J . Phys. Chem. 1993, 97, 5472-5481
5412
ARTICLES
-
Theoretical Studies of the Reactions H + CH C + H2 and C + H2 Global Ground-State Potential Surface for CH2
-
CH2 Using an ab Initio
Lawrence B. Harding Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439
Renee Guadagnini and George C. Schatz’J Department of Chemistry, Northwestern University, Evanston, Illinois 60208-31 13 Received: January 1 1 , 1993; In Final Form: March 16, 1993
Ab initio, multireference, configuration interaction (CI) calculations have been used to characterize the groundstate potential surface of methylene. The calculations employ a full-valence, complete-active-space reference wave function and a (4~,3~,2d,lf/3~,2p,ld) basis set. The calculations were carried out at -6000 points, and the resulting energies were fit to a many-body expansion including conical intersections between the 3B1 and 3A2 states for CZ,geometries and between the 3rIand 32-states for linear geometries. The calculations show conical intersection provides a zero barrier route for the C(3P) HZinsertion reaction. Quasiclassical that the trajectory studies of the title reactions using the global surface indicate that both reactions proceed without activation energy and that the thermal rate constants are nearly independent of temperature. The rate constants for H C H agree with high-temperature (2000 K) experimental studies but are substantially higher (factor of 10) than a measurement at 297 K. For C Hz, the CHZlifetimes at thermal energies are approximately 20 ps which is in agreement with an experimentally derived estimate.
+
+
+
I. Introduction Atomic carbon, CH, and CH2 are all important reactive species in hydrocarbon flames. It has been postulated that reaction R1 CH(%)
+ H(’S)
- [CH,]
C(3P) + H,
(Rl)
is an important source of atomic carbon in fuel-rich hydrocarbon flames.’ There have been a number of experimental studies2-’ of both this reaction and the reaction of C(3P) with H, to form ground-state methylene: C
+ H,
-
CH,
(R2) Braun et al.5 derived a collision efficiency for the C(3P) H2 insertion reaction of between 0.1 and 1.O. Very recently, Dean et ~ 1 have . ~studied C H2 in a shock tube at sufficiently high temperatures to measure the rate of reaction R1 in the reverse, endothermic, direction. By combining a pyrolysis technique for generating C(3P) at high temperatures with an excimer laser photolysis technique at lower temperatures, they were able to measure the rate of reaction R1 over the range 1504-2042 K. They found no temperature dependence to the rate constant and the value of their rate constant at 2000 K was in good agreement with an earlier value of Peeters and Vinckier.6 However, they note that their high-temperature rate constant is more than a factor of 10 above a room temperature measurement recently reported by Becker et ~ 1 using . ~ a photolysis flow reactor, suggesting that there may be a significanttemperature dependence between 300 and 1500 K. There have been a very large number of theoretical studies*-’3 of the methylene potential surface. Here we focus primarily on those which characterized the surface globally. The most accurate calculations to date on the methylene potential surface are those
+
Also Visiting Scientist, Argonne National Laboratory.
+
of Comeau et a1.I2which focused on only that part of the potential close to the minimum. They calculated 45 points on the triplet surface using a (5~4p3d2flg/3~2pld) basis set. These points were then fit and rotation-vibration energy levels calculated using the Morse oscillator rigid bender internal dynamics (MORBID) procedure. The calculated dissociation energy from these calculations is within the error bars (h0.8 kcal/mol) of the measured dissociationenergy. Jensen and Bunker14have varied 9 of the 24 parameters in this ab initio potential to improve the agreement between predicted and observed rotational-vibrational energy levels. This semiempirical potential is probably the most accurate description of the potential in the local region near the minimum that is currently available. The most accurate global potential to date for CH2 is that of Knowles, Handy, and Carterlo(KHC). They reported CASSCF calculations employing a (5s,3p,2d/2s,lp) basis set on the two lowest 3A” states. The calculated points were scaled to match the experimental dissociation energy and fit to a potential function in the form of a diagonalized 2 X 2 matrix. This form of the analytic potential function was chosen to correctly describe the conical intersections between the two lowest triplet surfaces that occur at linear geometries. A quasiclassical trajectory study of reaction 1 has been reported by Murre11 and DunneIs using this potential. The KHC calculations did not attempt to describe the conical intersection between the 3B1 and 3A2surface for C , geometries. They report a C2, barrier to the C(3P) + H2 insertion of -70 kcal/mol and a C, barrier of -40 kcal/mol. The latter results are in contrast to calculations reported by Harding who found a very small barrier to the insertion reaction due to a conical intersection between the 3B1and surfaces. The existence of a large insertion barrier on the KHC surface is important as it both changes the lowest energy mechanism for reaction R1 from addition-limination to direct (collinear) abstraction and it changes the lowest energy pathway for dissociationof methylene
0022-3654/93/2091-5472%04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5473
Ground-State Potential Surface of Methylene
'n
1%
A
A
I I
3 . =g
Figure 3. Schematic linear correlation diagram for H
'
+
Figure 1. Schemaic C2, correlation diagram for the C(3P) H2
-
CH ( ' 2 ) + H
+
Figure 2. Schematic linear correlation diagram for CH + Hz.
+H
-
C(3P)
(the reverse of reaction R2) from elimination of molecular hydrogen to CH bond cleavage. As alluded to above, there are several interesting topological features on theground-state (triplet) methylenesurfacethat result from conical intersectionsbetween different triplet surfaces.These are similar to those recently studied on the isoelectronic NH2+ surface.16 Starting with C(3P) and H2, at large separations there are threedegenerate triplet states, depictedschematicallyin Figure 1 for a C2uorientation. At small separations, the 3BIstate will drop below the other two. However, at larger separations, as discussed previously, the SA2state is lower in energy owing to a dative bonding interaction between the empty carbon p orbital and the H2. At large separations the 3B1state is expected to be quite repulsive because a CZ, insertion on this surface is Woodward-Hoffman forbidden. The 3Bz surface is expected to be the highest of the three and will not be characterized in this study. As has been discussed previously, the 3B1and 3A2surfaces must cross and it is this crossing that gives rise to low-energy route for the C(3P) H2 insertion reaction. A second surface crossing occurs for linear CHH geometries. Again at large separations there are three degenerate states, depicted schematically in Figure 2. The correlationbetween these states from the C H2 asymptote to the CH + H asymptote is also shown in Figure 2. As in the CZ,approach, in regions near the C H2 asymptote, the 32- state is lowest in energy owing to a similar dativebonding interaction. At the CH + H asymptote the 3Z- state correlates to the 42-state of CH as that state lies
+
+
+
-
CHI.
17 kcal/mol above the 211 ground state. Thus, the 32- and 3 l l surfaces must also cross in some intermediate region. A third surface crossing occurs for linear H-C-H geometries. At the H CH asymptote, the three lowest triplet states consist of a doubly degenerate 311 state and a higher lying 3Z-state. These states are depicted schematically in Figure 3. The correlation between these states and those of linear methylene shows that, as the two species come together, the 32surface drops below the 311surface, resulting in the third surface crossing. This crossing was recently studied in ref 13. In this study we will develop a global ground-state potential surface for CHI that accurately describes all regions of the potential surface up to energies significantly above the second dissociation limit, CH(211) H(2S). This includes the three conical intersections discussed above. This surface will allow, for the first time, theaccurate modeling ofthecompetition between the two dissociation pathways open to triplet methylene. We will then use the global surface with quasiclassical trajectory calculations to determine rate constants for reactions R1 and R2,and to characterize certain features of the reaction dynamics, such as the H2 product distributions for reaction R1, and the CH;! unimolecular lifetimes for reaction R2. On the global surface, there are two possible reaction mechanisms for reaction R1: direct abstraction, involving a linear CHH barrier, and CH2 complex formation (for which there is no barrier) followed by decay to C H2. The CHI lifetime in the latter mechanism is expected to be very short ( 2 80. At this point a second smaller minimum appears corresponding to the outer edge of the 3B1state. As RHHis further increased, the inner, 3B1,minimum grows and the outer, 3A2,minimum shrinks and eventually disappears. From these plots it is clear that much
+
-
+
Ground-State Potential Surface of Methylene
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5477
3
2.5 n 3
s. z I
2
0
IY
1.5
1
3
2.5 n 3
s. I
I
2
IYv
Figure 9. Schematic 01 .ita )lots of the C,,(H-C. I) and C,,(H-H-C) states. 1.5
1
2
3
5
4
6
(4
RH-H F i p e 7 . C,,(H-H-C) potentialsurfacesforthe311and32-states.Plotting conventions as in Figure 6 .
6
R,
= R,(CH 211)
4 n 3
&
n
>
2
0
-1
4
n
n 3
&
>
u
Figure 8. Schematic orbital plots of the &(H-H-C) states.
and C,,(H-H-C)
2
0 -6
-4
-2
0
2
4
6
z (4
of the energy release of the insertion reaction will not appear until R H His significantly extended, suggesting that vibrational excitation of the H2 may enhance the rate of reaction. G. Crossings with 'A, Surface. Although the primary topic of this paper is the ground state, triplet potential surface, it is relevant to note that this surface is crossed in several places by the 'Al potential surface. Figure 13 shows two-dimensional C2" cross sectionsof both the lowest triplet surface and the 'Al surface. At large RCM, the 'AIsurface correlates with C(lD) Hz which
+
Figure 10. H + CH interaction potentials for fixed R(C-H,). Plotting conventions as in Figure 5.
+
lies 29 kcal/mol above C(3P) H2. Unlike the triplet surface, the 'AIsurface drops rapidly as RCMdecreases, crossingthe triplet surface close to the long-range 3A2 minimum. At smaller RCM the triplet surface drops below the singlet, crossing it close to the 'Al minimum.
Harding et al.
5478 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 R,,
2l
c__1 I
44
>
= 3.50 au
2
0
4
c
F
R,,
au
n
n
,,= 3.00
= 1.70 au
I
4 n 3
3
a
a2
>
>-
2
0
0
6
R,,
= 2.50 au
A-.
'3'
s.
a2
>
>-
0 -4
Q
-2
2
0 , ., 2
4
z (4
Figure 11. Hz + C interaction potentials for fixed R(H-H). Plotting conventions as in Figure 6.
V. Detail8 of Trajectory Calculations Trajectory calculations were performed using a standard implementationof the usual quasiclassicalMonte Carlo method. In caseswhere conical intersectionsintroduce cusps in the potential surface, only the lower root was used in our trajectory calculations. There is no indication in our calculations of poor accuracy due to discontinuities in the first derivatives that occur at isolated points. The maximum impact parameter used for reaction R1 was 8 a. while that for R2 was 6 ao. For each reaction,calculations were done at translational energies E equal to 0.76, 1.52, 2.54, 5.07,and 10.1kcal/mol(O.35 kcal/mol was alsodone for (R2)). For each translational energy, four different choices of the initial diatomic rotational angular momentum (JCHor J H ~were ) considered,namely J = 1,3,6, and 12. These parameters coincide, for the most part, with parameters used by Murre11 and Dunne,ls which enablesdirect comparisons with their results. For reaction R1,we have multiplied all rate constants (but not cross sections) by the electronic factor 3/8 which reflects the statistical fraction of the surfaces accessed in CH H collisions which sample the 'A" surface that is responsible for reaction. For reaction R2,the corresponding electronic statistical factor is l/3. For reaction R1,once the reactive cross section Q ( E , J ~ H was ) determined, it was fit via least squares to linear functions of first E, then JCH,and the resulting fit was used to calculate rate constants through numerical integration of the usual expression
-6
,
I
-4
"
'
I
-2
"
I
'
'
I
2
0
4
"
I
6
(4
Figure 12. H2 + C interaction potentials for fixed R(H-H). Plotting conventions as in Figure 6.
6 5
+
2
1
0
( r p ) - ' / * C Q (E ,JCH)e-E/kTE dE (5) where QCHis the CH rotational partition function. For reaction R2,cross sections were defined for forming CH2 in the outer (shallow) well and the inner (deep) well. The outer
1
2
3
R C-H,
4
5
6
(au)
Figure 13. C2" potential surfaces for the lowest triplet ('B1 and 'A2) and the 'A, states. Plotting conventions as in Figure 5.
well cross section Q,(E,JH,)was defined using those trajectories which satisfy R 5 4.5 a0 (where R is the C-H2 Jacobi coordinate
Ground-State Potential Surface of Methylene
The Journal of Physical Chemistry, Vol. 97, No. 21, I993 5419
and R = 4.5 a. approximately locates the outer well boundary) when the H-C-H angle is between 45' and 135'. The inner well cross section Q(E,JH,)was defined by trajectories for which R I1.99 a. (R = 1.99 a0 corresponds to the location of the cusp which separates the3Azand3Blsurfaces) withthesameconstraint on the H-C-H angle. Note that all trajectories which contribute to Qi will necessarily have also contributed to Qo. Both Qi and Qo include contributions from direct and complex forming collisions. To determine the complex-forming part of these cross sections, we tagged each trajectory according to the time spent in the inner and outer wells and then calculated survival probability distributionsby binning trajectories based on these lifetimes.Plots of these survival probably distributions generally showed exponential behavior after an initial transient which was over within 0.1 ps. The slopes of these survival probability plots was then , the intercept was used to define the CHI lifetimes ~i and T ~while used to determine the fractions of Q and Qo that are associated with complex formation. We denote these complexcross sections by Qic and Qm,respectively. One feature of this approach is that the survival distribution function needs only to be calculated for a time long enough to determine the slope and intercept (typically requiring a time on the order of the unimolecular decay time). Trajectories surviving longer than this can be terminated. In our case we terminated all trajectories at 15 ps. The use of survival distribution functions in quasiclassical trajectory calculations to calculate association cross sections and unimolecular decay lifetimes has previously been used by Hu and Hase20in their study of H CHS CH4. In this and earlier studies by Hase and c0-workers,21 comparisons with classical and quantum versions of RRKM theory were used to determine the importance of quantum and nonstatistical effects. For H CH3, energy randomizes rapidly once the CH4 is formed, so the trajectory and classical RRKM lifetimes are in good agreement. In addition, there is only a 5-78 transient in the survival distribution plot, so there is little ambiguity in calculating the association cross section (Le., the results are nearly independent of how the association process is defined). However, quantum effects on the CH4unimolecular decay are important, as the CH3 zero-point energy is rapidly converted into energy that can be used for dissociation. This causes the trajectory lifetime for CH4 to be shorter than the quantum RRKM result. The present study is largely analogous to the earlier Hu and Hase study, except that C + H2 can form outer-well complexes which subsequently can transform into inner-well complexes. In the outer well, energy scrambling is slow, and the initial nonstatistical transient is large. This can lead to errors both in the association and unimolecular decay constants for the innerwell complexes. We will use tests of microscopic reversibility to examine the importance of quantum effects and nonstatistical behavior in our results. Trajectory rate constants for the C + H2 CH2 reaction have been calculated by substituting the inner well complex formation cross section Q c into eq 1 (appropriately modified to describe the HZdiatomic), using the same least-squares fitting and numerical quadrature as for H + CH. In addition, we used the complex lifetimes ~i to calculate a thermally averaged CHI unimolecular lifetime. In this case the appropriate Boltzmann average uses the E and JH,labeled decay rates l / r i ( E , J ~ , ) .
+
-
+
-
-+
VI. Trajectory Results
+
A. CH H C H2. Table IV presents the reactive cross sections Q associated with reaction R1 as a function of E and JCH.As might be expectedfor a reaction which involves no barrier and the formation of short-lived complexes, the cross section decreases slowly with E and with JCH. Murrell and Dunne15 have calculated some of the same cross sections in their study of CH + H, and their cross sections are generally a factor of 4 smaller than ours for low E and JCH.Their cross sectionsdecrease
TABLE Iv: Reactive Cross Sectiona (in eo2) for H + CH(E, J&+) C + Hz +
Elkcal mol-' = ~
JCH
0.76
1.52
2.54
5.07
1 3 6 12
42.4 47.8 45.0 37.6
45.8 38.9 41.4 25.8
43.3 41.2 32.8 25.2
32.3 27.8 27.4 28.4
5 & -10
-
10.1 ~
24.8 18.3 17.8 16.2
Y
-1 1
x
0
1
2
3
4
1000K/T Figure 14. Arrhenius plot of k in cm3/s versus 1000 K/T. The solid curve shows the present results, while the dashed curve is a trajectory result derived from ref 14. Experimental data include filled circles (ref 4), triangle (ref 6), and square (ref 3).
with increasing energy at about the same rate as ours, but they decrease with JCHmuch more rapidly. It seems likely that some of the differences noted here are due to the 0.1-eV barrier on the fitted surface used by Murrell and Dunne, although it seems surprising that there is no hint of activated behavior in their integral cross section. Figure 14 presents an Arrhenius plot of the thermal rate constant for reaction R1 as obtained using eq 1 . Included in the plot are three estimates of the rate constant that are provided by experimental measurement^,^,^,^ along with an estimate provided by Murrell and Dunne.I5 Our calculated rate constant is found to have essentially no dependence on temperature over the range considered in the plot (300-2000 K). At high temperature (close to 2000 K) our result is within the error bars of the two measurements4v6available at that temperature, and in addition we agree with the results of Dean et 01.4 which show no temperature dependence to the rate constant over the range 1504-2042 K. Our rate constants are substantially higher (factor of -3) than Murrell and Dunne,15which is consistent with the comparison of cross sectionsdiscussed above. They are also substantially higher (factor of 10) than the measured value at 297 K given in ref 3, which is rather surprising, as in the absence of a significant barrier to reaction, one would expect that thecorrect rateconstant shouldhave relatively weak temperature dependence. Our results show the expected weak temperature dependence, while a combination of the Becker et al. rate constant at 297 K with either the theory or experiment at 2000 K suggests a stronger dependence. Table V shows selected information concerning the product state energy partitioning for reaction R1. Included in this table are the product vibrational state-resolved cross section Q ( U H ~ ) , the average rotational quantum number ( J H * ( U Hfor ~ ) )each HZ vibrational state, the average energy in product vibration, rotation and translation ( ( E " ) ,( E r ) ,and ( E t ) ,respectively), the corresponding fractions of the energy available to the products andft), and the average HZvibrational and rotational quantum
-
-+
Harding et al.
5480 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
Product State Energy Partitioning for H
TABLE V
Elkcal mol-'
0.76 1
JCH
+ CH
0.76 6 45.0 19.7 18.9 6.4
-
8.3 6.6 3.4 9.0 10.8 7.1 0.33 0.40 0.27 0.70 6.9
TABLE VI: Complex Formation C r m Sections QE(in ao2) for C Hz --c C H I , and CHI Unimolecular Lifetimes (in ps)
+
Elkcal mol-' ~~
JH.
0.35 17.4" 17.5" 9.5 13.8 10.3 9.0 16.7 1.7
1 3 6 12
0.76 13.7 19.0 8.2 15.1 7.5 10.4 13.3 1.9
1.52 10.2 22.3 5.0 14.1 7.4 6.6 7.7 1.8
2.54 6.5 20.5 3.3 10.9 4.8 6.2 10.1 1.4
5.07 2.5 4.2 3.0 12.7 3.7 4.3 5.2 1.2
10.1 3.6 10.4 2.6 8.8 2.4 9.4 2.2 0.6
" Top entry is cross section; bottom is lifetime. numbers ( ( D H , ) and ( J H , ) ) .Theresultsindicatethat theavailable energy ends up being distributed somewhat evenly to the three degrees of freedom, with rotation getting the most. Note that the product distributions are not simply statistical, for if they were, the fractions f v , f i , andft would be 0.29,0.29,and 0.42, respectively (based on a rigid-rotor harmonic-oscillator model). The observed results indicate that rotation is favored and translation disfavored relative to the statisticalvalues. Variation of the results with respect to reagent translational energy and CH rotational state is small. Let us briefly consider the hydrogen exchange reaction H' + CH CH' H that occurs in parallel with reaction R1. As with reaction R1,this cross section does not vary rapidly with energy or with CH rotational state. For E = 1.52kcal/mol and J = 1 it has the value 1 1.1 ao2,which is 24% of the cross section for reaction R1. The corresponding value from Murre11 and Dunne is 1.1 ao2. The rate constant for exchange that has been calculated using our cross sections increases slowly with temperature from 2.7 X at 300 K to 5.6 X 10-" at 2000 K. B. C H2--cCH2. Table VI presentscross sections for complex formation, Qic, and CH2 unimolecular decay lifetimes, ~ i for , selected values of E and J H ~ These . all refer to inner-well complexes. The corresponding outer-well complexes have cross sectionsthat are typically about double those associated with the inner well, and lifetimes that are in the range 0.1-1.0 ps. It is noteworthy that the outer-well cross section is much smaller than the hard-sphere cross section associated with the outer-sphere capture radius (rb2 = 64 ao2). This means that only collisions with favorable orientations are able to be trapped in the outer well. Once trapped, they have a substantial probability of penetrating into the inner well. In fact the inner-wellcrosssections at low E and J H ,are actually larger than the hard-sphere cross section associated with the inner capture radius (12 a$). One way to define the importance of sequential trapping (first outer well, then inner) is to calculate the cross section for trajectories which first spend a specified time in the outer well and then cross
-
+
+
C
Hz 2.54 1
2.54 6
10.1 1
10.1 6
43.4 21.4 17.3 4.7 7.9 6.2 3.0 7.8 10.4 9.0 0.29 0.38 0.33 0.62 6.7
32.8 14.0 12.9 5.8
24.8 10.3 6.9 5.3 2.3 10.2 6.3 4.3 1.8 12.5 12.5 9.9 0.36 0.36 0.28 0.98 7.1
17.8 6.8 9.0 1.9 0.1 8.3 8.6 2.9 4.0 9.2 14.8 12.2 0.26 0.41 0.34 0.74 7.9
-
9.2 6.4 4.9
-
9.5 12.0 7.1 0.33 0.42 0.25 0.75 7.3
the inner well. If we choose this time to be 0.1 ps, which is long enough to give exponential survival distributions for the outer well, we find that the remaining cross section is 6040% of the total cross section for passing into the inner well at low energy (0.35 kcal/mol) dropping to 2040% at 10.1 kcal/mol translational energy. Table VI shows that the inner-well cross section is largest at ~ decreases rapidly as either E or J Hincreases. ~ low E and J Hand The corresponding lifetime is also largest at low E and J H ~with , a value of roughly 20 ps at 0.35 kcal/mol and J H =~ 1. This lifetime decreases to around 1 ps for E = 10.1 kcal/mol and J H ~ = 12. Thermal averages of the cross sections in Table VI give an associationrateconstant kz that is weakly temperaturedependent, varying from k2 = 1.7 X 10-11 at 300 K to k2 = 2.0 X 10-11 at 2000 K. The corresponding thermally averaged unimolecular decay lifetime (k-Z)-l varies from 17 to 6 ps over the same temperature range. One experimental estimate of the lifetime of CH2 has been given by Husain and Kirsch2based on measured values of the termolecular association rate constant. The value given, namely 1 ps, was characterized as an Yorderof magnitude" estimate, so its value is consistent with what we have reported. To check the importance of quantum and nonstatistical effects in the thermally averaged rate constants k2 and k-2, we have compared the ratio k2/ k-2 with the equilibriumconstant K which governs the C + H2 CH2 reaction, as these should be identical. Kmay be determined by standard methods of quantum statistical mechanicsusingproperties of CH2and HZthat are given in Tables I and 111. We have ignored anharmonicity in this evaluation as only a rough comparison between these quantities is desired. At 300 and 2000 K,we find K = 6.5 X lez4 and 1.7X 10-21 cm3, respectively. The corresponding ratio k2/k-2 is 2.9 X and 1.2X cm3at the same temperatures. As might be expected, the biggest discrepancy is at lower temperatures (300K)and the direction is such that either the rate constant k2 or the lifetime (k4-I is too high. It is easiest to explain this if we assume that the error is in k2, as this could easily be overestimated because zero-point energy scrambling in the outer well makes it too easy to cross to the inner well. By contrast, the zero-point problem should lead to CH2 lifetimes that are too shorr (as decay back to C + H2 can occur to give H2 with less than zero-point energy). Since the microscopic reversibility test indicates that the error is in the opposite direction, we conclude that at low temperatures theerror is in k2. At high temperatures (2000K)the discrepancy between K and k2/k-2 is smaller in magnitude, and it is reversed in direction compared to 300 K,so the suggestion here is that the error in (k&l is now more important.
-
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5481
Ground-State Potential Surface of Methylene
m. CODClUSiOM
+
The calculations predict no barrier for either the CH H addition reaction or the C H2 insertion reaction. The CH H addition reaction is found to have a very broad attractive, entrance channel. The long-range approach becomes repulsive only for orientations close to linear. A crossing between the 3A2 and 3B1 surfaces is predicted to play an important role in determining the topology of the surface in the vicinity of the C H2 insertion reaction path. At long range the jA2 surface is lowest in energy. On this surface there is no barrier to C H2 addition, forming a loosely bound complex. At shorter distances the 3A2 surface becomes increasingly repulsive. A crossing between the 3A2and 3B1surfaces provides a zero barrier route to the overall insertion reaction. It appears as though the dynamical bottleneck for this insertion will be located in the vicinity of this surface crossing. The trajectory calculations for reactions R1 and R2 show that the reaction kinetics is dominated by activationless processes (Le., insertion-elimination instead of abstraction for (Rl)), and the resulting rate constants are only weak functions of temperature. This is consistent with the zero-energy barriers found in the ab initio calculations, and it is therefore surprising that our rate constant for (Rl) disagrees with experiment at 297 K when it agrees at 2000 K. Thus it appears that the correct 297 K rate constant should be substantially higher than is suggested by the experiment, and probably close to what we have calculated. For reaction R2, the comparison with experiment is more indirect, but the one comparison of CH2 lifetimes indicates reasonable agreement with our 17-ps lifetimes at 300 K. The C H2 reaction is unusual for gas-phase reactions in that there is a precursor “outer” well that is quite shallow, and then a deep -inner’’ well corresponding to the CH2 product of reaction R2. This behavior does occur in other chemical problems, most notably in the chemisorption of molecules on metallic surfaces, where there is usually a precursor physisorptionwell that precedes chemisorption. For reaction R2, our studies indicate that the outer well does not influence the unimolecular decay lifetime, but it does influence the association rate constant by trapping molecules long enough for them to sample the inner well. As a result, the association cross sectionsand rate constants are larger than one might expect based on the magnitude of the capture radius using typical steric factors. Unfortunately, trapping in the outer well can lead to errors in the association rate constant
+
+
+
+
+
due to scrambling of the H2 zero-point energy so the large association cross sections and rate constants may not always be correct. We used a test of microscopic reversibility to estimate the magnitude of this effect and found that it is quite important at low temperatures. As a result, it seems likely that the rate constantsrepofled for reaction R2 and its reverse are not accurate at low temperature. Other methods, such as RRKM, may provide improved estimates of these rate constants, but at this point there are no experimental results that can be used to judge the accuracy of the results. Acknowledgment. This research was supported by the Department of Energy, Division of Chemical Sciences, under Contract W-31-109-Eng-38, and by NSF grant CHE-9016490. References and Notes (1) Gaydon, A. G. The Specrroscopy of Flames, 2nd ed.;Chapman and Hall: London, 1974. Thorne, L. R.;Branch, M. C.; Chandler, D. W.; Kee, R.J.; Miller, J. A. Symp. (In?.) Combust., [Proc.],15, 1974, 969. (2) Husain,D.;Kirsch, L. J. Tram.FurudaySoc. 1971,67,2025. Husain, D.; Young, A. N. J. Chem. SOC.Faraday Trans. 2 1975, 71, 525. (3) Baker, K.H.; Engelhardt, B.; Wiesen, P.; Bayes, K. D. Chem. Phys.
Lett. 1989, 154, 342.
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