1888
J . Phys. Chem. 1989, 93, 1888-1893
than the methyl isocyanide reaction. Hence, like ethyl isocyanide, DTBP should suppress the acetonitrile yield and raise P3. Only because, in the course of the reaction, DTBP produces methyl radicals does it enhance the acetonitrile yield and lower Py, This lowering of P3 is significant with only 0.7 Torr of DTBP lowering the threshold by 2 Torr.
Summary The effect of nonpolar bath gases on the methyl isocyanide isomerization is to decrease the yield of acetonitrile in the subthreshold region and to increase P3. It is found that the greater the partial pressure of a particular bath gas, the lower the yield. Results also indicate that the degree of suppression of the acetonitrile yield is related to the heat capacity of the addend and to the vibrational modes in the addend. These findings support the conclusion that rotational hole-filling is not significant in the reaction. It is also found that addition of polar addends fits the same general description as the nonpolar addends. The two reactive
addends, however, show different effects. Ethyl isocyanide shows an enhanced suppression of the acetonitrile yield due to its moderation of the radical reaction channel. Addition of DTBP, on the other hand, increases the acetonitrile yield and lowers P3 by introducing methyl radicals into the system, thus enhancing the radical channel. In conclusion, the primary effect of methyl isocyanide-addend collisions is to redistribute the energy and deactivate the methyl isocyanide.
Acknowledgment. Acknowledgment for partial support of this work is made to the National Science Foundation (Grant No. R11-8503811, M.J.S. and L.M.Y.) and to the Research Corp. M.J.S. acknowledges helpful discussions with Dr. David Crosley of the Stanford Research Institute and Professor Elizabeth J. Rock of Wellesley College. We also thank Susan Berets and Wei Jian for helpful discussions during preparation of the manuscript. Registry No. DTBP, 110-05-4; methyl isocyanide, 593-75-9;ethyl isocyanide, 624-79-3.
Theoretical Studies of the Insertion Reactions of Atomic Carbon and Silicon into Methane and Silane Shogo Sakai,? John Deisz, and Mark S. Gordon* Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105 (Received: March 11, 1988; In Final Form: August 8, 1988)
The mechanisms for the insertions of atomic (ID and 3P) carbon and silicon into the C-H and Si-H bonds of methane and silane are investigated by ab initio SCF methods, many body perturbation theory, and a localized molecular orbital (LMO) analysis. The LMO analysis shows that the insertion of 'D atoms into CH4 and SiH4 may be classified into two types: cationic hydrogen transfer and anionic hydrogen transfer. For the triplet atoms the LMO analysis suggests two different insertion reaction mechanisms: the near abstraction and the pull-push mechanisms.
I. Introduction The chemical reaction mechanisms for the reactions of atoms are a very active area for both experimental and theoretical investigations. For example, experimental studies of the reaction of atomic carbon with molecular hydrogen have shown the reaction to be very fast,' while ground-state 3P carbon is essentially unreactive' with CH,. It is known that atomic carbon reacts with saturated substrates through two primary mechanisms:* insertion and hydrogen abstraction. The first theoretical study of the reaction of atomic carbon with molecular hydrogen was reported by Blint and N e ~ t o n . They ~ found that the insertion of ID carbon follows a perpendicular (C,) minimum energy path with no energy barrier. For 3P carbon, formally a thermally forbidden process, there are two surfaces relevant to this reaction in the C, approach: The 3A2surface is lower in energy at large C-H2 separations, while the 3B1surface leads to the ground state of C H 2 with a large (91.7 kcal/mol) energy barrier. There is an avoided intersection of the 3A2and 3B, surfaces along the reaction path in C, symmetry. The reaction mechanism for the insertion of 'D carbon into molecular hydrogen may be understood by considering the interaction of the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO) for the atom and molecule, that is, in terms of a four-orbital, four-electron interaction. In this sense, the reaction mechanism is similar to that of the singlet carbene insertion into molecular hydr~gen."'~ In the case of the reaction of atomic carbon with methane, the simplest saturated hydro-
'Present address:
Osakagakuin University, Kishibe, Suita 564, Japan.
0022-3654/89/2093-1888$01.50/0
carbon, the symmetry is reduced to C,. Whereas the least motion C(3P) H2 insertion reaction is symmetry forbidden, the C(3P) + CH4 insertion is formally allowed. Here again, the reaction C CH, can be compared to the analogous carbene insertion reaction. Also, the reactions of atomic carbon with silane, and of atomic silicon with methane and silane, are of interest in order to study the differences between carbon and silicon reactivity. In this paper, we study the insertion reaction mechanisms for the following eight reactions:
+
+
+ CH4 C('D) + SiH4 Si('D) + CH, C('D)
Si('D)
+ SiH4
-
'HCCH3
(1)
'HCSiH3
(2)
'HSiCH,
(3)
'HSiSiH3
(4)
( 1 ) Braun, W.; Bass, A. M.; Davis, D. D.; Simmons, J. D. Proc. R. SOC. London A 1969, 312, 417. Husain, D.; Kirsch, L. J. Trans. Faraday SOC. 1971, 67, 2025. Husain, D.; Young, A. N. J. Chem. Soc., Faraday Trans. 2 1975, 71, 525. (2) Skell, P. S.; Havel, J. J.; McGlinchey, M. J. Acc. Chem. Res. 1973, 6 , 97. ( 3 ) Blint, R. J.; Newton, M. D. Chem. Phys. Lett. 1975, 32, 178. (4) Gordon, M . S . ; Gano, D. R. J . Am. Chem. Soc. 1984, 106, 5421. (5) Dobson, R. C.; Hayes, D. M.; Hoffmann, R. J. Am. Chem. SOC.1971, 93, 6188. (6) Kollman, H. Tetrahedron 1972, 28, 5893. (7) Bauschlicher, C. W.; Haber, K.; Schaeffer, H. F., 111; Bender, C. F. J. Am. Chem. SOC.1977, 99, 3610. (8) Kollmar, H. J . Am. Chem. SOC.1978, 100, 2660. (9) Kollmar, H.; Staemmler, V. Theor. Chim. Acta 1979, 51, 207. (IO) Jeziorek, D.; Zurawski, B. Int. J. Quantum Chem. 1979, 61, 277.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1889
Insertion Reactions C(3P)
+ CH4
C(3P) + SiH4
-
+ CH4 Si(3P) + SiH4 Si(3P)
+
+
+
3HCCH3
(5)
3HCSiH3
(6)
3HSiCH3
(7)
3HSiSiH3
(8)
TRANSITION STATE
PRODUCT
1.083"
11. Theoretical Approach C1 Ab initio calculations were carried out by use of the / 1.488 I G A U S S I A N S ~ "and GAMESS'~programs. The geometries were optimized by the use of analytically calculated energy gradients with restricted Hartree-Fock (RHF) and unrestricted HartreeFock (UHF) wave functions for closed and open shell systems, 1.932 respectively. Geometry optimizations and transition-state searches 1.478 n were performed with the split valence 3-21G13and the split valence plus d polarization 6-31G(d) basis sets,I4 using the Schlegel alCa gorithm.I5 The 6-3 1G(d) vibrational frequencies were obtained n from analytical second derivative procedures, and zero point vi11.088 brational energy corrections were obtained at this level. The complex R H F (CHF) method16 was used to describe 'D atoms. In order to obtain improved energy comparisons, additional calculations were performed at the HF-optimized structures with electron correlation incorporated through many body perturbation theory," with the 6-3 lG(d,p) basis set. The Moller-Plesset method through full fourth order (denoted MP4) was incorporated, excluding inner shells. Such single point energies are denoted cs MP4/6-3 lG(d,p)//SCF/6-3 1G(d). To interpret the results, a localized molecular orbital (LMO) analysis of the reactions was carried out following a method described elsewhere.l* The calculation of the localized orbitals was based on the Foster-Boys method,I9 in which the sum over all the orbitals of the average interelectronic separation between the two electrons in a given orbital, xi(+?(p)rFv+;(v)), is minimized. This requirement maximizes the separation between the CS C1 centroids R , Rj of two different orbitals, where Ri = ( + i ( p ) l ~ ~ i ( p ) ) Figure 1. Transition state and product geometries for the reactions 1-4. defines the position of the +iorbital centroid. The location of the Bond lengths are in & . and angles in degrees. The point group is indicated centroid, Ri, is used to represent the position of the electrons in below each structure. the following discussion. For the open shell U H F calculation, the Here, EMUIPZ(ID) is the complex MP2 energy of the ID atom, RMPn LMO's are determined independently for a and fl electrons. is the energy of the IS state of the atom within the R H F formalism, 111. Reactions of C(lD) and Si('D) with CH4 and SiH4 and UMPn is the open shell singlet energy of the atom within the (real) U H F formalism. This assumption, that the improvement Here we present a theoretical study of the insertion reactions in the 'D energy from second to fourth order may be estimated of C(ID) and Si('D) with CHI and SiH,. The 6-31G(d) structures by averaging the analogous improvements for the real closed and are displayed in Figure 1, and the MP4/6-3lG(d,p)//6-31G(d) open shell singlets, may be tested with the 6-31G(d) basis by activation energies and heats of reaction are listed in Table I. The replacing MP4 by MP2 and MP2 by S C F in eq 1. Then, the MP2 Moller-Plesset method based on C H F wave functions for ID atoms ('D) - S C F (ID) energy difference for carbon is estimated to be can be obtained only at the MP2 level with the current version -0.05795 using eq 1, as compared with -0.05851 by direct of G A U ~ I A N B Therefore, ~. the total MP4 energies for the 'D atoms calculation. The corresponding values for silicon are -0.042 91 were calculated from the following equation: and -0.046 97. It is expected that the absolute errors will be much smaller on going from MP2 to MP4, probably less than 1 EMPl(lD) = kcal/mol. All total energies used in this paper are listed in the E ~ p 2 ( l D ) 0.5[RMP4 - RMP2 UMP4 - UMP21 (9) Appendix. The force constant matrices for all cis saddle-point geometries (11) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Ragavachari, K.; have two negative eigenvalues, so these structures are not true Whiteside, R. A,; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIANBZ; transition states. One of the negative eigenvalues is a high-freCarnegie-Mellon University: Pittsburgh, PA, 1983. quency vibration in the C, symmetry plane and may result from (1 2) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCC Sofware Catalog the repulsion between the occupied p-type orbital of the A atom 1980, 1 , Program QGO1; Schmidt, M. W.; Boatz, J. A,; Baldridge, K. K.; Koseki, S.; Gordon, M. S.; Elbert, S. T.; Lam, B. Quantum Chemistry Proand the occupied X-H u bond of the XH4 molecule. The other gram Exchange Bull. 1987, 7, 115. imaginary frequency corresponds to the internal rotation motion. (13) Binkley, J. S.; Pople, J. A,; Hfehre, W. J. J . Am. Chem. SOC.1980, The force constant matrices for the trans saddle point geometries, 102, 1980. Gordon, M. S.;Binkley, J. S.; Pople, J. A,; Pietro, W. J.; Hehre, on the other hand, have just one negative eigenvalue, as expected W. J. J . Am. Chem. SOC.1982, 104, 2997. for transition states. It is verified that these transition states are (14) Hariharan, P. C.; Pople, J. A. Mol. Phys. 1974, 27, 209. Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. related to A XH4 and A H + XH3 by following the instrinsic J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. reation coordinate20 (IRC) from the transition state to reactants (15) Schlegel, H. B. J . Comput. Chem. 1982, 3, 214. and products. (16) Seeger, R.; Pople, J. A. J . Chem. Phys. 1977, 66, 3045. (17) Moller, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. Binkley, J. S.; In order to check the accuracy of the H F calculation for the Pople, J. A. I n f . J . Quantum Chem. 1975, 9, 229. Pople, J. A,; Binkley, J. singlet states, the energies of the insertion transition states and
i
i
+
+
+
S.; Seeger, R. I n f . J . Quantum Chem. 1976, SlO, 1 . Krishnan, R.; Pople, J. A. Inr. J . Quantum Chem. 1978, 14, 91. Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. (18) Sakai, S.; Morokuma, K. J . Phys. Chem. 1987, 91, 3661. (19) Foster, J. M.; Boys, S. F. Rev. Mod. Phys. 1960, 32, 296, 300.
(20) Fukui, K. J . Phys. Chem. 1970, 74, 4161. Ishida, K.; Morokuma, K.; Komornicki, A. J . Chem. Phys. 1977, 66, 2153. Schmidt, M. W.; Gordon, M. S.; Dupuis, M. J . Am. Chem. SOC.1985, 107, 2585.
1890 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Sakai et al.
H
H
the products with optimized geometries at the HF/6-31G(d) level were calculated with CHF/6-3 1G(d) wave functions. The differences in the total energies for the C H F vs R H F wave functions are listed in Table 11. The corresponding differences for ID carbon and silicon are 18.3 and 12.2 kcal/mol, respectively. Of course, the H F calculation for the 'D atom is not meaningful. The Si-CH4 transition state has the smallest CHF-RHF energy difference, because this is the latest of the four transition states and therefore the furthest removed from the A(ID) species. Note that the activation energies calculated at the MP4/6-31G(d,p)//HF/6-3 1G(d) and MP2/CHF/6-3 lG(d)//6-3 1G(d) levels (Table I) are similar to each other. Both sets of calculations suggest that the activation energy for the Si SiH, reaction is nearly zero, Next we compare our results with recent studies2I of the insertion reactions of methylene and silylene into methane and silane. The energetics for the latter reactions are listed in Table 111. The heats of reaction AHo for Si + CH4 and Si + SiH, are almost the same as those for SiH, + CH, and SiH, + SiH,, respectively. On the other hand, the AHo for C + CHI and C + SiH, are about 30-40 kcal/mol less exothermic than those for the CH, + CH, aqd CH, + SiH, reactions. These energy differences arise from es of the product carbenes relative to the silylenes. [he largest activation energy in Table I11 is that for the insertion of SiH2 into CH4. Likewise, the largest activation energy found in the current work (Table I) is for the insertion of Si into CH4. It has been that the LMO centroids analysis gives a simple and clear understanding of a chemical reaction mechanism. In order to obtain a qualitative analysis of the singlet insertion reaction mechanisms, the centroids of the 3-21G L M O s at the transition-state geometries were calculated. The core orbitals were not included in the LMO transformation. The centroids are shown in Figure 2, where H * and H denote the active (reacting) and inactive hydrogens, respectively. In the figure, the centroids of the LMO's for the X-H orbitals are omitted. The centroid of the C-H* LMO in TS1 and TS3 (attack on methane) is almost midway between C and H*, while the centroid of the Si-H* LMO in TS2 and TS4 (attack on silane) localizes much closer to the hydrogen. The vacant orbital of the A atom (dotted line) orients in the direction of the X-H* centroids. Thus, these reaction mechanisms may be understood in terms of HOMOLUMO interactions. The corresponding four reaction paths may be studied at the 3-2 IG level by determining the intrinsic reaction coordinate20 (IRC) and calculating the LMO centroids along the reaction paths. The latter are illustrated for reactions 1 and 2 in Figure 3. In the C + H*-CH3 reaction, the centroid of the breaking C-H* bond moves into the C-C bond area along the reaction path, and one lone pair of the C atom moves into the forming H*-C bond region. The reaction mechanism for Si + H*-CH3 (not shown) H*-CH3. For the C H*-SiH3 is similar to that for C reaction, the centroid of the breaking Si-H* bond moves into the forming C-H* bond region along the reaction path, and a lone pair of the C atom moves into the C-Si bond region. Thus, the active hydrogen in reactions 1 and 3 (insertion into methane) behaves as if the transfer was cationic, since the electron pair is left behind in the course of the IRC. On the other hand, reactions 2 and 4 (insertion into silane) behave as if they are anionic hydrogen transfers since the electron pair remains with H*. The difference in these reaction mechanisms comes from the polarization of the breaking C-H* and Si-H* bonds.
TS3
TS4
Figure 2. Location of charge centroids of localized orbitals for transition states of reaction 1-4 at the HF/3-21G level. Double-headed arrows are locations of one pair (a and p) of electrons. I4
+
+
+
(21) Gordon, M. S.; Truong, T. N.; Bonderson, E. K. J . Am. Chem. SOC. 1986, 108, 1421. Gordon, M. S.; Truong, T. N. Chem. Phys. Left., in press. (22) Ha, T.; Nguyen, M.; Hendrickx, M.; Vanquickenborne,L. G. Chem. Phys. Lett. 1983, 96, 261.
lS
I
I
t
t
Figure 3. Location of charge centroids of localized orbitals along the reaction paths of reactions 1 and 2.
As shown in a previous paper,23 there is only a qualitative correspondence between the Mulliken population analysis and this charge centroid analysis. The Mulliken population analysis deals with the total electron density on an atom, and the charge centroid analysis examines the location of electrons localized in the vicinity of reaction center. For example, the Mulliken population on the active hydrogen during reaction 1 changes from 0.80 (methane) (23) Kahn, S. D.; Hehre, W. J.; Rondan, N. G.; Houk, K. N. J . Am. Chem. SOC.1985,107, 8291. These authors have examined the charge on a migrating hydrogen in 1,5-sigmatropic shifts by obtaining electron density
surfaces and fitting them to nuclear-centered spheres. This approach should give results that are similar to ours.
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1891
Insertion Reactions
+
+
+ +
1.204 (11.1) 2.078 (40.0) 1.358 (23.9)
1.503 (1.5) 2.840 (49.8) 1.932 (77.1)
1.375 (26.9) 2.281 (19.1) 1.599 (5.3)
TABLE I: Bond Lengths, Activation Energies ( E , ) , and Enthalpy Differences (AH,) for the Reaction A(’D) XH4 (3) Si CHI (2) C SiH, (1) C CH4
R1W-X) RdX-A) R3W-A)
E , (Activation Energy: Includes Zero-Point Energy Differences) 32.0 18.3 33.3 23.5 14.6 33.0 29.9 18.2 31.7 MP2/CHF/6-31G(d)//HF/6-31G(d) 6.8 8.8 14.1 MP4/6-3 1G(d,p)//HF/6-3 1G(d) 8.6 7.3 14.0
HF/6-3 lG(d)//HF/6-3 1G(d) CHF/6-3 1G(d)//HF/6-3 1G(d) HF/6-3 lG(d,p)//HF/6-31G(d)
-
XHAH“*b (4) Si + SiH,
1.523 (2.9) 3.130 (29.9) 2.020 (33.2) 11.6 2.8 11.3 -1.9 2.4
AHo (Heat of Reaction: Includes Zero-Point Energy Differences) -67.0 -6.5.7 -40.3 HF/6-31G(d)//HF/6-31G(d) -67.3 -66.3 -40.3 HF/6-3 1G(d,p)//HF/6-3 1G(d) -84.2 -83.3 49.0 MP4/6-3 1G(d,p)//HF/6-3 1G(d)
-42.1 -42.1 -52.8
“Bond lengths are given in A. Values in parentheses are the percent increases in bond lengths at the transition state, relative to reactants (HX) or products (XA, HA). Energies in kcal/mol, corrected for zero point vibrational contributions. TRANSITION STATE
TABLE 11: ’E(HF)-’E(CHF) Energy Differences for Transition States and Products AE, kcal/mol AE, kcal/mol
Transition State C-CH4 8.2 C-SiH4 4.0 Si-CH4 0.4 Si-SiH, 9.2
HCCH, HCSiH, HSiCH, HSiSiH3
:
Y-
Products
0.0 0.0 0.0 0.0
PRODUCT
110.5 11 5 . 3
k
C”
n
-
TABLE 111: Activation Energies E , and Enthalpy Differences A H for the Reaction AH, XHA H A X H 3 E,, kcal/mol
+
reactions 3-21G 45.3 SiH2 + CHI SiH2 SiH4 15.8 9.1 CH,+CH4 CHI SiH4 2.1
+ +
MP4/MCAH, kcal/mol 6-31G(d) 31 IG(d,p) MP4/MC-31 lG(d,p) 43.1 22.2, -49.7a 0.0 -50.0b 9.1 0.0 -112.2c 0.0 -113.ga
“Gordon, M. S.; Truong, T. N. Chem. Phys. Lett., in press. bGordon, M. S.; Truong, T. N.; Bonderson, J. J. Am. Chem. SOC. 1986, 108, 1421. ‘Gordon, M. S.; Truong, T. N.; Pople, J. A. Chem. Phys. Lelt. 1986, 130, 245.
through 0.76 (TS) to 0.85 (HCCH,). In reaction 2, these changes are from 1.18 (silane) through 1.21 (TS) to 0.82 (HCSiH,). The population changes shown above indicate that in reaction 1 the population on the active hydrogen is a minimum at the transition state, while in reaction 2 the population is a maximum at the transition state. This observation is consistent with the idea of the “cationic hydrogen mechanism” in reaction 1 and the “anionic hydrogen mechanism” in reaction 2, deduced from the charge centroid analysis.
IV. Reactions of C(3P) and Si(3P) Atoms with CH4 and SiH4 Now consider the insertions of C(3P) and Si(3P) into CH, and SiH,, reactions 5-8. The saddle point bond lengths, activation
(7)
LS
1.401 1
CS
CS
Figure 4. Transition state and product geometries for reactions 5-8.
TABLE I V Bond Lengths, Activation Energies, E,, and Enthalpy Differences, AHo, for the Reaction AOP) + XH4 (7) Si + CH4 (5) C CH4 (6) C + SiH4 R1W-X) 1.546 (42.7) 1.579 (6.6) R2(X-A) 2.345 (57.9) 2.257 (22.4) R3W-A) 1.188 (10.7) 1.366 (27.3)
+
E, (Activation Energy: Includes Zero-Point Energy Differences) HF/6-3 lG(d)//HF/6-3 1G(d) 38.2 10.0 HF/6-3 lG(d,p)//HF/6-3lG(d) 36.5 8.4 MP4/6-3 1G(d,p)//HF/6-3 1G(d) 30.6 AHo (Heat HF/6-3 1G(d)//HF/6-3 1G(d) HF/6-3 1G(d,p)//HF/6-3 1G(d) MP4/6-3 IG(d,p)//HF/6-3 1G(d)
H
1
of Reaction: Includes Zero-Point Energy Differences) -6.1 -53.0 -65.8 -6.1 -53.2 -66.1 -6.2 -61.5 -75.4
-,XHgiH“.b (8) Si + SiH, 2.062 (39.3) 2.499 (6.6) 1.579 (6.5) 16.4 15.8 7.3 -17.1 -17.2 -19.4
“Bond lengths are given in A, values in parentheses are the percent increases in bond lengths at the transition state, relative to reactants (HX)or products (XA, HA). bEnergies in kcal/mol.
1892 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Sakai et al.
I
H
i
I
I i
t
t
\
Transition State
I Transition State
I
Transitlon State
'
i c\H/c\H
I
I
I
i
I
i
It
/""
\
i
1
t
\
I
t
I H
H
I
\
H
Reaction ( 6 )
Reaction ( 5 )
Reaction ( 8 )
Figure 5. Location of charge centroids of localized orbitals along the reaction paths of reactions 5,6, and 8. t and 1 are locations of a and fl electrons, respectively. Arrow within a circle designates location of an electron above the plane, and arrow with line through it is location of an electron under the plane.
TABLE V: Total Energies (hartree)" for Reactants level (1) (2) (3) (4) (5) (6) (7) (8)
C(lD)
Si('D)
-37.61777
-288.789 82
-37.676 28
-288.836 79
-37.697 36
C(W -37.68060
Si('P) -288.831 7 8
CH4 -40.195 17
SiH4 -291.22509
-40.201 70
-291.23083
-37.732 97
-288.87203
-40.33244 -40.364 62
-291.307 1 1 -291.33899
-37.749 98
-288.887 20
-40.385 48
-291.36425
-288.854 17
"The level of computation is defined as follows: ( 1 ) HF/6-31G(d)//6-31G(d); (2) CHF/6-31G(d); (3) HF/6-3lG(d,p)//6-3lG(d); (4) MP2/ CHF/6-3 1G(d); ( 5 ) MP2/6-3 1G(d)//6-3 1G(d); (6) MP2/6-3 1 G(d,p)//6-3 1G(d); (7) MP4/CHF/6-3 1G(d); (8) MP4/6-3 1G(d,p)//6-3 1G(d). energies, and heats of reaction a t the U H F / 6 - 3 1G(d) optimized geometries a r e listed in Table IV. All notations in Table IV a r e the same a s those in Table I. T h e transition state and product geometries for reactions 5-8 a r e shown in Figure 4. For the transition states, t h e force constant matrices each have just one negative eigenvalue. Note that on the triplet surfaces, the transition states for reactions 5 and 8 have cis, rather than trans arrangements. Based on the percent increases in R , , R2,and R3(Table IV), reactions 5 and 8 a r e late transition states and reaction 6 is an
early transition state. A transition state could not be found for reaction 7. T h e Hammond postulate24 would suggest a large barrier for this reaction. Therefore, it is possible that the 3Si CH4 transition states for the insertion and abstraction reactions coalesce. I t is also possible that this insertion reaction does not occur directly, but rather in two steps: abstraction (Si CH4 SiH CH,) followed by dimerization ( S i H CH,
+
-
+
(24) Hammond, G. S. J . Am. Chem. SOC.1955, 77, 334.
+
+
-
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1893
Insertion Reactions TABLE VI: Total Energies (hartree)” for Transition States and Products
level
C
+ CHd
C
+ SiHd
Si + CHa
Si + SiHd
Singlets: Transition States (1) (2) (3) (4) (5)
-77.76072 -77.773 85 -77.77021 -77.996 14 -78.06749
-328.81395 -328.82040 -328.81993 -328.970 13 -329.051 00
-328.92693 -328.927 61 -328.936 19 -329.13943 -329.21396
-579.99567 -580.010 37 -580.001 94 -580.14439 -580.21623
(1) (2) (3) (5)
-77.92237 -77.92237 -77.929 3 1 -78.21961
Singlets: Products -328.951 19 -329.04623 -328.951 21 -329.04623 -328.957 44 -329.052 78 -329.19883 -329.31585
-580.081 13 -580.081 13 -580.086 41 -580.30365
(1) (3) (5)
-77.783 15 -77.818 26 -78.08051
-328.821 50 -328.898 11 -329.12378
-579.951 46 -580.033 78 -580.236 78
-77.937 78 -77.97042 -78.236 56
Triplets: Products -328.951 88 -328.99633 -329.021 69 -329.041 65 -329.239 02 -329.28224
-580.01693 -580.090 16 -580.283 45
Triplets: Transition States
(1) (3) (5)
“The level of computation is defined as follows: (1) HF/6-31G(d)//6-31G(d); (2) CHF/6-3lG(d)//6-3lG(d); (3) HF/6-31G(d,p)/ /6-3 1G(d); (4) MP2/CHF/6-3 lG(d)//6-3 lG(d); (5) MP4/6-31G(d,~)//6-31G(d).
HSiCH3). The abstraction reactions will be considered in a separate paper.25 The energy barrier for reaction 6 is the smallest value of the other three triplet reactions at the S C F level, and this barrier disappears at the MP4 level of calculation. In order to analyze the insertion reaction mechanisms, the three triplet reaction paths have been investigated by determining the IRC and the LMO centroids at the UHF/3-21G level. Reactions 5 and 8 have C, symmetry throughout the reaction, and one of two radical orbitals localizes on a p orbital of the A atom. This a” radical orbital does not mix throughout the reaction. Therefore, in order to simplify the figure, the a” radical orbital was not included in the LMO transformation. Reaction 6 has C, symmetry at this computational level, and all valence electrons on carbon are included in the L M O transformation. The centroids along the reaction paths for reactions 5, 6, and 8 are shown in Figure 5. For reactions 5 and 8, five valence electrons are illustrated: three from the attacking A atom (ex(25) Sakai, S . ; Gordon, M. S., in preparation.
cluding the aforementioned a” electron) plus those in the XH* bond. For reaction 6, all four valence electrons on A plus the XH* electrons are illustrated. In the figure, the notation arrow within a circle is used to indicate that the electron is located above the AXH* plane, while an arrow with a line through it indicates the electron is located below the plane. From the motion of the centroids, the first step for reactions 5 and 8 is the hydrogen abstraction reaction by the atomic radical A. Then the recombination of AH and XH3 occurs. There is no barrier between these two steps. Reaction 6 appears to be a hydrogen anion transfer, followed by an ionic reaction between the anionic species, AH-, and XH3+. This might be termed a pull-push mechanism. The differences observed in the reaction mechanisms may be due to the very polar nature of the X+H- bond combined with the A-H+ nature of the forming bond in reaction 6.
V. Conclusions For the insertions of ID carbon and silicon atoms into methane and silane, there are nonzero activation energies except for Si SiH4. These four reactions are classified into two types based on the polarization of the breaking bond determined by the charge centroid analysis. One is the “cationic hydrogen transfer mechanism” for the insertions into methane (reactions 1 and 3), and the other is the “anionic hydrogen transfer mechanism” for the insertions into silane (reactions 2 and 4). For the insertions of 3P carbon and silicon atoms into methane and silane, the carbon insertion into methane (reaction 5) has a large barrier, while the silicon insertion into silane (reaction 8) has a small barrier. The insertion of carbon into silane (reaction 6) occurs with no energy barrier, while we were unable to find a transition state for the 3Si CH4 system, reaction 7. The triplet reactions are classified into two types by the charge centroid analysis. One is the “near abstraction mechanism” for reactions 5 and 8. Another is the “anionic hydrogen transfer mechanism” for reaction 6.
+
+
Acknowledgment. This work was supported by grants from the donors of the Petroleum Research Fund, administered by the American Chemical Society, the National Science Foundation (CHE86-40771), and the Air Force Office of Scientific Research (87-0049). The computer time made available by the North Dakota State University Computer Center is gratefully acknowledged. Appendix The total energies of the reactants and products and transition states are listed in Tables V and VI, respectively. Registry No. Carbon, 7440-44-0; silicon, 7440-21-3; methane, 7482-8; silane, 7803-62-5.
