J Phys. Chem. 1990, 94, 3242-3246
3242
Features of the Potential Energy Surface for Reactions of OH with CH,O Maribel R. Sotot and Michael Page* Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Code 4410, Washington, D.C. 20375-5000 (Received: October 17, 1989; I n Final Form: January 30, 1990)
We use ab initio multiconfiguration self-consistent-field (MCSCF) and multireference configuration interaction (MRCI) methods to investigate the potential energy surface for reactions of hydroxyl radical with formaldehyde. The appropriate minima, transition states, and products for hydrogen abstraction from formaldehyde and OH addition to the carbon or oxygen are located at the MCSCF level of theory with a double-[plus polarization (DZP) quality basis set. Dynamical correlation effects on the energetics are determined by single-point MRCI calculations at the MCSCF stationary points also with a DZP basis set. The contribution of zero-point vibrational energy to the energetics is estimated from analytical MCSCF harmonic vibrational frequencies. Our calculations predict a barrier height of 3.6 kcal/mol and an exothermicity of 21.7 kcal/mol for the abstraction reaction. The only other exothermic reaction channel involves radical addition to the carbon atom. This channel is predicted to have a barrier about 7 kcal/mol higher than the barrier for abstraction and is predicted to be exothermic by 13.8 kcal/mol. We also investigate the addition of hydroxyl to the oxygen atom of formaldehyde. This channel is endothermic by 40.9 kcal/mol and leads to a very shallow potential energy well which disappears when the effects of zero-point vibrational energy are considered
1. Introduction The bimolecular reaction of formaldehyde and hydroxyl radical H2CO O H H C O H2O (1)
+
+
+
along with the subssquent unimolecular decomposition of the formyl radical H + CO + M HCO + M (2) constitute key components of the chain processes for the combustion of hydrocarbons.lq2 Despite the well-recognized prominence of reaction 1, its rate is poorly characterized at combustion temperatures. Direct experimental studies from several laborat ~ r i e s now ~ - ~cover the temperature range 228-576 K. The rate is found to be only weakly dependent on temperature over this entire range, indicating that the reaction occurs essentially without activation. The rate in the combustion regime (> 1000 K), on the other hand, has been determined only by indirect methodss-I0 and is subject to substantial uncertainty. In particular, the kinetic modeling flame data of Peeters and Mahnen,* upon which the recommended value in the compilation of Tsang and Hampson2 is based, is considerably lower than the determinations of Vandooren and Van Tiggelen9 and of Westenberg and Fristom.'O These faster high-temperature results initially appeared to be inconsistent with the relatively temperature insensitive low-temperature results. However, by performing transition state theory (TST) calculations with adjustable frequencies, Zabarnick, Fleming, and Lin' were able to show that the two sets of data may be consistent with one another. Two low-frequencybending modes at the transition state, expected in such a low-barrier, highly exothermic abstraction reaction," essentially behave like classical (completely active) oscillators. This leads to substantial hightemperature curvature in the Arrhenius plot. It was noted, h ~ w e v e rthat , ~ the TST calculation does not predict as pronounced a temperature insensitivity below 600 K as do the measurements. In addition to its importance in combustion, the title reaction plays a well-recognized critical role in atmospheric chemistry, where formaldehyde is a pollutant and reaction with O H is a key source of its removal.12 A vexing problem at any temperature is that the mechanism of the reaction of OH with H 2 C 0 is not firmly established. Besides reaction I , the only other exothermic channel leads to formic acid, presumably prefaced by OH addition to the carbon atom yielding an intermediate radical complex: H,CO + O H H,C(OH)O (3) H,C(OH)O HC(0H)O H (4) +
+
+
+
'O N T i N R L Postdoctoral Associate. 0022-3654/90/2094-3242$02.50/0
These reactions were proposed by Horowitz, Su, and Calverti3 to account for the observed product formation in C H 2 0 / 0 2 mixtures photolyzed at 313 nm. In order to fit their results by computer modeling, reaction 3 was proposed to be twice as fast as reaction I . A number of studies have since attempted to ascertain the role of reaction 3 in reactions of OH and H 2 C 0 under various conditions. Any observation of pressure dependence in the rate constant would provide strong evidence for reaction 3 since the addition complex can be stabilized by collisions. A weak pressure dependence in the rate constant was in fact reported,I4 but the rate was later determined by the same authors to have been pressure independent within experimental uncertainty.'$ These authors also point out that the original justification for invoking reaction 3 by Horowitz was based on incorrect kinetic information concerning the formation of OH. Recently, Zabarnick et aL7 reported pressure independence over nearly an order of magnitude pressure range. Given the observed pressure independence and the lack of significant formic acid production at room t e m p e r a t ~ r e , ' ~there , ' ~ is no evidence that seems to demand a significant contribution from reaction 3. On the other hand, as pointed out by Stief et al.,5 pressure dependence in the formic acid route might not be observed if the addition complex proceeds
( I ) Glassman, 1. Combustion; Academic Press: New York, 1987. (2)Tsang, W.; Hampon, R. F. J . Phys. Chem. Ref.Data 1987, 15, 1087. (3) Morris, E. D.,Jr.; Niki, H . J . Chem. Phys. 1971, 55, 1991. (4) Atkinson, R.;Pitts, J. N. J . Chem. Phys. 1978, 68, 3581. (5) Stief, L. J.; Nava, D. F.; Payne, W. A,; Michael, J. V. J . Chem. Phys. 1980,73, 2254. (6) Temps, F.; Wagner, H. Gg. Ber. Bunsen-Ges. Phys. Chem. 1984.88, 415. (7) Zabarnick, S.; Fleming, J. W.; Lin, M. C. fnr. J . Chem. Kinet. 1988, 20, 117. (8) Peeters, J.; Mahnen, G . Symp. ( f n t . )Combust., [Proc.] 1973, 14rh, 133.
(9) Vandooren, J.; Van Tiggelen, P. J. Symp. (Int.) Combust., [Proc.] 1977, 16th. 1133. (IO) Westenberg, A. A.; Fristom, R. M. Symp. ( f n t . )Combust., [Proc.] 1965, loth, 473. ( 1 1 ) Dunning, T. H., Jr.; Harding, L. B.; Bair, R. A,; Eades, R. A.; Shepard, R. L. J. Phys. Chem. 1986, 90, 344. (12) Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Atmospheric Chemistry; Wiley: New York, 1986. (13) Horowitz, A.; Su,F.; Calvert, J. H. fnt. J . Chem. Kinet. 1978, 10, 1099. . .. .
(14)Niki, H.;Maker, P. D.;Savage, C. M.; Breitenbach, L. P. J. Phys. Chem. 1978.82, 132. (15) Niki, H.; Maker. P. D.; Savage, C. M.; Breitenbach, L. P. J. Phys. Chem. 1984, 88. 5342. (16) Morrison, B. M., Jr.; Heicklen, J. J. Photochem. 1980, 13, 189.
0 1990 American Chemical Society
Potential Energy Surface for O H
+ CHzO Reactions
The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 3243
to formic acid (reaction 4) faster than it decomposes back to reactants. At present, reaction 3 is not needed to explain any observations, but neither has it been ruled out. Whether, or under what conditions, the formic acid channel is able to compete with abstraction remains uncertain. In this paper, we report results of a b initio multiconfiguration (MC) SCF and large-scale multireference configuration interaction (MRCI) calculations of features of the potential energy surface for the abstraction reaction and the addition reaction. In addition, we investigate the addition of O H to the oxygen atom of formaldehyde to form a putative complex which is implicated as an intermediate in the reaction between CH3 and O2:I7 H2CO
+ OH
--+
HZCOOH
TABLE I: MCSCF/DZP Structural Parameters and Harmonic Vibrational Frequencies at the Stationary Points for H-Atom Abstraction
R(C,Oz), A R(C,HI),A R(C;H;), A R(H,Os), A R(OsH,), A LC,O,H,, deg LCIOZH,, deg L C I W ~deg . 4 0 5 H 6 ,deg
(5)
CASSCF/DZP Harmonic Vibrational Frequencies, cm-' 4067.5 4092.4 4204.6 3185.9 3 152.8 3862.2 2932.1 205 1.9 3006.1 2005.7 1594.0 2135.7 1609.9 1344.6 1737.5 1335.8 1201.6 1253.9 1295.0 879.5 519.5 384.0 156.0 152.7
In section 11, we describe details of the electronic structure methods used. This is followed by a description of the calculated results for each of the three channels considered. The results and conclusions are then summarized in the last section. 11. Theoretical Method The qualitative electronic structure changes taking place during abstraction (reaction 1 ) are predominantly confined to three electrons and three molecular orbitals (MOs). The equilibrium and transition-state structures as well as the harmonic vibrational frequencies have thus been determined by use of a three-electron, three-active-orbital complete active space (CASSCF) wave function.Is This is an MCSCF wave function formed by including all possible doublet configurations distributing the three active electrons among the three active orbitals. There are eight such configurations. At the reactants (OH + H2CO), the active MOs correspond to a C-H bonding and antibonding pair on formaldehyde and a radical orbital localized on the oxygen atom of OH. At the product these orbitals correspond to the bonding and antibonding orbitals for the incipient O H u bond in water and a singly occupied radical orbital on the formyl radical. The active space for the addition reactions is different than it is for abstraction. Here again we use a three-electron, threeactive-orbital CASSCF wave function, but the active orbitals for the reactants are the radical orbital on OH and the A and A* orbitals of formaldehyde. It is important to note that because the MCSCF configurations are different, calculated electronic energies for the two reaction channels cannot be directly compared to one another. Instead, energies for each of the channels must be compared directly to reactant energies calculated with the same MCSCF reference space. The overall energetics are determined from single-point calculations using CI wave functions involving all single and double excitations from all eight reference configurations. The MRCI wave functions employed in this study are all obtained within the frozen-core approximation: the orbitals that correlate with the Is core orbitals of the carbon atom and the oxygen atoms along with the associated virtual orbitals are excluded in the configuration selection and are thus forced to be doubly occupied and unoccupied, respectively. All of the calculations reported here use the same basis set, denoted DZP. This is the standard Dunning 4s/2p contractionI9 of the 9s/5p primitive set of Huzinaga20 on carbon and oxygen with single d-polarization functions with exponents 0.75 on carbon and 0.85 on oxygen and the corresponding unscaled 4s/2s contraction on hydrogen with a single p function of exponent 0.75. There are 63 contracted basis functions in the DZP basis set. The MRCI calculations described above include 735 306 doublet configurations. The electronic structure calculations were all carried out on the Cray XMP-24 at the Naval Research Labo-
(17) Zellner, R.; Ewig. F. J . fhys. Chem. 1988, 92, 2971. (18) Roos, B. 0.; Taylor, P. R.; Siegbahn, P. E. M. Chem. fhys. 1980,48, 152. (19) Dunning, T. H., Jr. J . Chem. fhys. 1970,53, 2823. Dunning, T. H.;
Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., 111, Ed.; Plenum Press: New York, 1977; Vol. 3. (20) Huzinaga, S. J Chem. Phys. 1965, 42, 1293.
HO + HzCO HO*.*H.**HCO Hi0 + HCO 1.1879 (1.1884)' 1.1735 (1.1737) 1.1618 (1.1619) 1.1188 (1.1154) 1.2860 (1.2694) 1.0955 (1.1154) 1.0975 (1.1201) 1.1064 (1.1308) 1.2859 (I .2963) 0.9649 (0.9679) 0.9571 (0.9793) 0.9548 (0.9794) 0.9466 (0.9679) 121.83 (122.06) 122.18 (122.57) 122.20 (122.06) 125.52 (125.14) 127.54 (126.65) 178.34 (177.79) 97.78 (96.29) 105.17 (103.62)
2927.91'
ZPE,b kcal/mol a
23.59
22.20
23.16
Parameters in parentheses are 7-in-7 CASSCF/DZP values from Zero-point vibrational energy.
ref 22.
ratory using the MESAZ' system of programs. 111. Abstraction The hydrogen abstraction from formaldehyde by hydroxyl occurs on a potential energy surface of *A' symmetry, for which all of the atoms remain in the plane of the formaldehyde. The unpaired electron on hydroxyl attacks one of the C H u bonds of formaldehyde. The two electrons in the CH bond become unpaired while one of these pairs with the O H radical electron to form the OH bond in water and the other remains as the radical electron in hydroxyl. As with many other hydrogen atom abstraction reactions," the predominant electronic structure changes are confined to three electrons and three MOs. We therefore use a three-electron, three-orbital (3-in-3) CASSCF reference description. The remaining electrons and MOs in the system can be regarded as spectators in the reaction: there are no major qualitative electron correlation changes for these electrons during the course of the reaction. There are, however, significant quantitative dynamical electron correlation effects involving these electrons. Dynamical correlation for all of the valence electrons is taken into account at the MRCI level. One consequence of adopting the 3-in-3 CASSCF reference description is that the correct molecular symmetry is nut recovered at the reactant and product asymptotes. For example, our calculated structures for formaldehyde and for water will not have Cz, symmetry because in each case, the two bonds to hydrogen are not treated equivalently. This inequivalent treatment is expected to have an insignificant effect on the energetics a t the MRCI level. The geometries for the reactants, the transition state, and the products were fully optimized at the 3-in-3 CASSCF level of theory. Structural parameters as well as the CASSCF/DZP harmonic vibrational frequencies are shown in Table I. Also shown are the 7-in-7 CASSCF/DZP structures reported by Dupuis and Lester2z(DL) as part of their study of hydrogen atom abstraction from formaldehyde. DL included in the active space of the MCSCF those electrons and orbitals necessary to ensure the proper asymptotic symmetry. The structures are fairty similar ~~
(21) MESA (Molecular Electronic Structure Applications); Saxe, Martin, R.;Page, M.;Lengsficld, 9. H. (22) Dupuis, M.; Lester, W. A. J . Chem. f h y s . 1984, 81. 847.
P.;
3244 The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 96,
Soto and Page TABLE 111: MCSCF/DZP Structural Parameters and Harmonic Vibrational Frequencies at the Stationary Points for OH Addition to Carbon
R(Ci02). A R(CiOh, A R(O,H4), A R(CIH&,A R(CiH6). A L C , O ~ Odeg ~, LC,O,H,, deg LHSClO2,deg LH&IO~,deg LH,O~C,O~, deg 4 C I 0 3 H 4 ,deg L H ~ C I O ~deg H~,
Figure 1. Structure of the saddle point on the 3-in-3 CASSCF/DZP potential energy surface for H-atom abstraction from formaldehyde by OH. TABLE 11: Relative Energies of the Reactants, Transition State, and Products for the Abstraction Reaction (kcal/mol) wave function HO + HzCO HO-H-.HCO H 2 0 + HCO H Fa 0.0 26.9 -9.2 3-in-3 CASSCF* 0.0 18.5 - I 2.5 7411-7 CASSCFO 0.0 15.2 -14.6 HF/SDCI" 0.0 9.3 -20.7 MRClb 0.0 3.6 -21.6 0.0 -0.0 -31.2 expt'
"Reference 22. bThis work. rHeat of formation: CH20, ref 23: CHO, ref 24; H20. OH, ref 25. at the two levels of theory. The transition-state structure at the 3-in-3 CASSCF/DZP level is shown in Figure 1. The three atoms involved in the transfer are nearly collinear, with an angle of 178.3' at the transition state. The incipient OH bond in water is stretched by 0.324 A at the transition state, or about 35% of its asymptotic length. The CH bond is stretched considerably less: 0.1 67 A or about 15% of its original length. The transition state is therefore somewhat early as one expects for an exothermic reaction. However, the true saddle-point structure probably resembles reactants more than do either of the calculated transition-state structures reported in Table 1. This is because the MCSCF wave function significantly underestimates the exothermicity of the reaction. The 19 kcal/mol error in the reaction exothermicity is reduced by about half upon performing the MRCI calculations based on the CASSCF reference orbitals. Table 11 shows the energetics, including corrections for zero-point vibrational energy differences, at several levels of theory and from experiment. Since all of the calculations represented in Table I1 use a DZP quality basis set the large differences between the different calculated barrier heights and exothermicities can be attributed to electron correlation effects. The single and double CI (SDCI) based on the Hartree-Fock (HF) reference orbitals provides substantially better energetics than either the H F or the CASSCF calculations and nearly reproduced the MRCI exothermicity. The barrier height is still considerably higher at the SDCI level than it is at the MRCI level, illustrating-as pointed out by DL-the importance of using a a multiconfiguration reference description for (23) Chuang, M. C.: Foltz, M. F.: Moore, C. B. J. Chem. Phys. 1987, 87,
3855.
(24) Baulch, D. L.; COX,R. A.: Crutzen, P. J.; Hampson, R. F., Jr.: Troe. J.; Watson, R. T. J. Phys. Chem. Re/. Data 1982, I / . 493. (25) J A N A F Thermochemical Tables, 2nd ed.: National Bureau of Standards: Washington, DC, 1971.
CH20 + OH 1.2089 0.9567 1.0923 1.0923 121.27 121.27
TS" 1.2694 1.8335 0.9556 1.0832 1.0832 98.64 102.09 1 18.66 1 18.66 0.00
103.66 -103.66
HzC(0)OH 1.3706 1.4108 0.9473 1.0846 1.0911 114.13 108.74 109.16 105.69 54 12 174.68 -65.76
CASSCF/DZP Harmonic Vibrational Frequencies, cm-l 4072.9 4083.0 4165.2 3253.3 3349.2 3286.3 3162.8 3247.5 3193.8 1856.1 1684.9 1588.6 1634.4 1441.1 1552.3 1449.8 1351.2 1320.I 1 124.0 1232.4 1167.5 1001.1 1 186.8 831.2 1078.4 348.3 973.2 109.3 566.0 982.I i 303.4 ZPE,*kcal/mol
23.67
26.50
29.42
Transition state. *Zero-pointvibrational energy. the CI. When DL apply a correction to the SDCI energies for quadruple excitations, the activation energy is lowered to 4.0 kcal/mol, much closer to the MRCI value of 3.6 kcal/mol. Second-order MRCI wave functions have been shown to be capable of nearly reproducing full-CI results, providing all the important references for nondynamical electron correlation are included.26 Given the nearly 10 kcal/mol errors in the reaction exothermicity at both the 3-in-3 MRCI level reported here and at the SDCI level corrected for effects of quadruple excitations reported by DL, much of the remaining errors are likely attributable to basis set effects. An important result emerges from the transition-state frequencies reported in Table I. Despite the likelihood of the calculated transition state being located too far toward products, the two nearly degenerate bending modes have very low frequencies: 153 and 157 cm-'. These low-frequency motions, which arise out of free rotations of the reactants, can be expected to have even lower frequencies at a level of theory for which the transition state more resembles reactants. Therefore, the frequencies of 139 cm-l that Zabarnick et al.' needed to assume in order show consistency between the low-temperature and faster high-temperature data are reasonable. IV. Addition to the Carbon Atom As mentioned previously, the CASSCF reference wave function includes different orbitals in the active space for the addition reactions than it does for the abstraction reaction. Here the OH radical electron attacks the formaldehyde A bond. The three active orbitals are thus the OH radical orbital and the A and A* orbitals. Unlike our treatment of the abstraction reaction, correct asymptotic molecular symmetry is recovered for the addition reactions. Structures for the reactants, transition state, and radical addition complex were fully optimized at the 3-in-3 CASSCF level of theory. Structural parameters, as well as harmonic vibrational frequencies and resulting zero-point vibrational energies, are given in Table 111. The initial approach up to and including the transition state for OH addition to the carbon atom has C, symmetry with the hydroxyl H atom eclipsing the 0 atom of form( 2 6 ) Bauchlicher, C. W : Taylor, P. R. J. Chem. Phys. 1987,86,
5600.
Potential Energy Surface for O H
+ C H 2 0 Reactions
The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 3245 TABLE I V MCSCF/DZP Structural Parameters and Harmonic Vibrational Frequencies at the Stationary Points for OH Addition to Oxygen
CH,O+OH
TS'
CHZOOH
I .2089
1.3570 1.5162 0.9508 1.0744 1.0778 107.20 98.00 116.80 11 5.53 -144.05 30.69 -121.89
1.3642 1.4851 0.9504 1.0771 1.0779 107.12 99.27 116.25 110.17 -120.20 -33.39 -174.30
R(C102)qA
A R(O3Hd+A R(CIHS),A R(CIH~),A R(Oz03).
Figure 2. Structures of the saddle point and the product on the 3-in-3 CASSCF/DZP potential energy surface for OH addition to the carbon atom of formaldehyde.
aldehyde. After the saddle-point region is traversed, the minimum energy path bifurcates, leading to one of two equivalent conformations for the addition complex which has no elements of symmetry. This behavior of the minimum energy path is reminiscent of that for the methoxy radical isomerization to the hydroxymethyl r a d i ~ a l . ~The * ~ ~resulting ~ H O C H 2 0 addition complex can best be described as having a gauche arrangement of the HOCO framework. The transition state and addition complex are shown in Figure 2. At the level of the CASSCF reference calculations, the zero-point energy corrected barrier and exothermicity for the addition of O H to the carbon atom of formaldehyde are 20.5 and 4.7 kcal/mol, respectively. MRCI/DZP energies were determined at the CASSCF/DZP geometries. The barrier for addition of O H to the carbon atom is found to be 10.4 kcal/mol including the correction for zero-point vibrational energy. The addition reaction is calculated to be exothermic by 13.8 kcal/mol. In addition to the cis-HOC0 path described above, one might also expect an O H approach for which the HOCO framework is in a trans configuration. We were unable to locate a transition state for a trans approach. We were able to optimize an anti conformation for the addition complex. This complex has A" symmetry: the radical orbital on the oxygen is out of the HOCO plane and thus this state does not correlate with dissociation back to the ground state of formaldehyde. At the MRCI level, this anti conformation is 2.7 kcal/mol above the gauche confirmation. The abstraction reaction is calculated to have a barrier of 3.6 kcal/mol and known experimentally to have essentially no barrier at all. The barrier for the addition reaction is not known experimentally. It is reasonable to make the assumption that the MRCl/DZP value for the difference between the barriers for the two channels is more reliable than the calculated values of the barriers themselves. On the basis of this assumption, the true barrier for OH addition to the carbon atom is estimated to be about 7 kcal/mol. A 7 kcal/mol barrier for this reaction is consistent with the lack of formic acid production observed for the OH H,CO reaction.6*15*16 Given a 7 kcal/mol difference in activation energies, the formic acid route, in fact, is unlikely to occur at any temperature. At low and moderate temperatures, this route is ruled out on energetic grounds. Also, the looser transition state for the abstraction reaction-in particular, the presence of two anomalously low frequency bending modes-and the concomitant rapid increase in the abstraction rate with temperature render the addition route leading to formic acid unlikely to be competitive at high temperature as well.
+
V. Addition to the Oxygen Atom I n their study of the CH, O2reaction," Zellner and Ewig
+
propose a mechanism consisting of C H 3 0 0 complex formation followed either by dissociation to C H 3 0 0 or by isomerization to C H 2 0 0 H with subsequent rapid dissociation to C H 2 0 + OH.
+
(27) Vaghjiani, G.L.; Ravishankare, A. R. J . Phys. Chem. 1989, 93, 1948. (28) Saebo, S.;Radom. L.; Schaefer, H. F. J . Chem. Phys. 1983,78,845. (29) Colwell, S. M.:Handy, N . C. J . Chem. Phys. 1985.82, 1281.
LC10203,deg ~ 0 ~ 0 ~ deg H4, L H ~ C ~deg O~, &C1Ozr deg L H ~ O ~ Odeg ~C~, L H ~ C , O ~deg O~, LH.&OA deg
0.9567 1.0923 1.0922 1 12.00 106.17 121.30 121.25
CASSCF/DZP Harmonic Vibrational Frequencies, cm-' 4072.9 3253.3 3162.8 1856.1 1634.4 1351.2 1167.5
ZPE,b kcal/mol
23.67
4141.0 3446.6 3301.7 1581.1 1410.3 1246.1 1205.7 713.8 659.0 457.8 175.8
I98.0i
4142.0 3427.6 3294.0 1565.1 1433.8 1280.4 1234.0 933.6 743.9 485.4 284.1 175.1
26.22
27.16
Transition state. Zero-point vibrational energy. These authors conclude that the isomerization channel dominates the reaction at all temperatures below 2800 K. Although it has no substantive consequence for the CH3 O2branching reaction, the structure and properties of the putative CHzOOH radical are not known, nor has its existence been established. Conceptually, this species is formed from O H and H 2 C 0 by breaking the formaldehyde n bond and forming a peroxy bond. One can use bond additivity to estimate the energy of this complex, but such rules give no information about whether or not the complex represents a minimum on the potential energy surface (PES). This is particularly pertinent since the energy of the peroxy bond is less than the C O *-bond energy forsaken to form the complex. There are some unusual features of the PES for formation of the CHIOOH addition complex from O H and H 2 C 0 that make the transition state particularly difficult to locate. Consider O H approaching the oxygen of formaldehyde. The reaction is overall uphill in energy, and therefore the initial approach must be repulsive; however, the approach is least repulsive if the CH2 group is oriented such that the maximum C O n overlap is retained as the 00 bond begins to form. Thus the CH2 group must bisect or nearly bisect the OOC plane. After considerable effort, it became apparent that although the energy profile-essentially as a function of 00 separation-nearly flattened out, it remained repulsive for all configurations meeting the above criterion. In order to reach a local minimum on the PES for the complex, after the reactants are brought into close proximity the p-type orbital of the C H 2 radical must be rotated away from the 00 bond to prevent any n-type stabilization with increased 00 separation. The net result is that there exists a shallow local minimum for CHzOOH which is separated from the dissociated products by an activation energy which is essentially a barrier to internal rotation of a terminal methylene group, about 1 kcal/mol. The motion corresponding to the eigenvector of the force constant matrix with negative eigenvalue has only a minor contribution from 00 separation. After the transition-state region is traversed from the complex, the energy becomes repulsive along the 00 separation direction and the reaction path turns to include a large component of 00 separation. * The structures of the transition state and the addition complex are shown in Figure 3 and the structural parameters are given in Table 1V. At the MRCI/DZP level of theory, the addition
+
Soto and Page
3246 The Journal of Physical Chemistry, Vol. 94, No. 8, 1990
40.9
40.8
i - --- --- -
CHzOOH
I
,
I
I
Figure 3. Structures of the saddle point and the product on the 3-in-3 CASSCF/DZP potential energy surface for OH addition to the oxygen
I I
