point geometries for the reaction of AIH3 with ethylene are illustrated in Figure 1. The
+
relative energies of these geometries are listed in Table I. At the first process in the reaction of AlH, with ethylene, the addition complex was produced without a barrier. The complex is a weak adduct between ethylene and AlH,, with the C-C bond length in the complex only 0.013 A longer than that in the isolated ethylene. This weak bound arises from an electron-donative interaction from the A orbital of ethylene into the empty p orbital of aluminum. Thus this reaction was described by the two-step mechanism, as shown in eqs 4 and 5. first step AIH, + H2C=CH2 complex I (4) second step complex I H2AICH2CH3 (5) At the transition state in the second step, the C-A1 bond distance is only 8% longer than that in the product. The C-H* bond distance is longer by 60% than that in the product, and the AI-H* bond distance is only 7% longer than that in the complex, where H* denotes the active (reacting) hydrogen. Therefore, only the
-
+
(16) Mdler, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. Binkley, J. S.; Pople, J. A. Int. J . Quant. Chem. 1975, 9, 229. Pople, J. A,; Binkley, J. S.; Seeger, R. Ibid. 1976, SIO,1. Krishnan, R.; Pople, J. A. Ibid. 1978, 14,91. Krishnan, R.; Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1980, 72, 4244. (17) Sakai, S.; Morokuma, K. J. Phys. Chem. 1987,91, 3661. Sakai, S.; Deisz, J.; Gordon, M. S. J . Phys. Chem. 1989, 93, 1888. (18) Foster, J. M.; Boys, S . F. Reu. Mod. Phys. 1960, 32, 296, 300.
The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991 177
Alumination Reaction of Ethylene
H
tl-JH
H$4 -O H COMPLEX
I
1
H
-I
j h t H H/+
TS-l
PRODUCT I - A
Figure 2. Location of charge centroids of localized orbitals for the complex, transition state, and product of reaction 1 at the HF/3-21G level: t is location of one pair (a and 8) of electrons.
C-AI bond has been formed at the transition state. In other words, this insertion reaction in the second step looks like two-stage process reaction; the first stage is the formation of the new C-A1 bond before reaching the transition state, and the second is the formation of the new C-H* bond and the breaking of the old AI-H* bond. If C, symmetry was preserved in the reaction path, product I-A was produced. The force constant matrix of product I-A has two imaginary frequencies (57i cm-I and 232i cm-I). One (57i cm-I) corresponds to the rotation of AIH2 around the AI-C axis, while the other (2323 cm-I) corresponds to the rotation of the methyl group. Therefore, the reaction path from the transition state to the product does not preserve a C, symmetry. The real product is product I-B. The energies of product I-A and product I-B are predicted to be very close, with product I-B slightly lower (3 kcal/mol) at the HF/3-21G level. It has been d e m o n ~ t r a t e d ~that ' , ~ ~the LMO centroids analysis gives a simple and clear understanding of a chemical reaction mechanism. The charge centroids of the 3-21G LMOs at complex I, TS I, and product I-A were calculated in order to obtain a qualitative analysis of the reaction mechanisms. The core orbitals were not included in the LMO transformation. The centroids are shown in Figure 2. The largest motion of the centroids between the complex and the transition state is that of the a electrons of ethylene part. The centroid of a electrons in the complex locates at almost the same position as in the isolated ethylene. In the transition state, the charge centroid of a electrons moves into the new C-AI bond region, while the centroid of the AI-H* LMO moves a little bit from the AI-H* bond region into the direction of the C-H* new bond region. From the LMO centroids analysis, it is concluded that the reaction in the second step (reaction 5) proceeds by a push-pull two-stage reaction mechanism. The first stage is the breaking of the a bond to form the C-AI new bond, while the second is the AI-H* bond breaking with the C-H* bond formation. Namely, the first stage is the moving of the a electrons into the new C-AI bond region, which creates a model state (transition state), as shown below. The second stage is the migration of anion, +CH,
'705
COMPLEX
H-, to the cation part, CH2+. 2. H2AICH3 H2C=CH2. The stationary point geometries for reaction 2 are shown in Figure 3. In the complex, the C-C bond of the ethylene part and the AI-C* (methyl group) do not lie on the same plane, and the plane of the C-C (ethylene part) bond and AI atom is perpendicular to the plane of the AI-C* (methyl group) bond and the middle point of the C-C (ethylene part) bond, because of the steric hindrance of the methyl group of CH3AIH2. The reaction of CH,AIH, with ethylene was also described by the two-step mechanism, the same as reaction 1: the first step is the formation of the complex and the second is the process of product insertion. At the transition state, the new C-AI bond distance is only 3.6% longer than that in the product, while the new C-C bond distance is 40% longer than that in the product. The breaking C-AI bond
+
(19) Ha, T.; Nguyen, M.; Hendrickx, M.; Vanquickenbrne, L. G . Chem. Lett. 1983, 96, 261.
- II
T S - II H
\>
1.605 1205
108.7
6.l23.1
c)H1'092
1.993
PRODUCT I 1
Figure 3. Geometries of reactants, complex, transition state, and products of reaction 2. 3 H$+H
f
\
-- .CH*
transition-state model
Phys.
\
k COMPLEX -11
H
TS
-
I1
Figure 4. Location of charge centroids of localized orbitals for the com-
plex and transition state of reaction 2.
distance is 8% longer than that in the complex. These structural features for the process from the complex to the transition state are the same as those in reaction 1. Namely, the first stage in the second step is the formation of the new C-AI bond before the transition state is reached, and the second stage is the AI-C* (methyl group) bond breaking with new C-C bond formation. The real product is a trans type (product 11). The force constant matrix of the cis-type product (not shown here) has two imaginary frequencies (56i cm-I and 155i cm-I). The LMO charge centroids at the complex, complex 11, and the transition-state geometries, TS-11, are shown in Figure 4. From the centroids in the complex, complex 11, this interaction is an electron-donative interaction from the .rr orbital of ethylene into the empty p orbital of the AI atom. In the transition state, the centroid of ?r electrons moves into the new AI-C bond region. These features of the charge centroids are the same as those of
178 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
Sakai
1 CI
\
/
2.180
CI
T 5
-
COMPLEX - Ill T S - 111 Figure 6. Location of charge centroids of localized orbitals for the complex and transition state of reaction 3 .
Ill
C!
\
2.188
0 =57.9
122.2
c1
COMPLEX -111
PRODUCT
Ill
Figure 5. Geometries of reactants,complex, transition state, and products of reaction 3.
reaction I . This reaction in the second step also proceeds by the push-pull two-stage reaction mechanism. From Table I, the binding energy of the complex in reaction 2 is almost the same as that in reaction 1, while the activation energy barrier at the transition state is about 17 kcal/mol higher than that in reaction 1 at the MP3/6-31G(d) level. The binding energies of both complexes, complex I and complex 11, arise from only an electron-donative interaction from the P orbital of ethylene into the empty p orbital of the AI atom. On the other hand, the active hydrogen atom in reaction 1 does not have the orientation for the new bond formation; the hydrogen atom has only the s orbital, and the methyl group in reaction 2 has to orient in the direction of ethylene for the new C-C bond formation. The transition state is four-centered, and the steric hindrance of methyl group exerts an influence on the activation energy in reaction 2. The heat of reaction for reaction 2 is about 8 kcal/mol less exothermic than that for reaction 1. This energy difference arises from the lower bond energy of the C - C relative to the C-H bond. Because the dissociation energies for H2AI+-- -CH,- and H2AI+-- -H- are predicted to be very close (277.7 kcal/mol and 276.5 kcal/mol at MP3/6-31G(d) level). On theother hand, the bond energies of the C-H in CH4 and the C-C in C2H6are 99 kcal/mo120 and 83 kcal/mol,20 respectively. Reactions 1 and 2 are qualitatively consistent with the Evans-Polanyi rule,2' since the more exothermic the reaction, the lower the energy barrier. The results are also consistent with the Hammond postulation,22 since the transition state of reaction 1 is seen to be reached somewhat earlier than is that of reaction 2. 3. CI2AIH H2C=CH2. In order to study the substituent effects per the aluminum metal, we studied the reaction of ClzAIH with ethylene. The stationary point geometries in reaction 3 are shown in Figure 5. In complex 111, the interaction between the P orbital of ethylene and the vertical p orbital of the AI atom is stronger than that in complex I, leading to a shorter AI-M (the middle point of the C-C bond) bond distance in pmplex 111. This reason comes from the difference of the electronegativity between
+
(20) Cottrell, T. L. The Strengths of Chemical Bonds, 2nd ed.; Butterworths Scientific Publications: London, 1958. (21) Evans, M. G.; Polanyi, M. Trans. Faraday Soe. 1935, 31, 875. (22) Hammond, G.S.J . Am. Chem. Soc. 1955, 77, 334.
hydrogen and chlorine atoms. Therefore the substitution of a chlorine is a favorable factor for the first process of the two-stage mechanism, i.e., the new C-AI bond formation, on account of its greater electronegativity. In the transition state, the C-AI bond distance in TS I11 is shorter by 0.09 A than that in TS I, and the AI-H* bond distance in TS I11 is about 0.03 A shorter than that in TS I. The C-H* bond distance in TS 111 is about 0.02 A shorter than that in TS I. From the above facts, the second process of two-stage reaction mechanism in reaction 3 is later than that in reaction 1. The AI-H* bond in HAlC12 is stronger than that in H,AI, where the dissociation energies of H2AI+-- -H- and CI2A1+-- -H- are predicted to be 276.5 kcal/mol and 298.6 kcal/mol at the MP3/6-31G(d) level, respectively. The difference of the dissociation energies of the AI-H* bonds exerts an influence on the activation energies in reactions 1 and 3. Namely, it is considered that the activation energy relates strongly to the dissociation energy of the breaking bond, the AI-H*.
IV. Conclusion The aluminations of ethylene were studied by ab initio M O methods. The reactions are described by the two-step mechanism: the formation of the addition complex without a barrier and the production of the insertion product. The second step is more important than the first one for the reaction rate. The LMO centroids analysis showed that the second step in the reactions proceeds by the push-pull two-stage reaction mechanism. The first stage is the new C-AI bond formation with P bond breaking, and the second is the old AI-H or AI-C bond breaking and the new C-H or C-C bond formation. The bond energy of the old breaking bond, AI-H or AI-C, is closely related to the activation barrier. Namely, the greater the dissociation energy of AI-R, AI+ + R-, the greater is the activation barrier. The structure of the Ziegler-Natta catalysis model was as shown below.
From above results, it will be considered that the role of A1(CHJ2 in the above model weakens the Ti-CH3 bond and accelerates the reaction process. Acknowledgment. This research was supported by the Grant-in-Aid for Cooperative Research from the Ministry of Education of Japan, for which we express our gratitude. The numerical calculations were carried out at the Computer Center of the Institute for Molecular Science (IMS). Supplementary Material Available: Tables listing total energies, vibrational energies, and full geometry information (7 pages). Ordering information is available on any current masthead page.
