J. Phys. Chem. 1983, 87, 1081-1085
1081
Hydrogen Abstractions from Methyl Groups by Atomic Oxygen. Kinetic Isotope Effects Calculated from MNDO/UHF Results and an Assessment of Their Applicability to Monooxygenase-Dependent Hydroxylations Andrew 1.Pudrlanowskl+ and Gllda H. Loew” Life Sciences Dlvlslon, SRI International, Menlo Park, Californie 94025 (Received: May 11. 1982; In Flnal Form: September 14, 1982)
The semiempirical MNDO SCF-MO method has been applied to the calculation of kinetic isotope effects for methyl-hydrogen abstraction reactions involving O(,P) and CH,, propene, toluene, CHCl, and acetone. Transition states for these abstractions were characterized, and appropriate deuterium and tritium substitutions were made so as to permit comparisons of inter- and intramolecular isotope effects. A tunneling correction was used, and, while internal rotor corrections are discussed for propene, toluene, and acetone, they could not be fully applied due to the tendency of MNDO to underestimate internal rotation barriers. The applicability of isotope effects derived from this triplet oxene model to monooxygenase hydroxylations is discussed.
Introduction The abstraction of a methyl or methylene hydrogen by atomic oxygen in its ground state, R3C-H + O(3P) R3C. + .OH, is an interesting atom metathesis reaction from a theoretical standpoint in that it is expected to proceed through a “tight” transition state (TS) and have an appreciable activation energy.’ It is also deceptively simple to study, since a three-center (C-H-0) TS should be easy to locate on an energy surface. An accurate ab inito description, however, is extremely costly because of the importance of electron correlation in calculating a triplet surface. The magnitude of the problem is amply demonstrated by the recent CHI + O(3P) calculations of Walch and Dunning., One obviously wishes to study molecules larger than methane, but, apart from that, the size of the problem increases d r a m a t i d y when kinetic isotope effects are considered because force constant (Hessian) matrices for the TS and a reactant are required. Not surprisingly, then, recent calculations of kinetic isotope effects directly from a molecular surface have made use of semiempirical molecular orbital t h e ~ r y . A ~ subsequent study applied the MNDO formalism4to the calculation of isotope effects for hydrogen metathesis, with methyl and trifluoromethyl radicals5 as the abstracting species. The resulta achieved by Brown et al. in that study encouraged us to apply the same techniques to O(3P) hydrogen abstractions. In the present study we report calculated isotope effects for the following five reactions:
-
-
CH4 + O(3P)
CH,
+ OH
(1)
+ O(3P) H2C-CH-CH2 + OH PhCH3 + O(3P) PhCH, + OH CC13 + OH CHC1, + O(,P)
H&=CH-CH,
H3C-C-CH3
II 0
f O(3Pl
-
H~C-C-CHZ
II0
f OH
(2)
(3) (4) (5)
Reactions 1 , 4 , and 5 are observable in the gas phase at ordinary temperatures, reaction 5 being apparently the only gas-phase O(,P) hydrogen abstraction for which deuterium kinetic isotope effects have actually been measured! Reactions 2 and 3, however, are not observable Present address: The Squibb Institute for Medical Research, New Brunswick, N J 08903. f
0022-3654/83/2007-1081$01.50/0
in the gas phase at room temperature because the addition of O(3P)to the a system is much faster than abstraction. These reactions have been included because of interest in O(3P),or triplet oxene, as a simple model for the active oxygen species of cytochrome P450 enzymatic oxidat i o n ~ . ~Allylic -~ and benzylic hydroxylations, for which reactions 2 and 3 serve as prototypes, are characteristic P450-mediated reactions, and kinetic isotope effects have been measured for a number of such hydroxylations.1° Thus, the present study should be of direct interest to physical chemists who are concerned with gas-phase reactions, but it may also serve as a starting point for assessing the extent to which enzymatic isotope effects may be connected with model oxidation mechanisms. It must be kept in mind, however, that enzymatic kinetic schemes are seldom straightforward, and measured isotope effects may be complicated functions of the rates of several individual steps.l’ In fact, enough measurements are available for P450-mediated benzylic hydroxylations to show that their deuterium isotope effects are not consistent, the kH/KD values ranging from unity to approximately 11, with values of around 2 more common between the extremes.1°J2 Thus, if the triplet oxene model has validity beyond its already demonstrated qualitative usefulness in mechanistic studiesF9 the kinetic isotope effect intrinsic to a given hydroxylation step may be of interest. Deuterium and tritium kinetic isotope effects are reported here for reactions 1-4, while only the deuterium effect was calculated for reaction 5. All calculations employed the so-called Wigner correction for tunneling,13J4 which was found to be important for these hydrogen ab(1) S. W. Benson, “Thermochemical Kinetics”, 2nd ed., Wiley-Interscience, New York, 1976. (2) S. P. Walch and T. H. Dunning, Jr., J . Chem. Phys., 72, 3221 (1980). (3) M. J. S. Dewar and G. P. Ford, J.Am. Chem. SOC.,99,8343 (1977). (4) M. J. S. Dewar and W. Thiel, J . Am. Chem. SOC.,99,4899 (1977). (5) S. B. Brown, M. J. S. Dewar, G. P. Ford, D. J. Nelson, and H. S. Rzepa, J . Am. Chem. SOC.,100, 7832 (1978). (6) J. H. Lee and R. B. Timmons, Znt. J. Chem. Kinet., 9,133 (1977). (7) A. T. Pudzianowski and G. H. Loew, J. Am. Chem. SOC.,102,5443 (1980). (8) A. T. Pudzianowski and G. H. Loew, J . Mol. Catal., 17, 1 (1982). (9) A. T. Pudzianowski, G . H. Loew, B. A. Mico, R. V. Branchflower, and L. R. Pohl, J . Am. Chem. SOC.,in press. (10) J. Daly in “Handbook of Experimental Pharmacology XXVIII/2”, B. B. Brodie and J. R. Gillette, eds.; Springer-Verlag,West Berlin, 1971, p 285. (11) D. B. Northrop, Biochemistry, 14, 2644 (1975). (12) L. M. Hjelmeland, L. Aronow, and J. R. Trudell, Biochem. Biophys. Res. Commun., 7 6 , 541 (1977). (13) E. Wigner, 2.Phys. Chem., Abt. E , 19, 203 (1932). (14) L. Melander and W. H. Saunders,Jr., “Reaction Rates of Isotopic Molecules”, Wiley-Interscience, New York, 1980.
0 1983 American Chemlcal Society
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The Journal of Physical Chemistry, Vol. 87,
No. 6, 1983
stractions. Intramolecular isotope effects were also calculated for reactions 1-3 and were found to be somewhat smaller than the intermolecular effects. Corrections for internal rotations, which could be significant for reactions 2 and 3 and particularly reaction 5, are possible in principle1J5but could not be applied due to the tendency of MNDO to underestimate barriers to internal rotation. Thus, the calculated kinetic isotope effect as a function of temperature is definitely overestimated for reaction 5 and may be for reactions 2 and 3 as well, although probably to a lesser extent.
Theoretical Methods We are interested in bimolecular reactions whose rate is governed by the combination of reactant species A and B to form a transition state (AB)*,as expressed in pseudoequilibrium form: A +B (AB)* (6) If one of the reactants, e.g., A, is isotopically substituted, absolute reaction rate theory and statistical mechanics give the following expression for the rate constant ratio: l4
Pudzianowski and Loew H1
"1
T
El
gr
CJV
d '
+
Figure 1. Optimized structures for CH, and CH, 0 TS (reaction 1). In this and subsequent figures, the nuclear displacements of the transition mode (reaction coordinate) are given as arrows originating at the nuclei involved. Ail distances are in angstroms and angles are in degrees.
-
L
where the isotopic substitution is denoted by primes and M, Q,, and Q, denote respectively molecular weights and rotational and vibrational partition functions in the rigid rotor-harmonic oscillator approximation. Note, however, that Q, as used above differs from the Q, employed in thermodynamics calculations by a factor of exp(-E,/RT), where E,, is the zero-point energy.14 Equation 7 neglects tunneling effects, but, since we are interested in hydrogen metathesis at a relatively low temperature, we cannot justify this approximation. The socalled Wiper correction13J4is a multiplicative factor which may be written as follows:
t = 1+ (1/24)(hc~*/kT)~
(8)
where U * is the modulus of the imaginary transition mode frequency in cm-l, h, k,and c are respectively Planck's and Boltzmann's constants and the speed of light, and T i s the absolute temperature. Thus, the isotope effect of eq 7 may be corrected for tunneling in the following way: (k/k?t = (t/t3(k/k? (9) The standard statistical mechanical treatment1@applies to molecules with no internal rotations. When such rotations are present, corrections should be made to the partition functions for vibration and rotation, the form of the corrections depending on whether the internal rotation is free or hindered.l In the hindered case, the potential barrier for the rotation must be known, and both the free and hindered cases require moments of inertia for the molecule as a whole and for the internal rotor itself, which may be calculated according to the method of Herschbach et a l l 5 Thus, all the necessary quantities for internal rotor corrections can, in principle, be obtained from the molecular surface under investigation. In practice, however, such corrections are extremely sensitive to the performance of the molecular calculation with respect to internal rotation barriers. All molecular calculations were carried out within the MNDO f ~ r m a l i s mopen , ~ shells being treated by the un(15)D. R. Herschbach, H. S. Johnston, K. S. Pitzer, and R. E. Powell, J. Chem. Phys., 26, 736 (1956). (16)N. Davidson, "Statistical Mechanics", McGraw-Hill, New York, 1962.
C,-H,
1.228
n,-c
1.347
C,C,C,
126.4
i C,C,H,
124.0
L L
H,C,H,
113.9
H,C,C,
108.6
i
H,C,C,
115.5
i
Flgure 2. Optimized structures for propene and propene + 0 aiiyi abstraction TS (reaction 2).
restricted (UHF-based) method." These included total optimizations of molecular geometry for reactants and transition states, with calculations of force constant matrices and normal vibrational modes for all geometry-optimized species as discussed elsewhere.8J8 We have noted previously8 that TS geometries obtained from MNDO/UHF calculations on CH4 and O(3P) and CzH4+ O(3P) compare very well with ab initio results for the same systems2J9 and also that calculated absolute entropies of activation are close to the corresponding experimental values.*J9 Entropies are reproduced well partly because MNDO can often furnish optimized geometries of very good quality: molecular structure is directly involved in the rotational partition function, which is usually orders of magnitude larger than the thermodynamic vibrational function. Thus, when errors on the order of 1 cal/(mol K) or larger appear in So for reactant internal rotors, we should begin to suspect these as cases requiring internal rotor corrections since the optimized geometry will probably not be a significant source of error. The Fortran programs MNDO and NDTS" were used respectively to locate minima and saddle points on MNDO enthalpy surfaces, while the NDFOR~O program was used to calculate force constant matrices, normal vibration modes, and principal moments of inertia for all reactants and transition states. Geometry optimization was always continued until a root-mean-square enthalpy gradient of 5 X lo4 hartree/A or less was obtained. Symmetry num(17) J. A. Pople and D. L. Beveridge, "Approximate Molecular Orbital Theory", McGraw-Hill, New York, 1970, p 52. (18)M. C. Flanigan, A. Komomicki, and J. W. McIver, Jr. in "Modem Theoretical Chemistry", Vol. 8, G. A. S e d , Ed., Plenum Press, New York, 1977,p 1. (19)M. Dupuis, J. J. Wendoloski, T. Takada, and W. A. Lester, Jr., J. Chem. Phys., 76,481 (1982). (20) W. Thiel, G. P. Ford, M. McKee. D. Nelson. S. Olivella. H. S. Rzepa, end M. J. S. Dewar. These versions were originally obtain& from the NRCC at Lawrence Berkeley Laboratory and modified in our labor atory .
The Journal of Physical Chemistiy, Vol. 87, No. 6, 1983
Hydrogen Abstractions from Methyl Groups
1083
TABLE I: Calculated Isotope Effects at 298 K with Maximum Isotopic Substitution of Methvl Hvdroeens AH*,
AS*,
reaction
kcal/mol
Cal/(mOl K)
kH/kD
kH/kT
1
27.4 (8.4)a 24.7 (5.5)b 21.8 (4.8)c 29.1 (2.6)d
-23.7 (-20)a - 29.2 -29.9 -27.7
8.82 5.54 7.36 8.94
22.6 16.0 16.3 22.8
2 3 4
W*D,
W*T,
cm-I
1842 (2525)e 1742 (2364) 1694 (2300) 2006 (2752)
Experimental values given in Herron and Huie.*l Estimated value.' Estimated value.g e w * values in parentheses are for unsubstituted TS.
cm-
( k H /k D t
1547 1473 1433 1694
14.8 9.02 11.9 15.2
(kH /kT
t
48.9 33.1 33.4 50.7
Estimated value, based on reaction 2 A H values.
4
i V
L C3ClC, L O,C,C, L n,c,c, L n,c,c,
H/
121.5
114.3 108.1.
Figure 5. Optimized structures for acetone and acetone (reaction 5).
c,
L C,C,C, L c,c,c, L C,C3C, L c,c,c, L n,c,c, L nIc,c,
117.8
121.1 UO.9
TABLE 11: Comparisons of Inter- and Intramolecular Isotope Effects at 298 K for R-CH,D and R-CH,T
120.3
119.8 108.8
kH/
EaC-
iiw.
Flgure 3. Optimized structures for toluene and toluene abstraction TS (reaction 3).
+ 0 TS
+ 0 benzyl
tiOn kD 1 inter 33.8
kH/ kT
W*T,O
Cm-'
Cm-'
25.8 5.41 8.13 7.99 8.47
1858 (2519) 1760 (2359) 1712 (2290)
( k ~ / (kH/
kD)t
1568 55.8 (2517) 42.4 2 inter 1495 8.67 intra (2356) 13.0 3 inter 1455 12.8 intra (2286) 13.4 w values in parentheses are for R-HDC-H-0 or R-HTC-H-0 TS. intra
83.8 63.4 13.3 20.3 18.45 21.5
U*D?
kT)t
178 133.8 27.0 40.9 37.0 42.7 ~~
*
c3v
L
ClCH
CIV
108.6
L ClCH
Figure 4. Optimized structures for Ci,CH and C1,C-H-0 4).
106.8
TS (reaction
bers1J8 were consistently used in evaluating rigid rotor rotational partition functions.
Results The optimized reactant and transition-state geometries for reactions 1-5 are given in Figures 1-5, and the nuclear displacements for the transition mode (reaction coordinate) are given with each TS. These modes indicate that all five reactions are simple, collinear hydrogen abstractions, and each TS falls within Benson's suggested criteria1for a tight transition state: the C-H bonds are stretched by slightly more than 0.1 A and the 0-H distances are about 0.4 A longer than the MNDO/UHF value for the OH radical (0.938 A). Calculated isotope effects are given in Table I for reactions 1-4. In each case the maximum number of methyl hydrogens possible has been isotopically substituted for the calculation. Calculated activation enthalpies and entropies are also reported, but comparison with experimental data27is possible only for reaction 1. The AH* (21)J. T. Herron and R. E. Huie, J. Phys. Chem. Ref. Data, 2, 467 (1973). (22)J. R. McNesby, J . Phys. Chem., 64, 1671 (1960).
values for reactions 2-4 are compared with our own estim a t e ~ It . ~is~certain ~ that MNDO seriously overestimates AH* for a number of bimolecular reaction^,^^^^^ probably because the present parametrization exaggerates the repulsions in three-center interactions characteristic of the transition states. The net effect on the metathesis reactions studied so far seems to be that the AH* barrier is made too high, without significantly distorting the position of the TS along the reaction coordinate. Thus, calculated activation e n t r ~ p i e s have ~ , ~ generally been within 3 cal/(mol K)of observed values. Table I1 compares inter- and intramolecular isotope effects calculated for reactions 1-3 with only one methyl hydrogen isotopically substituted. The intramolecular isotope effect compares R-H2C-D, for example, with RHDC-H; hence, the resulting cancellations in eq 7 leave only the ratio of partition functions for transition states to be evaluated. The intermolecular effect calculated here compares R-H2C-D and R-H2C-T with R-CH3. (Note that comparison of R-HDC-H, e.g., with R-CH, would constitute evaluation of a secondary isotope effect.) The isotope effect for reaction 5 refers to acetone-d,, and the temperatures given in Table I11 are those at which Lee
-
(23)T.E.Sharp and H. S.Johnston, J. Chem. Phys., 37,1541(1962). (24)H. S.Johnston and E. Tschuikow-Roux, J.Chem. Phys., 36,463 (1962). (25)L.R. Pohl, J. W. George, J. L. Martin, and G.Krishna, Biochem. Pharmacol., 28, 561 (1979). (26)A. I. Pilyashenko-Novohatniy, A. N. Grigoryan, A. P. Kovalyev, V. S. Byelova, and R. 1. Grozdev, Dokl. Akad. Nauk SSSR,245, 1501 (1979). . (27)J. E. Gander and G. J. Mannering, Pharmacol. Ther., 10, 191 (1980).
1084
Pudzianowski and Loew
The Journal of Physical Chemistry, Vol. 87, No. 6, 1983
TABLE 111: Kinetic Isotope Effects for Reaction 5a as a Function of Temperature k ~ l k ~ (MNDO)
T, K 614.0 564.0 555.0 517.0 298.15 a w
* =~2587
3.142 3.448 3.511 3.828 9.397
cm-',
W*D =
~HI~D 1.394 1.431 1.438 1.469 1.680
1 8 8 8 cm-'.
(kH/kD)t (MNDO)
kH/k% (exptl)
4.380 4.934 5.049 5.623 15.79
2.85' 3.21 3.51 3.72'
AH*,
A&'*,
kcalimol
cal/( mol K)
27.6 ( 4.4)b
-28.1 (-24.4)b
Values f r o m data o f Lee and T i m m o w 6
TABLE IV: MNDO Results for Internal Rotations at 298 K
Average of t w o values6
TABLE V : Effect of Tunneling Corrections on the Deuterium Isotope Effects for Hydrogen Abstraction by CD, and CF,
MNDO
so(cor), SovoV,- (MNDO), cal/ (exptl),Q (MNDO), (exptl),Q Cali (mol cal/ kcal/mol kcal/mol ( m o l K ) K) (mol K) 9-
species propene acetone toluene
0.2 0.1
2.0 0.8 0
65.5 72.3 80.7
63.4 69.6 77.8
63.8 70.5 76.6
F r o m Benson's tabulations.'
CD, 563 604 611 666 760 G
and Timmons6 carried out their measurements. The results for reaction 5 are given in Table I11 and compared with the corresponding experimental values. Even with the tunneling correction, the MNDO kH/kDvalues for this reaction are N 1.5 times the experimental value at a given temperature. (It should be noted that the limiting value of the MNDO isotope effect, as T approaches infinity, is given by the ratio of transition mode frequencies u * H / u * D = 1.37. The calculated values for all five reactions considered fall in the range 1.34-1.37, while u * ~ / uvalues *~ fall in the range 1.56-1.63.) A likely reason for this discrepancy is the tendency of MNDO to underestimate barriers to internal rotation, as manifested explicitly in the very low barriers found for acetone and propene (Table IV). Thus, the methyl group is essentially a free rotor in the MNDO description, and this turns up implicitly in the lowest frequency normal modes obtained from force constant calculations. The internal rotations are mixed with rigid rotor rotational modes and translational modes; hence, the vibrational partition function Q, is unduly biased by the presence of spurious low-frequencycalculated "vibrational" modes, and the isotope effect given by eq 7 is directly affected. Table IV also shows the effect on calculated entropies of including explicit corrections for internal rotation. Propene and acetone were treated as restricted rotor cases: equivalent oscillator frequencies were calculatedl from the experimental V,, values and substituted for the lowest calculated vibrational frequency (the two lowest in the case of acetone), after which the entropies were recalculated and entered as S"(cor) in Table IV. Toluene was treated as a free rotor: the MNDO entropy was recalculated after deletion of the lowest frequency vibrational mode, and the free rotor entropy contribution' was added to this value to give So(cor). The entropies given as S"(MND0) are the uncorrected calculated values: these are improved significantly when corrections are made. As an example of the possible effect of such corrections on resulta calculated from eq 7 for a restricted rotor case, we note that the corrected Q, for acetone at 298 K is 0.336 times the uncorrected value (Table S5). (See paragraph at end of text regarding supplementary material.) Full incorporation of internal rotor corrections requires that these be extended to the transition states. In hydrogen abstractions yielding planar radicals, such as allylic and benzylic cases, the rotation of the methyl group involved "stiffens" in the transition state.l In principle, then,
2.97 2.76 2.73 2.52 2.26 1.35
CF, 325 422 588 710 1015 1710 1880 m
5.63 3.93 2.73 2.32 1.84 1.53 1.49 1.35
+ C,H
/C2D6 1.434b6 4.26 1.405 3.88 1.388 3.79 1.364 3.44 1.312 2.96 1 1.35
+ CH,/CD, 1.587' 1.494 1.360 1.287 1.172 1.070 1.059 1
8.93 5.87 3.71 2.99 2.16 1.64 1.58 1.35
3.86d 3.56 3.65 3.12 2.79
18.5e 7.59 3.56 2.69 2.09 1.57 1.54
a Values calculated b y Brown et al.' From5 W * H = 2728 c m - ' and W * D = 2 0 2 0 cm-'. Froms W * H = 2411 cm-' and W * D = 1 7 9 2 cm-'. Data of McNesby.Z2 e Cited by Brown et al.' as referring to r e a c t i o n ~ of ~~'~ CHD, and CH,D, with CF,.
the restricted rotor formalism applies, but MNDO cannot be relied upon for even approximate estimates of the relevant barriers.
Discussion In the case of hydrogen metathesis reactions, there are few experimental data against which MNDO isotope effects may be compared. The single O(3P)study available6 involves acetone, whose two internal methyl rotors create difficulties for MNDO, probably accounting for much of the error in the final calculated isotope effects. With propene and toluene we observed less mixing of the single internal rotation with translational and rotational modes in the normal mode analysis; hence, we expect that the calculated isotope effects for these compounds are overestimated to a lesser extent than are the acetone effects. The MNDO results of Brown et aL5are concerned with hydrogen metathesis, but these authors did not include a tunneling correction. Table V reproduces their results, to which we have now applied the tunneling factors given by eq 8 and 9. For CD3 + CzH6/C2D6,which corresponds directly to the experimental reaction,22 the tunneling correction brings the MNDO results much closer to the experimental values: the corrected MNDO results overestimate the isotope effect by a range of 4-10%. The corrected results for CF3 + CH4/CD, seem worse, particularly at the lower temperatures, until we realize that the measured isotope refer to CDBHand CH2D2,not to CD,. Our own results for O(3P)reactions with CH,/CD,/CT, and CH4/CH3D/CH3T(Table I and intermolecular effect, Table 11) imply that the primary isotope effect for CH, increases with decreasing isotopic substitution. This makes good sense, since CH, is very light, and the effect
The Journal of Physlcal Chemistry, Vol. 87, No. 6, 1983 1085
Hydrogen Abstractions from Methyl Groups
on Q, of a single deuterium or tritium is more pronounced in a less substituted methane. There is also an effect on Q,: vibrational frequencies involving C-D and C-T bonds are lower than those for C-H bonds, and the vibrational levels are more populated at a given temperature in the isotopic methanes. As the temperature increases, this difference is expected to become less important, which would seem to be the trend shown in Table V at temperatures higher than 588 K. Thus, if the MNDO force constant calculations of Brown et al.s had actually been carried out on CD3H and CH2D2to correspond to the experimental reactions, the low-temperature isotope effects in Table V would undoubtedly have been closer to the observed values. Taking these results into consideration, we expect that the calculated isotope effects for the CH, and CHC1, O(,P) reactions, reactions 1and 4, respectively, are acceptable, and we note that these predictions could be directly tested in gas-phase experiments. The allylic and benzylic abstractions, reactions 2 and 3, respectively, are probably characterized by deuterium isotope effects of -7-8 at 298 K, assuming that the values in Tables I and I1 are overestimated by somewhat less than 50%. As expected, the tunneling correction is quite signifcant for all five reactions studied here as well as those investigated by Brown et al.s Kinetic isotope effects have been observed for a number of enzymatic oxidations involving monooxygenases. Besides the range of deuterium effects for benzylic hydroxylations mentioned in the Introduction, the cytochrome P450-mediated oxidation of CHC13has a deuterium effect of -2 both in vivo and in vitr0.2~The enzyme methanemonooxygenase from Methylococcus capsulatus is reported to have a CH4/CD4isotope effect of 5 at room temperature.26 The deuterium effects calculated for the corresponding gas-phase triplet oxene reactions are both -15 (Table I). A direct connection between the calculated isotope effects and those observed for monooxygenase reactions can only exist under the following two assumptions: (a) The triplet oxene model gives, coincidentally or otherwise, a precise description of the enzymatic active oxygen species. (b) The enzymatic kinetic isotope effect is directly linked to a hydrogen abstraction, which is the rate-limiting step for the monooxygenase reaction sequence. Assumption a is an exaggeration of what we have so far o b ~ e r v e d , namely, ~-~ that triplet oxene serves as a good qualitative model with which to examine possible mechanisms for enzymatic oxidations. These observations suggest that the active oxygen species of P450-mediated oxidations behaves like an oxygen radical, perhaps resembling somewhat the oxygen in an OH radical. The active oxygen is presumably bound, however fleetingly, to a heme iron which is itself coordinated to a porphyrin ring. The presence of the porphyrin may introduce steric effects such as stacking of aromatic substrates with the 7~ system of the porphyrin ring, which the triplet oxene model alone cannot account for but which could have a pronounced effect on observed substrate reactivity or selectivity. Assumption b is generally untenable. In his analysis of steady-state enzyme kinetics and isotope effects,’l Northrop considers a mechanism involving only five individual steps, from which he derives a relation between the steady-state isotope effect associated with C-H bond cleavage and the isotope effect on the overall maximal velocity V. From this relation it is clear that VH/VDisotope effects on the order of 2 or 3 can easily arise when the C-H bond cleavage is not rate-limiting, particularly when another step is only 10 times faster, at which point
-
-
the effects of all “intrinsic” kH/kDvalues converge to VH/ VD values of 2-3. Therefore, our predicted intrinsic values for allylic and benzylic triplet oxene abstractions cannot be unambiguously related to enzymatic hydroxylations displaying small intermolecular deuterium effects. The same thing is true of the calculated deuterium effect for CHC13 O(,P) and the observed values for P450 oxidation of chloroform.26 Making some allowance for overestimation, we may safely assume that the predicted inter- and intramolecular deuterium effects for the benzylic abstraction reaction 3 are both 10 (Table 11). This corresponds rather well with the intramolecular effect observed by Hjelmeland et a1.12 for a P450-mediated benzylic hydroxylation. These authors have argued that intramolecular competition provides a better measure of the intrinsic isotope effect by isolating the hydroxylation step in the enzymatic sequence. They have also suggested that the large effect observed in this manner may be indicative of a radical abstraction-recombination mechanism. Our results are consistent with these observations. If we accept the qualitative validity of the triplet oxene model for cytochrome P45O-mediated oxidations, the present study indicates that the intrinsic kinetic isotope effects for enzymatic hydroxylations are expected to be large. This conclusion has some applicability in that small intermolecular enzymatic isotope effects would indicate that the hydroxylation step is not rate limiting for the given substrate. Northrop’s analysis” leads to a lower limit of VH/VD 8 for assignment of rate-limiting status to C-H bond cleavage. Such high values have been observed in some benzylic hydroxylations12but not in others.1° Furthermore, the presence or absence of an isotope effect in P450-mediated hydroxylations can depend on apparently steric factors, such as the size of substrate side chains,12and on the nature of the agent used to biologically induce enzyme p r o d u ~ t i o n . ~All ~ of this implies that the C-H bond cleavage may be rate limiting in some cases but is definitely not in others. If it is possible to identify those cases in which it is not, perhaps attention can then be directed toward the other important factors that influence the overall rate. However, we now expect that further intramolecular isotope effect studies, such as those of Hjelmeland et a1.,l2 will show that the intrinsic effect for hydroxylations is large.
+
-
-
Acknowledgment. Computations were performed on the CDC 7600 computer at Lawrence Berkeley Laboratory and the Computer Resources VAX 11/780 at SRI International. We thank Dr. Dale Spangler for useful discussions, and assistance, and Dr. George Ford for his timely intervention in putting some initially incongruous results right. Informal discussions with Dr. David Golden served to stimulate our interest in gas-phase oxidation kinetics. Support from NIH Grant No. GM 27943-02 and NCI Contract No. N01-CP-15730 is gratefully acknowledged. Registry NO.CHI, 74-82-8; H&=CH--CH,, 115-07-1;PhCH3, 108-88-3; CHC13, 67-66-3; H3C-C(0)-CH3, 67-64-1; O(3P), ima-80-2.
Supplementary Material Available: Tables Sl-S5 giving the molecular weight, principal moments of inertia for the MNDO-optimized structure, modulus of the transition mode frequency, and rotational and vibrational (with zero-point energy factor) partition function for the reactants and transition states of reactions 1-5 (5 pages). Ordering information is given on any current masthead page.
