J. Phys. Chem. 1994, 98, 11465-11489
11465
Calculations of Rate Coefficients for the Chemically Activated Reactions of Acetylene with Vinylic and Aromatic Radicals Hai Wang and Michael Frenklach* Fuel Science Program, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Received: June 15, 1994; In Final Form: August 19, 1994@
Semiempirical quantum mechanical AM 1 calculations were performed for the chemically activated reactions of acetylene with vinyl, 1-buten-3-yn-1 -yl, 1,3-butadien-l-y1, phenyl, 1-ethynylphenyl, 2-naphthyl, and 4-phenanthryl radicals. The reaction rate coefficients were then calculated on the Rice-Ramsperger-KasselMarcus (RRKM) level of theory, using the AM1 molecular parameters corrected to reproduce available experimental data. The results obtained support the hypothesis that reactions of multiring aromatic species are in principle similar to those of benzene and phenyl. The calculated rate coefficients are tabulated for the conditions of interest to combustion modeling.
Introduction Understanding of the processes underlying the formation and growth of polycyclic aromatic hydrocarbons (PAHs) is of practical concern. Formed during combustion, PAHs constitute an important class of pollutants, many of which have been found to be mutagenic and carcinogenic.'s2 PAHs have been suggested to be the precursors to soot in hydrocarbon flame^.^,^ PAH chemistry is also important to other fields, such as astrophysical Figure 1. Schematic diagram of the hydrogen-abstraction-acetyleneaddition reaction mechanism of PAH formation and growth.* environment^,^ diamond film synthesis,6 and fullerene~.~ It has been s u g g e ~ t e dthat ~ , ~ PAH molecular mass growth in assignments of rate coefficients for detailed kinetic modeling, hydrocarbon pyrolysis and oxidation follows a sequential twoa similar analysis was performed for reactions of acetylene with step process: hydrogen abstraction which activates the aromatic vinyl, l-buten-3-yn-l-y1, and 1,3-butadien-l-y1 radicals. molecules and acetylene addition which propagates molecular The calculated rate coefficients were calibrated against growth. It has been demonstrated that this H-abstraction-CzHzexperimental data when available. The obtained rate coefficient addition (HACA) mechanism, depicted in Figure 1, is capable expressions are tabulated for conditions typical of hydrocarbon of describing near-quantitatively the observed PAH peak combustion. The results obtained for 1-buten-3-yn-1-yland 1,3concentrationsl0-lZand soot profiles13-15 in a number of laminar butadien-1-yl are compared to the QRRK calculations of premixed acetylene and ethylene flames. The same model has Westmoreland et al.,19who showed that the addition of acetylene also met with success in explaining the sooting limits of ethane, to these species can form directly benzene and phenyl via ethylene, and acetylene flames16 and in predicting the soot yield chemically-activated processes. The implication of the present under the condition of natural-gas fueled Diesel combustion. l7 analysis to PAH formation in flames is discussed. While the attention on the mechanism of the first aromatic Method ring (Le., benzene and phenyl) formation has been intensified in recent year^,'^-*^ little is known on the subsequent reactions Quantum Mechanical Calculations and Vibrational Freof the aromatic species and their rate coefficients. The quencies. Semiempirical quantum mechanical calculations were hypothesis advanced to facilitate the initial s t ~ d i e s ~ - was ' ~ ~ ~ ~ performed ~'~ by using the AMlz4 (Austin Model 1) Hamiltonian that the reaction kinetics of larger PAHs are analogous to those of the MOPAC 527 and AMPAC (version 3.01)28 programs. of benzene and phenyl. In pursuit of testing this hypothesis Stable species considered in the present calculations are listed and considering that the key reaction step of the HACA in Table 1 along with their formulas and structures. For mechanism is the addition of acetylene to an aromatic radical, aromatic species, a nomenclature system developed earliefl3 is the objective of the present work was to investigate systematiused to assist discussion. This nomenclature is straightforward cally the reaction of acetylene with a series of one- and multiand intuitive. For example, Ai is an aromatic molecule of i ring aromatic radicals, namely, phenyl, 1-ethynylphenyl, 2-naphfused rings, Ai- its radical, and AiC2H with a hydrogen atom thyl, and 4-phenanthryl. replaced by an ethynyl group. The transition-state structures were also determined at the The analysis was performed by first employing semiempirical AM 1 level. For additioddissociation reactions, the transitionquantum mechanical calculationsz4 to obtain the molecular geometries and vibrational frequencies, followed by systematic state structures were obtained by assuming a reaction coordinate along the forminghreaking bond and optimizing the structures corrections applied to the obtained frequencies and then by rate along this coordinate. For isomerization reactions, the transitioncoefficient calculations using the unimolecular Ricestate geometries were obtained with the SADDLE option of Ramsperger-Kassel-Marcus (RRKM) t h e ~ r y . ~ To~ check ,~~ the MOPAC and AMPAC programs. the adequacy of the methods employed and to be consistent in The moments of inertia and vibrational frequencies of the stable species and transition states were calculated from the Abstract published in Advance ACS Abstracts, October 15, 1994. @
0 1994 American Chemical Society 0022-3654/94/2098-11465$04.50/0
Wang and Frenklach
11466 J. Phys. Chem., Vol. 98, No. 44, 1994
TABLE 1: Species Considered in the Present Study and Their Standard-State (298 K, 1 atm) Thermodynamic Properties
~ species hydrogen acetylene vinyl ethylene 1-buten-3-yn-lyl 1-buten-3-yne 1,3-butadien-l-y1 1,3-butadien-2-y1 1,3-butadiene 3-hexen-l,5-diyne 1,3-hexadien-5-yn-l-y1 1,3-hexadien-5 -yne 1,3,5-hexatrien- 1-yl 1,3,5-hexatriene o-benzyne
formula
structure HCWH
H~C=~H HzC=CHz
HC=C-HC=~H HCEC-HC=CH2
H~C=CH-CH=CH H2C=CH-&CHz H*C=CH-CH=CHz HCW-CH=CH-CWH HC=C--CH=CH-CH=~H H~C=ECH-CH=CH-CWH
H~C=CH-CH=CH-CH=~H HZC=CH-CH=CH-CH=CH~
0 1
~
~p p . 2 9 8 cal , ~mol-' ~ K-'
~
, cal mol-' K-I this work"
S0298,
kcalmol-l
lit.
this work"
52.1b 54.5' 71.7' 12Sd 127.1' 68.P 85.4' 77.4e 26.3d 123.5' 140.9' 81.8' 99.3' 40.2' 106.W
4.976 10Sd 10.4 10.4d 17.78 17Sd 18.88 18.18 19.W 24.6' 25.9' 26.1' 27.4' 27.6' 18.P
10.5 10.6 10.5 17.7 17.5 18.7 18.0 18.2 25.1 26.1 26.2 27.2 26.6 19.2
27.396 48.W 56. If 52Sd 67.88 66.8d 69.38 68.38 66.6d 77.0' 80.8' 79.6' 82.1' 79.4' 67Sk
47.9 56.0 52.5 68.0 66.6 69.5 68.5 66.4 76.8 80.5 79.4 82.1 79.8 67.9
18.V"
18.5
69.G"
68.6
lit.
phenyl
6
78.6'
benzene
0
20.0'J
19.6"'
19.5
64.9"
64.4
49.9"
20.6"
219
72.0°
72.0"
2-ethynylphenyl
133.2'
26.8"
26.2
78.8"
78.0
phenylacetylene
73.8'
27.5"
27.7
76.2"
76.4
2-phenylvinyl
94.6'
28.5"
27.9
85.0"
86.0
129.0'
35.5"
35.3
84.7"
84.5
4-ethynylphenyl-1-vinyl
149.5'
39.7"
39.6
9 1.4"
91.5
naphthyne
119.74
1-naphthyl
94.7'
3 1.Or
30.3
84.1'
83.2
naphthalene
35.8'
3 1.7s
31.6
80.2s
80.2
1-ethynylnaphthalene
90.6'
39.7'
39.6
91.4'
91.2
112.3s
40.7'
39.9
100.2'
100.8
62.1'
37.6'
36.4
87.0'
86.4
naphthylvinyl
acenaphthylene
30.5
82.2
J. Phys. Chem., Vol. 98, No. 44, 1994 11467
Calculations of Rate Coefficients
TABLE 1 (Continued) cal mol-' K-I this work" 90.2
Cop,~98. cal mol-'
Soz98,
kcal mol-' 103 f 5"
lit.
lit.
4-phenanthryl
107.5'
43.5"
42.6
96.5"
97.1
4-ethynylphenanthrene
109.1'
51.8"
51.9
103.7"
105.3
53.9'
48.5"
48.6
96.2"
95.8
130.34
539
51.7
112.5"
112.9
AfWz98,
species
formula
structure
pyrene
phenanthrylvinyl
96 f 5"
K-I this worko
37.8
49.6
102.6
Unless otherwise indicated, these properties are calculated with the AM1 rotational constants and corrected AM1 vibrational frequencies (see f Reference 33. g This text). Reference 29. Reference 30. Reference 3 1. Based on %H-H bond dissociaqtion energy of 111.2 kcaUm01.~~ work, based on the ab initio HF/6-31G** rotational constants and vibrational frequencies. Average of those recommended in refs 34-36. Group additivity with group values derived from CzH, and C4H, species. j Reference 37. I; Group additivity, ref 19. Reference 38. Group additivity, reference 35. * Reference 39. Reference 40. p Calculated with the uncorrected AM1 vibrational frequencies. 4 Evaluated by using the AM1-GC method of reference 38. Group additivity based on values fitted to naphthalene. Group additivity with updated group values of reference 41. Reference 42. Estimated by using the AM1-GC method,38with the group correction value for >CH--tH- equal to that of the similar group in 1,3-cyclohexadin-5-y1radical. The uncertainty range is estimated. optimized AM1 geometries. For comparison and verification, a limited number of ab initio calculations were also performed. These calculations were carried out by using Gaussian 8844at the Hartree-Fock (HF) level with a 6-31G** basis sei? (splitvalence plus d-type polarization functions on heavy atoms and p-type on hydrogen). The computed AM1 and ab initio vibrational frequencies and moments of inertia are presented in Table 2 for a number of representative species. Experimental data for these species, whenever available, are also provided. Inspection of the data presented in Table 2 indicates that the rotational constants are largely in reasonably good agreement among different calculational methods (with the exception of C2H3 and i-C4Hs) and the experimental data. The AM1 vibrational frequencies, on the other hand, show marked deviations from the experimental data and the more reliable ab initio results. Since the accuracy of the frequencies is one of the key factors in the rate coefficient calculations, classification of the errors and corresponding corrections of the AM1 frequencies were undertaken. The deviations of the AM1 frequencies shown in Table 2 can be classified into four kinds. The first kind applies only to the vinyl radical whose lowest AM1 frequency, 312 cm-', is a factor of 2.6 smaller than the ab initio value. This lowest frequency was replaced by the ab initio value, 824 cm-'. The second kind is applicable to radicals like n-C4H5 and i - C d s , which contain a C-C torsional rotation. The AM1 frequencies of this motion are a factor of 2-2.5 smaller than the ab initio results. For example, AM1 predicts a frequency of 97 cm-' for the torsional rotation of the HzC=CH and
CH&H moieties in n-C4H5, while the ab initio HF-6/31G** calculation gives 203 cm-' for the same motion. The correction adopted in this case was to multiply the corresponding AM1 frequencies by a factor of 2. We note that a hindered internal rotor treatment may be more appropriate for this kind of vibrational mode. However, since the potential energy for this motion cannot be established reliably through semiempirical or low-level ab initio calculations, and since the ab initio values calculated for these frequencies are above the recommended threshold of -150 cm-' suggested by Gilbert and Smith,26we treated these degrees of freedom as vibrations. The third kind is applicable to the AM1 results for the lowerlying ring-deformation frequencies in aromatic species. The AM1 frequencies are about 10% smaller than the experimental values (cf.Benzene: AM1, 371 cm-'; experiment, 410 cm-'. Naphthalene (not shown in Table 2): AM1, 164 cm-'; experiment, 176 cm-'). This deviation was corrected by multiplying the AMI ring-deformation frequencies by a factor of 1.1. The last kind is due to the harmonic approximation in the frequency calculations. Inspection of the data shown in Table 2 indicates that most of the calculated frequencies are slightly larger than experimental values and that these deviations cannot to be corrected by applying a single multiplier, f = all molecules and all vibrational modes. Taking the AM1 results for acetylene as an example, f is equal to 0.76 for the two smallest frequencies but increases to 0.97 for the largest frequency. It is obvious that to correct each individual frequency would be a dubious, if not impossible task. Therefore,
11468 J. Phys. Chem., Vol. 98,No. 44, 1994
Wang and Frenklach
TABLE 2: Comparison of Rotational Constants and Vibrational Frequencies species method" CzH2 CzG C4H4
C&
AMI 1.19 1.19 ab initio 1.21 1.21 expt.& 1.18 1.18 AM1 0.83 1.00 e ~ p t . 0.83 ~ ~ 1.00 AM1 0.15 0.16 abinitio 0.15 0.16 expt.4' 0.14 0.16 AM1 0.13 0.15
4.90 4.86 1.68 1.72 1.68 1.39
expt46 Ai
AM1
0.19 0.19 0.095
expt.46 0.19 0.19 0.094 C1H3
AM1 abinitio n-C4H3 AM1 abinitio i-C4H3 AM1 abinitio n-C& AM1 abinitio i-C4H5 AM1 abinifio
v , cm-I
cm-'
0.96 0.94 0.16 0.15 0.14 0.14 0.14 0.14 0.13 0.13
1.06 1.07 0.17 0.16 0.14 0.14 0.16 0.16 0.15 0.14
9.46 7.74 1.91 2.13 9.64 5.73 1.56 1.48 1.53 1.84
804 799 612 835 826 248 252 217 87 3184 162 3055 371 1579 410 1486 312 824 241 250 200 168 97 203 121 299
804 799 612 874 943 340 366 304 325 3215 301 3087 371 1767 410 1596 769 884 384 366 239 260 263 315 321 328
929 877 730 1056 949 598 606 539 490 3217 512 3101 618 1767 606 1596 853 958 454 595 449 272 434 524 470 516
929 877 730 1068 1023 681 773 618 538
2182 2243 1974 1167 1236 837 795 625 702
3423 3585 3289 1388 1342 837 811 677 952
3475 3697 3374 1413 1444 959 938 874 963
1827 1623 981 1094 927 991
3153 2989 1055 1120 974 1004
3186 3026 1178 1197 1096 1052
3210 3103 1303 1432 1312 1054
3218 3106 1414 1566 1415 1291
1842 1844 1599 1303
2372 2408 2111 1325
3138 3323 3030 1403
3181 3344 3068 1444
3216 3415 3116 1832
3454 3645 3330 1875 3142 3159 3180
522 770 894 908 912 976 990 1013 1196 1280 1294 1381 1438 1596 1630 2984 2992 3003 648 3184 606 3047 996 1188 659 656 602 409 563 587 562 553
648 3187 673 3047 1342 1403 806 680 738 428 568 719 695 761
745 3188 703 3062 1853 1627 827 754 841 515 797 904 864 936
891 3195 849 3063 3111 3256 845 856 889 857 876 924 938 997
891 3195 849 3063 3170 3352 894 888 1001 893 965 955 955 1005
989 3206 975 3068 3471 3408 1130 1104 1039 1082 980 1018 983 1063
990 1012 1028 1146 1146 1179 1222 1222 1276 1329 1368 1579 975 992 995 1010 1038 1038 1150 1178 1178 1310 1326 1486
1206 1312 1359 1536 1057 1030 1075 1071
1864 1529 2024 1643 1183 1247 1099 1276
2376 2074 2226 1726 1238 1285 1270 1398
3113 3266 3103 3270 1321 1357 1329 1468
3438 3419 3159 3366 1396 1479 1398 1586
3464 3621 3422 3595 1852 1577 1818 1663
1870 1657 2110 2055
3113 3300 3094 3270
3172 3308 3122 3276
3187 3322 3171 3323
3218 3400 3195 3380
3457 3401 3223 3414
The AM1 and ab initio vibrational frequencies are as calculated without adjustments. The ab initio calculations were performed on the HF/ 6-31G** level.
an overall, yet structurally-dependentcorrection, described next, was applied to fit the standard-stateentropies and heat capacities. It was found that when the AM1 frequencies of acetylene are multiplied by a constant factorfequal to 0.78, the standardstate entropies (s0298)and heat capacities (c0p,298)match closely the corresponding literature data (see Table 1). Similarly, a constant multiplier of 0.96 can be applied to both ethylene and benzene. For molecules containing both double and triple C-C bonds, we explored a number of mixture rules and found that the following formula can be applied to accurately reproduce the SO298 and COp.298 data,
f = 0.78"""O. 96"""O. 85n3/" where nl is the number of acetylenic carbon (ZC-) atoms and hydrogen atoms bonded to them; n2 the number of ethylenic and peripheral, H-bonded aromatic carbon (e
