Chemical Physics 282 (2002) 305–314 www.elsevier.com/locate/chemphys Ab initio and RRKM calculations for the decomposition channels of CH3OBr and BrCH2OH Demetrios K. Papayannis, Evangelos Drougas, Agnie M. Kosmas * Physical Chemistry Laboratory, Department of Chemistry, University of Ioannina, 45110 Ioannina, Greece Received 8 March 2002 Abstract Quantum mechanical and RRKM calculations are carried out to study the potential energy surface and the kinetics for the six most important decomposition channels of methyl hypobromite ðCH3 OBrÞ. Optimized geometries, vibrational frequencies, and relative energies have been obtained for the various stationary points. The O–Br bond scission to CH3 O þ Br products and the 1,2 elimination pathway leading to HCHO þ HBr appear to be the most important dissociation channels. Analogous paths from the isomeric BrCH2 OH are also examined. The calculations are compared with the results for the other two similar systems, CH3 OF and CH3 OCl. Ó 2002 Elsevier Science B.V. All rights reserved. 1. Introduction The species CH3 OX (X ¼ halogen atom), especially those with X ¼ Cl, Br were early recognized to play a significant role in several of the processes involved in stratospheric ozone depletion cycles [1– 15]. Thus, numerous studies have been devoted to the theoretical and experimental investigation of the properties of these compounds [16–29]. Also several studies have been devoted to the examination of the potential energy surface for the decomposition and isomerization pathways of two of the members of this series, CH3 OF [30,31] and CH3 OCl [32–35] and the experimental investigation of the related association reactions CH3 O þ X and CH3 þ OX, X ¼ F, Cl, Br [8–11,14,15,36,37]. * Corresponding author. Fax: +30-5109-8798. E-mail address: [email protected] (A.M. Kosmas). Hence, to contribute to the completion of this family, the decomposition and isomerization pathways of CH3 OBr are investigated in the present work. As in the case of the other two similar compounds, CH3 OF and CH3 OCl, there are six main channels in the decomposition scheme of CH3 OBr: CH3 OBr ! HCHO þ HBr ð1Þ CH3 OBr ! BrCH2 OH ð2Þ CH3 OBr ! cis–HCOBr þ H2 ð3Þ CH3 OBr ! CH3 O þ Br ð4Þ CH3 OBr ! CH3 þ OBr ð5Þ CH3 OBr ! CH2 þ HOBr ð6Þ In addition, the following production pathways of the isomeric bromomethanol are of interest, i.e., 0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 7 2 0 - 6 306 D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 the four-center 1,2 HBr elimination, (7), the 1,2 HH elimination, (8), and the isomerization to CH3 OBr, (9) BrCH2 OH ! HCHO þ HBr ð7Þ BrCH2 OH ! H2 þ BrCHO ð8Þ BrCH2 OH ! CH3 OBr ð9Þ These processes are also examined as being closely associated with the corresponding pathways of CH3 OBr system. 2. Quantum mechanical calculations and results The geometries of all reactants, products, and stationary points have been fully optimized at the UMP2(full)/6-311+G(d, p) level of theory. Harmonic frequency calculations were carried out at the same level of theory and the zero-point energies were determined. To improve the reliability of the energetics, single-point energies at the QCISD(T)/ 6-311+G(d, p) and UMP2(full)/6-311+G(3df, 2p) levels of theory were calculated at the optimized geometries. Based on these values G2MP2 theory [38] was employed and the G2MP2 energies were obtained. All calculations were performed with the Gaussian 98 series of programs [39]. Optimized geometries for the stationary points on the potential energy surface and BrCHO product are shown in Fig. 1 and the reaction energy profile is depicted in Fig. 2. Like the other members of the CH3 OX family, CH3 OBr possesses a trans-structure in Cs symmetry in consistency with the literature results and a cis-conformation located 2.8 kcal mol1 higher. The second energy minimum, BrCH2 OH, is located 34.5 kcal mol1 lower than CH3 OBr. Calculated harmonic vibrational frequencies and moments of inertia are listed in Table 1. Our geometrical and frequency results for CH3 OBr are within 5% of the B3LYP/ 6-311++G(3d2f, 3pd) results of Guha and Francisco [21,29] and the results of Messer et al. [22] and Espinosa-Garcia [22,26]. In addition to the energy minima five tight transition state structures have been determined, labeled according to the associated pathway as TS1, TS2, TS3, TS7, and TS8. The stable structures are characterized by positive frequencies and the transition states possess one imaginary frequency. The MP2/6311+G(d, p) and G2MP2 total electronic energies and the relative energetics with respect to CH3 OBr minimum for all decomposition channels studied, (1)–(9), along with the corresponding ZPE corrections, are listed in Table 2. The structural and frequency results obtained for H2 ; CH2 ; CH3 ; CH3 O, and HCHO are in good agreement with previous studies of other CH3 OX systems [30–33] and they are not depicted here for space reasons. Also the results for HBr and HOBr are in good agreement with literature results [22,23,26,40]. As in both CH3 OF and CH3 OCl, an important decomposition channel in CH3 OBr is the 1,2 hydrogen halide elimination process to HCHOþ HBr products, channel (1). The mechanism involves first the isomerization to the cis-form through a rotation about the C–O bond and the subsequent elimination of HBr via a four-member ring-type, tight transition state, TS1, located about 49 kcal mol1 . TS1 has Cs symmetry with an imaginary frequency 3253i cm1 . The O–Br and , C–H bonds are elongated by 0.672 and 0.128 A respectively, and the forming H–Br bond is 0.991 longer than the equilibrium bond length in HBr A molecule [40]. CH3 OBr is unstable with respect to products HBr þ HCHO by 26 kcal mol1 . Channel (2) involves the isomerization to bromomethanol via the tight transition state, TS2, located about 67 kcal mol1 higher with an imaginary frequency 808i cm1 . The mechanism involves the simultaneous migration of H atom to O and of Br atom to C. The high isomerization barrier makes CH3 OBr kinetically stable with respect to BrCH2 OH but the isomeric bromomethanol is thermodynamically more stable than methyl hypobromite by about 34 kcal mol1 . The third channel (3) is a 1,1 HH elimination process leading to H2 þ cis-HCOBr through the transition state TS3, located at 71 kcal mol1 with an imaginary frequency 1410i. The two breaking C–H bonds are , respectively, and the forming 1.281 and 1.492 A , i.e., only 0.367 A H–H bond length is 1.105 A longer than the equilibrium bond length in H2 . The high transition state barrier in combination with the considerable endothermicity, 32 kcal D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 307 Fig. 1. Optimized UMP2(full)/6-311+G(d, p) structures for stationary points on the potential energy surface. Distances are in ngstr€ A om and angles in degrees. mol1 , makes this channel highly improbable at thermal energies. Pathways (7) and (8) represent similar decomposition channels of bromomethanol, quite analogous to (2) and (3) of CH3 OBr. Thus, channel (7) is also a 1,2 elimination process to HCHO þ HBr through the ring-type transition state TS7 and channel (8) a 1,2 HH elimination to H2 þ BrCHO through TS8. In TS8 the C–H and 308 D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 Fig. 2. Potential energy surface for CH3 OBr and BrCH2 OH decomposition. , O–H bonds are elongated to 1.341 and 1.388 A respectively. The other three decomposition channels (4)–(6) represent barrierless dissociation processes and no detectable energy barriers could be determined, like the similar processes in CH3 OF and CH3 OCl systems. Channels (4) and (5) involve simple bond fissions of O–Br and C–O bonds, respectively, and channel (6) occurs through an H-shift mechanism producing 1 CH2 and HOBr. The calculated potential energy surface shows that methyl hypobromite is very stable with respect to the products of these three channels at thermal reaction energies. As already said, these pathways take place without tight transition state configurations and they represent cases of unimolecular dissociations for which the reverse association reactions are also barrierless. Such cases have been an extensively treated subject and various variational approaches have been suggested within the frame of RRKM theory to handle the absence of a well-defined critical configuration in the initial addition step [41–45]. In the present work we have adopted the variational procedure of Schatz and coworkers [46]. Following this approach, we have examined energies, geometries, and frequencies at several reaction points RPij , i ¼ 4, 5, and 6, j ¼ a; . . . ; f , along the minimum energy path for each of routes (4)–(6) by increasing the relevant bond coordinate [47]. The highest energy points in each pathway, labeled RP4, RP5, and RP6 respectively, have been the points where the minimization of the microcanonical rate constant has been achieved as we shall see in the following section. In other words, these points have been used, each, as a loose critical point configuration for the pathway under consideration. Their properties are also collected in Table 1. Of interest is the comparison of the potential energy surface of the present system with CH3 OF [30,31] and CH3 OCl [32–35], with which significant similarities and differences are observed. Thus, as in CH3 OF and CH3 OCl; CH3 OBr is thermodynamically stable with respect to all decomposition channels with the exceptions of the 1,2 hydrogen halide elimination, channel (1) and the isomerization channel to the corresponding halogenated methanol, channel (2). However, the associated energy barriers for processes (1)–(4) are located lower in CH3 OF [30,31] than in the other two methyl hypohalites. Hence, larger values of the microcanonical rate coefficients have been indeed obtained in CH3 OF [31] than in the other two systems. Among the important dissociation pathways of bromethanol, the 1,2 elimination to HCHO þ HBr appears to be the major channel followed by the D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 309 Table 1 2 ) for reactants, products, and stationary UMP2(full)/6-31++-G(d, p) harmonic frequencies ðcm1 Þ and moments of inertia (amu A points Frequencies CH3 OBra cis-CH3 OBr BrCH2 OH TS1 TS2 TS3 TS7 TS8 RP4 RP5 RP6 CH3 CH2 cis-HCOBr BrCHO HOBr OBr HBr CH3 O HCHO H2 3186, 3100, 3226, 3878, 3078, 3996, 3211, 3336, 3120, 3087, 3359, 3174, 3370, 3439, 3075, 3106, 3828, 750 2742 3140, 3052, 4533 CH3 OBr BrCH2 OH TS1 TS2 TS3 TS7 TS8 RP4 RP5 RP6 Ia 12.59 13.12 16.18 9.43 12.37 15.89 12.23 14.23 23.20 21.30 3156, 3083, 3203, 3235, 2988, 3241, 2688, 3187, 2360, 3086, 3358, 3079, 3370, 3206, 2068, 1799, 1143, 3067, 3012, 3108, 3133, 1680, 3127, 1746, 2740, 2059, 3049, 3166, 2983, 3177, 1145 1028, 1345, 681 1524, 1506, 1557, 1517, 1539, 1536, 1517, 1613, 1593, 1535, 1457, 1490, 1444, 1484, 1463, 1546, 1410, 1275, 1271, 1301, 1428, 1355, 1426, 1455, 1348, 1444, 1481, 1200, 1187, 1048, 581, 319, 253 1456, 1187, 1170, 1009, 592, 316, 234 1513, 1210, 1167, 1040, 592, 353, 258i 1355, 1196, 1126, 940, 625, 426, 306 1246, 1213, 970, 524, 356, 245, 3253i 1207, 1012, 950, 417, 415, 237, 808i 1087, 929, 847, 382, 315, 209, 1410i 1460, 1182, 1031, 894, 510, 250, 642i 1280, 1051, 885, 617, 551, 272, 2259i 1390, 1176, 1150, 1011, 213, 200, 200i 968, 687, 569, 540, 191, 68, 265i 895, 632, 475, 375, 250, 125, 153i 461 705, 348, 206 929, 663, 370 3103, 3020, 1545, 1430, 1423, 1136, 984, 809 2981, 1764, 1559, 1279, 1206 Ib 120.50 133.48 156.13 179.76 165.78 162.88 144.10 206.10 160.51 148.69 Ic 134.20 142.22 168.79 185.70 172.42 176.29 150.79 217.25 180.90 167.93 Ir 8.4 8.9 9.2 9.5 9.3 9.3 9.2 10.2 9.4 9.3 a The first line contains the results of present work while the second line contains the results of Ref. [28] at the B3LYP/6311++G(3d2f, 3pd). 1,2 HH elimination to H2 þ BrCHO. The isomerization process is much less probable since the associated isomerization transition state, TS2, is located much higher in the potential energy surface compared to TS7 and TS8 for the elimination processes. Two other fragmentation routes are possible in principle as in chloromethanol [35], the C–O and C–Br bond fission pathways, but the products are very high located and they may become significant only at very large reaction energies under photogragmantation conditions as in the ClCH2 OH case. 3. Unimolecular decomposition rate constants The energy-specific microcanonical rate constants, ki ðJ ; EÞ, for the reaction channels (1)–(9) were evaluated using the RRKM (Rice–Ramsperger–Kassel–Marcus) theory. For a given reaction step at an initial reactant energy E, ki ðJ ; EÞ is given by ki ðJ ; EÞ ¼ Wi ðJ ; EÞ=h.M ðJ ; EÞ; ð10Þ where J is the reactant rotational state, h is the Planck’ s constant, .M ðJ ; EÞ is the density of states 310 D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 Table 2 Total (Hartree) and relative (kcal mol1 ) energies and ZPE corrections ðkcal mol1 Þ for optimized species involved in CH3 OBr and BrCH2 OH decomposition channels Species Total energies including ZPEa CH3 OBr BrCH2 OH TS1 TS2 TS3 TS7 TS8 HCHO þ HBr cis-HCOBr þ H2 CH3 O þ Br CH3 þ OBr CH2 þ HOBr BrCHO þ H2 )2687.679082 )2687.743011 )2687.592982 )2687.618816 )2687.568812 )2687.680516 2687.602980 )2687.730792 )2687.626162 )2687.613421 )2687.543548 )2687.544343 )2687.726733 )2687.325622 )2687.386647 )2687.246238 )2687.216675 )2687.207924 )2687.326688 )2687.233295 )2687.368818 )2687.248742 )2687.267483 )2687.198105 )2687.181029 )2687.357843 )2687.461075 )2687.516156 )2687.382534 )2687.353863 )2687.347751 )2687.457151 )2687.376669 )2687.502526 )2687.388554 )2687.386790 )2687.335309 )2687.317277 )2687.497782 DEb ZPE 0.0 )34.5 49.2 67.2 71.1 2.5 52.9 )26.0 45.4 46.6 78.8 90.2 )23.0 25.2 26.0 20.4 21.2 19.4 24.9 20.4 19.9 15.7 22.6 19.2 18.1 17.3 a First column gives the optimized MP2/6-311+G(d, p) results, the second column the single point QCISD(T) results and the third column the G2MP2 results. All electronic energies include the ZPE corrections. b Energy differences listed correspond to G2MP2 values. The reliability of these energy differences may be appreciated from the comparison of the theoretical and experimental reaction enthalpies at 298 K for CH3 O þ Br ! HCHO þ HBr, which are )72.1 and )65.7 [15] kcal mol1 , respectively. available to the minimum, M ¼ CH3 OBr or M ¼ BrCH2 OH, at a reactant energy E and Wi ðJ ; EÞ is the number of states for the active degrees of freedom of the transition state TSi being involved in the considered reaction step i ¼ 1; . . . ; 9. The calculations have been carried out employing the corresponding algorithm by Zhu and Hase [48]. The required input for the calculations includes the relative energies, the vibrational harmonic frequencies, and the moments of inertia, which are all collected in Tables 1 and 2. RRKM theory was directly applied to the decomposition channels (1), (3), (7) and (8) and the interisomerization processes (2) and (9), which were found to proceed via the tight transition state configurations, TS1, TS3, TS7, TS8, and TS2. Processes (4)–(6) take place via barrierless decomposition pathways and for the examination of these channels the principles of variational RRKM theory were employed as described in the previous section. According to variational theory, the bottleneck of a reaction occurs at the point along the minimum energy path where the number of states available, and hence the microcanonical rate constant, is at a minimum [41–47]. Consequently, calculations have been done at several reaction points along the minimum energy path for each Fig. 3. Microcanonical rate constants kðJ ; EÞ for pathways (1)– (6). D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 production pathway until a minimum in the rate is found, thereby defining the reaction bottleneck. Like in previous variational RRKM calculations for radical-molecule and radical–radical barrierless association and decomposition reactions we have found that the minimum in the rate occurs at a reaction point, RPj , located at the highest energy point along the minimum energy path [46,47]. These points labeled RP4, RP5, and RP6 have been used for the evaluation of the microcanonical rate coefficient for channels (4)–(6), respectively. The calculations have been carried out in the range of energies from E0 to 300 kcal mol1 and J ¼ 50. The lowest energy value was set just equal to the first dissociation potential threshold and the selected J value was taken to be the highest populated rotational quantum number at 300 K. The resulting microcanonical rate constants are shown in Figs. 3 and 4 for CH3 OBr and BrCH2 OH decomposition, respectively. Due to the lowest dissociation threshold, k4 which corresponds to the O– Br bond scission, assumes the greatest value of all channels at the lowest energies but it is readily followed by k1 the 1,2 HBr elimination. Thus, k1 , and k4 soon cross and k1 rises fast dominating the overall dissociation process for a large energy range up to 200 kcal mol1 . Above this value most channels begin to compete and become important with the exception of the O–Br bond scission, channel (4) and the isomerization channel (2) that fall lower. In the BrCH2 OH case things are more Fig. 4. Microcanonical rate constants kðJ ; EÞ for pathways (7)– (9). 311 clear and the resulting kðJ ; EÞ rise more slowly, demonstrating the greater stability of bromomethanol. The most important decomposition process remains the 1,2 elimination to HBrþ HCHO throughout the interesting energy region. The increasing contribution to the centrifugal barrier with increasing J results in a considerable drop of the microcanonical rate coefficient, kðJ ; EÞ and hence a strong J dependence is obtained. To demonstrate the effect of the J dependence, another series of calculations were carried out at two additional J values, J ¼ 0 and 20, focused on channels (1) and (4) that are the most interesting production pathways of CH3 OBr decomposition. The calculated k1 and k4 values are depicted in Fig. 5 which shows nicely the rapid drop of both rate coefficients with increasing J and the faster decrease of k1 as the result of the tighter transition state TS1 intervening in this process [49,50]. In channel (4) where a loose transition state is accounted for, a weaker dependence is obtained [49,50], since the large moments of inertia decrease the rotational constants and weaken the J effect. Detailed k values are also listed in Table 3 where the same phenomena may be seen. Table 3 also shows the decreasing significance of J as the energy rises. Above 100 kcal mol1 the decrease in the k’s with increasing J is much milder and the J effect is much less dramatic in the high energy region. A final comment may be made regarding the energy ordering of the critical configurations for the important decomposition channels, namely the 1,2 hydrogen halide elimination, the isomerization to halogenated methanol and the oxygen–halogen bond scission leading to methoxy radicals and halogen atoms. This ordering may have an interesting influence on the reactions of methoxy radicals with X, X ¼ F, Cl, Br since the mechanism of these reactions involves the intermediate formation of CH3 OX and its subsequent decomposition following the potential energy surface studied. Indeed, the various experimental studies [8,11,14, 15,36,37] have produced quite different values for the bimolecular rate coefficient of each such reaction. A large rate constant, ð1:5 0:8Þ 1010 cm3 molecule1 s1 [36], almost unit probability in every collision, was obtained in the CH3 O þ F ! HCHO þ HF reaction where the associated tran- 312 D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 Fig. 5. Microcanonical rate constants kðJ ; EÞ for pathways (1) and (4) for different J values. D.K. Papayannis et al. / Chemical Physics 282 (2002) 305–314 313 Table 3 Microcanonical rate coefficients, k1 and k4 in s1 for different J values E (kcal mol1 ) 50 52 54 56 58 60 62 64 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 k4 k1 J ¼0 20 50 J ¼0 20 50 5.65E8 5.34E9 2.38E10 7.57E10 1.95E11 4.38E11 8.82E11 1.64E12 2.85E12 7.43E12 1.13E13 1.67E13 2.39E13 3.33E13 4.55E13 6.09E13 8.01E13 1.04E14 1.32E14 1.67E14 2.08E14 2.56E14 3.12E14 3.76E14 4.51E14 5.35E14 6.31E14 7.39E14 8.61E14 2.52E8 3.56E9 1.78E10 6.02E10 1.62E11 3.73E11 7.68E11 1.45E12 2.56E12 6.81E12 1.04E13 1.55E13 2.23E13 3.14E13 4.30E13 5.79E13 7.64E13 9.92E13 1.27E14 1.61E14 2.00E14 2.47E14 3.02E14 3.65E14 4.38E14 5.21E14 6.16E14 7.22E14 8.42E14 2.63E6 5.06E8 4.35E9 1.97E10 6.44E10 1.71E11 3.90E11 8.01E11 1.51E12 4.44E12 7.08E12 1.09E13 1.61E13 2.33E13 3.27E13 4.48E13 6.03E13 7.96E13 1.03E14 1.32E14 1.67E14 2.09E14 2.58E14 3.15E14 3.81E14 4.57E14 5.43E14 6.42E14 7.52E14 7.75E9 2.66E10 7.08E10 1.60E11 3.21E11 5.91E11 1.02E12 1.66E12 2.57E12 5.58E12 7.87E12 1.08E13 1.46E13 1.93E13 2.50E13 3.19E13 4.02E13 5.00E13 6.15E13 7.49E13 9.02E13 1.08E14 1.28E14 1.50E14 1.75E14 2.03E14 2.34E14 2.69E14 3.06E14 5.37E9 2.02E10 5.67E10 1.33E11 2.74E11 5.14E11 8.99E11 1.48E12 2.33E12 5.14E12 7.29E12 1.01E13 1.37E13 1.81E13 2.36E13 3.03E13 3.83E13 4.78E13 5.89E13 7.19E13 8.68E13 1.04E14 1.23E14 1.45E14 1.70E14 L97E14 2.28E14 2.62E14 2.99E14 1.04E9 5.74E9 2.02E10 5.55E11 1.29E11 2.66E11 5.00E11 8.76E11 1.45E12 3.46E12 5.06E12 7.19E12 9.98E12 1.35E13 1.80E13 2.35E13 3.02E13 3.82E13 4.77E13 5.89E13 7.20E13 8.70E14 1.04E14 1.24E14 1.46E14 1.71E14 1.99E14 2.30E14 2.64E14 sition state barrier TS1 in the exit pathway is located about 9 kcal mol1 below the reactant energy level, CH3 O þ F [30,31]. On the other hand, in CH3 OCl and CH3 OBr systems, the quantum mechanically calculated transition states TS1 for the similar decomposition pathways to HCHO þ HCl and HCHO þ HBr, respectively, are calculated to be around 2.5 kcal mol1 higher than the CH3 O þ Cl [32–35] or CH3 O þ Br reactants. The calculated small energy differences cannot claim to be of chemical accuracy but they are in fair consistency with the varying but lower in general, experimental rate constants measured [11,14,37] in the Cl and Br cases. To summarize, we believe that the present work contributes to the understanding of the dissociation pathways of halogen hypohalides but we feel that the description of these sys- tems is yet incomplete and more work is needed for their full elucidation. 4. Summary The potential energy surface for the important decomposition channels of isomeric CH3 OBr and BrCH2 OH molecules is investigated at the G2MP2 level of theory. 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