J. Phys. Chem. 1993,97, 5040-5045
5040
Theoretical Characterization of the Reaction of HOz with Formaldehyde E. M. Evleth,’J C. F. Melius,* M. T. Rayez,s J. C. Rayez,s and W. Forsts Luboratoire de Dynamique des Interactions Molbculaires (ER 271, CNRS), Universitb Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris, France, Sandia National Luboratories, Livermore, California 94550, and Laboratoire de Physicochimie Thborique (UA503, CNRS), Universitb de Bordeaux, 33405 Talence Cedex, France Received: December 16, 1992; In Final Form: February 24, 1993
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The reaction of HO2 formaldehyde is characterized at both the semiempirical and a b initio levels. It is shown that semiempirical methods do not furnish the information necessary to rationalize the kinetics of the formation of 0 0 C H 2 0 H . The mechanism of this reaction is rationalized at both the MP4/6-31G** and BAC MP4/ 6-31G** levels. The critical transition state for this reaction involves the simultaneous addition of the terminal oxygen atom of HO2 to the carbon of the C O bond and transfer of a proton from OOH to the oxygen of this same bond. It is shown that the previously proposed mechanism involving the intermediate formation of the HOOCH2O radical is incorrect. Kinetic modeling indicates that the critical transition state has an energy close to the incoming HO2 CH2O channel and that a large deuterium isotope effect should occur in the reaction of DO2 CH20.
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1. Introduction
The addition reaction of the peroxy radical, H02, with formaldehyde has been experimentally investigated by a number of experimental groups’-5 with a short overview presented recentlya6 This reaction yields a structure characterized as 0 0 C H 2 0 H with a measured A.HHr,300of -16.3 kcal/m01.~ However, an undetected intermediate alkoxy radical, HOOCHzO, was proposed to be first formed by the addition of HOz to the C-0 bond followed by intramolecular hydrogen atom transfer to yield the peroxy radical, 0 0 C H 2 0 H (eq 1). H02
+ H2C=0
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[HOOCH20]
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Universitb Pierre et Marie Curie.
* Sandia National Laboratories. 1 UniversitC
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O O C H 2 0 H (1)
That an intermediate is formed in this reaction is indicated by the kinetic expression for the forward reaction of the hydrogenated components, kk = 7.7 X 10-15e625*550/T cm3 molecule-] SKI. No deuterium isotope effect has been measured in this system. The combination of a negative activation energy and a low preexponential factor indicates that a complex is formed prior to a transition state which has a tight configuration but has an energy less than the incoming channel. Another condition for this kind a behavior is that the incoming channel giving the complex has no appreciable activation energy. This is described schematically by Figure 1A. Although mechanism 1 is generally accepted,6 several factors mitigate against it. First, the application of Benson’s group additivity rules’ allows predicting that the U f , 3 0 0 of 0 0 C H 2 0 H is-39.5 kcal/mol, which is within 1 kcal/mol of the experimental value of -38.8 kcal/m01.~ The A H f , 3 0 0 of HOOCH20 cannot be accurately estimated, but based on the bond energy differences between H-OC and H-OOC, it should be 15-20 kcal/mol less stable than 00CH20H. This places the AHf,3m of HOOCH20 near that of the reactants, H 0 2 + H2C=0. Second, one theoretically expects a significant barrier for the nearly isoergetic reaction H02 + H2C=O HOOCH20. These factors make HOOCH20 a poor candidate structure for the complex. If so, this still leaves the question as to what other structures could serve as this intermediate. +
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de Bordeaux.
0022-3654/93/2097-5040$04.00/0
B Figure 1. (A) Schematic potential energy surface for an indirect reaction: (1) location of transition state for entrance channel; (2) intermediate complex; (3) transition state between intermediatecomplex and product. In mechanism 2, there is no J = 0 potential energy barrier. (B) Definition of the energy quantities Eo, AE, and AEz. Both AE and AEz are indicated downhill and are therefore negative; however, they may be uphill as will be shown in the text and Table VI.
The initial theoretical studies4were done using the MIND0/3 semiempirical parameterization which yielded a A.Hr,jm for reaction 1,-17 kcal/mol, in near agreement with the experimental value. However, later workshowed a high barrier for thereaction H 0 2 + H2C=0 HOOCH20. The idea of using DZP level ab initio calculations was previously rejected since reaction enthalpies and activation energies cannot be generally accurately calculated at this level. However, the recent development of the ab initio bond additivity correction (BAC) method* gives heats of formation and activation energies generally accurate to within 2 kcal/mol. Therefore, a more definitive ab initio theoretical study is now possible and reported here.
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0 1993 American Chemical Society
Reaction of H 0 2 with Formaldehyde
The Journal of Physical Chemistry, Vol. 97, No. 19, I993 5041
We will theoretically demonstrate here that the accepted mechanism (eq 1) for this reaction is probably incorrect. We will show that probably no HOOCHzO intermediateisever formed in this reaction. We show that the probable intermediate is a hydrogen-bonded complex between H02 and H2C=0 and that this intermediate rearranges directly to give OOCH20H. The theoretically determined mechanism is (2).
HO,
+ H,C=O
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[H,C=OHOO]
- "TS"
O O C H 2 0 H (2)
2. Technical Details The ab initio calculationsreported here were performed using Gaussian 90.9 The BAC calculations were calculated using Gaussian 90 archives as input to a program developed by C. F. Melius.s The BAC-MP4 protocol uses geometries optimized at the HF/6-31G* level. The HF/6-31G* frequencies are scaled (0.89) and the thermodpamic quantities are computed in a normal fashion with the exception that a hindered rotor approximation can be applied to certain rotationally loose coordinates. Although this approximation was applied here, the differences obtained assuming that all vibrations were harmonic were less than 0.1 entropy unit. The electronic energies are obtained at the MP4/6-31G**//6-31G* level. For radical species, a S2spin error correction was applied at the PMP3/6-31G** level plus an additional spin correction of 3 kcal/mol. The PM3 and AM1 semiempirical calculations were performed using AMPAC 214.'&'* This program also allows for doing a configuration interaction calculation using a selected number of the most interacting configurations found by searching from the entire single- and double-configurationalspace. The use of CI at the AM1 or PM3 level runs counter to their parameterization protocols but allows one to test whether the system responds in an extraordinary manner to a correlation correction (see also ref 13).
3. Results and Discussion
A. A Semiempirical Energetic Analysis. Here we will show that the semiempiricalmethods employed yielded results which mislead us at the initial stages of this study. Although AM1 and PM3 use the most recent parameterization for organic systems containing hydrogen, carbon, and oxygen, they are logical extensions of the earlier MIND0/3 and MNDO methods. The most recent parameterizations represent overall improvements in theestimationof AHr,3~ofalargeclassof structures. However, for the systems treated here, this evolution in parameterization has not produced increasing precision. In the case of HO2, the AHr,3Wof the H 0 2radical is calculated at -2.8, -10.2, -1 1.2, and -2.0 kcal/mol using, respectively, MIND0/3, MNDO, AM1, and PM3 and can be compared with +3.5 kcal/mol experimentally.' As seen in Table I, the AM1 and PM3 AHr,300 errors are accumulative when viewed globally, 10-20 kcal/mol for the 1 M 1 , 3 0 0 of H 0 2 H2CO or for the radical 0 0 C H 2 0 H (111). Therefore, in contrast to the impression given by the average statistical precision cited for AM1 and PM3 (ca. 6 kcal/mol),'OJ1 the errors can be much larger in particular cases and render the methods useless for even approximate thermochemical kinetic exploitation. The same structures, I-V, were encountered using semiempirical and ab initio methods. These are shown in their general forms in Figures 2 (1-111 and V) and 3 (IV). We will not report the semiempirical structures since these can be easily calculated initiating optimization from the ab initio structures (Table 11). The first structure encountered on the reaction path taking HO2 H2CO to OOCHzOH is the hydrogen-bonded complex, I, in which the H atom of the HO2 radical is complexed to the oxy8en of the C = O bond. Two product structures, I1 (HOOCHCH20) and I11(00CH20H), were found along with two transition states,
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TABLE I: Semiempirical Heats of Formation, AHf,% kcal/mol structure H02 HzC=O H0z HzC=O AHreI HzC=O:HOO (I) AH~I HOOCHzO (11) AHreI OOCHzOH (111) AHreI TS (IV) CIlOO AHrel TS (V) AHrel
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AM 1 -11.2 -31.5 -42.7 0 -47.3 -4.6 -31.3 +11.4 -61.8 -19.1 -26.1 -33.1 4-9.6 -13.1 +29.6
PM3
exptl"
-2.0 -34.1 -36.1 0 -38.7 -2.6 -36.6 -0.5 -42.2 -6.1 -2.8 -8.6 +27.5 -6.2 +29.9
+3.5 -25.6 -22.5 0
-38.8 -16.3
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References 4 and 7. CIlOO (see text), lOOXl00 selected configurations. AHre',enthalpy relative to reactants.
IV and V. Transition state IV conceptually connects I to 111. Transition state V connects HO2 H2CO to 11. In order to put the semiempirical calculations in their best light, one can set the relative heat of formation of HO2 H2C0 at zero, which yields AM1 and PM3 AHr,300 values for the reaction H 0 2 + H2CO OOCHzOH (111) of -19 and -6 kcal/mol, respectively. The AM1 value is close to the experimental value of -16 kcal/mol. However, using AMI, structure I1 was found to be 11 kcal/mol less stable than H 0 2 + H2CO but approximately at the same energy using PM3. Using either method, theactivationenthalpies for the two transition states, structures IV and V, were calculated to be much larger than zero. Moreover, using CI only on the TS (IV) structureandnot on thereactants did not reduce the transition state to near or below zero as found in the ab initio study discussed below. The semiempiricalmethods lead to the conclusion that neither mechanism 1 nor mechanism 2 explains the experimentalresults. B. An ab Initio Energetic Analysis. Table I1 shows the detailed UHF and UMP level energetics and structures for the HOz and HzCO reactants and the products and transition states, I-V, discussed above. Table I11 shows the BAC-calculated thermodynamic properties. Table IV gives the overall enthalpies of reactions for HO2 H2C0, yielding structures I-V at the UHF and various MP levels along with the BAC values. The first item of note is that all levels of ab initio calculations give the A Z f r , 3 ~of structure I11 values of between -15.2 and -16.5 kcal/mol, in agreement with the experimental value of -16.3 kcal/mol. The AHr,3w for structure I1 is also relatively correlation insensitive and approximately equal to the energy of the entrance channel, HO2 H2CO. The only complex candidate found in the ab initio calculations was that for the H-bonded complex, H2CO-HOO (I). The computed complexation enthalpies for the formation of this complex, on the order of -9 kcal/mol, were larger than we anticipatedby several kilocalories/mole. However, the formation of this complex from the reaction of HO2 + H2CO should be without an activation energy. Therefore, we conclude that the only candidate structure for the complex responsible for the negative activation energy in the kinetic studies is I and not 11. Structure I has a planar cisoid configuration (Figure 2). However, we also characterized (not shown here) a slightly higher energy planar transoid (zero negative frequencies) and a r-H-bonded (two negative frequencies) complex which had ZPE-corrected UHF energiesto within 1-2 kcal/mol of I. This gives the picture of an extremely loose complex in which the nonthermalized dynamics allow all these structures to play a conceptual role. The calculationsof the transition states IV and V encountered technical and conceptual difficulties. First of all, our initial assumption was that any transition state for the reaction of HO2
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Evleth et al.
5042 The Journal of Physical Chemistry, Vol. 97, No. 19, 1993
