1688
Organometallics 1995, 14, 1688-1693
Conformations of (q3-Cyclohexenyl)palladiumSystems. A Molecular Mechanics (MM2) Study Bjorn Bikermark” and Johan D. Oslob Department of Chemistry, Organic Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Per-Ola Norrby” Department of Medicinal Chemistry, Royal Danish School of Pharmacy, Universitetsparken 2, DK-2100 Copenhagen, Denmark Received November 29, 1994@ The primary products from palladium(I1)-assisted nucleophilic addition to 1,4-cyclohexadienes ((y3-cyclohexenyl)palladiumcomplexes) have been investigated by molecular mechanics (MM2). The observed coupling constants can best be explained by a rapid equilibrium between chair- and boatlike conformations. Methods to estimate the relative amounts of the boat and chair conformations of the complexes are presented. Palladium allyl complexes have been found to be very versatile and important reagents in organic i3ynthesis.l Several palladium-catalyzed conversions of unsaturated substrates proceed via y3-allyl complexes. Included in the range of reactions available are functionalizations of cyclohexenes, l,&cyclohexadienes,and l,4-cyclohexaIn the dienes, as well as acyclic 1,4- to 1,7-diene~.~ palladium-catalyzed nucleophilic displacement of allylic acetates, another facile reaction with (y3-allyl)palladium intermediates, optically active products can be obtained by introduction of chiral ligand^.^^^ In most cases, (y3-allyl)palladiumcomplexes will react with nucleophiles to form allylic products. We have previously studied ways to control the configuration of the product double bond and the regioselectivity of the nucleophilic a t t a ~ k Complications .~ arise from the fast dynamic equilibria in the y3-allyl moiety,6 the rates of which, depending on reaction conditions, are often comparable to the rate of nucleophilic a t t a ~ k . ~ The selectivities in these reactions are determined by the energies and reactivities of the different isomers of the intermediate y3-allyl. In order to rationalize some of these effects, we have recently created a molecular mechanics (MM2) force field for the (y3-ally1)palladium moiety.8 The conformational preferences of the q3-allyl intermediates are especially important for rationalization and prediction of enantioselectivity in the reaction. Abstract published in Advance ACS Abstracts, March 1, 1995. (1)Trost, B. M.; Verhoeven, T. R. In Comprehensive Organometallic Chemistry; Wilkinson, G., Ed.; Pergamon: Oxford, U.K., 1982; Vol. 8, pp 80’2-853. (2)(a) Backvall, J.-E. Acc. Chem. Res. 1983, 16, 335-342. (b) Larock R. C.; Takagi, K. J. Org. Chem. 1984,49,2701-2705. (c) Hall, S. S.; h e r m a r k , B. Organometallics 1984,3, 1745-1748. (3) (a) Godleski, S. A. In Comprehensive Organic Synthesis; Trost, B. M., Fleming, I., Eds.; Pergamon: Oxford, U.K., 1991; Vol. 4, Chapter 3.3, pp 585-661. (b) Harrington, J. P. Transition Metals in Total Synthesis; Wiley: New York, 1990. (4)Peiia-Cabrera, E.; Norrby, P.-0.; Sjogren, M.; Vitagliano, A.; deFelice, V.; Oslob, J.; h e r m a r k , B.; Helquist, P., manuscript in preparation. (5) Sjogren, M.; Hansson, S.; Norrby, P.-0.; h e r m a r k , B.; Cucciolito, M. E.; Vitagliano, A. Organometallics 1992, 11,3954-3964. (6) Hansson, S.; Norrby, P.-0.; Sjogren, M. P. T.; h e r m a r k , B.; Cucciolito, M. E.; Giordano, F.; Vitagliano, A. Organometallics 1993, 12, 4940-4948 and references cited therein. (7) Sjogren, M. Ph.D. Thesis, The Royal Institute of Technology, Stockholm, Sweden, 1993. @
0276-7333/95/2314-1688$09.00/0
In order to elucidate these effects, it is advantageous to study systems where the above-mentioned complications arising from the fast isomerizations in the system (e.g., the y3-y1-y3 isomerization) are absent. This is true in, for example, the y3-cyclohexenylmoiety, where the position of the side groups are locked by the ring. We have recently observed enantioselectivity in the palladium-catalyzed nucleophilic substitution of unsubstituted cyclohexenyl acetate in the presence of a chiral l i g a ~ ~ d The . ~ J enantioselectivity here clearly arises from a conformationally induced reactivity difference between the allyl termini in the (y3-cyclohexenyl)palladium ~ o m p l e x .It~ is therefore very important to us to be able to correctly describe the conformations of the (y3cyclohexeny1)palladium complexes. It has also been reported that the conformation of (y3-cyclohexenyl)palladium complexes governs the mode of attack by acetate.9 (y3-Cyclohexenyl)palladium complexes (e.g. 1) are intermediates in a palladium-assisted functionalization of 1,4cyclohexadieneswhich we reported earlier (Scheme 1).2cJo In the course of this investigation,2cJ0a large number of (y3-cyclohexenyl)palladiumcomplexes were isolated and characterized. The conformation of these complexes was unclear but was assigned as overall “pseudochair”or “pseudoboat”from the vicinal couplings between allyl and ring methylene protons. However, in most cases the supposed diaxial couplings between ring methylene protons (H5 to H4 and H6) were suspiciously low. The numbering of the protons in the cyclohexenyl system is shown in the figure in the lower right corner of Chart 1. For example, in the prototypical compound 1,the couplings J41,52 and J 4 2 , 5 2 were 7.8 and 5.7 Hz, respectively (Table 1). These values are in reasonable agreement with a previously observed palladium cyclohexenyl species in a chair conf~rmation,~ (8)(a) Norrby, P.-0.; h e r m a r k , B.; Haeffner, F.; Hansson, S.; Blomberg, M. J.A m . Chem. SOC.1993,115, 4859-4867. (b) Norrby, P.-0. Ph.D. Thesis, The Royal Institute of Technology, Stockholm, Sweden, 1992. (9) Grennberg, H.; Langer, V.; Backvall, J.-E. J.Chem. SOC.,Chem. Commun. 1991,- 1190- 1192. (10)(a) Siiderberg, B. C.; h e r m a r k , B.; Hall, S. S. J. Org. Chem. 1988, 53, 2925-2937. (b) Soderberg, B. C. Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 1987.
0 1995 American Chemical Society
Conformations of (r,J-Cyclohexenyl)palladium Systems
Organometallics, Vol. 14, No. 4, 1995 1689
Table 1. Calculated Percentages of the Boat Conformation, Together with Observed and Calculated Coupling Constants calcd ~
eq 1"
~
~~
eq 2b method
le
2d
3'
4f.g
1'
2d
3'
4fh
obsd'
100.0 3.1 5.6 3.3 5.5
0.0 11.9 6.6 12.0 6.3
65.7 6.1 5.9 6.3 5.8 0.99
50.0 7.5 6.1 7.6 5.9 0.15
47.5 7.5 5.9 7.7 5.7 0.08
45.1 7.6 5.7 7.7 5.5 0.15
100.0 2.8 3.2 3.1 3.2
0.0 9.9 6.7 10.1 6.4
65.7 5.3 4.4 5.5 4.3 1.88
31.9 7.7 5.6 7.8 5.4 0.26
44.7 7.5 5.9 7.7 5.7 0.08
45.6 7.5 5.9 7.7 5.8 0.08
7.6 5.8 7.6 5.8
100.0 4.8 2.3
0.0 6.6 12.4
21.5 6.2 10.2 3.00
62.3 5.5 6.1 0.34
69.9 6.0 6.0 0.00
57.8 5.1 6.2 0.62
100.0 2.4 1.4
0.0 5.6 9.4
21.5 4.9 7.7 1.41
34.9 4.5 6.6 1.15
78.9 6.0 6.0 0.00
47.0 4.9 6.4 0.84
6 6
100.0 12.7 4.9 12.8 4.9
0.0 2.2 7.9 2.2 8.0
99.4 12.7 4.9 12.7 4.9 0.74
89.9 11.7 5.2 11.7 5.2 0.02
89.8 11.7 5.2 11.7 5.2 0.00
92.4 12.0 5.1 12.0 5.1 0.19
100.0 12.1 4.1 12.1 4.1
0.0 1.1 7.1 1.2 7.0
99.4 12.0 4.1 12.0 4.1 0.80
94.1 11.4 4.3 11.5 4.3 0.68
89.2 11.7 5.2 11.7 5.2 0.01
89.1 10.9 4.4 10.9 4.4 0.79
11.7 5.2 11.7 5.2
100.0 3.0 5.7 3.0 5.7
0.0 12.0 6.4 12.0 6.5
49.6 7.6 6.1 7.5 6.1 0.63
58.3 6.8 6.0 6.8 6.0 0.30
52.8 6.8 5.6 6.8 5.6 0.01
53.5 6.8 5.6 6.8 5.7 0.04
100.0 2.8 3.4 2.8 3.4
0.0 10.1 6.5 10.0 6.5
49.6 6.5 5.O 6.4 5.0 0.5 1
42.2 7.0 5.2 7.0 5.2 0.30
56.1 6.8 5.6 6.8 5.6 0.01
55.5 6.8 5.6 6.8 5.6 0.02
6.8 5.6 6.8 5.6
100.0 5.7 12.4 5.7 12.4
0.0 7.1 2.3 7.1 2.3
97.5 5.8 12.2 5.8 12.2 2.40
65.3 6.2 8.9 6.2 8.9 0.58
71.4 5.4 8.8 5.4 8.8 0.00
68.6 5.8 8.8 5.8 8.8 0.26
100.0 5.9 10.5 5.9 10.5
0.0 4.7 1.8 4.7 1.9
97.5 5.9 10.3 5.9 10.3 1.10
79.9 5.7 8.8 5.7 8.8 0.18
83.8 5.4 8.8 5.4 8.8 0.00
69.6 6.3 8.7 6.3 8.7 0.66
5.4 8.8 5.4 8.8
100.0 4.9 3.0 5.7
0.0 6.6 12.0 6.5
66.9 5.4 6.0 6.0 1.83
33.0 6.0 9.0 6.3 0.37
25.9 5.6 9.1 5.8 0.08
27.5 5.7 9.1 5.9 0.11
100.0 2.5 2.8 3.4
0.0 5.5 9.9 6.6
66.9 3.5 5.2 4.5 1.10
11.8 5.1 9.1 6.2 0.46
13.8 5.2 9.1 6.3 0.46
27.0 5.5 8.8 6.6 0.66
5.7 9.1 5.7
100.0 5.7 2.7 6.2
0.0 5.7 12.2 6.0
48.6 5.7 7.6 6.1 1.51
26.6 5.7 9.7 6.1 0.91
26.5 4.1 9.7 6.1 0.01
26.6 5.3 9.7 6.1 0.68
100.0 4.7 1.6 5.3
0.0 3.2 11.6 5.3
48.6 3.9 6.7 5.3 1.77
19.9 3.5 9.6 5.3 0.59
25.4 4.2 9.7 6.0 0.11
27.0 4.4 9.7 6.1 0.16
4.1 9.7 6.1
100.0 4.8 3.4 5.4
0.0 6.5 12.0 6.2
54.9 5.6 7.3 5.8 0.72
42.1 5.8 8.4 5.9 0.29
36.1 5.5 8.5 5.5 0.01
36.4 5.5 8.5 5.5 0.02
100.0 2.5 3.2 3.1
0.0 5.6 10.1 6.3
54.9 3.9 6.3 4.6 1.66
20.3 5.0 8.7 5.7 0.32
29.6 5.2 8.5 5.8 0.27
36.1 5.3 8.4 6.0 0.30
5.5 8.5 5.5
100.0 3.0 5.7 3.3 5.5
0.0 12.0 6.6 11.9 6.4
61.3 6.4 6.1 6.7 5.9 1.42
38.8 8.5 6.2 8.6 6.1 0.22
36.7 8.5 6.1 8.6 5.9 0.19
33.9 8.5 5.9 8.6 5.7 0.24
100.0 2.7 3.4 3.1 3.2
0.0 10.0 6.6 9.9 6.5
61.3 5.5 4.6 5.7 4.5 2.3 1
19.5 8.5 6.0 8.6 -5.9 0.20
22.3 8.5 6.1 8.6 5.9 0.19
33.2 8.3 6.4 8.5 6.2 0.29
8.3 5.9 8.8 6.1
100.0 2.9 5.9 3.0 5.7
0.0 11.9 6.6 11.8 6.8
31.8 9.0 6.4 9.0 6.4 0.69
41.6 8.1 6.3 8.2 6.3 0.30
35.7 8.2 5.9 8.2 5.9 0.19
36.7 8.2 6.0 8.2 6.0 0.24
100.0 2.7 3.6 2.8 3.3
0 9.9 6.7 9.8 6.9
31.8 7.8 5.7 7.6 5.8 0.44
23.9 8.2 6.0 8.1 6.1 0.09
20.2 8.2 5.8 8.2 6.0 0.19
37.5 8.0 6.3 8.0 6.4 0.29
8.2 5.9 8.2 5.9
100.0 4.8 3.3 5.5
0.0 6.5 12.0 6.3
68.5 5.4 6.0 5.8 2.05
36.9 5.9 8.8 6.0 1.25
18.0 4.9 9.1 4.8 0.84
31.2 5.6 8.9 5.7 1.06
100.0 2.4 3.1 3.2
0.0
5.5 10.0 6.4
68.5 3.4 5.3 4.2 2.46
18.6 4.9 8.7 5.8 0.69
9.8 4.3 9.2 5.3 0.42
34.2 5.2 8.4 6.1 0.95
3.8 9.2 5.8
100.0 5.5 2.9 6.1
0.0 5.9 12.3 5.8
49.9 5.7 7.6 5.9 2.00
17.4 5.8 10.6 5.8 0.93
16.8 4.2 10.7 5.8 0.09
17.2 5.4 10.7 5.8 0.70
100.0 4.6 1.8 5.1
0.0 3.3 11.7 5.1
49.9 4.0 6.8 5.1 2.34
11.0 3.5 10.6 5.1 0.66
17.6 4.3 10.7 5.9 0.10
17.9 4.4 10.7 5.9 0.10
4.2 10.7 6
compd 1
% boat J41.52 J42.52 J52.61 J52.62
lllls
2
% boat J42.52 J52.61
llllS
3
% boat J42.51 J42.52
J51.62 352.62
llllS
4
% boat J42.51 J42.52
J42.52 J52.62
llllS
5
% boat J41.51 J42.51 J51.61 J5 I ,62
llllS
6
% boat J42.52 J52.61 J52.62 llllS
7
% boat J42.52
J52.61 J52.62 llllS
8
% boat J42.52 J52.61 J52.62 RllS
9
% boat J41.52 J42.52 J52.61 J52.62 ITXlS
10
% boat J41.52 J42.52 J52.61 J52.62 IlllS
11
% boat J42.52 J52.61 J52.62 llllS
12
% boat 542.52 J52.61 J52.62 llllS
method
h e r m a r k et al.
1690 Organometallics, Vol. 14, No. 4, 1995 Table 1 (Continued) calcd eq 1"
eq 2h method
compd 13
% boat J41.52 J42.52 J52.61
J52.62
% boat J41.52 J42.52 J52.61 J52.62
% boat 341.52 J42.52 J52.61 J52.62
% boat 542.32 152.61 J52.62
4'8
50.9 1.2 7.2 5.7 0.01
49.5 1.2 5.6 7.2 5.6 0.08
100.0 2.9 3.2 3.O 3.2
1'
2"
3'
4@
obsd'
0.0 10.0 6.5 10.0 6.5
84.6 4.0 3.1 4.1 3.7 2.64
36.8 1.4 5.3 7.4 5.3 0.30
52.3 1.2 5.7 1.2 5.7 0.02
50.5 1.2 5.7 7.2 5.6 0.04
7.2 5.7 7.2 5.1
84.6 4.5 5 .l 5.6 1.91
54.4 1.2 6.0 7.2 5.9 0.18
100.0 3.0 5.7 3.2 5.5
0.0 12.0 6.5 12.0 6.4
41.2 8.3 6.1 8.4 6.0 0.75
53.1 7.2 6.0 7.3 5.9 0.09
51.8 7.2 6.0 7.4 5.8 0.06
48.2 7.3 5.7 1.4 5.6 0.20
100.0 2.8 3.3 3.0 3.2
0.0 10.1 6.6 10.0 6.5
41.2 7.1 5.2 7.1 5.1 0.52
35.1 7.5 5.4 1.6 5.3 0.39
54.0 7.2 5.9 7.4 5.8 0.05
48.6 1.3 5.8 7.4 5.7 0.12
1.3 5.9 1.3 5.9
100.0 3.1 5.6 3.1 5.6
0.0 11.9 6.6 11.9 6.5
52.7 7.3 6.1 7.3 6.1 0.19
49.0 1.3 5.8 7.3 5.8 0.00
41.7 7.3 5.7 1.3 5.7 0.01
100.0 2.8 3.3 2.8 3.3
0.0 10.0 6.6 10.0 6.6
64.0 5.4 4.5 5.4 4.5 1.62
35.1 7.5 5.5 1.5 5.5 0.26
47.8 7.3 5.8 7.3 5.8 0.01
48.6 7.3 5.8 1.3 5.8 0.02
7.3 5.8 1.3 5.8
100.0 4.9 3.4 5.3
0.0 6.5 12.0 6.4
64.0 6.3 6.0 6.3 6.0 0.14 44.0 5.8 8.2 5.9 0.57
33.7 6.0 9.1 6.0 0.24
28.4 5.7 9.2 5.7 0.01
27.8 5.7 9.2 5.7 0.03
100.0 2.5 3.3 3.0
0.0
44.0 4.2 7.0 4.9 1.59
11.0 5.1 9.3 6.1 0.40
18.0 5.3 9.1 6.2 0.38
27.0 5.5 9.0 6.3 0.41
5.7 9.2 5.7
ITIS
16
3'
0.0 12.0 6.5 12.0 6.5
rmS
15
2"
100.0 3.1 5.5 3.2 5.5
rmS
14
method
1C
rmS
4.5
5.1
5.5
10.0 6.5
Reference 12. Reference 14. Boltzmann weighted average; eq 3. Adjusted for best fit to observed couplings; eqs 4 and 5. e As in method 2, allowing for a variable systematic error in the Karplus equation. As in method 2, but adjusting each coupling by a fixed value. g Couplings adjusted by 0.4 Hz. * Couplings adjusted by -0.8 Hz. Reference 10. (1
Scheme 1
ate the accuracy of the molecular mechanics method for relative energies of different conformations of (v3-allyl)palladium complexes. The second goal is especially important to us, since we are using this force field in the development of new chiral ligands for palladiumcatalyzed reaction^.^,^
PdC12(CH&N)2
MM2 Calculations Pd 1
c
C02Me
v
but a (cyclohexeny1)molybdenum complex in a chair conformation has been shown to have a diaxial coupling of 11.4 Hz,ll in good agreement with a value calculated from the published X-ray structure using a modification of the Karplus equation.12 Also, the compound 3, which is believed to prefer a boat conformation, has a diaxial coupling of 11.7 HZ.~~JO It can be assumed that the observed coupling constants result from a fast equilibrium between boat and chair conformations in solution. According to preliminary MM2 calculations using the previously developed parameter set,8 both conformations are minima on the energy hypersurface for the compounds in Chart 1. In view of the above, we decided to reinvestigate the previously determined NMR coupling constants using a combination of molecular mechanics and Karplus type equations. The goal of this investigation is twofold: first, to elucidate the conformational preferences of (73cyclohexeny1)palladiumcomplexes, and second, to evalu(11)Faller, J. W.; Murray, H. H.; White, D. L.; Chao, K. H. Organometallics 1983, 2 , 400-409. (12)Bothner-By, A. A. Adu. Mugn. Reson. 1966, 1 , 195. The modified Karplus equation is shown in eq 1.
We have recently shown, for a related system, that coupling constants calculated from molecular mechanics structures can be used to both verify structural assignments and determine the position of a fast equilibrium.13 The molecular mechanics calculations on our y3-cyclohexenyl complexes were performed using a recently developed force field which has been parameterized for very similar systems.8 For most of these simple structures, all minima on the energy hypersurface could easily be located by hand, but in a few cases (e.g., 8 ) dihedral driver calculations were used to verify that all relevant conformations were found. For all conformations generated, vicinal couplings in the saturated part of the cyclohexenyl ring were calculated by two different Karplus-type methods: the simple relationship in eq 112 and the more complex are given by eq 2.14
+ 5 COS 20 3J = 13.7 cos2 0 - 0.73 COS 0 + 3J = 7
- COS
0
(1)
CA\xi{0.56 - 2.47 COS' 0(&3 +.16.9"1Axil)) (2) Here f3 is a H-C-C-H
dihedral angle, Axi is the
(13)Martin, J. T.; Norrby, P.-0.;h e r m a r k , B. J.Org. Chem. 1993, 58, 1400-1406. (14) Haasnoot, C. A. G.; de Leeuw, F. A. A. M.; Altona, C. Tetrahedron 1980, 36, 2783-2792.
Conformations of (~3-Cyclohexenyl)palladiumSystems
Organometallics, Vol. 14, No. 4, 1995 1691
Chart 1. Complexes Investigated in This Work” 1
Pd
6’@
Pd
\
7’@
Pd\ eC(d
Meom Me0
41
3 a The numbering of substituents in the cyclohexenyl moiety is given at the lower right. Protons trans to palladium have the second index “1”:Drotons cis to Dalladium have “2”in methvlenes. When a carbon has only one proton bound to it, the second index is left out (e.g.,H-5 in allstructures except 3).
difference in electronegativity between hydrogen and one substituent on the ethane fragment under study, and & is a positional “sign” (+1or -1) for one substituent.14 Under the assumption of fast conformational equilibrium, time-averaged coupling constants can now be calculated by taking a population-weighted average over all conformations (eq 3, where p i is the population of, and J i a coupling in, conformer i).
(3)
Alternatively, errors in the calculated energies can be compensated for by treating the relative populations of the two major conformations (boat and chair) as variables and fitting the calculated coupling constants to the observed values by least-squares methods (eqs 4 and 5, where x is the fraction in the boat conformation and e(x) is the error in x).13
X =
C(Jboat
- Jchair)(Joba - Jchair)
(5)
C(Jboat - Jchair)2
A few considerations must be made when calculating the Boltzmann populations (pi) in eq 3. The Boltzmann factors should be calculated from free energies, whereas most molecular mechanics packages calculate a steric energy, which is similar but not identical with enthalpy. The simplest procedure is to just ignore the difference and calculate the populations directly from the steric energies. This will be designated as method 1 in this work. When the conformations are structurally similar, this may be a valid procedure. Even in the absence of normal mode analysis, a qualitative estimate of the difference in relative free energies between conformers can be obtained by driving some key torsional angles and comparing the curvature of the potential wells. A shallow well should lead to a higher entropy term and thus a higher population in one specific conformer.
The Jboat and Jchalr values are calculated using method 1. We still assume that energy error differences are negligible within one class of conformations. The accuracy of the relative populations thus obtained can be estimated from eq 6, where e(&t is a total coupling constant error, both experimental errors in the observed value and all errors in the coupling constant calculation. We assume this value to be 1-2 Hz, mainly due to the inaccuracy of the Karplus equations. As an ideal example, if two conformers are calculated to exist in a 50/50 equilibrium at ambient temperature and the maximum calculated coupling constant difference between the two conformers is 10 Hz, the error in the free
1692 Organometallics, Vol. 14, No. 4, 1995 energy difference between the conformers can be expected to be 1-2 kJ/mol. In some cases, usually due to linearly dependent systems and/or inaccuracies in the Karplus equation, meaningless values for the population (e.g., negative) can result. It is good practice to check the populations against those obtained from method 1 and, if possible, identify the sources of any differences. Very often, the populations simply display a small shift toward conformers with a more shallow minimum, that is, entropically favored conformers. As an additional refinement, it is possible to compensate for small systematic errors in the Karplus equation. This is especially useful in a system like this, where a group with unknown properties (the allyl) is connected to the ethane fragment under study. This is most easily done by allowing a nonzero intercept in the linear regression, corresponding t o a constant adjustment to the Karplus equation (method 3). A more ambitious project would be to try to determine the correct electronegativity of the allyl group from the available data, but no such attempt was made in the current work. Already addition of a nonzero intercept has to be considered an overinterpretation of the available data. Great care should be used when analyzing the results of this regression. For some of our compounds, we actually fit a line to two data points only. However, it was noted that in many cases the intercepts were very similar between different sets of data, possibly corresponding to a real systematic error in the application of the Karplus equations to these systems. As an additional way of determining relative populations (method 41, we therefore applied one fixed correction, corresponding to the median of the corrections determined by method 3, to all coupling constants before performing the least-squares fit (eq 5). The arguments presented here depend on the validity of the Karplus e q ~ a t i 0 n s . lAlthough ~ the general form of the equation is well-established, there is considerable variation in the literature on the values of the coefficients in the equation. It is certainly well-known that there are substituent effects on the coeffkients16 and that electronegative substituents on the HC-CH fragment cause a slight decrease in the observed coupling,16aJ7thus giving somewhat lower maximum possible values for J . Our system is, in essence, three steps removed from the original Karplus ethane fragment;15 that is, it contains a six-membered ring, a methoxy group, and a q3-allylsystem. Equation 1takes the first of these points into account,12whereas equation 2 also ~ accounts for the influence of the methoxy g r 0 ~ p . lThe good agreement in this paper (see below) suggests that, at least for protons on C4, C5, and C6, the coefficients are quite reasonable and that the couplings are not drastically affected by the presence of a q3-allyl group at the other end of the ring. The median correction (not considering differences in conformation) obtained from method 3 is less than 1 Hz for both Karplus-type equations. We have also seen a fairly large experimental value for J (11.7 Hz in 3,Table 11, again suggesting (15)Karplus, M.J . Chem. Phys. 1969,30,11-15. (16)(a) Karplus, M. J. Am. Chem. SOC.1963, 85, 2870-2871. (b) Abraham, R. J.; Pachler, K. G . R. Mol. Phys. 1963-64,7, 165-182. ( c ) Abraham, R. J.; Thomas, W. A. Chem. Commun. 1966,431-433. (17)Williamson, K.L.J . Am. Chem. SOC.1963,85, 516-519.
h e r m a r k et al.
no large decreases in the Karplus coefficients due to the allyl group. Calculations were done for all dimeric complexes (116). In some cases (compounds 7-9) dihedral driver calculations were performed in order to find all possible minimum energy conformations with respect to rotation of side groups. For computational efficiency, calculations were not performed on the true dimers but on complexes consisting of one palladium-cyclohexenyl moiety connected to another palladium atom via two chloride bridges. The results from these calculations are shown in Table 1, together with the observed couplings.1° A few calculations of the full dimers verify that the structures and relative energies of conformations in one ring are unaffected by the presence of a second ring.
Results and Discussion The results in Table 1nicely illustrate the advantage of utilizing the observed coupling constants in the calculation of relative populations according to eq 4 (method 2) instead of the more common reliance upon calculated energies (eq 3, method 1). In all cases, the expected error in populations estimated from eq 6 is low, due t o the presence of at least one coupling constant with a large range of attainable values (a diaxial coupling in equilibrium with a diequatorial coupling). A comparison of the two Karplus-type equations (eqs 1 and 2) shows surprisingly little difference. For the fitted methods (methods 2-41, this is in part due to the fitting, since a systematic error in the coupling constant calculation to some extent can be compensated by a shift in the predicted populations. However, this probably is not the only reason for the almost negligible difference between the simple eq 1and the more recent eq 2. The explanation may be found in the way the two equations treat the electronegativity of the two substituents. It seems for eq 1 that the error from ignoring the large electronegativity of the methoxy group is to some extent cancelled by ignoring also the opposite effect of the allyl group, whereas eq 2 includes the large effect from the methoxy but not the small effect from the allyl. If, for each conformation, the two groups would affect the coupling in opposite directions, with the absolute effect of the allyl being about half that of the methoxy, both equations should give approximately the same error, but with opposite signs. The true magnitude of this effect can be estimated from the application of method 3. It should be stressed again that, for each case taken alone, method 3 is very prone to give spurious, false results. For this reason, we use the median instead of the mean as an estimator of the underlying systematic error in the Karplus-type equation. This estimated error is actually larger for the more elaborate eq 2, indicating a significant electronegativecontrihution to the coupling constants from the allyl group. It should be noted that when this correction is applied t o the individual couplings before populations are calculated (method 41, the two Karplus-type equations yield almost identical calculated populations. The two main outliers are compounds 3 and 5, as should be expected from the structural difference between these two compounds and the rest of the data set. Compound 3 lacks a methoxy group, and therefore the cancellation of errors in eq 1 no longer occurs, whereas the corrected eq 2 (method
Conformations of (~3-Cyclohexenyl)palladi~m Systems 4) should still give accurate results. In compound 5, the only compound in the series where the methoxy group is cis to the palladium, the dihedral relationship between the methoxy group and the observed protons has changed. The systematic difference between eqs 1 and 2 cannot, therefore, be expected to be the same for compounds 3 and 5 as for the other compounds in the investigation. The results of the MM2 calculations allow us to come to some very useful conclusions. Because the geometry and energy calculations indicating an equilibrium significantly improve the agreement between the observed couplings and the model, we can say that the q3cyclohexenyl ring in our palladium system is probably undergoing rapid conformational change between chair and boat conformations. Furthermore, these calculations also show that the J52,42 coupling constant should be essentially unaffected by the conformation of the ring. Rather, it is J52,41 that provides a clue to the equilibrium between chair and boat. In our earlier work, we assigned the chair and boat conformations on the basis of the axia1,axial vicinal couplings and on the values of the H-3,H-41 and H-3,H42 (or H-l,H-6) couplings.2cJ0 In this paper, we have shown that the axial,axial couplings are better described by invoking fluxionality. The J3,41 values for boat conformations were -6 Hz, while J3,42 values were usually -0 Hz, the latter corresponding to a dihedral angle of -90". This assignment is certainly reasonable, and this coupling pattern was seen for 3 in this paper and for several compounds with endo substituents on C-5 that should force the ring into a boat conformation.2cJ0 In a chair conformation, the dihedral angles H-3-C-3-C-4-H-41 and H-3-C-3-C-4-H-42 would be quite similar and so the assumption was made
Organometallics, Vol. 14,No. 4, 1995 1693 that the coupling constants would be similar. This assumption is not nearly so reasonable, since the presence of the n-bond to the palladium from C-3 might be expected to affect the angular dependence of the coupling constant on the underside of the ring in quite a different way than on the top side of the ring. In addition, 3Jallylic couplings in conventional organic systems are not known to be especially reliable indicators of bond angles.18 We feel, therefore, that the use of H5 couplings is a better indicator of conformation and that the J 3 , 4 couplings are useful only when one coupling is -0 Hz to indicate a system with the equilibrium very heavily in favor of the boat conformation.
Computational Details All MM2 calculations were carried out using the MacMimid MM2(91) packagelg on a Macintosh Quadra, with added parameters for the (~,?-allyl)palladium moiety.* Coupling constants according to eq 1 were calculated with a homedeveloped macro in Microsoft Excel, whereas MacroMode120 was used to calculate couplings according to eq 2. In this implementation, the electronegativity of the v3-allylmoiety is ignored.
Acknowledgment. Support from the Trygger Foundation and the Danish Medical Research Council is gratefully acknowledged. J.D.O.thanks the Royal Institute of Technology for a research scholarship. OM940910N (18)Garbisch. E. W.. Jr. J. Am. Chem. SOC.1961.86.5561-5564. (19)MacMimic/MM2(91); Instar Software AB, IDEON Research Park, S-22370 Lund, Sweden. (20) MacroModel V4.0: Mohamadi, F.; Richards, N. G. J.; Guida, W. C.: Liskamu, R.: Caufield, C.; C h a w- , G.: Hendrickson, T.: Still, W. C . J . Comput.-Chem. 1990,11, 440.
