10549
J. Phys. Chem. 1995, 99, 10549-10556
Ab Initio Calculations of the Potential Surface for the Thermal Decomposition of the Phenoxy1 Radical Santiago Olivella,*v+Albert Sol4,*9*and Angel Garcia-Raso* Departaments de Quimica Orgbnica i Quimica Fisica, Universitat de Barcelona, Marti i FranquEs I , 08028-Barcelona, Catalunya, Spain, and Departament de Quimica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain Received: March 30, 1 9 9 9
The thermal decomposition of the phenoxyl radical (1)to form CO plus C5H5', a key reaction in the hightemperature oxidation of benzene, has been studied using ab initio quantum mechanical electronic structure methods. The complete active space (CAS) SCF method was used for geometry optimization of 10 stationary points on the ground-state potential energy reaction surface and computing their harmonic vibrational frequencies. Subsequent calculations using the multireference second-order perturbation theory based on a CASSCF reference function (CASPT2) with 6-3 lG(d,p) basis set established the energetics along the two altemative reaction paths proposed by Benson and co-workers. The energetics were further corrected for zero point vibrational energy at the CASSCF level of theory. The present study predicts the decomposition of 1 to occur preferably through an electrocyclic cyclization mechanism involving the formation of the 6-oxobicyclo[3.1 .O]hex-3-en-2-y1radical (2) as intermediate, rather than by a ring-opening process leading to 1-yl radical (4) intermediate. In contrast to early reported experimental kinetic the (3~)-6-0~0-1,3,5-hexatriendata, the preexponential factor of the thermal Arrhenius expression of the rate constant for the unimolecular decomposition of 1 is predicted to have a normal value (A > 10'3.5s-I).
SCHEME 1
I. Introduction
A
The unimolecular decomposition of the phenoxyl radical (1) by reaction eq 1 is currently believed to be a very important step in the high-temperature oxidation of aromatic hydrocarbons, which are important ingredients of lead-free gasoline.1*2
Recent studies of benzene oxidation at high temperatures with detailed product analyses have indicated that phenol (CSH5OH) is the most important early stage oxidation p r ~ d u c t . ~In - ~view of its known weak OH bond,6 the C&OH generated in the early oxidation process is expected to produce 1 very readily either unimolecularly or bimolecularly via reactions with atomic and radical specie^.^ Its decomposition product, C5H5', is believed to be a major precursor of cI-c4 hydrocarbon fragments observed in the oxidation proce~s.43~ The understanding of the kinetics and mechanism of 1 at high temperatures is therefore one of the major steps toward the ultimate goal of elucidating the complex benzene oxidation chemistry. The rate constant for the decomposition of 1 by reaction eq 1 was first determined by Benson and co-workers* to be 10 f 5 s-l at 1000 K. Further kinetic studies by Lin and Lin7 on the thermal decomposition of anisole (C&OCH3) as a source of 1 gave rise to the parameters A = 10 12.0*o.2 s-l and Ea = 47.7 f 1.4 kcal/mol for the thermal Arrhenius expression of the rate constant of reaction eq 1, covering the 1010-1430 K range of temperature. In a subsequent kinetic study, employing both C&OCH3 and allyl phenyl ether (C&OCHCH2) as 1 sources, the latter authors gave the Arrhenius parameters A = 1011.4*0.2 s-l and Ea = 43.9 f 0.9 kcal/mol at 1000-1580 K.9 Departament de Quimica Orghnica, Universitat de Barcelona. Departament de Quimica Fisica, Universitat de Barcelona. 8 Departament de Quimica, Universitat de les Illes Balears. @Abstractpublished in Advance ACS Abstracts, June 1, 1995.
4
Two altemative mechanisms can be proposed for reaction eq 1 (see Scheme 1). In one of these (hereafter called mechanism A) the reaction proceeds through a cyclization of 1 to form the 6-oxobicyclo[3.1.O]hex-3-en-2-y1 radical (2) as intermediate which undergoes a ring opening of the cyclopropanone moiety to give (2,4-cyclopentadienyl)carbonylradical (3). The other mechanism (hereafter called mechanism B) involves a ring fission of 1 to form the (3z)-6-oxo-1,3,5hexatrien-1-yl radical (4) and subsequent cyclization of this intermediate to 3. The last step of both mechanisms consists in the CO elimination from 3 to give cyclopentadienyl radical (5). On the basis of a thermochemical kinetic estimate, Benson and co-workers*suggested that the reaction occurs most likely via mechanism A. The apparent low A factors determined by Lin and Lin seem to render a very strong support for a tight transition state mechanism such as TS1 of mechanism A, which involves the formation of two rigid rings. The alternative mechanism B, involving initially the ring opening of 1, is expected to have a looser transition state (i.e., TS3) with perhaps a more normal preexponential factor (A 1. 10'3.5s-l). At this point we note that the above arguments implicitly assume that the first step in each reaction path, namely 1 2 for mechanism A and 1 4 for mechanism B, is the rate-detedning one. The validity of these assumptions has not yet been confirmed
-
0022-3654/95/2099-10549$09.00/00 1995 American Chemical Society
-
Olivella et al.
10550 J. Phys. Chem., Vol. 99, No. 26, 1995 theoretically. Furthermore, the A factor values of 10'2.0*o.2 and 10'1.4*0.2s-I determined by Lin and Lin lead to an activation entropy ranging from - 10.8 to - 11.7 cal mol-' K-I at 10001580 K for the cyclization of 1 to 2. However, there are good reasons for believing that these values are abnormally too negative. In fact a theoretical studylo of the ring opening of bicyclo[3.1 .O]hex-3-en-2-y1radical (6) to give cyclohexadienyl radical (7)predicted an activation entropy of -0.298 cal mol-' K-I at 298 K for the reverse reaction, namely the rearrangement 7 6 , which is structurally related to the cyclization 1 2.
-
-
H
H'
6
'H
7
Since it is likely that the both rearrangements involve a similar transition structure, there is no a priori structural reason that the corresponding activation entropies differ in more than ca. 10 cal mol-' K-'. To ascertain the crucial points of the conclusions drawn by Benson and co-workers, as well as by Lin and Lin, it is felt that a rigorous theoretical study of the C6H50. reaction potential energy hypersurface in the region conceming the thermal unimolecular decomposition of 1 is of much importance. While there have been many theoretical studies''-'7 on the structure of 1 as well as on its ESR, IR, and UV-vis spectra, no theoretical study has been devoted yet to the decomposition reactions of 1. Here we report the first theoretical investigation of the two altemative thermal decomposition modes of 1. Specifically, we report a complete characterization of 10 stationary points on the C6H50' ground-state potential energy hypersurface, including predictions of geometrical structures, harmonic vibrational frequencies, absolute entropies, and relative energies of minima and transition states, using high-level quantum mechanical methods. Energy differences between the two decomposition pathways are obtained and rationalized in terms of the structural features shown by the radical intermediates and transition states involved. Finally, the activation parameters and rate constant for the rate-determining step of the energetically preferred decomposition pathway are compared with the available experimental data.
11. Computational Details The equilibrium structures of 1-5 and the transition structures TS1-TS5 were initially optimized by using the spin-unrestricted Hartree-Fock (UHF)28version of the AM1 semiempirical selfconsistent field (SCF) molecular orbital (MO) method29 as implemented in the AMPAC program30 and then further optimized within the framework of the UHF method with the 3-21G split-valence basis set3' employing analytical gradient procedure^.^^ All these ab initio calculations were performed with the Gaussian 90 system of programs33 on the IBM 3090/ 6005 computer at the Centre de Supercomputacio de Catalunya (CESCA). The UHF wave function of the 10 optimized structures was subjected to very serious spin contamination, ranging from 0.979 to 1.677 as compared to 0.75 for a pure doublet state. This can be taken as an indication of strong nondynamical electron correlation effects. One may then question the reliability of the geometries calculated for these structures. Consequently, all the geometries were reoptimized by use of multiconfiguration SCF (MCSCF) wave functions of the
complete active space (CAS) SCF class.34 The CASs were selected following the procedure suggested by Pulay and Hamilton,35based on the fractional occupation of the natural orbitals of the UHF wave function (designated UNOs). These indicated a number of active orbitals which varied from 3, for the equilibrium structure 2, to 9, for the transition state TS3. The distribution among the active orbitals of the corresponding number of active electrons led in each case to CASSCF wave functions formed as a linear combination of a number of doublet spin-adapted configuration state functions which varied from 8 (2) to 8820 (TS3). The 3-21G basis set was used for the CASSCF geometry optimizations. To investigate the effect of the d polarization functions (at the carbon and oxygen atoms) on the geometry of the calculated structures, additional geometry optimizations at the CASSCF level with the 6-3 1G(d) basis set36were performed for the most relevant stationary points. The normal modes and harmonic vibrational frequencies of the structures optimized at the CASSCF level were obtained by diagonalizing the massweighted Cartesian force constant matrix calculated numerically by finite differences of analytical gradients.37 All CASSCF calculations were carried out by using GAMESS system of programs38on the IBM 3090/600J computer at the CESCA. To incorporate the effect of dynamical electron correlation on the relative energy ordering of the calculated stationary points, second-order multiconfigurational perturbation theory based on the CASSCF reference function (CASPT2)39was used at the CASSCF optimum geometries with the 6-31G(d,p) basis set.36 The full Hartree-Fock matrix was used in the construction of the zeroth-order Hamiltonian The dimensions of the first-order interaction space in the CASPT2 calculations varied from 3 846 830 for 2 to 5 086 324 for TS3. The CASPT2 calculations were performed with the MOLCAS version 2 quantum chemistry package40 on a IBM RS/6000-58H workstation. The harmonic vibrational frequencies computed at the SCF level of theory typically overestimate the experimentally observedfundamental frequencies by an average of about 12%, due to a combination of electron correlation and vibrational anharmonicity effects. In order to predict more reliable zeropoint vibrational energies (ZPVE), the raw theoretical harmonic frequencies are currently scaled by 0.89.4' Due to the lack of any survey on the accuracy of the vibrational frequencies predicted by ab initio CASSCF calculations, the harmonic vibrational frequencies computed at the latter level of theory were also scaled by a factor of 0.89. Temperature corrections and absolute entropies were obtained, assuming ideal gas behavior, from the scaled harmonic frequencies and moments of inertia by standard methods4* Thus the temperature correction to the sum of the CASPT2/6-31G(d,p) energy and the ZPVE was evaluated as a sum of the translational and rotational energies at the absolute temperature T and the change in the vibrational energy in going from 0 to T K, while the absolute entropies (S) were evaluated by the relation S = S,,
+ S,, + S,,,
- R In CJ
+ R In m
(2)
where S,,,S, and S b I b are the translational, rotational, and vibrational contributions, respectively, R is the ideal gas constant, u is the rotational symmetry number,43and m is the multiplicity of the electronic ground state. A standard pressure of 1 atm was taken in the S calculations. The first-order rate constants (k(7')) for the unimolecular decomposition of 1 (eq 1) were computed using the activated complex theoryu assuming that the transmission coefficient is equal to 1, as expressed by the following relation
J. Phys. Chem., Vol. 99, No. 26, I995 10551
Thermal Decomposition of the Phenoxy1 Radical
k(7'j = (kT/h) exp(As'/R) exp(-&/RT)
(3)
where A,?? and A$ are the energy and entropy changes between 1 and the transition structure of the rate-determining step, k is the Boltzmann constant, and h is the Plank constant. A,?? was calculated as follows:
A d = v'+ AZPVE
+ AE(T)
(4)
where is the potential energy barrier (calculated at the CASPT2/6-31G(d,p) level) and AZPVE and A,??(r) are the differences between the transition state and reactant ZPVEs and temperature corrections, respectively. Finally, the activation energy (Ea) and preexponential factor (A) of the thermal Arrhenius expression of the rate constant were calculated by the following relations:
E,=&+RT
(5)
A = (ekT/h) exp(As'/R) 111. Results and Discussion Molecular Geometries. Selected bond lengths (in A) of the 10 stationary points located in this study are depicted in Figure 1, which shows computer plots of the geometries optimized at the CASSCF level with the 3-21G basis set. For comparison, the bond distances obtained from the geometries optimized at the CASSCF level with the 6-31G(d) basis set for 1, TS1, 2, TS2, 3, TS5, and 5 are shown in parentheses. The full optimized geometries are available as supplementary material. The atomic labels used throughout this paper are defined in the first structure of Figure 1. Overall, the structures of 1, TS1,2, TS2, 3, TS5, and 5 calculated using the 3-21G basis sets are similar to those calculated with the larger 6-31G(d) basis set. Unless otherwise noted, the following discussion refers to the geometries calculated with the 3-21G basis set. For the sake of brevity, only the geometrical features of the relevant stationary points involved in the predicted minimum energy reaction path, namely mechanism A, are succinctly discussed in this section. As noted in previous theoretical s t ~ d i e s ,the ~ ~calculated ,~~ equilibrium structure of 1 is particularly sensitive to the basis set utilized. Hence, in going from a split-valence 3-21G to the polarized 6-31G(d) basis the CO bond length is shortened by 0.057 A and the C5Cll distance is lengthened by 0.025 A, although there is little change in the C3C4 or C4C5 bonds. In a recent study, Chipman et al.27 have shown that further extension of the basis set to the much larger 6-31 1G(2d,p) basis leads to essentially the same equilibrium structure obtained with the 6-31G(d) basis. The CASSCF/6-31G(d) geometry reported here for 1 is therefore expected to be reliable. The CO distance of 1.236 A is slightly elongated as compared to the values typical of a carbonyl double bond in benzoquinone~~~ (-1.22 A), indicating that is very close to that of a regular CO double bond. As regards the heavy-atom skeleton, Chipman et al. have concluded that 1 is similar in some respects (C2C3 and C3C4 distances) to the aromatic structure of benzene, in other respects (ClC2 and C4C5 distances) to the quinoid structure of p benzoquinone, and in still other respects (ClC11 and C5Cll distances) is intermediate between them.27 The most noteworthy geometrical features of the transition structure calculated for the formal electrocyclic rearrangement of 1 to 2, namely TS1, are the remarkable differences in the lengths of the bonds which in 1 and 2 are equal by symmetry (e.g., C1C2 and C4C5, C2C3 and C3C4, and C l C l l and C5C11). This C, symmetry transition structure indicates an
asynchronous ring closure/opening similar to that found for the interconversion between 6 and 7.1° In principle, during the cyclization of 1 to give 2 the methine hydrogen atoms adjacent to the forming CC bond might move in either a disrotatory or conrotatory fashion. However, owing to the severe geometrical constraints in 2, only the disrotatory motion can take place. Figure 2 shows the correlation diagram for the two highest occupied MOs of 1 (x3 and x4) and 2 ( x ~and x2), which are the MOs most directly involved in the disrotatory conversion of 1 into 2. Each of these orbitals is classified by symmetry labels (S, symmetrical; A, antisymmetrical) relating to the symmetry plane that is maintained along the conventional disrotatory process, namely the plane bisecting the inter-ring CC bond in 2. Alternative symmetry labels appropriate to the irreducible representations of the corresponding point groups (Le., CzYfor 1 and C, for 2) are also given in parentheses. Since the single occupied MOs of 1 and 2 are of different symmetry, it follows that the electronic ground states of these molecules do not correlate to each other. Therefore, if it is assumed that the cyclization of 1 into 2 proceeds through a pathway conserving the symmetry plane bisecting the inter-ring CC bond, it becomes apparent that the thermal reaction is both orbitalsymmetry forbidden and state-symmetry forbidden. Perturbation by not fully concerted changes in the geometrical parameters along the reaction path can lead to complete annulment of the symmetry, and consequently, this allows an interaction between the two highest occupied MOs of 1, which should force the correlation between the ground states of 1 and 2. On the basis of the noted differences in the bond lengths of the structure calculated with the 3-21G basis set for TS1, it can be concluded that the necessary interaction between the n3 and x4 MOs of 1 takes place at the transition state. The unpaired electron in TS1 is unequally spread out among C1, C2, and C4 atoms. In clear contrast, the structure calculated with the 6-31G(d) basis set for TS1 shows nearly C, symmetry and the unpaired electron is equally distributed between C2 and C4 atoms. The ground electronic configuration is found to be that of the resulting radical 2, indicating that the x3-x4 orbital interaction occurs before the transition state is reached. However, in view of the nearly identical energy calculated at the highest level of theory for the structures optimized with the 3-21G and 6-31G(d) basis sets for TS1, the importance of the question concerning the different symmetry found for these structures is lessened. The structure of the bicyclic radical intermediate 2 is akin to that calculated at the same level of theory for 6. The unpaired electron in both C, structures is distributed between C2 and C4 atoms. As a result, the bond lengths in the cyclopenta-3-en2-yl part of 2 are similar to those calculated for 6. Moreover, the tilting angle (1 11.2") of the cyclopropanone ring with regard to the cyclopenta-3-en-2-yl ring in 2 is close to the tilting angle (109.3') of the cyclopropane ring with regard to the cyclopenta3-en-2-yl ring in 6. However, the fusion C1C5 bond (1.581 A) in 2 is significantly elongated as compared to either a regular CC single bond or the length calculated for the fusion CC bond of 6 (1.527 A). The CASSCF calculations with the 6-31G(d) basis set also predict for 2 a long (1.572 A) C1C5 bond length. This result may be attributed to the expected largest strain of the cyclopropanone ring in 2 as compared to cyclopropane ring in 6. This point is supported later by the calculated strain energies of these three-membered rings. Regarding the CO bond in 2, it is noteworthy that both the 3-21G and 6-31G(d) basis sets give distances (1.193 and 1.178 A), respectively) which are only 0.01 A shorter to those found in the transition structure TS1. Despite the common geometrical features shared by the
10552 J. Phys. Chem., Vol. 99, No. 26, 1995
Olivella et al.
-
H8
a
1.202
Figure 1. Computer plots of the CASSCF/3-2 1G-optimized structures for the thermal unimolecular decomposition of phenoxyl radical.
calculated at the same level of theory for the ring opening of 6 to give cyclopentadienylmethyl radical (8).1° In both transition
H
8 %
Figure 2. Molecular orbital correlation diagram for the disrotatory interconversion between phenoxyl and 6-oxobicyclo[3.1 .O]hex-3-en2-yl radicals.
equilibrium geometries of 2 and 6, it is important to mention that the lower harmonic vibrational frequencies calculated for these structurally related bicyclic radicals are quite different. Hence the smallest (scaled) frequency (VI)calculated for 2 (170 and 138 cm-', respectively with the 3-21G and 6-31G(d) basis sets), which corresponds to a torsional vibration consisting in a bending of the CO bond with respect to the ClC11C5 plane coupled with a in-phase bending of this plane with respect to the cyclopenta-3-en-2-yl ring. Of course this vibration is absent in the theoretical IR spectrum of 6. Furthermore, the smallest (scaled) frequency of 330 cm-l calculated (CASSCFl3-21G) for 6, which corresponds to the torsion of the cyclopropane ring with respect to the cyclopenta-3-en-2-yl plane, is shifted to the value of 242 cm-I (250 cm-' with the 6-31G(d) basis set) in 2 and is the second smallest frequency ( ~ 2 )of its theoretical IR spectrum. These lower vibrational frequencies V I and v2 play a crucial role in the argument given latter to rationalize the unexpectedly large absolute entropy calculated for 2. In contrast to the noted significant differences between the geometries calculated for TS1 with the 3-21G and 6-31G(d) basis sets, in the case of TS2, which appears to be the transition structure of the rate-determining step for the global unimolecular decomposition of 1, both basis sets predict an almost identical geometry. The unpaired electron is unequally spread out among C2, C4, and C11 atoms. It is worth noting that in going from 2 to TS2 the C5Cll bond has stretched to 1.858 A, the C2C3 and C4C5 distances decrease by 0.030 and 0.088 A, respectively, while the C3C4 distance lengthens by 0.042 A. These changes are nearly identical to those observed for the transition structure
structures one of the two CC double bonds (i.e., C2C3) of the resulting intermediate radical is notably formed. On the other hand, the CO bond length in TS2 does not change almost as compared to that in 2. The salient geometrical feature of the resulting intermediate radical 3 is that the optimization with both the 3-21G and 6-3 1G(d) basis sets yields an equilibrium structure which is close to Cssymmetry but slightly distorted. The small deviation from C, symmetry is due to the fact that the dihedral angle (0) between the 012Cl1, C11C1, and C1H6 bonds is calculated to be 110.3" (99.8" with the 6-31G(d) basis set) rather than 0" or 180". Within the C, s y h e t r y constraint, two additional stationary points were found for 3, which correspond to the syn (0= 0") and anti (0= 180") conformers. The harmonic vibrational analysis proved that the corresponding structures have an imaginary frequency. The nuclear displacements associated to both frequencies lead to the C1 equilibrium structure of 3 shown in Figure 1. This conformational preference is akin to that found for 8.1° It is worth noting that 3 is a geometric and electronic analog of 8 with the two hydrogen atoms of the methylene group replaced by an oxygen atom. In both radicals the unpaired electron is located on the C11 atom. The 3-21G and 6-31G(d) basis sets leads to essentially the same transition structure, TS5, for the CO loss from 3. In going from 3 to TS5 the CC bond undergoing cleavage has elongated to 1.921 A and the CO bond is shortened by 0.027 A, while the cyclopentadienyl ring does not change almost, except the C1H6 bond which becomes nearly coplanar to the carbon skeleton. In the resulting cyclopentadienyl radical, 5, the C1C2 and C1C5 bond distances are shortened by about 0.047 A, as compared to those in TS5. The change in the C2C3, C3C4, and C4C5 bond distances in going from TS5 to 5 are less significant (K0.013 A). Finally, it is noteworthy to recall that
J. Phys. Chem., Val. 99,No. 26, 1995 10553
Thermal Decomposition of the Phenoxy1 Radical
TABLE 1: Total Energies (E, hartrees), Zero-Point Vibrational Energies (ZPVE, kWmol), and Relative Energies (Erel, kcdmol) Calculated for CASSCF/3-21G Optimized Structures E
structure 1 TSl 2 TS2 3 TS3 4 TS4
point group CzV CI C,
CI CI CI CI
state 'BI 'A" 'A A ' 'A 'A
A '
TS5
CI CI
5
CzV
A ' 'BI
C,,
IZ+
co
'A
nao' 7 5
3 5 5
9 7 7 7 5 0
CASSCFI 3-21G -303.339 19 -303.19329 -303.185 03 -303.185 18 -303.236 77 -303.250 26 -303.214 04 -303.196 98 -304.240 32 -191.16480 -112.093 30'
CASSCFI 6-31G(d,p) -305.04141 -304.910 12 -304.900 11 -304.896 45 -304.952 51 -304.952 60 -304.919 89 -304.901 10 -304.956 35 -192.24637 -112.737 26d
Ere1
CASFT21 6-31G(d,p) -305.93758 -305.85240 -305.865 64 -305.848 46 -305.890 07 -305.823 41 -305.822 61 -305.814 47 -305.879 82 -192.87004 -113.027 18'
ZPVEb 54.1 51.6 53.1 52.1 53.1 52.1 51.4 50.8 51.5 46.1 2.9)
CASPT21 6-31G(d,p)
CASPT21 6-31G(d,p) + ZPVE
0.0
0.0
53.5 45.1 55.9 29.8 71.6 72.1 77.3 36.2 25.3
51.0 44.1
53.9 28.8 69.6 69.4 74.0 33.6 20.6
a Number of active orbitals. Obtained from calculated CASSCFl3-21G harmonic vibrational frequencies scaled by 0.89. SCFl3-21G energy. SCF/6-31G(d) energy. e MP2(fu11)/6-31G(d) energy.
at the SCF level of theory the 3-21G and 6-31G(d) basis sets give an equilibrium CO distance of 1.129 and 1.114 A, respectively, for the carbon monoxide molecule. Therefore, the CO bond distance is still further shortened by about 0.0260.023 8, in passing from TS5 to the resulting CO molecule. Energies. The CASSCF and CASFT2 energetics for the 10 stationary points optimized with the 3-21G basis sets are presented in Table 1. The relative energies calculated without including the ZPVE corrections are given in the penultimate column of Table 1, while those including such a correction are given in the last column. Unless otherwise noted, the relative energies given hereafter in the text refer to the CASPT2/631G(d,p) level plus ZPVE correction values. The credibility of the calculated relative energies can be assessed in part by comparing the relative energies of 44.1 and 28.8 kcaumol predicted for the intermediate radicals 2 and 3, respectively, with the values of 43.6 and 29.4 kcal/mol obtained from the heats of formation at 298 K of 1-3 derived by Benson and co-workers from thermochemical data.8 Furthermore, the 20.6 kcal/mol predicted for the global energy of reaction eq 1 agrees closely with the reaction enthalpy of 20.0 kcal/mol at 298 K estimated by the same authors. In agreement with Benson and co-workers proposal,8 the results of the present calculations clearly indicate mechanism A to be energetically favored with respect to mechanism B. Hence, the transition structure of the rate-determining step of mechanism B, namely TS4, is predicted to lie 20.1 kcaYmol above the energy calculated for the transition structure of the rate-determining step of mechanism A, namely TS2. The calculated higher energies of the transition structures TS3 and TS4, as compared to those of TS1 and TS2, is clearly related to the higher energy calculated for the radical intermediate 4 (69.4 kcal/mol) as compared with that of 2 (44.1 kcdmol). A major reason for the predicted large energy difference (25.3 k c d mol) between 2 and 4 is due to the lack of any delocalization of the unpaired electron in the latter radical. As noted above, the unpaired electron in structure 2 is distributed between C2 and C4 atoms at the n2 MO (see Figure 2). Thus, the delocalization of the 3 n-type electrons in the C2C3C4 part of 2 is akin to that of a substituted allyl radical. In contrast, the unpaired electron in structure 5 is located on a a-type orbital of C5 atom, so this radical can be regarded as a substituted vinyl radical. It is well-known that, in general, the allyl radicals are less energetic than the vinyl radicals.46 The relatively small potential energy barrier of 4.8 kcal/mol, calculated for the CO elimination from the intermediate radical 3 seems consistent with the exoergonicity of 8.8 kcdmol calculated for this reaction. Interestingly, Benson and co-
--
workers speculated the possibility that the two-step sequence 2 3 5 CO may occurs concertedly. Our results clearly show that the radical intermediate is a true potential energy well. However, the large exoergonicity of 15.3 kcdmol predicted for the ring opening step 2 3, along with the low potential energy barrier of 4.8 kcdmol predicted for the CO loss from 3, suggests that it should be difficult to establish experimentally the intermediacy of 3. At this point, it is noteworthy that Benson and co-workers assumed that the rate-determining step of mechanism A is the cyclization 1 2 rather than the ring opening 2 3. However, we find that TS2 lies 2.9 kcal/mol above TSl. To investigate the effect of the geometries on the calculated relative energies, additional CASPT2 calculations using the geometries optimized with the 6-3 1G basis set were carried out for the seven stationary points involved in mechanism A. The results are presented in Table 2. In comparing Tables 1 and 2 it is observed that the relative energies calculated at the CASPT2/6-31G(d,p) level using the geometries optimized with the 3-21G and 6-31G(d) basis sets are very close, varying at most by 1.3 kcal/mol (5 CO). In particular, at this level the difference between TS2 and TS1 changes from 2.4 to 1.7 kcal/mol. Inclusion of the ZPVE correction to the CASFT2/6-3 lG(d,p)//CASSCF/631G(d) relative energies leads to an energy difference between TS2 and TS1 of 2.1 kcdmol. Therefore it is concluded that TS2 is the transition structure of the overall reaction eq 1. It is instructive to compare the potential energy barrier calculated for the 1 2 rearrangement with that of the structurally related rearrangement 7 6. At the CASFT2/63 lG(d,p)//CASSCF/3-21G level, the potential energy barriers for these rearrangements are calculated to be 53.5 (see Table 1) and 36.9 kcal/mo1,4' respectively. Could there be a specific reason why the potential energy barrier for the cyclization 1 2 is notably (16.6 kcal/mol) higher than that of the 7 6 cyclization? The simplest explanation is based on the expected differences in the strain energy of the three-membered ring formed in each cyclization. To assess the strain energies of the three-membered ring units of 6 and 2, we have calculated the homodesmotic strain energies48of cyclopropane ( c - C ~ H ~ ) and cyclopropanone (c-C~H~O). Thus the homodesmotic strain energy of c-C&, defined by the formal reaction eq 7, was
+
-
-
-
+
-
-
--
C-C&
+ 2 CH3CH3
-
CH3CH,CH3 4-CH,CH,CH,CH,
(7)
calculated at the second-order Moller-Plesset perturbation theory49 (MP2) with the 6-31G(d) basis set to be 30.5 kcaY mol, while the homodesmotic strain energy of c-C3&0, defined
Olivella et al.
10554 J. Phys. Chem., Vol. 99, No. 26, 1995
TABLE 2: Total Energies (E, hartrees), Zero-Point Vibrational Energies (ZPVE, kcdmol), and Relative Energies (Erel, kcaymol) Calculated for CASSCF/6-31G(d) Optimized Structures E point group
structure
state
naoa
CASSCFI 6-31G(d)
CASSCFI 6-31G(d,p)
-305.035 74
-305.044 56
-304.902 79 -304.892 24 -304.889 01 -304.945 08 -304.948 67 - 192.237 45 -1 12.737 88'
-304.911 87 -304.901 38 -304.898 06 -304.954 10 -304.957 71 -192.246 74 -112,73788'
Ere1 CASPT21 6-31G(d,p) -305.938 -305.853 -305.864 -305.849 -305.889 -305.878 -192.870 -113.025
23 01 95 62 77 57 78 14d
ZPVEb 53.7 51.9 53.2 52.3 53.2 51.7 45.9 3.1)
CASPT21 6-31G(d,p)
CASPT21 6-31G(d,p) ZPVE
0.0 53.5
+
0.0
46.0 55.2 30.4 37.4
51.7 45.5 53.8 29.9 35.4
26.6
21.9
Number of active orbitals. Obtained from calculated CASSCFl6-3 lG(d) harmonic vibrational frequencies scaled by 0.89. SCFl6-3 1G(d) energy. MP2(fu11)/6-31G(d) energy.
TABLE 3: Activation Parameters and Rate Constants (k, s-l) Calculated" for the Unimolecular Thermal Decomposition of 1 at Various Temperatures temp (K) APb A F Eab logA k 298
54.17 53.38 53.05
1000 1200
2.11 0.70
0.38
54.77 55.37 55.44
13.69 13.91 13.92
3.5 x lo-?' 6.4 x IO' 6.6 x IO3
Using the geometries and harmonic vibrational frequencies (scaled by 0.89) calculated at the CASSCF/6-3lG(d) level and the energies calculated at the CASPT2/6-31G(d.p) level for 1 and TS2. In kcaU mol. In cal mol-' K-I. 'j
by the formal reaction eq 8, was calculated at the same level to
-
+
c - C ~ H ~ O2 CH,CH, CH,C(O)CH,
+
T = 298 K 1 TS1 2 TS2 3
39.503 39.503 39.503 39.503 39.503
26.820 26.754 26.670 26.795 26.957
1 TS1
45.515 45.515 45.515 45.515 45.515
30.427 30.361 30.277 30.402 30.564
+ CH,CH2CH,CH,
46.420 46.420 46.420 46.420 46.420
30.971 30.904 30.820 30.945 31.108
8.782 9.263 10.002 9.543 13.114
1.377
0 0 0 0
1.377 1.377 1.377 1.377 1.377
75.105 76.896 77.552 77.218 80.95 1
1.377 1.377 1.377 1.377 1.377
122.823 123.601 125.716 123.526 129.006
1.377 1.377 1.377 1.377 1.377
132.795 133.273 135.708 133.174 138.965
T = 1000 K
2
TS2 3
(8)
be 48.8 kcaVm01.~~ Therefore, the difference of 18.3 kcaVmol between the calculated homodesmotic strain energies of C-C3&0 and C-C& is consistent with the difference of 16.6 kcaVmol between the potential energy barriers calculated for the cyclizations 1 2 and 7 6. Activation Parameters. The activation parameters and rate constants calculated for the unimolecular decomposition of 1 at various temperatures are given in Table 3. These parameters were calculated assuming that the thermal decomposition of 1 takes place via mechanism A and that TS2 is the transition structure of the the rate-determining step for the global process. The activation energies of 55.37 and 55.44 kcaVmol calculated at 1000 and 1200 K, respectively, are about 7.7 kcal/mol higher than the experimental value of 47.7 f 1.4 kcallmol covering the 1010-1430 K range of temperatures, reported by Lin and Lin.' If one takes as the experimental activation energy the last value of 43.9 i 0.9 kcaVmo1 at 1000-1580 K reported by Lin and L i r ~ ,the ~ difference between the calculated and experimental activation energies increases up to 11.5 kcallmol. On the basis of the recently proved accuracy of the CASPT2 method in predicting activation energies for various cyclization reaction^,^'-^^ such a large discrepancy is quite surprising. Moreover, the preexponential A factors of lOI3 91 and l O I 3 92 s-l calculated at 1000 and 1200 K, respectively, are substantially larger than the experimental values of and 10" 4*02 s-l covering the temperature ranges 1010-1430 and 10001580 K, respectively, reported by Lin and However, the rate consistent of 64 s-' calculated at 1000 K seems reasonable as compared with the experimental value of 10 f 5 s-l reported by Benson and co-workers.8 As noted in section I, the relatively low A factor of 10' I 4*0 s-l determined by Lin and Lin, which leads to a ca. activation entropy ranging from -10.8 to -11.7 cal mol-' K-' at 10001580 K, was attributed to the assumption that the reaction takes +
TABLE 4: Contribution@to the Absolute Entropies (cal mol-' K-l) Calculatedbfor CASSCF/6-31G(d) Optimized Structures at Various Temperatures structure S, S, Svlb -R In u R In m S
1 TSl 2 TS2
3
46.880 46.349 48.547 46.232
51.550 T = 1200 K 55.403 54.571 57.090 54.431 60.059
1.377
0 0 0 0 1.377
0 0 0 0
" See eq 2. Using the harmonic vibrational frequencies (scaled by 0.89) calculated at the CASSCF/6-31G(d) level.
place via a rather tight transition state initially involving the formation of an intermediate possessing two rigid rings (2).This of course agrees with current intuition, which in assessing the entropies of two isomeric molecules such as 1 and 2 attributes less entropy to the isomer possessing a bicyclic structure. To ascertain the validity of this hypothesis, the absolute entropies of 1, TS1, 2, TS2, and 3 calculated at various temperatures from the scaled CASSCF/6-3 1G(d) harmonic frequencies are given in Table 4. The different contributions to the absolute entropies (see eq 2 ) are also included in Table 4. The salient result here is that in going from 1 to 2 the absolute entropy increases by about 2.9 cal mol-' K-I. It is interesting to analyze this unexpected result in terms of the changes undergone by the S v l b and R In 0 contributions. Firstly, we note that in going from 1 to 2, Svtb increases by about 1.7 cal mol-' K-' in the 1000-1200 K range of temperatures. As mentioned above, 2 shows two remarkably small torsional frequencies ( V I = 138 and v2 = 250 cm-I). These frequencies are significantly smaller than the values of = 179 and v2 = 358 cm-' calculated at the same level of theory for the two lowest vibrational frequencies of 1. At this point it is recalled that the largest contributions to Sv,b are from the lower vibrational frequencies. At 1000 K, for instance, the contributions of V I and v: to the &b of 1 are calculated to be 4.692 and 3.330 cal mol-' K-I, respectively, whereas in the case of 2 the contributions are 5.207 ( V I )and 4.030 (v2) cal mol-' K-I. Therefore, it becomes clear that the difference between the S \ l b of 1 and 2, and hence the difference between the absolute entropies themselves, is due
Thermal Decomposition of the Phenoxy1 Radical mainly to the significantly distinct values of the lower torsional frequencies of these structures. Secondly, we note that in going from 1 to 2 the rotational symmetry number u changes from 2 to 1 due to the lowering of the molecular symmetry point group from C2"to Cs.Consequently, its contribution to the absolute entropy changes from 1.377 to 0 cal mol-' K-I. At variance with current intuition, it turns out that the absolute entropy of 2 is larger than that of 1 due to both the smaller values of the lower torsional frequencies in structure 2 and its lower molecular symmetry. A major consequence of this peculiar feature is that the relatively low values of the preexponential A factor determined by Lin and Lin are not supported by theory. The noted disparities between the calculated and experimental Arrhenius parameters, combined with the reasonable correspondence found between the calculated rate constant with the experimental value at 1000 K reported by Benson and coworkers, suggest that the Arrhenius parameters determined by Lin and Lin might be in error. In this regard it should be mentioned that Lin and Lin pointed out that there is a notable uncertainty in the measured decomposition rates of 1 due to the effects of secondary reactions which can competitively alter the concentration of 1, so they recommend further study of this reaction system using a heated shock tube to alleviate the low vapor pressure problem associated with the system? In the light of the results of our theoretical study, there is clearly a need for a critical reevaluation of the 1 decomposition rate measurements.
IV. Conclusions Our computational exploration of the C&O' potential energy hypersurface in the region concerning the thermal unimolecular decomposition of the phenoxyl radical reveals several important points: (1) The minimum energy pathway on the potential energy hypersurface for the thermal decomposition of the phenoxyl radical involves initial electrocyclic cyclization to a bicyclic radical intermediate (6-oxobicyclo[3.1.O]hex-3-en-2-y1 radical), lying about 45 kcaYmol above the phenoxyl radical, followed by a ring opening of its cyclopropanone moiety leading to the (2,4-cyclopentadienyl)carbonylradical, which lies about 30 kcaY mol above the phenoxyl radical. This ring opening is the rate determining step of the global decomposition process. Finally, the (2,4-cyclopentadienyl)carbonylradical undergoes CO elimination yielding cyclopentadienyl radical. At the highest level of theory employed in this study, namely CASPT2/6-31G(d,p)/ /CASSCF/6-3 1G(d) level plus ZPVE correction, the global decomposition reaction is predicted to be endoergonic by 21.9 kcal/mol with an energy barrier of 53.8 kcaYmol, an activation energy of 55.4 kcal/mol, and an activation entropy of 0.7 cal mol-] K-' at 1000 K. (2) The altemative decomposition pathway involves initial ring opening of the phenoxyl radical by homolytic scission of a CC bond, leading to a hexatrienyl radical intermediate ((32)6-0xo-l,3,5-hexatrien-l-y1 radical) which lies about 69 kcaY mol above the phenoxyl radical, followed by an intramolecular addition of the radical center to the substituted terminal carbon atom of the ketene group, yielding the (2,4-~yclopentadienyl)carbonyl radical found on the minimum energy pathway. This intramolecular radical addition is the rate-determining step of the this altemative pathway. At the CASPT2/6-31G(d,p)// CASSCF/3-21G level plus ZPVE correction, the overall energy barrier of this pathway is predicted to be 74.0 kcumol. This high potential energy barrier, in comparison with that of the minimum energy pathway, is attributed to the much higher
J. Phys. Chem., Vol. 99, No. 26, 1995 10555 energy of the (3z)-6-oxo-1,3,5-hexatrien-l-yl radical intermediate, as compared with that of the 6-oxobicyclo[3.1.O]hex-3-en2-yl radical. A major reason for the predicted large energy difference (25.3 kcaYmol) between these intermediates is due to the lack of any delocalization of the unpaired electron in the former radical. (3) In contrast to current intuition, which in assessing the absolute entropies of the isomeric radicals phenoxyl and 6-oxobicyclo[3.1.O]hex-3-en-2-y1 attributes a smaller entropy to the bicyclic isomer, the present calculations predict that in going from the former to the latter radical the absolute entropy increases by about 2.9 cal mol-' K-' at 1000-1200 K. This unexpected result is due to the lowering of the molecular symmetry and the smaller values of the lower torsional frequencies in the structure calculated for the 6-oxobicyclo[3.1.0]hex-3-en-2-yl radical. A major consequence of this peculiar feature is that the relatively low values of the preexponential A factor determined by Lin and Lin are not supported by theory. (4) At the highest level of theory employed in this study, the Arrhenius parameters for the thermal unimolecular decomposition of the phenoxyl radical are predicted to be Ea = 55.4 kcal/ mol and A = 10'3.9s-I at 1OOO- 1200 K. These are significantly higher than the values Ea = 47.7 f 1.4 and 43.9 f 0.9 kcal/ mol, A = 10'2.0*o.2 and 1011.4*0.2 s-I, covering the temperature ranges 1010-1430 and 1OOO-1580 K, respectively, determined by Lin and Lin. However, these authors pointed out that there is a notable uncertainty in the measured decomposition rates of the phenoxyl radical due to the effects of secondary reactions which can competitively alter the concentration of this radical. In light of the results of our theoretical study, there is clearly a need for a critical reevaluation of the phenoxyl radical decomposition rate measurements.
Acknowledgment. We are grateful to the Spanish DGICYT for financial support of this research (Grant PB92-0796-C0201). The authors thank the CESCA for a generous allotment of computer time on the IBM 3090/6005. We are indebted to Dr. Michael W. Schmidt for providing us a copy of his greatly extended version of the GAMESS system of programs. Supplementary Material Available: Cartesian coordinates of the CASSCF/3-21G optimized structures 1-5 and TS1TS5 and the CASSCF/6-31G(d) optimized structures 1, TS1, 2, TS2,3, TS5, and 5 (8 pages). Ordering information is given on any current masthead page. References and Notes (1) Glassman, I. Combustion, 2nd ed.; Academic Press: New York, 1986. (2) Brezinsky, K. Prog. Energ. Combust. Sci. 1986, 12, 1. (3) Bittner, J. D.; Howard, J. B. Symp. (In?.) Combust., [Proc.], 18, 1980 1981, 1105. (4) Venkat, C.; Brezinsky, K.; Glassman, I. Symp. (1nt.j Combust., [Proc.],19, 1982 1983, 143. (5) Bittner, J. D.; Howard, J. B.; Palmer, H. B. "NATO Conference Series, 6: Materials Science"; Plenum Press: New York, 1983; Vol. 7, p 95. (6) McMillen, D. F.: Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493. (7) Lin, C.-Y.; Lin, M. C. Int. J. Chem. Kinet. 1985, 17, 1025. (8) Colussi, A. J.; Zabel, F.; Benson, S. W. Inr. J . Chem. Kinet. 1977, 9, 161. (9) Lin, C.-Y.; Lin, M. C. J. Phys. Chem. 1986, 90, 425. (10) Olivella, S.; SolB, A. J . Am. Chem. SOC.1991, 113, 8628. (1 1) Hinchliffe, R. E.; Steinbank, R. E., Ali, M. A. Theor. Chim. Acta 1966, 5, 95. (12) Pople, J. A.; Beveridge, D. L.; Dobosh, P. A. J . Am. Chem. SOC. 1968, 90, 4201. (13) Chang, H. M.; Jaffe, H. H. Chem. Phys. Lett. 1973, 23, 14.
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