J. Phys. Chem. 1994,98, 7513-7522
7513
Thermal Stereomutations of Cyclopropane and of Isotopically Labeled Cyclopropanes Assessed through ab Initio Computational Methods and Kinetic Isotope Effect Calculations John E. Baldwin,*J Yukio Yamaguchi,* and Henry F. Schaefer III*** Department of Chemistry, Syracuse University, Syracuse, New York 13244, and the Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 Received: July 6, 1993; In Final Form: May 27, 1994"
New a b initio computational efforts to understand the thermal stereomutation reactions shown by isotopically labeled cyclopropanes have provided energies, geometries, and harmonic vibrational frequencies for cyclopropane and for five trimethylene diradical stationary points: one second-order stationary point, one intermediate, and three transition structures. The calculated vibrational frequencies for cyclopropane and the three trimethylene transition structures, and for the various cyclopropane-1,2-4 and -1,2,3-d3 and the 43 distinct trimethylene transition structures derived from them through carbon-carbon bond cleavages, led to calculated kinetic isotope effect values for the elementary reactions taking place by way of these transition structures. A kinetic model for net one-center and two-center thermal epimerizations utilizing the relative transition structure energies obtained from the ab initio computations and the calculated kH/kD effects on elementary reactions gave a predicted ratio kl/klz of 1.06/ 1 for cyclopropane. Deuterium-labeled cyclopropanes are predicted to behave similarly. The net one-center versus two-center thermal epimerization balance in these cyclopropanes results from the participation of multiple kinetically significant reaction paths.
Introduction Chambers and Kistiakowsky postulated in a 1934 paper that the trimethylene diradical might be an intermediate for the thermal conversion of cyclopropane to propene.' When the thermal interconversion of the cis and trans isomers of cyclopropane- 1,2-d~was uncovered in 1958, deuterium-labeled trimethylene diradicals were recognized as possible intermediates which could serve to rationalize the isomerization.2 Early thermochemical considerationssuggested that the trimethylene diradical would exist in a substantial energy well, permitting rotations about C-C bonds in the diradical to occur much faster than ring c l o s ~ r ebut , ~ more recent estimationsbased on improved values for the heat of formation of the ethyl radical place the intermediate in a very shallow depression on the energy surface, on the order of 1 kcal/mol deep.415 Hoffmann applied orbital symmetry considerations and extended Hiickel calculations to distinct conformers of the trimethylene system.6~~ The edge-to-edge (EE, or '0,O") form was H H
H H
v
\:
Hfi.H H
H
H EE
or optical isomerization by way of EE, was favored, while reaction by way of EF(ts),giving one-centeror geometricalisomerization, was slower but quite competitive: the C2-symmetric transition structure for the conrotatory process, close to EE in geometry and energy, was found to be only 0.6 kcal/mol lower than EF(ts). The disrotatory path for two-center epimerizationwas calculated to be less competitive. In 1972 these theoretical insights were thought to accord well with experimental evidence showing that rate constants for geometrical (one-center) and optical (twocenter) thermal epimerizations in 1,2-disubstitutedcyclopropanes are generally of comparable magnitudeas The relationships between reaction modes, net one-center and two-center stereomutations,and the corresponding rate constants kl, k2, and k12 according to the Salem model are shown diagrammatically in Figure 1. At the center, a cyclopropane with two specific hydrogens highlighted, is the reactant; it may give kl2 products in two ways, through clockwise and counterclockwise conrotatory paths, extendingdiagonally to two corners of the plot. The kl and k2 products are formed by way of EF(ts) structures through processes which start in conrotatory fashion but are disrotatory in the transition state region. According to the model of Figure 1, the kl/k12 balance should be dictated by competition between two reaction modes, and the EE trimethylene intermediate should either give klz product or revert to starting material. Two subsequent experimental studies, however, contradicted the generalization that kl, k2, and k12 for stereomutations of substituted cyclopropanes are of comparable kinetic significance: deuterium-labeled phenylcyclopropanes and cyclopropanes were reported to isomerize thermally either predominantly or exclusively through two-center epimerizations.9 For deuteriumlabeled phenylcyclopropanesat least 78-82% of the epimerization at the phenyl-substituted C(l) was thought to occur with synchronous epimerization at the deuterium-labeled C(2), according to experimental evidence and some needed enabling assumptions? for the kinetic situation was characterized by two observables, ki and k,, and three kinetic parameters, kl2, (k2 + kzs),and (kl k13). The ratio of rate constants for ki and k, for (+)-(S,S)-cyclopropane-d2at 422.5 OC in the gas phase was found to be kJk, = 1.07 f 0.04.9 To interpret this kinetic result in terms of the relative magnitudes of rate constants for one-
H
ET (tr)
found to be an intermediate; the lowest energy barrier between this intermediate and cyclopropane, only about 1 kcal/mol high, corresponded to a conrotatory motion of the terminal methylene groups.7 Other theoretical efforts extended these results and found that the C,-symmetric edge-to-face (EF, or '0,90") form of trimethylene was a transition structure for epimerizationof cyclopropane at only one carbon. Salem and co-workerss explored the 21dimensional hypersurface for cyclopropane stereomutations and found that the synchronous conrotatory path, giving two-center *SyracuseUniversity. *Universityof Georgia. Abstract published in Aduunce ACS Abmucrs. July IS, 1994.
0022-3654/94/2098-75 13$04.50/0
+
@ 1994 American Chemical Society
Baldwin et al.
7514 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994
(ki/k12) + (ki/k12)(kl’/kd + (k13/ki2))/(1 + (ki/kiz) + & I / k12)(kl’/kl) (kl3/k12)). The experimental ratio is a function of (kl/kl2), (kl’/kl), and (kl3/kl2)* Assumptions about (kl’/k1) and (k13/k12) were made and employed, and the authors concluded that the double-rotation mechanism predominates by a substantial factor; data were fit to a model characterized by 98% of double rotation and “contaminated” by only 2% of single methylene r o t a t i ~ n .The ~ double-rotation mechanism was held to predominate by a substantial factor. In phenylcyclopropaneand cyclopropane, it was claimed, the theoretically predicted double-rotation mechanism predominates.9 These landmark investigations framed all discourse on the cyclopropane stereomutation problem for the next decade.l0 Yet they posed two challenging questions that seemed deserving of further attention. First, one of experimental design: how could one approach the thermal stereomutations of deuterium-labeled versions of phenylcyclopropane and of cyclopropane so that experimentally based determinationsof all kj and kjl rate constants could be attained?’] How might one work past the =twoobservables, three or more unknowns” dilemma inherent in the experimental designs adopted?g Thesecondquestion relates topattemsof reactivity: why should deuterium-labeledphenylcyclopropanesand cyclopropanessuffer thermal stereomutations with k12 >> kl while every other 1,2disubstituted cyclopropane investigated shows a diametrically opposed kinetic behavior, with the sum of the rate constants for one-center epimerization events (kl + k2) being invariably comparable to or greater than k12?l2 Further experimental work on isotopically labeled phenylcyclopropanes has shown that they suffer thermal stereomutations through one-center as well as two-center epimerizations. The stereomutation rate constants for phenylcyclopropane-1,2,3-d3 at 309 ‘C are kl = 0.36, k2 = 0.87, k12 = 0.20, and kz3 = 0.0, all X s-l; the one-center epimerization events are of greatest kinetic import.” To secure these results through experiment alone, two chiral versions of phenylcyclopropane-2-d, all three optically inactive forms of phenylcyclopropane-1,2,3-d3,(2R,3R)phenylcyclopropane- 1,2,3-d3, and (lR,2S3R)-phenylcyclopropane-[2-13C]1,2,3-d3 were synthesized and studied kinetically: together they provided assumption-free derivations of the individual epimerization rate constants.14 With the deuterium-labeled phenylcyclopropanesthus shown to adhere to the normal pattern, with substantial contributions from both one-center and two-center thermal epimerizations in evidence, the discordant reactivity propensities of all other 1,2disubstituted cyclopropanesand the k12 >> kl inequality inferred for cyclopropanes- 1,2-d29 thus begged for an explanation. Additional experimental work with isotopically labeled cyclopropanes finally answered the experimental design issues in theory and in New synthetic routes and improved analytical methods involving vibrational circular dichroism and tunable diode laser infrared spectroscopy for following optical and geometrical isomerizations facilitated kinetic experiments with chiral cyclopropanes- [ l-13C] 1,2,3-d3,I6l8 optically active cyclopropanes having one deuterium at each carbon, thus providing two experimental observables, k, = (4k12 + 4kl) and ki = (4k12 + 8k1),for deriving the two kinetic unknowns (Scheme 3). The stereomutation rate constants kl and klz measured at 407 ‘C were essentially identical. Schemes 1-3 explicitly take into account symmetry considerations so that all the rate constants for geometrical and optical isomerizations require no further symmetry corrections; all rate constant terms relate to epimerizationsconsequent to the cleavage of a specific carbon4arbon bond. The experimental determination1618that kl klz for isomerizations among cyclopropane-[1-13C]1,2,3-d3 isomers at 407 ‘C prompted intense scrutiny of the assumptions regarding isotope
+
H
FHlz
H
H
Figure 1. Schematic representation of reaction paths for cyclopropane stercomutations,following Salem and co-workem8The variables 81 and 82 refer to rotations about terminal methylene groups. Changes in the angle are significant but not shown in this simplified C( 1)-C(3)-C(2) projection onto two dimensions of the surface. SCHEME 1
k = kl
+
kl’
+
k13
SCHEME 2
PD k12
ll
s, s D k = kl
+ kl’ + k13
center and two-center epimerizations, some assumptions were necessary, for once again the kinetic situation was one characterized by only two observable rate-constant-dependent quantities (Scheme 1). All eight nonvertical arrows in Scheme 1 are associated with the same rate constant, (kl + kl’ + kl3) = (k2 + k2’ + kz3); kl refers to one-center epimerization at C( 1) when C( 1)-C(2) breaks, and kl’ to one-center epimerization at C ( l ) when C( 1)-C(3) breaks. The representation of the kinetic situation shown in Scheme 1 is based on a convention: the cis isomer is shown twice, with each depiction of the cis form representing half of the total cis isomer present. The equivalent representation which eschews this convention, shown in Scheme 2, includes the cis form only once, but now has unequal rate constants to and from the cis isomer and each antipode of trans-cyclopropane-1,2-d2. The experimentally estimated rate constants and the rate constants of Schemes 1 and 2 are related by the equalities k, = (2k12 2k) and ki = 4k. The ratio ki/k, is then given by 2{-
+
-
Thermal Stereomutations of Cyclopropane
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7515 1.4974 1.5031 1.4985 1.51001(77)
SCHEME 3 D
P
I
114.02 114.38
114.44 115.85(11)
SY*
I
I
1.0758 1.0777 1.0722 1.07415(98)
C31G*-SCF DD-SCF Tzzp-SG EXpE"T
Figure 2. Predicted equilibrium geometry for closed shell singlet D3h-
symmetric cyclopropane. Experimental values are from ref 35. Values in parentheses denote three standard deviations and apply to the last digits of the constants. D
D
effects and kinetic paths used by Berson, Pedersen,and Carpenter? but no inadequacies in the 1975 analysis have been identified. If one takes the cy~lopropane-d2~ versus [13C]~yclopropane-d~~~~~ kinetic results as both precise and accurate and treats them according to the original assumptions and model? one is led ineluctably to the inference of an impossibly large secondary B deuterium isotope effect for the isomerizations of cyclopropane1,2-d~,estimated as 2.2 at 696 K, or 6 at room temperature. An isotope effect of this magnitude can hardly be correct, and thus 104.75 104.98 1.0916 one must question whether all the experimentally determined 104.93 1.0926 1.0888 rate constants for both the ~yclopropane-d2~ and the [13C]~yclopropane-d3~"~* isomerizations are as precise and accurate as reported. 1.5005 6-31Gb-TCSCF These issues and uncertainties have been addressed through ab initio and secondary deuterium and carbon-13 kinetic isotope effect calculations by Getty, Davidson, and Borden:19they found 115.43 115.54 1.0730 moderate and normal isotope effects on the several modes of 1.0760 cyclopropane stereomutation and concluded that a common 1.0706 mechanistic interpretation of the reported experimental results H H for the cyclopropane-d2and [ 13C]cyclopropane-d3is not possible. 121.73 1.0729 1.0759 The present manuscript extends our earlier computational 1.0701 efforts directed toward understanding cyclopropane stereomuFigure 3. Predicted geometry for the closed shell singlet Cb-symmetric tations through ab initio calculations,20921 calculates secondary edge-to-edgetrimethylene diradical EE, a second-order stationary point deuterium kinetic isotope effects, and develops and applies an structure. appropriate kinetic model. tions with single- and double-excitation (CISD) energies were determined at theSCF-optimizedgeometries. At this CISD level Theoretical Approach of theory the three lowest occupied molecular orbitals [C(ls)like orbitals] were held doubly occupied (frozen cores) with all Three basis sets, labeled 6-31G*, DZP, and TZZP, were three basis sets. For the DZP and TZ2P basis sets the employed in the present study. The 6-31G* basis set was from corresponding three highest lying virtual orbitals [C( ls*)-like Hariharan and Pople22and was used to reproduce the work by atomic orbitals] were also deleted (frozen virtuals) in all Getty, Davidson, and Borden.19 The double-{basis set (DZ) was configurations. Thus the DZP- and TZ2P-CISD wave functions from the standard Huzinaga'-Dunningu contraction of Gaussian with the TCSCF reference for the transition state structure in functions and is described as (9s5p/4s2p) on carbon and (4s/2s) C, symmetry2' included 160 526 and 552 746 configurations, on hydrogen. The triple-{ basis set (TZ) was again from respectively. These CI wave functions were determined via the H~zinaga23-Dunning~~ and is described as (9s5p/5s3p) on carbon shape-driven graphical unitary group approach.30 For the EF and (4s/3s) on hydrogen. In both the DZ and T Z basis sets the isomer all spin eigenfunctions were included in the CI space in hydrogen s functions have been scaled by the standard factor of order to reproduce the calculations of Getty, Davidson, and 1.2. The DZP basis set was constructed by augmenting the DZ Borden.19 It should be noted that, in our previous only basis set with a single set of d functions for each carbon atom configurationswithin the Hartree-Fockinteracting ~ p a c e 3 ~ Jwere 2 [ad(C) = 0.751 and a single set of p functions for each hydrogen included in the CI wave functions for the EF isomer. In order atom [ap(H) = 0.751. The TZ2P basis set was the T Z basis set to estimate approximately unlinked quadruple excitations, augmented with two sets of d functions for each carbon atom Davidson's correction33.34 was applied, and this type of energetic [~yd(C)= 1.50,0.375] and two sets of p functionsfor each hydrogen prediction is abbreviated as CISD+Q. atom [ap(H)= 1.50.0.3751. SetsofsixCartesiand-like functions were used throughout. Results and Discussion For the cyclopropane and trimethylene diradical stationary point structures, complete structural optimizations were carried The geometries determined for cyclopropane and five triout using SCF2S and TCSCF26 analytic first-derivative methods. methylene diradical stationary points are summarized in Figures Harmonic vibrational frequencies were determined via analytic 2-7. In these six figures, bond lengths are in angstroms and bond second-derivativet e c h n i q ~ e s . ~ ~The ~ ~ configuration ~-2~ interacangles are in degrees. The 6-3 1G*-SCF reoptimized geometries
tit:::
Baldwin et al.
7516 The Journal of Physical Chemistry, Vo1.98, No. 31, 1994
105.07 ~. 105.23 105.18
105.80 I 06.00 105.96
~
1.0885
1 18.69 118.90 118.86
1.0931
109.31
110.87 110.54 110.56
-.._.
H
H
Ha i 19.80 120.23
*a
120.18
'
...' :$::; ,. 109.38
120.31 120.4 1 120.37
1.5006 W - T C S C F
115.28 115.41 116.50 117.03 117.04
1.0861 1.0875 1.0834
I .0745 1.0771 1.0717
110.85 110.86
1.0756 1.0780 1.0727
116.95 117.41 117.41
119.24 119.53 119.48
1.0753 1.0779 1.0726
'
29.54 HaCCC ?6.30 26.43
-176.38 HbCCC -176.41 -176.47
Figure 4. Equilibrium geometry for a closed shell singlet Crsymmetric trimethylene diradical intermediate, C;(int).
T S y c 50.20
t
47.43 47.44
%ccc
-151.52 -151.50 151.84
-
Figure 6. Predicted geometry for the closed shell singlet C,-symmetric
trimethylene diradical transition structure C;(ts),
105.01 105.18
g:;; 119.73 119.59
.. **..
1.0898 1.0908
n 10927 110940
H
H
108.90 108.69
' e * ..
1.5024
1os.44
1.5050
105.73
119.06
105'69
n
1.0776 117.63 117.88
H
.---...116.60
.... e-...
H
1.0895 1.0905 1.0865
1.0781 121.21
1.5084 6-31G*-SCF 1.5108 DZP-SCF 1.5066 TZ2P-SCF
119.95 113.94 113.85 113.90
1.0738 1.0769 1.0714
H
Figure 5. Predicted geometry for the closed shell singlet Cl-symmetric
trimethylene diradical transition structure C~(ts).~~ are included for comparison with ref 19. The energies estimated through these ab initio calculations are summarized in Table 1. The calculations find a reactive intermediate, C;(int), a trimethylene of Cspoint group symmetry very close in geometry and energy to the Ca-symmetricEE trimethylene. The difference in energy between C;(int) and EE is quite small (Table 1); at the higher levels of theory, applied to the geometries for EE and C;(int) found using 6-31G* and DZP TCSCF wave functions, EE appears to be even slightly lower in energy! One may wonder whether reoptimization of geometry for the EE structure at the highest levels of theory would reveal it to be an intermediate, or still a second-order stationary point. The vibrational mode in C;(int) correspondingto an asynchronouspassage of one terminal methylene through the plane common to the carbon atoms is
...--..-109.21 109.19
1.0723 1.0753 1.0698
121.64 121.62 121.60
1.0756 1.0781
'-, '
ti;:: 119.43
116'43 116.85 116.87
'
H,CCC 76.91 78.13 78.04
Figure 7. Predicted geometry for the edge-to-faceopen shell singlet C,symmetric trimethylene diradical transition structure EF(ts).
calculated to be only 102 cm-1 (6-31G*) or 96 cm-1 (DZP);it is a very low energy torsional motion.
+H
+H
-H
-H
Thermal Stereomutations of Cyclopropane
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7517
TABLE 1: Total Energies (in hartrees) and Relative Energies (in kcal mol-’) for Cyclopropane and Trimethylene Diradical structures calculation
cyclopropane
EE
c. (ht)
6-31G*-(TC)SCF
-117.058 865 (0.0) -1 17.082 530 (0.0) -117.091 539 (0.0) -117.438 281 (0.0) -1 17.480 647 (0.0) -117.491 109 (0.0) -117.539 395 (0.0) -117.537 902 (0.0) -1 17.592 057 (0.0)
-1 16.988 882 (43.91) -117,016 268 (41.58) -117,023 922 (42.43) -1 17.342 694 (59.98) -117.381 176 (62.42) -1 17.399 461 (57.51) -1 17.443 594 (60.12) -117.445 613 (57.91) -1 17.495 986 (60.28)
-1 16.989 696 (43.40) -117.016 721 (41.30) -117.024411 (42.12) -117.342 140 (60.33) -1 17.380 360 (62.93) -1 17.399 357 (57.57) -1 17.443 405 (60.23) -1 17.445 114 (58.22) -1 17.495 308 (60.71)
DZP-(TC)SCF TZZP-(TC)SCF 6-31G*-CISD 6-31G*-CISD+Q DZP-CISD DZP-CISD+Q TZ2P-CISD TZ2P-CISD+Q
This facile torsional motion would interconvert two equivalent C;(int) structures, and the resulting single intermediate would have CZ,molecular symmetry.36 Neither the depth of the energy well for the intermediate nor the question of whether the intermediate is really of CZ,point group symmetry or only of CZ, molecular symmetry is essential to the kinetic analysis that follows: that analysispresupposes a short-lived intermediate, but the precise structural characteristics of that intermediate are not of critical importance. It seems clear that very small changes in displacementsof terminal methylene hydrogens from the plane defined by the three carbon atoms and small variations in the C-C-C bond angle have little impact on the energy of the intermediate: these vibrational or * torsional modes for the intermediate lend it some dynamic character but do not allow any 180° rotations of terminal methylene groups.
Chapuisat and Jean found EE to be a secondary minimum along the synchronous conrotatory path for optical isomerization, yet they suggested that it is not a true minimum, since it could react further with “practically no activation energyn.3’ The reality of the trimethylene intermediate is suggested, however, in theoretical chemical dynamics modeling of cyclopropane stereomutations37 using trajectory techniques on quantum mechanical potential energy surfaces.38 Many reactive trajectories show that the trimethylene intermediate undergoes several oscillations of the C-C-C angle bending mode about the optimum value as the trimethylene traverses the distance between one C2symmetric transition state and another, leading to a k12product, as in Figure 12 of ref 37. The duration of this transit was estimated” to be 3.3 X 10-13 s, a value comparable to 100 cm-I. It may require higher levels of theory, or computationsof the free energy rather than the potential energy surface near EE, before all details concerningthe trimethylene intermediate are resolved. All three trimethylene transition structures are found to be very similar in energy. The lowest energy transition structure, C1(ts),19 arises when the reaction channel leading from cyclopropane toward EE through a conrotatory motion of terminal methylene groups encounters a bifurcati0n3~and C2 symmetry is lost as two equivalent paths diverge. There are two identical transition states associated with the C3H6 Cl-trimethylene transition structure for each initially conrotatory approach to the trimethylene intermediate, and two more (mirror image versions of the first pair) for passage from the intermediate on to the net k12 product.
CI(t.9) -1 16.989 538 (43.50) -117.016 660 (41.33) -1 17.342 523 (60.09) -1 17.380 855 (62.62) -1 17.399 493 (57.49) -1 17.443 576 (60.13)
CAt.9) -1 16.988 759 (43.99) -117.015 807 (41.87) -1 17.023 474 (42.71) -1 17.340 999 (61.04) -117.379 151 (63.69) -1 17.398 282 (58.25) -1 17.442 290 (60.93) -117.443 861 (59.01) -1 17.493 939 (6 1.57)
EF(t.9) -1 16.987 686 (44.67) -1 17.014 936 (42.42) -1 17.022 499 (43.32) -1 17.340 826 (61.15) -1 17.379 364 (63.56) -1 17.398 016 (58.42) -1 17.442 355 (60.89) -1 17.443 690 (59.12) -117.494 182 (61.42)
The trimethylenes C;(int) and Cl(t.9) are essentially equal in potential energy at the higher levels of theory (Table 1). Passage from the intermediate to this transition state would require only the proper phase relationshipsof thevibrationalmodes; the lifetime of the intermediate would thus be limited more by entropic than by energetic factors. At the four higher levels of theory for which all structures were considered, DZP-CISD and DZP-CISD+Q calculations with 6-31G* and DZP basis sets (Table l), C;(ts) is 0.90 f 0.14 kcal/ mol higher than the Cl(ts)alternative, and EF(ts) is 0.92 0.12 kcal/mol higherthan Cl(ts).Thus thereis nosignificantenergetic advantage favoring C;(ts) over EF(ts), or vice versa; at 407 OC, (or, very nearly, at 422.5 “C) the 0.9 kcal/mol difference in energy (taking AAE’ as a fair approximation to AAG*) corresponds to the rate constant ratios k(C,)/k(Cl)= k(EF)/k(Cl) = 0.5. While these ratios cannot be considered more than qualitative estimates, they are the ratios suggested by the ab initio computations and are utilized consistently without adjustments or scalingsof any sort in the kinetic analyses below. These rate constant ratios correspond to competitive passages over alternative transition states, whether the reactant is a cyclopropane or a trimethylene intermediate.
*
Kinetic Model These rate constant ratios imply a more complicated kinetic scheme for stereomutationsthan has been applied previously, for cleavage of a particular C-C bond of cyclopropane or of an isotopically labeled cyclopropane may occur to generate a trimethylene intermediate along six paths. Each of the four trimethylene intermediates formed may then partition between six exit channels to regenerate starting material or form k l , k2, and kl2 products. In addition, each kj one-center epimerization product may be formed by two paths involving EF(ts) structures. In place of the kinetic model of Figure 1,one has the more intricate multiple-path model of Figure 8. One may exercise this model and a conventional steady-state kinetic treatment to deduce a theoretical kl/k12 rate constant ratio for cyclopropane itself; the prediction is not one that can be tested directly through experiments, but it may serve as a useful preparation for the analysis of one-center and two-center epimerization reactions shown by deuterium-labeled cyclopropanes to follow. For now, no isotope effects are at issue; only the deduction of a theoretical kllk12rate constant ratio based on the ab initio computational results and the corresponding kinetic situation (Figure 8) is of concern. Formation of kl2 product with cleavage of C( 1)--C(2) may take place through initial conrotatory motions, either clockwise or counterclockwise; each may progress over two Cl-symmetric transition states to form a trimethylene intermediate; and the
Baldwin et al.
7518 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994
TABLE 3: Calculated ( k ~ / kand ~ )(kdkd-1 Val- for Cyclopropane-1,2,3-4 Involving Trimethylene Transition Structures at 407 OC trimethylene ( k ~ l k ~DZP ), ( k ~ l k ~6-31G* ), (kHlkD)-I
H
L;pI‘H
Figure 8. Schematic representation of reaction paths for cyclopropane stereomutations. The trimethylene transition structures are located approximately on the potential energy projection through symbols( , CI; @, C,) or an abbreviation (EF). Each of the four regions surrounded by six transitions states defines a trimethylene intermediate potential well.
TABLE 2 Calculated k ~ / and k ~(k~/k~)-l Values for Cyclopropane-1,2-& Involving Trimethylene Transition Structures at 422.5 OC
. --,
-,
CI-dz-1 9-dz-2 Cl -d2-3 Cl-dz-4 CI-dz-5 CI-dz-6 Cl-d2-7 9-d2-8 C1-dz-9 Cl-dz-10 9-d2-11 CI-dz-12
1.390 1.415 1.484 1.464 1.131 1.151 1.207 1.192 1.106 1.096 1.125 1.115
1.391 1.413 1.480 1.462 1.140 1.159 1.209 1.198 1.105 1.101 1.124 1.118
0.72 0.7 1 0.68 0.88 0.87 0.83 0.84 0.90 0.91 0.89 0.90
C,-dz- 1 Cs-d2-2 Cs-dz-3 CJ-dz-4 crdz-5 Ccd2-6 CS-dz-7
1.110 1.240 1.078 1.204 1.166 1.299 1.473
1.115 1.244 1.080 1.206 1.167 1.303 1.469
0.90 0.81 0.93 0.83 0.86 0.77 0.68
EF-d2-1 EF-dz-2 EF-dz-3 EF-dz-4 EF-dz-5 EF-d2-6
1.395 1.091 1.086 1.460 1.148 1.086
1.374 1.107 1.089 1.438 1.163 1.088
0.72 0.91 0.92 0.69 0.87 0.92
0.67
0.70 0.66 0.86 0.81 0.89 0.88 0.88 0.79 0.91 0.82 0.83 0.75 0.66
a Structural representations for the enumerated isomeric dz-labeled trimethylenes aredisplayedin Chart 1. Reference 19, based on unscaled 6-31GS calculated frequencies. fraction of this intermediate which progresses to form the klz product isgiven by{2k(C1)/(4k(C1) 2k(C,))J. Thekl~product may also be reached by two different disrotatory processes to give trimethylene intermediates and further reaction of these intermediates over a second C, transition state {k(CS)/(4k(C1) + 2k(Cs))Jof the time. Thus, k12 products are formed at a rate proportional to 4k(C1)(2k(C1)/(4k(C1) + 2k(C,))J + 2k(C,)(k(Cs)/(4k(C1) 2k(C,)}. With k(CJ taken to be 0.5k(C1),as estimated from the energies of Table 1, the k12 rate constant is proportional to 1.7k(C1). Formation of kl products may be traced in a similar fashion: 2kl is proportional to 4k(C1)(2k(C,)/(4k(Cl) + 2k(C,))J + 2k(C,)(4k(C1)/(4k(CI) 2k(C,))} + 4k(EF). Recalling that the relative value of k(EF) was estimated to be 0.5k(C1),this expression reduces to kl being proportional to 1.8k(C1). The theoretical rate constant ratio kl/k12 is thus 1.8/1.7, or 1.06/1. The calculated energies for Ct(ts),c(ts),and EF(ts) (Table 1) and the kinetic model based on a trimethylene intermediate and
+
Cl-d3-l Cl-d3-2 C1-d3-3 Cl-d3-4 Ci-d3-5 Cl-d3-6 Cl-d3-7 C1-d3-8
1.528 1.507 1.555 1.534 1.235 1.231 1.256 1.25 1
1.527 1.510 1.552 1.536 1.242 1.233 1.263 1.254
0.65 0.66 0.64 0.65 0.8 1 0.81 0.80 0.80
Crd3-l Crd3-2 CrQ-3 Cr-d3-4 Crd3-5 Crd3-6 EF-ds- 1 EF-d3-2 EF-d3-3 EF-d3-4
1.207 1.351 1.526 1.171 1.310 1.481 1.501 1.173 1.501 1.173
1.213 1.356 1.529 1.175 1.313 1.482 1.480 1.191 1.480 1.191
0.83 0.74 0.66 0.85 0.76 0.68 0.67 0.85 0.67 0.85
a Structural representations for the enumerated isomeric d3-labeled trimethylenes are displayed in Chart 2.
the steady-state assumption predict that the rate constants for net onecenter and two-center thermal epimerization events for cyclopropane itself are nearly the same. There is, it will be noted, no contradiction between this conclusion and the prediction made in 1968 by Hoffmann’ that the easiest passage from the trimethylene intermediate to the much deeper valleyof the cyclopropaneisvia a conrotatory motion of both methylene groups. The calculated fraction of the trimethyleneintermediate going to cyclopropane by “conrotatory” pathsis (4k(C1)/(4k(C1) 2k(C,))J, or 0.8. Thereisnot, however, such a marked predominanceof k12 over kl because a trimethylene intermediate may be formed through k(C,) as well as via k(C1) paths, and because k(EF) also plays a non-negligible role.
+
Secondary Deuterium Jhetic Isotope Effects The ab initio calculations for cyclopropanesand trimethylenes provided vibrational frequencies for unlabeled and deuteriumlabeled versions of equilibrium and transition state structures, and these were used to calculate kinetic isotope effects on rate constants k(C1), k(C,), and k(EF) given in Tables 2 and 3. These calculations were done for each system using vibrational frequencies from the 6-31G* and DZP SCF or TCSCF computations; the frequencies were scaled by a factor of 0.9.40 Isotope effects were calculated using a standard formulation based on application of the Teller-Redlich product theorem (eq l).41 In eq 1, all
=-
X
+
+
symbols have conventional definition^.^' The calculated isotope effects were not especially sensitive to which of the two sets of frequencies was employed. In Tables 2 and 3 the deuteriumlabeled trimethylenes are labeled 9 , C,, or EF to identify the geometry,d2 or d3 to specify the extent of labeling, and an arbitrary
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7519
Thermal Stereomutations of Cyclopropane
CHART 2
CHART 1 D H
D H
H D
\r
\r
H
D
D
C1-d2-1
H
C1-d2-2
D H
D H
H D D* H
H
D
F
\r
H
”f H
H
‘b D
H
I
b
H
H
D H
\r
D H
H D
\r
\r
H
C1-d2-8
D H
H D
n
D
\r
/c\ D.
Cl-dz-7
\r
H
H
H D
\r
hH
D H
\r
Q..
H D
\r
C1-d2-6
H H
I?
A
I “ “b
ti
Cl-dz-5
H H
..
D H
\?
\r
cS-d3-1
~ ~ d 3 - 2
C,-d3-3
C,-d3-5
CS-d3-6
EF-dj-1
D H
D H
CS-d3-4
\r
H
Ct-d2-10
D H
CI-d2- 11
D H
\r
CS-d2-1
C1-d2-12
H D
\r
EF-d3-2
I?
CS-d2-2
CS-d2-5
Tables 2 and 3 also give the reciprocals of the calculated ( k ~ / k ~values, ) which are the rate constantsfor passage of a particular deuterium-labeled trimethyleneover the specified transition state, relative to the rate constant appropriate to the unlabeled trimethylene. With these relative rate-constant terms one can readily calculate theoretical ki/ki, ratios for reactions involving a deuterium-labeledcyclopropane isomerizing through cleavage of a particular C-C bond.
CS-d2-6
D H
\r
Diastereoselective Kinetic Isotope Effects H EF-d2-1
H H
EF-d2-2
H H
H H
EF-dp-4
EF-d2-5
\r
EF-d2-3
The values of ( k ~ / ksummarized ~) in Tables 2 and 3 imply some very large dia~tereoselective~~ secondarydeuterium kinetic isotope effects. For the two C1-d2-i systems attainable from 1,2trans-cyclopropane-d2 through cleavage of C( 1)-C(2) through conrotatory motion, c1-4-3 and C1-4-8,reaction over the second
EF-dp-6
integer to indicate just which labeled form is involved. The correlations of labels with structures are given in Charts 1 and L.
These calculations treat cyclopropane- 1,2,3-d3 and trimethylene- 1,2,3-d3diradicals, rather than lCd3-labeled cyclopropanes and trimethylenes. Getty, Davidson, and Borden have shown that the calculatedcarbon-13 kinetic isotope effects are negligibly small;19 if W,d3 systems were treated explicitly, many more structures would need to be considered (50 rather than 18), with scant gain. Where direct comparisons are possible (Table 2), the present calculated ( k ~ l k d - 1values are generally quite close to those calculated earlier.19 Calculations of equilibrium isotope effects for cis and trans isomers of cyclopropane-1,2-d2 and for syn and anti forms of cyclopropane-112,3-dpshowed that they were negligible.
c1-d2-3
C1-d2- 8
transition state is calculated to be faster by a factor of 1.25. The corresponding pairs of C1-d3-i structures, C1-4-1 and Ci-d3-6, and C1-4-3 and C1-4-8, favor the second of each of the two alternatives by the same factor, 1.25. Deuterium-labeled cyclopropanes lead to these transition structures with substantial preferences for one conrotatory rotational sense over the other. Comparisons of entries in Tables 2 and 3 for other C1-d~-iand Cl-d3-i trimethylenes indicate that the large diastereoselective effect is associated with the nearly planar terminal methylene group. It makes little kinetic differencewhich of the two possible
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994
7520
dispositionsof a CHD unit at thecentral position or at the strongly canted terminal position of a C1-trimethylenetransition structure is adopted. Similar large effects are calculated for isomeric EF transition structures: reaction by way of EF-4-1 is faster than by the EF4 - 2 alternative by a factor of 1.26; the related pair EF-4-4 and EF-4-5 show the same large relative rate factor. The corresponding EF-Q systems are predicted to have the same preference by a factor of 1.27.
H
A D
%HH
EF-dz- 1
Baldwin et al.
+
EF-4
'
DA %HH
H
EI-d2-2
With the C,-symmetric transition structures, comparably large diastereotopic effects are seen, but they now favor terminal deuterium labels in an "interiorm disposition rather than in a peripheral location: thus formation of e - 4 - 5 is favored kinetically over C,-4-7 by a factor of 1.27, with the same preference shown for c-4-1over e-d3-3, and of e-4-4over e-4-6.
Figure 9. Schematic mapping of transition structures and products for stereomutationsof syn-cyclopropane-1,2,3-d3. Relative ( k ~ / k ~ )terms -l appropriateto the various trimethylene-d3transition structuresare listed in Table 3.
EF- 4
Cs-d2-5
C.-d2-7
These diastereoselective secondary deuterium kinetic isotope effects are among the largest calculated for simple hydrocarbon reactions and will be considered in greater detail in a subsequent report.
Figure 10. Schematic mapping of transition structures and products for stereomutationsof tranr-cyclopropane-l,2-d2 when the C( l)-C(2) bond ) - l appropriate to thevarious trimethylenebreaks. Relative ( k ~ / k ~ terms d2 transition structures are listed in Table 2.
Calculated k,/kg Ratios for Deuterium-Labeled Cyclopropanes With the calculated ( k ~ / kvalues ~ ) for trimethylene42 and
-4available (Tables 2 and 3), one may readily predict the relative importance of one-center and two-center epimerization events for the corresponding cyclopropane-1,2-d2 and 1,2,3-d3; the relative rate constants ~ ( C I ) k(C,), , and k(EF) defined for unlabeled cyclopropane and the C1, C,, and EF trimethylene transition states are modified for each trimethylene by a factor of ( k ~ / k ~ )(Tables -l 2 and 3). One simply has to apply the kinetic analysis used for stereomutations of the unlabeled system with the isotope-effect modified rate constants. For these predictions, transition structure symmetry factors play no role, for (sH*/sD*) will always be unity; all trimethylenedo and thus necessarily all trimethylene-d, transition structures are devoid of rotational symmetry. Consider, for example, stereomutations originating from the syn isomer of cyclopropane-1,2,3-d3 (Figure 9). This molecule may cleave C(l)-C(2) and then reach a k12 product in four different ways. For conversion to the k12 product in the upper right-hand or the lower left-hand corner of Figure 11, the rate constant is proportional to (0.66 + 0.80)k(C1)((0.65 0.81)k(C1))/((0.66 + 0.80 + 0.65 + 0.81)k(Cl) + (0.74 + 0.76)k(C#))],or l.162k(CI). The two reactions giving k12 product initiated by disrotatory ring opening occur with rates proportional to 0.83k(C8)(0.124) and 0.68k(C,)(O.O85). The four pathssum to give klz proportional to 1.243k(Cl). A similar summation of contributions for net one-center events over the 12 possible paths gives 2kl proportional to 2.71k(C1). The ratio kl/k12 is thus predicted to be 1.09/ 1,close to the 1.06/ 1 predicted for unlabeled cyclopropane. There are substantial isotope effects on individual
-
+
D
1
Figure 11. Schematic mapping of transition structures and products for
stereomutationsoftrans-cyclopropane-l,2-d2when theC( 1)-C(3) bond / terms appropriate to the varioustrimethylenebreaks. Relative ( k ~kD)-1 d2 transition structures are listed in Table 2. components of the stereomutations taking place, yet the overall balance between one-center and two-center epimerizations is hardly changed (according to this model) for cyclopropane-do compared with cyclopropane1 ,2,3-d3. The kinetic model predicts a kl/kl2 ratio for cyclopropane-l,2,3-d3at 407 OC which is within experimental uncertainty identical with the experimental value found through kinetic work with [ l-13C]cyclopropane-l,2,3-d3 at this temperature. For the isomeric cyclopropane-1 , 2 4 one must consider separately reactions involving C(1)-C(2) and other possibilities involving C(2)-C(3), as exemplified in Figures 10 and 11 for the trans reactant. The results of tracking the modifications in net
Thermal Stereomutations of Cyclopropane
The Journal of Physical Chemistry, Vol. 98, No. 31, I994 7521
TABLE 4 Calculated Relative Rate Constants for Net One-Center and Two-Center Stereomutations of Deuterium-Labeled Cyclopropanes cyclopropane klb kiz ki" kl3 k3 do cis- 1,2-dz trans-1,2-d2 syn-1,2,3-d3
1.800 1.392 1.392 1.355
1.700 1.284 1.284 1.243
Relative to ~ ( C I ) . When C(l)-C(2) breaks.
1.800 1.505 1.505 1.355
1.700 1.439 1.439 1.243
1.800 1.61 1.61 1.355
breaks. When C(l)-C(3)
TABLE 5: Calculated Deuterium Kinetic Isotope Effects for Net One-Center and Two-Center Stereomutations of Labeled Cyclopropanes cyclopropane kdkn: kla k12 Wb kin ka 1,2-d2 1,2,3-d3 When C(l)-C(2)
1.293 1.328
1.324 1.368
1.196 1.328
1.181 1.368
breaks. When C(l)-C(3)
breaks.
1.118 1.328
one-center and two-center stereomutations induced by secondary deuterium kinetic isotope effects are summarized in Table 4. In all cases, the results are consistent with the pattern deduced theoretically for stereomutations of cyclopropane itself even though there are some large secondary deuterium kinetic isotope effects associated with particular transition structures, they are of minor net impact on theoverall one-center/two-center balance. Thecalculated relative rate constants of Table 4 indicate small fl secondary deuterium kinetic isotope effects on both kl and k12: kl(d2)/kl(d3) = 1.027 and k12(d2)/ki~(d3)= 1.033. The relative rate constants of Table 4 may be restated in terms of kH/kD effects on net kl and kl2 processes, as summarized in Table 5 . For the cyc1opropane-l12-d2,the a effects are substantial: 1.18 per deuterium on kl and 1.13 per deuterium on klz. The ratio k13(d*)/kl~(d2)is predicted to be 1.12,a value in excellent accord with the calculated value of 1.13 (at 422.5 "C) reported by Getty, Davidson, and Borden19 for optical isomerization taking place through the various Cl(ts) possibilities and thus based on a very different kinetic model. The kl'/kl ratio for cyclopropane-1,2d2 from the entries of Table 5 is 1.08, slightly smaller. Both values are quite close to the 1-10assumed for both ratios in 1975.9
Conclusions The kl/k12ratio of thermal stereomutation rate constants for cyclopropane is predicted to be 1.06 at 407 OC. This computational result is based on the energies of three distinct types of trimethylene diradical transition structures calculated by refined ab initio methods and a kinetic model which includes a shortlived trimethylene intermediate and kinetically competitive rates for reactions proceeding by way of the three kinds of trimethylene transition structures. For cyclopropane-l,2-d2 and -1,2,3-d3, the corresponding kl/k12 ratios are calculated to be only slightly different, 1.08 and 1.09. These theoretically based predictions agree well with experimental work on the kinetics of thermal interconversionsof the four isomers of [ 1J3C] cyclopropane-1,2,3d3which demonstrated that kl- k12.lf-~* Recent highlycorrelated single-reference-based ab initio molecular orbital calculations led to similar con~lusions.4~ More accurate experimentalkinetic parameters, more powerful computational methods, or more sophisticated treatments of dynamical effects may in time modify the understandings of cyclopropane thermal stereomutations now offered, but the essential features of these reactions now seem reasonably well defined. The overall balance between net one-center and twocenter epimerizations is governed by multiple kinetically competitive paths, and the two types of stereomutations take place with essentially equal rate constants: kl = k12.
Acknowledgment. We thank the National Science Foundation for support of this work through Grant CHE-9 100246at Syracuse University andGrant CHE-9216754 at theuniversity of Georgia, and many individuals who helped clarify some of the issues encounted as this manuscript was in preparation, including Professors J. A. Berson, W. T. Borden, B. K.Carpenter, T. B. Freedman, A. Halevi, D. K.Lewis, L. A. Nafie, S.E. Novick, and Dr. Steven J. Cianciosi. References and Notes (1) Chambers, T. S.;Kistiakowsky, G. B. J. Am. Chem. Soc. 1934,56, 399405. (2) Rabinovitch, B. S.;Schlag, E. W.; Wiberg, K. B. J. Chem. Phys. 1958, 28, 504505. (3) Benson, S . W. J. Chem. Phys. 1961, 34, 521-526. (4) Doering, W. von E. Proc. Natl. Acad. Sci. U.S.A. 1981, 78. 52795283. Doering, W. von E. Peter A . Leemakers Symposium Lecture; A.C.S. Science Symposium Series; Wcaleyan University, 1981. (5) Seetula, J. A.; Russell, J. J.; Gutman, D. J . Am. Chem. Soc. 1990, 112, 1347-1353. Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.; Krasnoperov, L. N. J. Phys. Chem. 1992, 96,9847-9855. (6) Hoffmann, R. Tram. New York Acad. Sci. 1966, 475479. (7) Hoffmann, R. J. Am. Chem. SOC.1968, 90, 1475-1485. (8) Horsley,J.A.;Jean,Y.;Moser,C.;Salem,L.;Stevens,R.M.;Wright, J.S. PureAppl. Chem. (23rdCongr.,Boston) 1971,SuppI.l, 197-217.Horsley, J. A.; Jean, Y.; Moser, C.; Salem, L.; Stevens, R. M.; Wright, J. S.J . Am. Chem. Soc. 1972,94, 279-282. Salem, L. In The New World of Quantum Chemistry; Pullman, B., Parr, R., Eds.;D. Reidel: Dordrecht, Holland, 1976; pp 241-269. Independent work, based on ab initio calculations using the GVB method (Hay, P. J.; Hunt, W. J.; Goddard, W. A. J. Am. Chem. Soc. 1972, 94,638-640) came to the same conclusion: the barrier height for degenerate isomerization of cyclopropane 'is essentially the same ... whether one or both of the terminal CH, groups are rotated after opening of the CC bond." (9) Berson, J. A.; Pedersen, L. D. J. Am. Chem. Soc. 1975,97,238-240. Berson, J. A,; Pedersen, L. D.; Carpenter, B. K. J . Am. Chem. Soc. 1975,97. 240-242. Berson, J. A.; Pedersen, L. D.; Carpenter, B. K. J . Am. Chem. Soc. 1976, 98, 122-143; 1977, 99, 7399. See also: Wood, J. T.; Army, J. S.; Cortes, D.; Berson, J. A. J. Am. Chem. Soc. 1978,100, 3855-3860. (10) Berson, J. A. Annu. Reu. Phys. Chem. 1977.28, 111-132. Berson, J. A. In Rearrangements in Ground and Excited States; de Mayo, P., Ed.; Academic Press: New York, 1980; pp 31 1-390. Borden, W. T. In Reactiue Intermediates; Jones, M., Moss,R. A., Eds.; Wiley: New York, 1981; Vol. 11, Chapter 5. Gajewski, J. J. Hydrocarbon Thermallsomerizations;Academic Press: New York, 1981; pp 2742. Dervan, P. B.; Dougherty, D. A. In Diradicals; Borden, W. T., Ed.; Wiley: New York, 1982;Chapter 3. Carpenter, B. K. Determination of Organic Reaction Mechanisms; Wiley: New York, 1984; pp 62-67. (1 1) For the first clear recognition that experimental determinations of kj and $1 rate constants for cyclopropane stereomutations could be of telling mechanistic significance, see: Setser, D. W.; Rabinovitch, B. S.J. Am. Chem. Soc. 1964.86, 564569. (12) Baldwin, J. E. J. Chem. SOC.,Chem. Commun. 1988, 31-32 and references therein. See also: Baldwin, J. E.; Selden, C. B. J. Am. Chem. Soc. 1993, I IS, 2239-2248. (13) Baldwin, J. E.; Patapoff, T. W.; Barden, T. C. J. Am. Chem. Soc. 1984,106,1421-1426. Baldwin, J. E.;Barden,T. C.J. Am. Chem.Soc. 1984, 106,5312-5319. Baldwin, J. E.; Barden, T. C. J. Am. Chem. Soc. 1984,106, 6364-6367. (14) See also: Carpenter, B. K. In The Chemistry of the Cyclopropyl Group, Part 2; Rappaport, Z., Ed.; Wiley: Chichester, 1987; pp 1027-1082. (15) Cianciosi, S. J.; Spencer, K. M.; Freedman, T. B.; Nafie, L. A.; Baldwin, J. E. J . Am. Chem. Soc. 1989, 111, 1913-1915. Spencer, K. M.; Cianciosi, S.J.; Baldwin, J. E.; Freedman, T. B.; Nafie, L. A. Appl. Spectrosc. 1990,44235-238, Cianciosi, S.J.; Ragunathan, N.; Freedman, T. B.; Nafie, L. A.; Baldwin, J. E. J. Am. Chem. SOC.1990, 112, 8204-8206; the 95% confidence interval for .k estimated in this communication from only three kinetic points using a standard two-parameter nonlinear least-squares s-I, is too imprecise to be of any mechanistic calculation, (3.9-20.8) X relevance. (16) Cianciosi, S. J.; Ragunathan, N.; Freedman, T. B.; Nafie, L. A.; Lewis, D. K.; Glenar, D. A.; Baldwin, J. E. J . Am. Chem. SOC.1991, 113, 18641866. (17) Freedman, T. B.; Cianciosi, S.J.; Ragunathan, N.; Baldwin, J. E> Nafie,L. A. J. Am. Chem.Soc. 1991,113,8298-8305. Baldwin,J. E.;Cianciosi, S . J. J. Am. Chem. SOC.1992,114,9401-9408. Baldwin, J. E.; Cianciosi, S. J.; Glenar, D. A.; Hoffman, G. J.; Wu, I-W.; Lewis, D. K. J. Am. Chem. SOC. 1992,114, 9408-9414. (18) Cianciosi, S.J. Ph.D. Dissertation, Syracuse University, 1990; Diss. Abstr. In?. B 1991, 52, 832. (19) Getty, S.J.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1992, 114,2085-2093. In Scheme 1, the first-order rate constant for conversion of cis-cyclopropane-l,2-d* to each antipode of the trans isomer is a factor of 2 too large. See also: Getty, S.J.; Davidson, E. R.; Borden. W. T. J. Am. Chem. SOC.1994, 116, 1521-1527. (20) Yamaguchi, Y.; Osamura, Y.; Schaefer, H. F. J. Am. Chem. Soc. 1983, 105, 7506-7511.
7522 The Journal of Physical Chemistry, Vol. 98, No. 31. 1994 (21) Yamaguchi, Y.;Schaefer, H. F.; Baldwin, J. E. Chem. Phys. Lett. 1991,185, 143-150. The reaction coordinate for EF(b)depicted in Figure Sa is not correct; it is the wagging motion of the planar CH2 group, as given in Table 3. (22) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973,28,213-222. (23) Huzinaga, S . J. Chem. Phys. 1966,42, 1293-1302. (24) Dunning, T. H. J. Chem. Phys. 1970,53,2823-2833. (25) Osamura, Y.; Yamaguchi, Y.Schaefer, H. F. J. Chem. Phys. 1982, 77, 383-390. (26) Goddard, J. D.; Handy, N. C.; Schaefer, H. F. J. Chem. Phys. 1979, 71, 1525-1530. (27) Pople, J. A,; Krishnan, R.; Schlegel, H. B.; Binldey, J. S.Int. J. Quantum Chem. 1979, Symposium 13, 225-241. (28) h m u r a , Y.; Yamaguchi, Y.; Saxe, P.; Vincent, M. A.; Gaw, J. F.; Schaefer, H. F. Chem. Phys. 1982, 72, 131-139. (29) Osamura, Y.; Yamaguchi, Y.;Saxe, P.; Fox, D. J.; Vincent, M. A.; Schaefer, H. F. J. Mol. Struct. 1983, 103, 183-196. (30) Saxe, P.; Fox, D. J.; Schaefer, H. F.; Handy, N. C . J. Chem. Phys. 1982,77, 5584-5592. (31) Bunge, A. J. Chem. Phys. 1970,53, 20-28. (32) Bender, C.F.; Schaefer, H. F. J. Chem. Phys. 1971,55,4798-4803. (33) Davidson, E. R. In The WorldofQuantum Chemistry; Daudel, R., Pullman, B., Eds.; Reidel: Dmdrecht, Holland, 1974; pp 17-30. (34) Langhoff, S.R.; Davidson, E.R. lnt. J. Quantum Chem. 1974,8, 61-72.
Baldwin et al. (35) Endo, Y.;Chang, M.C.; Hirota, E. J. Mol. Spectrosc. 1987,126, 63-7 1. (36) Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic Press: New York, 1979. (37) Chapuisat, X.; Jean, Y. Top. Curr. Chem. 1976,158, 1-57. (38) Wang, I.S.Y.; Karplus, M.J. Am. Chem.Soc. 1973,95,8160-8164. (39) Miller, W. H.J. Phys. Chem. 1983,87,21-22.Gamtt,B. C.;Truhlar, D. G.;Wagner, A. F.; Dunning, T. H. J. Chem. Phys. 1983,78,4400-4413. Hoffman, D.K.;Nord, R. S.; Ruedenberg, K. Theor. Chim. Acta 1986,69, 265-279. Valtazanoe, P.; Ruedenberg, K.Theor. Chim. Acta 1986,69,281307. Kraus, W. A.; DcPristo, A. E. Theor. Chim. Acta 198669,309-322. (40) Grev, R. S.;Jansaen, C. L.; Schaefer, H. F. J . Chem. Phys. 1991,95, 5128-5132.seCalso. Hess,B.A., Jr.;Schaad,L. J.;Carsky,P.;Zahradnik, R. Chem. Rm. 1986,86,709-750. (41) Melander, L.; Saunders, W. H., Jr. Reaction Rates of Isotopic Molecules; Wiley: New York, 1980; pp 19-20. (42) Baldwin, J. E.; Reddy, V. P.; Heee, B. A., Jr.; Schaad, L. J. J. Am. Chem.Soc. 1988,110,8554. Baldwin,J. E.;Reddy, V.P.;Schaad, L. J.; Hess, B. A., Jr. J. Am. Chem. Soc. 1988,110, 8555-8556. (43) Replogle, E. S.;Pople, J. A. Abstracts, 203rd ACS NationaIMeeting, San Francisco, April 1992; PHYS 245. Replogle, E. S. Ph.D. Dissertation, CamegicMellon University, 1992.
