Ab Initio Calculations on Hydroaromatics: Hydrogen Abstraction and

Near degeneracy causes UHF-based calculational methods to predict incorrectly energies for the open shell molecules. Two observations distinguish the ...
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10506

J. Phys. Chem. B 1999, 103, 10506-10516

Ab Initio Calculations on Hydroaromatics: Hydrogen Abstraction and Dissociation Reaction Pathways Paul H. A. Schimmel,† Paul J. A. Ruttink,‡ and Bernard H. W. S. de Jong*,† Institute for Earth Sciences and Vening Meinesz Institute for Geodynamic Research, Utrecht UniVersity, Budapestlaan 4, 3508 TA, Utrecht, The Netherlands, and Department of Chemistry and Debye Institute, Utrecht UniVersity, Padualaan 14, 3584 CH, Utrecht, The Netherlands ReceiVed: September 10, 1999

Three hydrogen abstraction reactions on cyclohexene, cyclohexadiene, and propene involving hydrogen radicals, and five bond dissociation reactions on cyclohexene, cyclohexene-3-yl, 1,3-cyclohexadiene, 1,3-cyclohexadiene5-yl, and propene were studied using ab initio quantum chemical methods. The aim was to indicate possible reaction pathways for aromatization processes during oil and gas generation as well as coalification in natural processes. 3-21G and DZP basis sets were used for the unrestricted Hartree-Fock (UHF), restricted HartreeFock (RHF), second-order Møller-Plesset perturbation (MP2), and singles and doubles configuration interaction (SDCI) calculational methods. SDCI with size consistency corrections yielded a barrier of 9, 8, and 11 kcal/ mol for hydrogen abstraction on cyclohexene, 1,3-cyclohexadiene, and propene, respectively. Near degeneracy causes UHF-based calculational methods to predict incorrectly energies for the open shell molecules. Two observations distinguish the transition state for the selected aromatic molecules from the geometries for saturated hydrocarbons. First the abstracted hydrogen atom remained closer to its parent C atom in the aromatic molecules, and second, their transition state has a lower activation energy barrier. Both effects are due to delocalization, which is possible in aromatic systems in the transition state as well as the final products. This study ascertains that abstraction reactions are feasible for aromatization processes in kerogen under naturally occurring temperature and pressure conditions. Two step reactions contribute to the magnitude of the overall ratelimiting step of 57 kcal/mol for this reaction pathway. The first one accounts for 49 kcal/mol, and can be attributed to endothermic bond dissociation following the initial hydrogen abstraction. The second one accounts for 8 kcal/mol and can be attributed to the second hydrogen abstraction reaction.

Introduction Hydrogen transfer reactions involve the addition or abstraction of hydrogen atoms from aliphatic or aromatic hydrocarbons. These reactions are important in natural oil and gas generation as well as during coalification, combustion, and oil refining.1-3 They explain the formation of saturated and unsaturated hydrocarbons from a hydroaromatic substance, i.e., a hydrocarbon possessing both a saturated and an unsaturated hydrocarbon moiety. Abstraction reactions on saturated and unsaturated hydrocarbons have been particularly well studied both experimentally and theoretically as the summary of Litwinowicz et al.4 indicates. As a result of these studies, the experimentally determined activation energies are well-known for hydrogen abstraction on the increasingly less saturated hydrocarbon molecules methane, ethene, and ethyne, being 12-13,5 12-14,6-8 and 22-24 kcal/mol,7,8 respectively. Neither experimental nor theoretical data are available for hydrogen abstraction reactions of saturated carbon moieties in the presence of unsaturated ones. In kerogen maturation, i.e., the oil, gas, and coal forming process within the earth, such reactions may be of importance because of the ubiquitous occurrence of both hydroaromatics and radicals in natural environments.9-12 Previous authors have † Institute for Earth Sciences and Vening Meinesz Institute for Geodynamic Research. ‡ Department of Chemistry and Debye Institute.

suggested the importance of hydrogen abstraction reactions in this maturation process13,14 in order to explain the formation of fully aromatic hydrocarbons from hydroaromatic ones.15,16 Abbott et al.17 showed experimentally the important role of radicals in this process. In their experiment sulfur radicals abstracted hydrogen from a monoaromatic steroid to form a triaromatic steroid. In the present study we focus on the mechanism of hydrogen abstraction in hydroaromatics. Our principal goal is to test the feasibility of such a mechanism for aromatization of hydrocarbons under natural conditions of temperature and pressure. Our secondary goals are to provide a benchmark calculation for future semiempirical calculations on larger molecules and, from a more theoretical perspective, how a π-system adjacent to a reactive carbon atom affects the activation energies in hydrogen abstraction reactions. In order to implement these goals we have carried out ab initio molecular orbital calculations on three key reactions, selected because they exhibit the essential elements postulated to play a role in aromatization. The calculations concern initial, transition, and final states for each of these reactions. The canonical molecules participating in these reactions are cyclohexene (CH), cyclohexadiene (CHD), and propene. As a hydrogen atom approaches the selected molecules to abstract another hydrogen atom, a hydrogen molecule and a hydroaromatic radical are formed according to the following abstraction reactions (AB1-AB3):

10.1021/jp993213n CCC: $18.00 © 1999 American Chemical Society Published on Web 11/06/1999

Ab Initio Calculations on Hydroaromatics

Besides hydrogen abstraction reactions we have also considered simple bond dissociation (BD) reactions on hydroaromatics in which a hydrogen atom and a hydroaromatic radical or molecule are formed. These reactions are simple and efficient hydrogen transfer reactions and may be important intermediate steps in the aromatization of hydroaromatics via abstraction. In addition there are experimental data for such reactions either available or easily estimated from other dissociation reactions, a crucial asset in ascertaining the reliability and veracity of our calculations. Rather than carrying out saddle point calculations for bond dissociation reactions, which tend to have no or a small reverse activation energy barrier,18 we have evaluated the initial and final state ab initio calculational results for the following simple bond dissociation reactions, designated BD1-BD5:

J. Phys. Chem. B, Vol. 103, No. 47, 1999 10507 UHF 3-21G saddle point calculations were carried out for the three abstraction reactions AB1, AB2, and AB3 using the geometrically optimized local minima structures assuming an initially linear reaction center. The structures were partially optimized after positioning the abstracting hydrogen at various fixed distances from each moiety. After lifting the linear reaction constraint, true saddle point calculations were carried out starting with the structure estimated to be closest to the saddle point. In order to check the effect of the spin contamination, the procedure was repeated with RHF. Second-derivative calculations were carried out at the 3-21G UHF level on all resulting UHF structures, and at the 3-21G RHF level on all resulting RHF structures allowing a check on whether true local minima or saddle points were reached. Zeropoint vibrational energies (ZPE) were also obtained from these calculations. Former studies have shown that at UHF, ZPEs are about 10% too high.22 Therefore only 90% of the ZPEs were added to calculate total energies. Additional single point calculations for the resulting structures were done on the Cray C98/4256 computer at SARA in Amsterdam with a GAMESS-UK Unicos version 2.1. The 1s orbitals of the carbon atoms were fixed as core orbitals. The calculations included second-order Møller-Plesset perturbation theory (MP2)23,24 with an UHF reference wave function, and singles-doubles configuration interaction (SDCI)25a,b calculations with a RHF reference wave function. In the single point calculations the HF/DZP energies were retrieved as an intermediate calculation step. Additionally, the results of the first iteration in the CI Davidson diagonalization were retrieved to represent an approximation to a second-order restricted perturbation theory calculation. We wanted to check if RMP2 would be a better method for obtaining energies for our open shell molecules as our MP2 were proven to be very unreliable. Final single point SDCI/DZP calculations were also done for two points on the reaction pathway for hydrogen abstraction on methane. For the first point the transition state geometry proposed by Litwinowicz et al.4 was selected, because this one is considered to be the saddle point geometry. For the second, the reaction center abstraction coordinates were replaced with those found for AB3. This allowed a check on the influence of transition state (TS) geometry differences on activation energies. Results

Methods Calculations were carried out on a HP-750 computer with the GAMESS-UK HP 350 version 5.1 software package.19 The Pople 3-21G20 and the Dunning DZP basis sets21 were used with a set of six-component d functions with an exponent of 0.75 on the carbons and 1.0 for the p set on hydrogen. The geometries of cyclohexene (CH), cyclohexene-3-yl (CH-3-yl), cyclohexadiene (CHD), 1,3-cyclohexadiene-5-yl (CHD-5-yl), propene, propenyl, and H2 were first optimized at the unrestricted Hartree-Fock (UHF) computational level with a 3-21G basis set. The same procedure was repeated for the open shell molecules cyclohexene-3-yl, 1,3,-cyclohexadiene-5-yl, and propenyl using restricted Hartree-Fock (RHF) with a 3-21G basis set. All variables were allowed to relax after the initial configurations were set at C1 symmetry, except for benzene, which was forced to be D6h. Although GAMESS-UK did not find any of the anticipated symmetries, detailed inspection showed the conformations to be close to the ideal ones. The GAMESS-UK optimization procedure stops optimization before higher symmetry states are reached.

The calculated UHF, RHF, and available experimental data for the conformations of the stable molecules are shown in Figure 1a-g and in Table 1. The structure of CHD-5-yl shows a planar carbon skeleton. All carbon atoms except one lay approximately in a single plane in the CH-3-yl skeleton. In cyclohexadiene a slight twisting of the π-system occurs to relax some angle strain located at the sp3 hybridized carbon atoms, which have angles larger than the ideal 109.5°. This twisting causes the four hydrogen atoms attached to the unsaturated carbon atoms to be nonplanar. The conformations for the three transition states are shown in Figure 1h-m. Their bond lengths and bond angles are given in Tables 2 and 3. The three transition state reaction centers, C-H-H, are almost linear. The incoming hydrogen atom is slightly deflected from the π-system. S-squared values obtained at the 3-21G/DZP UHF level are shown in Table 4. Selected total energies for the UHF optimized stable and transition state structures and their 3-21G zero-point energies are shown in Table 5. Table 6 shows the RHF, ZPE, and cumulative energies with a 3-21G basis-set for both the RHF and UHF optimized open shell molecules. True minima

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Ab Initio Calculations on Hydroaromatics J. Phys. Chem. B, Vol. 103, No. 47, 1999 10509

Figure 1. Structure and symmetry group designation for all molecules as calculated with HF/3-21G. Simple angles are shown outside, dihedral angles are shown inside the structure. The first figure shows all (dihedral) angles for the carbon atoms, the second figure the remaining (dihedral) angles for the hydrogen atoms. When two values are given, the first represents the calculated and the second the experimental value. When a choice of dihedral angle exists, the dihedral angle with alpha hydrogens (H1) is taken. For example, -64.7 at C4-C5 for (a) means that the dihedral angle for H1-C4-C5 and the C4-C5-H1 plane is 64.7°. For the transition state in AB3 only simple angles are shown. (a) Cyclohexene; (b) cyclohexene-3-yl (UHF); (c) cyclohexene-3-yl (RHF); (d) 1,3-cyclohexadiene; (e) 1,3cyclohexadiene-5-yl (UHF); (f) 1,3-cyclohexadiene-5-yl (RHF); (g) benzene; (h) transition state AB 1 (UHF); (i) transition state AB 1 (RHF); (j) transition state AB2 (UHF); (k) transition state AB2 (RHF); (l) transition state AB3 (UHF); (m) transition state AB3 (RHF).

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TABLE 1: Calculated HF/3-21G and Experimental Bond Lengths (Å) for the Stable Reaction Intermediates (Figure 1a-g) CH

CH-3-yl

CHD

CHD-5-yl

bond

calcd UHF

exptla

calcd UHF

calcd RHF

calcd UHF

exptlb

calcd UHF

calcd RHF

C1-C2 C2-C3 C3-C4 C4-C5 C5-C6 C6-C1 C1-H1 C2-H1 C3-H1 C3-H2 C4-H1 C4-H2 C5-H1 C5-H2 C6-H1 C6-H2

1.318 1.515 1.541 1.540 1.541 1.515 1.075 1.075 1.086 1.088 1.085 1.084 1.084 1.085 1.089 1.089

1.335 1.504 1.515 1.550 1.515 1.504 1.093 1.093 1.093 1.093 1.093 1.093 1.093 1.093 1.093 1.093

1.390 1.390 1.514 1.544 1.544 1.514 1.073 1.075 1.073

1.433 1.334 1.514 1.543 1.544 1.508 1.071 1.074 1.074

1.322 1.476 1.322 1.519 1.544 1.518 1.073 1.075 1.073

1.350 1.468 1.350 1.523 1.534 1.523 1.082 1.082 1.082

1.372 1.417 1.417 1.372 1.513 1.513 1.073 1.073 1.072

1.089 1.085 1.084 1.084 1.089 1.085

1.089 1.085 1.084 1.084 1.088 1.085

1.085

1.082

1.083 1.088 1.089 1.083

1.096 1.096 1.096 1.096

a

TSinAB1

TS inAB2

bond

UHF

RHF

UHF

RHF

C1-C2 C2-C3 C3-C4 C4-C5 C5-C6 C6-C1 Cl-H1 C2-H1 C3-H1 C3-H2 C4-H1 C4-H2 C5-H1 C5-H2 C6-H1 C6-H2 H2-H3 H3-H2-C3-H1a H3-H2-C5-H1a

1.344 1.474 1.540 1.540 1.549 1.515 1.074 1.074 1.082 1.276 1.087 1.084 1.084 1.085 1.088 1.085 1.029 78.4

1.322 1.485 1.526 1.540 1.541 1.515 1.075 1.074 1.081 1.311 1.088 1.084 1.084 1.084 1.088 1.085 0.943 90.6

1.362 1.436 1.374 1.469 1.537 1.515 1.073 1.073 1.073

1.323 1.470 1.327 1.483 1.532 1.515 1.073 1.073 1.072

1.073

1.073

1.080 1.252 1.083 1.090 1.070

1.080 1.306 1.091 1.085 0.954

72.9

83.4

Dihedral angle (deg).

TABLE 3: Calculated HF/3-21G Bond Lengths (Å) and Dihedral Angles (deg) for the Transition State in AB3 (Figure 1l,m)

a

exptlc

1.333 1.433 1.434 1.333 1.511 1.511 1.073 1.073 1.070

1.385 1.385 1.385 1.385 1.385 1.385 1.072 1.072 1.072

1.393 1.393 1.393 1.393 1.393 1.393 1.084 1.084 1.084

1.073

1.073

1.072

1.084

1.074

1.073

1.072

1.084

1.091 1.091

1.091 1.091

1.072

1.084

Reference 26. b Reference 27. c Reference 28.

TABLE 2: Calculated HF/3-21G Bond Lengths (Å) and Dihedral Angles (°) for the Transition State Conformation in AB1 and AB2 (Figure 1h-k)

a

benzene calcd UHF

bond

UHF

RHF

C1-C2 C2-C3 C1-H1 C1-H2 C2-H1 C3-H1 C3-H2 C3-H3 H1-H4 H2-C1-C2-H1a H1-C1-C2-C3a H1-C3-C2-H1a H4-H1-C3-C2a

1.345 1.469 1.074 1.073 1.076 1.286 1.080 1.080 1.020 -0.3 1.9 -80.8 -168.4

1.320 1.480 1.074 1.073 1.075 1.324 1.079 1.079 0.934 -0.3 1.6 -76.9 -137.4

Dihedral angle (deg).

were obtained for all reaction intermediates as no imaginary frequencies were found with second derivative calculations. Table 7 shows the vibrational frequencies for the transition states. Only one imaginary frequency was found for each transition state associated with the displacement of the inter-

TABLE 4: UHF S2 Expectation Values for the 3-21G and DZP Basis Sets structure

3-21G

DZP

CH CH-3-yl CHD CH-5-yl benzene propyl TS in AB1 TS in AB2 TS in AB3

0.000 0.976 0.000 1.225 0.000 0.975 0.969 1.421 0.993

0.000 0.952 0.000 1.194 0.000 0.959 0.936 1.381 0.961

mediate hydrogen atom along the reaction coordinate. Figure 2 shows the Mulliken charge distribution for the transition state in AB3. ZPE-corrected bond dissociation energies are shown in Table 8. The experimental bond dissociation energies for cyclohexene and cyclohexene-3-yl (BD1 and BD3) in this table are deduced from the dissociation energy for propene and the reverse energy for a butadiene hydrogen addition reaction, respectively. Because cyclohexene has a higher order carbon atom from which hydrogen dissociates, we assume in this study a 2 kcal/mol lower bond dissociation energy. The same is true for cyclohexene-3yl, but as we took the reverse of an addition reaction, we added 2 kcal/mol to the bond dissociation value. The activation energies for abstraction, corrected for ZPE, are shown in Table 9. In Table 10 we summarize our main findings and compare them to methane. The SDCI/DZP single point energies for abstraction on methane corrected for ZPE are 16.2 kcal/mol for the transition state structure found by Litwinowicz et al.4 and 14.1 kcal/mol for the structure in which we have replaced the reaction center abstraction coordinates. Discussion We shall divide this discussion into two main parts. In the first one we shall cover the theoretical chemical methods used and the validation of such models. We shall start by dealing with the conformation and chemistry of the moieties observed in abstraction reactions, followed by the problem of spin contamination in our calculations, the sensitivity of bond dissociation and abstraction activation energies to the calculational methods employed, and finally the energy lowering in the activated complex. In the second part we shall discuss the implications of our results for the oil maturation or kerogen breakdown process. In

Ab Initio Calculations on Hydroaromatics

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TABLE 5: Selected Total Energies (at DZP Unless Otherwise Noted) and Uncorrected ZPEs (au) for UHF Optimized Geometries structure

RHF(3-21G)

RHF

UHF

SDCI/Poplea

FICIb

ZPE(3-21G)

CH CH-3-yl CHD CH-5-yl benzene propene propyl TS in AB1 TS in AB2 TS in AB3 H2 H

-231.721 95 -231.106 14 -230.643 23 -229.931 22 -229.419 44 -116.424 01 -115.797 15 -232.187 01 -230.999 64 -116.878 22 -1.122 96 -0.496 20

-233.067 61 -232.442 96 -231.877 38 -231.264 58 -230.744 15 -117.098 60 -116.469 68 -233.526 82 -232.335 89 -117.553 93 -1.131 33 -0.498 19

-233.067 61 -232.466 32 -231.877 38 -231.294 24 -230.744 15 -117.098 60 -116.493 83 -233.539 55 -232.358 52 -117.567 65 -1.131 33 -0.498 19

-233.955 83 -233.315 13 -232.730 28 -232.103 30 -231.558 72 -117.554 86 -116.910 25 -234.436 70 -233.211 59 -118.032 69 -1.165 70 -0.498 19

-233.759 33 -233.114 80 -232.540 71 -231.908 87 -231.374 82 -117.485 10 -116.835 62 -234.229 10 -233.007 88 -117.953 16 -1.165 10 -0.498 19

0.157 48 0.141 51 0.132 00 0.115 37 0.108 65 0.085 80 0.069 86 0.153 76 0.126 59 0.082 12 0.010 64 0.000 00

a

Reference 25b. b First-order iteration energy in the SDCI Davidson diagonalization (ref 35).

TABLE 6: 3-21G RHF, ZPE, and Cumulative Energies (au) for the RHF and UHF Optimized Open Shell Molecules RHF geometries

a

UHF geometries a

structure

RHF

ZPE(RHF)

cum E

CH-3-yl CH-5-yl propyl TS in ABI TS in AB2 TS inAB3

-231.10907 -229.93433 -115.80058 -232.18602 -231.00147 -116.87737

0.14226 0.11756 0.06986 0.15530 0.12998 0.08383

-230.98104 -229.82853 -115.73771 -232.04625 -230.88490 -116.80192

RHF

ZPE(UHF)

cum Ea

-231.10614 -229.93122 -115.79715 -232.18701 -231.99964 -116.87822

0.14151 0.11537 0.06986 0.15376 0.12659 0.08212

-230.97878 -229.82739 -115.53428 -232.04863 -230.88571 -116.80431

The ZPEs were scaled by a factor 0.9 (ref 22).

TABLE 8: Calculated, ZPE Corrected,a and Experimental Bond Dissociation Energies (kcal/mol) at Different Levels of Theory

Figure 2. Electron densities according to Mulliken population analysis of the UHF/3-21G wave function for TS/AB3.

TABLE 7: UHF/3-21G Transition State Vibrational Frequencies for the Three UHF Optimized Abstraction Transition States reaction

frequencies, cm-1

AB1

-2262, 175, 281, 325, 375, 479, 535, 557, 744, 799, 850, 909, 925, 953, 1035, 1072, 1111, 1120, 1143, 1179, 1265, 1289, 1325, 1345, 1394, 1425, 1477, 1495, 1502, 1510, 1518, 1560, 1632, 1652, 1658, 1662, 3179, 3193, 3206, 3223, 3246, 3253, 3265, 3315, 3339 -2160, 168, 264, 365, 425, 545, 591, 620, 714, 799, 871, 890, 968, 985, 1007, 1037, 1103, 1121, 1151, 1241, 1264, 1288, 1337, 1362, 1431, 1507, 1516, 1528, 1540, 1580, 1633, 1656, 3152, 3234, 3277, 3334, 3341, 3356, 3368 -2350, 178, 379, 460, 660, 668, 993, 1000, 1059, 1069, 1161, 1296, 1303, 1383, 1476, 1487, 1574, 1623, 1684, 3244, 3307, 3314, 3330, 3394

AB2

AB3

this part we shall discuss the height of the activation barrier for abstraction and dissociation and its consequences for aromatization in kerogen maturation, and the selection criteria of our canonical molecules as to their relevance in rationalizing this process. (i) Conformations and Chemical Properties. Figure 1 and Table 1 show a satisfactory agreement between calculated HF/ 3-21G and experimentally determined molecular conformations, i.e., the closed shell molecules, except for two bond types. The first is the C-C bond distance present in cyclohexene between atom numbers C3-C4 and C5-C6, which is almost 0.03 Å larger in the calculated geometry than observed experimentally. In cyclohexadiene we found that the C-C bond distance between atom numbers C1-C2 and C3-C4 is about 0.03 Å

UHF/3-21G UHF/DZP RHF/3-21G RHF/DZP MP2/3-21G MP2/DZP SDCI/3-21G SDCI/DZP FI CI(321-G)b FI CI(DZP)b experiment

BD1

BD2

BD3

BD4

BD5

55.0 55.7 70.6 70.3 -75.7 -42.9 74.5 80.4 62.9 82.8 84.3c

52.1 51.6 36.5 36.9 189.6 173.2 42.0 49.0 38.8 42.3 46.9d

42.7 43.9 63.3 62.5 -30.9 -27.7 66.9 71.4 69.8 74.5 73.0e

26.6 28.8 6.0 10.1 112.1 117.1 18.6 25.3 13.7 18.7 21.3f

55.2 56.0 71.4 71.1 117.7 71.4 75.0 81.1 78.8 84.2 86.3e

a The ZPEs were scaled by a factor 0.9 (ref 22). b First-order iteration energy in the SDCI Davidson diagonalization (ref 35). c Dissociation energy for propene (ref 30) with 2 kcal/mol extra stabilization energy for higher order carbon molecules. d Reverse of butadiene hydrogen addition energy (ref 31) minus 1 kcal/mol additional stabilization energy for first order carbon. e Reference 30. f Reference 32.

smaller than experimentally observed. The open shell reaction intermediates show expected conformational changes, such as an alternating lengthening and shortening of the carbon-carbon bonds as reflected in the varying bond orders. The more uniform π-bond lengths in the UHF-optimized molecules indicate that UHF tends to delocalize the free electron over the present π-system whereas RHF tends to form a localized π-bond, with the corresponding shorter bond distance. Consequently we find for the RHF optimized conformation of CH-3-yl not the expected C2 but a C1 symmetry. Except for this feature, the conformations found by UHF and RHF are almost identical. The transition state carbon moieties resemble the reactant most in accordance with the Hammond principle,33 yet have dihedral angles, and bond lengthening and shortening variations which lay in between those for reactants and products (Tables 2 and 3 and Figure 1h-m). UHF optimization again yields more uniform bond lengths for the π-bond lengths than RHF just as for the stable reaction intermediates mentioned above. The

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TABLE 9: Calculated, ZPE Corrected,a Activation Energies (kcal/mol) for Hydrogen Transfer Reactions at Different Levels of Theory level

AB 1

AB 2

AB 3

UHF/3-21G UHF/DZP RHF/3-21G RHF/DZP MP2/3-21G MP2/DZP SDCI/3-21G SDCI/DZP FI CI(3-21G)b FI CI(DPZ)b

13.4 14.4 22.0 22.4 -136.5 -123.8 10.8 8.8 16.2 15.7

5.9 7.6 21.9 21.8 -58.8 -68.1 9.8 7.5 16.7 16.4

15.7 16.2 24.3 24.8 13.1 14.1 28.3 10.7 30.3 16.8

a The ZPEs were scaled by a factor 0.9 (ref 22). First-order iteration energy in the SDCI Davidson diagonalization (ref 35).

positions of the reacting atoms relative to the carbon framework in the transition state for each of the abstraction reactions are similar, except for transition state conformation in AB3 where the dihedral angle H4-H1-C3-C2 differs about 30° between the RHF and UHF calculations; in UHF the calculated H-H distances are around 1.05 Å, i.e., 1.4 times the equilibrium H-H distance (0.74 Å), and the calculated C-H distances are around 1.26 Å i.e., 1.2 times their equilibrium distance (1.09 A). In RHF the H-H distances are around 0.96 Å, and the C-H distances around 1.31 Å. We designated d(C-H)-d(H-H) as the reaction coordinate to compare the moments for each of the transition states. It is handy to do so because the cumulative C-H and H-H distances in the UHF and RHF studies are approximately 2.3 Å. The value of this coordinate is negative before reaction and positive upon completion. For the UHF saddle points of AB1, AB2, and AB3 we find reaction coordinates of 0.25, 0.18, and 0.27, respectively. Thus in UHF, the transition state is reached first by reaction AB2, followed by AB1 and AB3 which have identical moments. For the RHF saddle points of AB1, AB2, and AB3, the reaction coordinate is 0.37, 0.35, and 0.39, respectively, a negligible difference although AB2 still reaches the saddle point first. The different values for our calculated reaction coordinates can be rationalized by the extra stabilization energy generated in the reaction products. Hueckel theory predicts that, in reactions AB1 and AB3, a resonance stabilization energy of 0.86 β, and in AB2 of 0.98 β, is generated. This stabilization results from the formation of a partial π-system with some resonance in the reaction products. The overall gain in reaction energy in these exothermic reactions increases, or in other words the reaction is more exothermic than anticipated. Thus the conformation of the activated complex will look more like that of the reactants which represent the least negative energy state. This is perfectly affirmed by our UHF calculated reaction coordinates: an increasing stabilization energy in the reaction products is reflected in a lower reaction coordinate. In fact it is surprising how similar the transition state moments of AB1 and AB3 are, 0.25 and 0.27 respectively, though the reacting carbon atom is connected to only one C atom in AB3 and to two C atoms in AB1. Apparently the presence of an identical π-system dominates the transition state moment. For RHF the situation is different. The reaction coordinate has a higher value for each of the abstraction reactions, corresponding to a later transition state moment. As noted before, RHF tends to localize the electron in one single bond and not over the entire π-system. Therefore each of the reaction products experiences the same and comparatively lower resonance stabilization energy, resulting in a more identical higher reaction coordinate. Actually the

reaction coordinate only affirms the increasingly less positive hydrogen dissociation energy for propene, CH, and CHD respectively. Propene has the highest dissociation energy, and the latest transition state moment. CHD has the lowest dissociation energy and the earliest transition state moment. (ii) Spin Contamination. Perusal of Table 4 shows that UHF calculations on the radicals and on the transition state structures yield with both basis sets an 〈S2〉 value which deviates considerably from the theoretical value of 0.75. This deviation points to the strong influence of a higher spin state, caused by near degeneracy. The high 〈S2〉 is accompanied by an artificial lowering of the corresponding energies. The 〈S2〉 value for the AB2 transition state is 0.4 higher than for the other transition states. Substantial spin contamination may also yield improper conformations. The quartet-state conformation may accordingly contribute substantially to the UHF optimized conformation. This effect may be especially important for the transition state structures, where different conformations influence energies significantly. We can make an estimate of the energy effects due to different geometries when we compare the RHF/3-21G and ZPE/3-21G energies for the UHF and RHF optimized geometries. Table 6 shows that the cumulative energies for both the UHF and RHF obtained geometries with RHF energies differ in the third decimal. The highest difference we find between the two is only 2.2 kcal/mol, suggesting that the influence of geometry on calculated energies during the transition tends to be minor. We therefore conclude that is there is no problem using the UHF optimized geometries for our further study. (iii) Predicted Bond Dissociation and Abstraction Activation Energies. Though we use the UHF optimized geometries, the energies retrieved by UHF can suffer considerably from high spin contamination. The absolute AB2 RHF abstraction activation energy is 14 kcal/mol less negative than that calculated by UHF as shown in Table 9 and for AB1 and AB3; 8 and 9 kcal/ mol less negative, respectively. When we consider the S2 expectation values for the three abstraction reactions in Table 4, we see that these differences directly reflect the degree of spin contamination in the transition state. Additionally, the AB2 UHF activation energy is about 7 kcal/mol more negative relative to that for the other abstraction reactions, but this difference disappears if RHF is used. From this we can only conclude that our UHF energies depend largely on spin contamination and are not suitable for the calculation of open shell hydroaromatics energies. We used the UHF functions as reference functions in our MP2 calculations, but the high 〈S2〉 values disqualified them as such. Consequently our MP2 calculations are also prone to error. The negative bond dissocation energies in Table 8 and abstraction activation energies in Table 9 at MP2 confirm this. Even though the value for abstraction in AB3 is reasonable, this agreement is fortuitous and cannot be trusted. The near-degeneracy problems can be circumvented by employing perturbation theory based on spin-restricted zeroorder wave functions. Though we did not carry out such calculation, we can estimate its effect by evaluating the energies at specific intermediate calculation steps in the SDCI, in which we used RHF reference wave functions. The result of the first iteration in a SDCI Davidson (FICI) diagonalization35 may be interpreted as an approximation to a second-order perturbation theory calculation. These intermediate energies are uncorrected for size consistency and only indicate the expected trends. The bond dissociation energies obtained via this method turn out to be far better than those obtained from MP2 results as perusal

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J. Phys. Chem. B, Vol. 103, No. 47, 1999 10513

TABLE 10: Overview of the Abstraction Center Bond Lengths (Å) and Activation Energies for the Hydroaromatic Molecules in Comparison to Methane distances (Å) RHF(3-21G) cyclohexene 1,3-cyclohexadiene propene methane a

UHF(3-21G)

activation energy (kcal/mol)

d(H-H)

d(C-H)

d(H-H)

d(C-H)

RHF/DZP

SDCI/DZP

0.943 0.954 0.934 0.87a

1.300 1.306 1.324 1.37a

1.029 1.070 1.020 0.927b

1.276 1.252 1.286 1.37b

22.4 21.8 24.8 38a

8.8 7.5 10.7 16.1c

Reference 34. b Reference 4. c Reference 36.

of Tables 8 and 9 indicates. Use of a DZP basis set raised the bond dissociation energies, yielding an even better fit between experiment and calculation. The bond dissociation energies are reproduced within 5 kcal/mol of their experimental value. We therefore recommend RMP2 calculations for open shell hydroaromatic molecules for future use. Both the open and closed shell RHF-based bond dissociation energies differ considerably from experimental values. They are all more negative than experimentally observed. The relative difference in RHF calculated reactivity of the open and closed shell dissociation is in better agreement with experiments as we found that closed shell dissociations are more endothermic than open shell ones. Predicted activation energies for hydrogen abstraction are about 22 kcal/mol with either basis set. When correlation energy is incorporated in SDCI/3-21G, the closed shell bond dissociation energies increase with 4 kcal/ mol and the open shell ones with 6-8 kcal/mol relative to RHF/ 3-21G. The effect of incorporating correlation energy is unanticipated. Normally when correlation is included, this increases the bond dissociation energies for closed shell molecules (i.e., BD1 and BD3) by ca. 23 kcal/mol and does not alter the bond dissociation energies for open shell molecules (i.e., BD2 and BD4) when compared to RHF results. Here both predicted closed shell and open shell dissociations energies change when correlation is incorporated. The SDCI/3-21G abstraction energy barriers for AB1-AB3 are 40-50% of their respective RHF/3-21G values. Basis set improvement to DZP reduces the activation energies even further to about 8 kcal/mol. SDCI/DZP closely reproduces experimentally determined bond dissociation energies. SDCI results are also not dependent on effects beyond control due to high spin contamination on predicted total energies, because of its use of a restricted reference wave function. Additionally, in contrast to all other methods employed here, SDCI/DZP reproduces the experimental abstraction activation energy of 12 kcal/mol for methane best.5,34,36 We therefore consider the SDCI/DZP results also to mimic closest the experimental activation energy for abstraction reactions on hydroaromatics. (iv) Activation Energy Lowering. In Table 10 we compare the main findings from our study with those on methane. Notice that both calculational methods on our hydroaromatic molecules give a lower activation energy than calculated for methane in a comparable study. Comparison of transition state geometries for the reacting atoms indicates that the H-H distances in our molecules are longer and the C-H distances shorter with both optimization methods. We find for methane a reaction coordinate of 0.5 using RHF and 0.44 for UHF optimized molecules, indicating that the transition state occurs later for this molecule than for hydroaromatics. The SDCI/DZP activation energy for propene is 5 kcal/mol more negative than the activation energy for methane at the same computational level. We can distinguish two effects which contribute to this more negative energy. The first is the

Figure 3. Illustration of the two distinguishable contributing effects to the activation energy lowering for hydrogen abstraction on propene relative to abstraction on methane according to SDCI/DZP results.

difference between the transition state conformations of the two abstraction reactions. We can make an estimate of its contribution to the decrease in activation energy by considering the SDCI/DZP energy of the methane abstraction structure in which the reaction atoms are placed at the same location as in the transition state of AB3. The energy of this complex is 14.1 kcal/ mol less negative than the total energy of the reactants. The conformational difference therefore lowers the transition state by 16.1-14.1 ) 2.0 kcal/mol as shown in Figure 3. The second contribution, accounting for the remaining 3.4 kcal/mol, is rationalized by the formation of an extended π-system. Hueckel theory predicts that the linear combination of the original π-system with the newly emptied π-lobe stabilizes the product. We tried to trace such a combination in the transition state. To do so, we extracted from the three MO’s which change their bonding character during reaction, the AO’s that constitute in the main these MOs. These AOs are illustrated in Figure 4, in which MO A contributes to the C-H bond in the reactant, and will contribute to the H-H bond in the product, whereas MO B contributes to the π-system in the reactant, and will contribute to the π-system without nodal plane in the product. MO C is the HOMO, has the 1s character of the approaching H-atom before reaction, and constitutes the π-system with a nodal plane in the products. The AO coefficients in the HOMO (MO C) suggest the partial formation of a π- system with one nodal plane in the transition state, possibly stabilizing the activated complex. In MO A we also notice π-character on the central C-atom allowing for delocalization potential. We cannot exactly state the extent to which this π-lobe interacts with the π-lobe on the reacting C-atom, as the latter also forms a σ(C-H-H) bond. In Figure 4 we do not see the above-mentioned linear combination of the original π-system with the π-lobe on the reacting carbon atom in MO B. The exact nature of the calculated stabilization is therefore still open to discussion. (v) Abstraction Mechanism. The calculated low, 8 ( 1 kcal/ mol, SDCI/DZP-based activation energy suggests that abstrac-

10514 J. Phys. Chem. B, Vol. 103, No. 47, 1999

Figure 4. Cartoon of extracted RHF/DZP atomic orbital coefficients for the three principal MOs participating in the hydrogen abstraction on propene during the transition state. Coefficients which contribute between |0.15| and |0.25| are shown small. Contributions over |0.25| are shown larger. (a) Doubly occupied MO which constitutes a σ-(CH-H) bond. (b) Doubly occupied MO which forms a π-system molecular orbital, without nodal plane. (c) Singly occupied MO, the HOMO, which shows coefficients for the approaching hydrogen atom and additional coefficients for a π-system with nodal plane.

tion reactions on hydroaromatics in the presence of hydrogen radicals must readily occur under any ambient conditions within the earth. We therefore expect during aromatization of hydroaromatics that removal of the first hydrogen atom requires an abstraction reaction pathway whereas the second hydrogen removal involves a simple hydrogen bond dissociation from the resulting radical. Removal of both hydrogen atoms by abstraction is not likely as the hydroaromatic radical has a strong affinity for an approaching hydrogen atom. Additionally this mechanism requires a continuous source of abstracting hydrogen atoms. The mechanism of hydrogen abstraction coupled with bond dissociation is self-sustaining as it regenerates radicals. The mechanism can be terminated by disproportionation and addition reactions. Abstraction by hydrogen may account for the presence of molecular hydrogen which is common in natural gas resources,37,38 though study of its provenance tends to have been neglected. For full aromatization of a hydroaromatic initially resembling cyclohexene, the abstraction reaction and bond dissociation must be repeated. In Figure 5 the SDCI/DZPderived energy diagram for the full aromatization of cyclohexene via this pathway is shown. The aromatization process is initiated by an exothermic abstraction reaction which yields a molecule with extra delocalization possibilities. As we remove the hydrogen atom via an abstraction rather than a dissociation reaction, the reaction changes from endothermic to exothermic with an energy difference of over 100 kcal/mol. In Figure 5 the highest cumulative energy barrier is situated between the reaction products of AB1 and the transition state of AB2. The cumulative height of this barrier is 57 kcal/mol and is formed by two reaction steps, i.e., the first dissociation reaction, endothermic by 49 kcal/mol, and the second exothermic abstraction reaction, which has an activation energy of 8 kcal/mol. We expect the experimental activation energy to be similar to 57 kcal/mol if the aromatization mechanism is indeed first order with negligible influences of initiation and termination processes as presumed

Schimmel et al.

Figure 5. SDCI/DZP energy diagram relative to reactants for the aromatization of cyclohexene by a pathway in which a hydrogen is removed alternatingly by two abstraction and simple dissociation reactions. The energy of the reaction step is obtained by subtracting the energies of all reaction products formed from the sum of the energies of cyclohexene and a hydrogen atom. The dashed lines are estimated transition states energies for the bond dissociation reactions, which generally have no or a low reverse activation energy.18 (I) Cyclohexene. (II) Cyclohexene-3-yl. (III) 1,3-Cyclohexadiene. (IV) 1,3-Cyclohexadiene-5-yl.

in this model. The 48 kcal/mol39 found experimentally is of the same magnitude, our study thus affirming the role of abstraction reactions for the aromatization of monoaromatic steroids. Aromatization is finally completed by a last simple bond dissociation reaction. Both dissociation steps profit from the formation of an extended π-system, requiring respectively 47 and 21 kcal/mol only as opposed to the 80-90 kcal/mol normally needed for C-H dissociation. The mechanism studied here agrees in detail with available experimental data. When not enough energy is available to overcome the rate-determining step, a resonance-stabilized radical will persist unless a hydrogen or different addition reaction occurs. This accounts for the observed high concentration of resonance stabilized radicals in kerogen,12 which are stable reaction intermediates during aromatization reactions. Our reaction mechanism also accounts for the rare observation of steroids in kerogen corresponding to the CHD;9 these steroids are the reaction intermediates in the rate-limiting step.20 The overall reaction enthalpy for aromatization is positive. In the natural gas, oil, and gas forming environment of kerogen the energy needed for aromatization is provided as thermal energy by the thermal gradient within the earth. The different aggregation states and separation of the reaction products presumably prevent backward reactions. In our study two phases are formed, benzene, and molecular hydrogen. For kerogen either two or three different phasessdepending on the original reactant moleculessare formed, i.e., natural gas, oil, and coal. In studying aromatization mechanisms we recognized two elements which add to its plausibility. First, two exothermic abstractions with low activation energies remove two hydrogen atoms. Their removal by simple dissociation reactions requires 84 and 73 kcal/mol energy input, respectively (cf. BD1 and BD3). Second, the abstraction products, i.e., the two hydroaromatic radicals, need little energy input to lose a hydrogen atom to form a closed shell molecule. As the dissociation and the subsequent abstraction are rate limiting, it allows for additional initiating reaction steps. For example, besides hydrogen radicals, other radicals-can cause aromatization reactions. Abstracting radicals may be hydrocarbon radicalsswhether resonance stabilized or notsor other

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J. Phys. Chem. B, Vol. 103, No. 47, 1999 10515

Figure 6. Observed aromatization of a monoaromatic steroid in kerogen maturation. The observed behavior is not restricted to the presented molecule; other monoaromatic steroids behave similarly.9

heterogeneous radicals as in the experiment performed by Abbott et al.5 We can also postulate that an abstraction reaction on a saturated carbon atom, either directly or indirectly linked to a π-system, can initiate aromatization. For a carbon atom indirectly linked to a π-system a discrete number of hydrogen shifts following the abstraction reaction may yield the radical which can lose a hydrogen. We emphasize that the rate-limiting step may not change in this process. The situation is slightly different for the second abstraction. For this step the activation energy is low and presumably any abstraction on a nonaromatic hydrocarbon followed by hydrogen shifts raises the activation energy barrier. Although energetically not preferable, this process may be important in the natural maturation process as the complexity of natural kerogen molecules ensures many abstraction centers. Finally we should point out that in kerogen, atoms and functional groups other than hydrogen are present which may serve as leaving groups. These different groups commonly need less energy to dissociate than a C-H bond, such as many monoaromatic steroids which possess alkyl groups; cf. Figure 6. Taking this into account, we may reduce or eliminate the difference between the observed and calculated activation energies. (vi) Relevance for Kerogen Maturation. Classically, kerogen is a general name for a hydrocarbon complex which originates from humic and fulvic acids which are randomly reworked, defunctionalized, and polymerized during early diagenesis and which cannot be extracted from rock samples with simple extraction methods.40 More recent studies indicate the importance of selective preservation of molecules resistant to biomolecular action for the formation and composition of kerogen.41 During catagenesis, i.e., the process following diagenesis, in which no microbiological action is involved, kerogen breaks down into aromatic and saturated moieties as a function of temperature only. In the course of this process kerogen fragments lose most of their hydrogen, functional groups, and saturated hydrocarbon moieties, and form linked aromatic structures which contain one to six carbon rings with little chemical diversity. The hydrogen initially present in kerogen now resides in molecular hydrogen and saturated hydrocarbons and, at more elevated temperatures, primarily in molecular hydrogen and methane. This is the ultimate thermodynamically stable state of the system.42 Essential in attaining this state is the removal of hydrogen from the kerogen nucleus, which in this process becomes richer in condensed aromatic structures. The principal hydrogen transfer processes which remove hydrogen from the kerogen nucleus are cyclization and aromatization. The study of dehydrogenation reactions in kerogen are thus essential in understanding the natural maturation process. As stressed by other authors, radical abstraction reactions may explain the aromatization of the hydroaromatic steroids.13,14 To study aromatization in kerogen with quantum chemical methods via this pathway, we have to deal with several constraints. Among these are that the large kerogen molecules

are due to their size not suited for quantum chemical calculations and that chemically meaningful results are next to impossible to extract from such large multifunctional molecules. The principal difficulty in carrying out studies of this nature is therefore to select the smallest molecules with the essential chemical entities necessary to rationalize kerogen aromatization. Another difficulty is, conceptually, how to constrain the complex nature of aromatization mechanisms. We have chosen a mechanism with the most general applicability, which may serve as a basis for study, with slight modifications, of alternative aromatization pathways. Finally, to study maturation we must take molecules with the same general maturation characteristics as kerogen, and for which the results can directly be linked to experimental observations. Molecules which meet these constraints are monoaromatic steroids. These steroids are present in kerogen and can be directly linked to their precursors in biological systems. Initial aromaticity is thought to originate from biological actions or from the influence of heterogeneous atoms during diagenesis.43 During catagenesis these steroids aromatize sequentially toward their fully aromatic homologues and additionally generate hydrogen-rich moieties in molecular hydrogen and saturated hydrocarbons (Figure 6).15,16 The steroids thus mimic kerogen evolution in detail and provide a solid base to describe the progress of reaction. However, even these steroids are too large to introduce directly into quantum chemical calculations. We therefore extracted from these molecules the essential molecular entities needed for aromatization. These are principally both saturated and unsaturated hydrocarbon moieties. The first ones are needed as the aromatization reaction cannot occur without them. The need for the presence of unsaturated hydrocarbons can be inferred from the fact that related steroids without aromaticity tend not to aromatize during early catagenesis. The presence of an aromatic ring may be especially important as it renders the molecule inert to hydrogen addition. The most simple prototype molecule which meets the above requirements is propene. We have additionally chosen cyclohexene and 1,3-cyclohexadiene, which also have these properties and still are small enough to be introduced in ab initio calculations. The last two molecules allow us to monitor the development of full aromaticity from hydroaromatic molecules. The results can be implemented into the original hydroaromatic steroid structure. The molecules can be thought to represent the ring next to the present π-system which aromatizes first. The choice of hydrogen as abstraction radical is rationalized by its simplicity for abstraction reactions. We have placed the abstraction center directly next to the π-system. Doing so, we expected the largest effect of the neighboring π-system on the activation energy for abstraction. For propene of course there is no other possible abstraction center. We have replaced an aromatic structure by one or two single unsaturated bonds and stated that the reaction is typical. This may cause confusion. The presence of aromaticity is important

10516 J. Phys. Chem. B, Vol. 103, No. 47, 1999 only as it inhibits alternative addition reactions on the hydroaromatic. CH and CHD each experience a different energy lowering in the products due to extension of the π-system. The calculated activation energies differ by only 1 kcal/mol. This shows how minor the effect of the size of the π-system is on the predicted activation energy. We therefore conclude that the calculated activation energies can indeed be extrapolated to monoaromatics. Conclusions and Recommendations Of all methods considered here SDCI predicts bond dissociation and abstraction activation energies on hydroaromatics most reliably. Abstractions on hydroaromatics are facilitated by the neighboring π-system. With an SDCI ab initio calculation we found activation energies for our three abstraction reactions clustered around 8 kcal/mol. The occurrence of extra delocalization possibilities in the products lowers the reaction coordinate as reflected in a more open geometry. This difference in geometry accounts for a lowering of the transition state activation energy by 2 kcal/mol. Delocalization is also present in the activated complex and lowers the saddle point by about 3 kcal/mol. Further studies must be done to allocate delocalization in the transition state. Spin contamination on open shell hydroaromatic molecules yielded incorrect energies when UHF and MP2 were used. UHF and RHF calculational results show similar optimized geometries for the stable intermediates, but the transition states geometries for the three abstraction reactions considered occur later in RHF. This difference, however, has a negligible effect on the value of the activation energies. Abstraction, whether located directly next to the π-system or located somewhere else with subsequent hydrogen shifts, followed by a simple hydrogen bond dissociation is a feasible pathway for aromatization of hydroaromatics. Geologically this study affirms the importance of this reaction pathway for the partitioning of kerogen in saturated and unsaturated hydrocarbons. The reaction is rate limited by simple hydrogen bond dissociation and subsequent hydrogen abstraction. The energy demands for this reaction via such pathway is 57 kcal/mol, agreeing reasonably well with those experimentally observed for hydroaromatic aromatization. Acknowledgment. GAMESS-UK is a package of ab initio programs written by M. F. Guest, J. H. van Lenthe, J. Kendrick, K. Schoffel, and P. Sherwood, with contributions from R. D. Amos, R. J. Buenker, M. Dupuis, N. C. Handy, I. H. Hillier, P. J. Knowles, V. Bonacic-Koutecky, W. von Niessen, R. J. Harrison, A. P. Rendell, V. R. Saunders, and A. J. Stone. The package is derived from the original GAMESS code due to M. Dupuis, D. Spangler, and J. Wendoloski, NRCC Software Catalog, Vol. 1, Program No. QG01 (GAMESS), 1980. References and Notes (1) Olah, G. O. Hydrocarbon Chemistry; Wiley: New York, 1995. (2) Hucknall, D. J. Chemistry of Hydrocarbon Combustion; Chapman and Hall: London, 1985. (3) Wamatz, J. In Combustion Chemistry; Gardines, W. C., Ed.; Springer-Verlag: New York, 1984.

Schimmel et al. (4) Litwinowicz, J. A.; Ewing, D. W.; Jurisevic, S. J. J. Phys. Chem. 1995, 99, 9709-9716. (5) Kerr, J. A., Moss, S. J., Eds. CRC Handbook of Bimolecular and Termolecular Gas Reactions; CRC Press: Boca Raton, FL, 1981; Vol. 1. (6) Benson, S. W.; Weissman, M. A. J. Phys. Chem 1988, 92, 40804084. (7) Tsang, W.; Hampson, R. F. J. Phys. Chem Ref Data 1986, 15, 1087-1279. (8) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just, T.; Kerr, J. A; Pilling, M. J.; Troe, F.; Walker, R. W.; Warnatz, J. J. Phys. Chem. Ref. Data 1992, 21, 411-734. (9) Simoneit, B. R. T. In Biological Markers in the Sedimentary Record; Johns, R. B., Ed.; Elsevier: Amsterdam, 1986; pp 43-99. (10) Ungerer, P. Org. Geochem. 1992, 16, 1-25. (11) Burnham, A. K.; Braun, R. L. Org. Geochem. 1992, 16, 27-39. (12) Marchand, A.; Conrad, J. In Kerogen, Insoluble Organic Matter from Sedimentary Rocks; Durand, B., Ed.; Technip: Paris, 1980; pp 243270. (13) Johns, W. D.; Almon, W. R. AdV. Org. Geochem. 1975, 7, 157171. (14) Seifert, W. K.; Moldowan, J. M. AdV. Org. Geochem. 1979, 9, 229237. (15) Mackenzie, A. S.; Lamb, N. A.; Maxwell, J. R. Nature 1982, 295, 223-226. (16) Mackenzie, A. S.; Hoffman, C. F.; Maxwell, J. R. Geochim. Cosmochim. Acta 1981, 45, 1345-1355. (17) Abbott, G. D.; Lewis, C. A.; Maxwell, J. R. Nature 1985, 318, 651-653. (18) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1976. (19) Dupuis, M.; Spangler, D.; Holmes, J. L.; Radom, L. J. Am. Chem. Soc. 1986, 108, 1767-1770. (20) Pople, J. A.; Binkley, J. S.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939-947. (21) Dunning, T. H., Jr. J. Chem. Phys. 1970, 53, 2823-2833. (22) Pople, J. A.; Schlegel, H. B.; Krishman, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F., Jr.; Hehre, W. J. Int. J. Quantum Chem. 1981, 15, 269-278. (23) Rice, J. E.; Amos, R. D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F. J. Chem. Phys. 1986, 85, 963-968. (24) Dupuis, J.; Watts, J. D. J. Comput. Chem. 1988, 9, 158-170. (25) (a) Lenthe, J. H.; Saunders, V. R. Mol. Phys. 1983, 48, 923-954. (b) Pople, J. A.; Seeger, R.; Krishman, R. Int. J. Quantum Chem. 1977, QS11, 149. (26) Chiang, J. F.; Bauer, S. H. J. Am. Chem. Soc. 1969, 91, 18981901. (27) Oberhammer, H.; Bauer, S. H. J. Am. Chem. Soc. 1969, 91, 1016. (28) Langseth, A.; Stoicheff, B. P. Can. J. Phys. 1956, 34, 350. (29) Reference not given. (30) Golden, D. M.; McMillen, D. F. Annu. ReV. Phys. Chem. 1982, 33, 493-532. (31) Kerr, J. A.; Parsongae, M. J. EValuated Kinetic Data on Gas Reactions; Butterworth: 1972; p 46. (32) Tsang, W. J. Phys. Chem. 1986, 90, 1152-1155. (33) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334. (34) Morokuma, K.; Davis, R. E. J. Am. Chem. Soc. 1972, 94, 10601067. (35) Davidson, E. R. J. Comput. Phys. 1975, 17, 87-94. (36) Siegbahn, P. E. M.; Niblaeus, K.; Roos, B. O. Chem. Phys. 1977, 26, 59-68. (37) Kravchik, T. E.; Zinger, A. S. Geokhim. 1962, 10, 890-898. (38) Nechayeva, O. L. Dokl. Adad. Nauk. SSSR. 1968, 179, 961-962. (39) Mackenzie, A. S.; McKenzie, D. Geol. Mag. 1983, 120, 417-465. (40) Tissot, B. P.; Welte, D. H. Petroleum Formation and Occurrence; Springer-Verlag: Berlin, 1984. (41) Derenne, S.; Kerp, H.; Largeau, C.; Leeuw, de J. W.; Tegelaar, E. W. Geochim. Cosmochim. Acta 1989, 53, 3103-3106. (42) Hunt, J. M. Pet. Eng. 1975, 47, 112-127. (43) Baas, M.; Leeuw, de J. W. In Biological Markers in the Sedimentary Record; Johns, R. B., Ed.; Elsevier: Amsterdam, 1986; pp 101-123.