Organometallics 1996, 14, 1834-1839
1834
Density Functional Study of Intermediates in the Nickel-Catalyzed Homo-Diels-Alder Reaction of Norbornadiene with Alkenes M. M. Gugelchuk" and J. Wisner Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N 2 L 3G1 Received November 28, 1994@
A theoretical study of proposed organonickel intermediates in the nickel-catalyzed homoDiels-Alder reaction has been carried out employing density functional theory (DFT) methods t o investigate the mechanism of this reaction. Predicted geometries and relative energies of various ground-state complexes important to the mechanistic pathway are discussed. The effects of the level of theory (local or nonlocal, gradient versus SCF corrections) and integration mesh size on relative energies, dipole moments, and Mulliken atomic charges were also investigated. Calculations using the local density approximation were insensitive to the mesh size. However, there are very large variations in the calculated total energies with nonlocal methods t h a t were dependent on both the mesh size and whether the nonlocal corrections were applied in a gradient manner or self-consistently. Dipole moments and atomic charges were much less sensitive. All calculations gave approximately the same relative ordering of the energetics. Some intermediates have been shown to follow a more energetically feasible pathway than others and can be useful in rationalization of the experimentally observed stereo- and regioselectivity. Introduction
series of intermediate organonickel complexes having discrete metal-carbon o bonds. It is evident that a The nickel-catalyzed homo-Diels-Alder reaction of major gap exists in understanding the mechanistic norbornadienes (NBD) with electron-deficient olefins details of this reaction. The organometallic intermedi(shown in eq 1)has been reported to proceed with high ates have been postulated mainly on the basis of degrees of stereo- and even enantioselectivity.1,2 In plausibility arguments or in relation to known stable , ~ ~catalytic ~~ contrast to the uncatalyzed p r o c e ~ s the molecules (cf. Figure l ) . l ~Early ~ on, Schrauzer put forth reaction affords the exo isomer predominantly and the concept of a concerted, n-complex multicenter endo-exo isomerization of the products is negligible mechanism5 which involves a single intermediate (1) under the reaction conditions. This stereoselectivity is arising from the simultaneous coordination of NBD, the influenced by the steric nature of an added phosphorus olefin, and the phosphorus ligand. This simple model * ~ useful to rationalize the propensity for exo stereoligandlb and the steric bulk of the olefin s u b s t i t ~ e n t . ~ ~ ~ was A particularly attractive synthetic aspect of this chemchemistry by assuming that tetrahedral coordination of istry is in the construction of polycyclic natural products NBD and the olefin takes place in the less-hindered with well-defined stereochemistry via cycloadditionconfiguration between the olefin substituent and phosfragmentation sequences. Recently, the influence of phorus ligand. However, later investigations have norbornadiene substituents on regio- and stereoseleclargely discredited the idea of such a concerted pathtivity in the deltacyclane product has been examined wayalc>6,7 with encouraging r e s u l t ~ . ~Because ~ , ~ of its synthetic On the basis of work with quadricyclane, Noyori potential, delineation of the factors responsible for the proposed a stepwise mechanismlcinvolving a nortricyobserved selectivity is quite desirous. clane complex (2) formed from 1by an internal oxidative coupling process. This type of complex had been suggested earlier in the catalytic isomerization of quadriNi(O)L, - 2 PR3 'EWG
While formally a [2+2+23 cycloaddition, this reaction most likely occurs through a sequence of steps and a Abstract published in Advance ACS Abstracts, March 15, 1995. (1)(a) Yoshikawa, S.; Kiji, J.; Furukawa, J. Bull. Chem. SOC.Jpn. 1976,49, 1093. (b)Yoshikawa, S.; Aoki, K.; Kiji, J.; Furukawa, J. Bull. Chem. SOC.Jpn. 1975,48,3239. (c) Noyori, R.; Umeda, I.; Kawauchi, H.; Takaya, H. J . A m , Chem. SOC.1975,97, 812. (2) Brunner, H.; Muschiol, M.; Prester, F. Angew. Chem., Int. E d . Engl. 1990,29, 652. (3) ( a ) Kobuke, Y.; Sugimoto, T.; Furukawa, J.; Fueno, T. J . A m . Chem. SOC.1972,94,3633. (b) Cookson, R. C.; Dance, J.;Hudec, J. J . Chem. SOC.1964, 5416. @
0276-7333l95/2314-1834$09.oo/o
(4) (a) Lautens, M.; Edwards, L. G. Tetrahedron Lett. 1989,30,6813. (b) Lautens, M.; Tam, W.; Edwards, L. G. J . Chem. SOC.,Perkin Trans. 1 1994, 2143. (c) Lautens, M.; Edwards, L. G. J . Org. Chem. 1991, 56, 3761. (5) (a) Schrauzer, G . N. Adu. Catal. Relat. Subj. 1968, 18, 373. (b) Schrauzer, G. N. Adu. Organomet. Chem. 1964, 2, 1. (c) Schrauzer, G. N.; Glockner, P. Chem. Ber. 1964, 97, 2451. (d) Schrauzer, G. N.; Eichler, S. Chem. Ber. 1962, 95, 2764. (6)Cassar, L.; Halpern, J. J . Chem. SOC.,Chem. Commun. 1970, 1082. (7) (a) Pardigon, 0.; Buono, G. Tetrahedron: Asymmetry 1993, 4, 1977. (b) Duan, I.-F.; Cheng, C.-H.; Shaw, J.-S.; Cheng, S.-S.;Liou, K. F. J . Chem. SOC.,Chem. Commun. 1991, 1347. (c) Brunner, H.; Prester, F. J . Organomet. Chem. 1991, 414, 401. (d) Lautens, M.; Lautens, J. C.; Smith, A. C. J . A m . Chem. SOC.1990, 112, 5627. (e) Lautens, M.; Crudden, C. M. Organometallics 1989,8,2733. (0 Lyons, J. E.; Myers, H. K.; Schneider, A. Ann. N.Y. Acad. Sci. 1980,333,273. ( g ) Lyons, J. E.; Myers, H. K.; Schneider, A. J . Chem. SOC.,Chem.
Commun. 1978,636.
0 1995 American Chemical Society
Density Functional Study of Diels-Alder Intermediates
ti+L
tl+L
i s
L
Figure 1. Possible stepwise mechanisms of nickelcatalyzed cycloaddition of olefins with NBD. cyclane t o norbornadiene by rhodium.6 Insertion of the coordinated olefin into the Ni-C u bond of the metallocycle would give intermediate 4. Associative reductive elimination (through complex 5) would yield the cycloaddition product. Support for complexes 4 and 5 arises from related cobalt-catalyzed cycloadditions7 of ethylene to NBD which yields vinyltricyclanes presumably through p-elimination from these type of intermediates. The insertion of unsaturated molecules into the Ni-C u bond of nickelacycles is well documented.8 Alternatively, oxidative coupling of one n bond of NBD with the coordinated olefin could produce a n-homoallylic nickel(I1)intermediate (3)that undergoes electronic reorganization to give 4 or 5. n-Homoallylic norbornadienyl palladium complexes have been isolated, and closure to the nortricyclenyl system has been demonstrated upon addition of a donor ligand such as pyridine or phosphine^.^ Whether electronic reorganization occurs prior to or as a result of ligand association is unknown. A final possibility is that the complexed olefin could add to NBD in a concerted manner (or stepwise through 3) t o form complex 6, which, via reductive elimination, would complete the three-membered ring. Some evidence for such a manifold can be found in the isolation of such complexes from homoDiels-Alder addition of alkynes to NBD-rhodium complexes. lo (8) Campora, J.; Gutierrez, E.; Monge, A,; Palma, P.; Poveda, M. L.; Ruiz, C.; Carmona, E. Organometallics 1994,13, 1728 and references therein. (9)( a ) Green, M.; Hancock, R. I. J . Chem. SOC.A 1967,2054. (b) Coulson, D. R. J . Am. Chem. SOC.1969,91,200. (c) Forsellini, E.; Bombieri, G.; Crociani, B.; Boschi, T. J . Chem. Soc., Chem. Commun. 1970,1203. (d) Hines, L. F.; Stille, J. K. J . Am. Chem. SOC.1972,94, 485.
Organometallics, Vol. 14, No. 4, 1995 1835 The direct involvement of bis(phosphine) nickel complexes has not been determined but may be plausible since the catalyst systems typically used contain Ni/P in a 1:2 ratio. Related to this issue, studies by Grubbs and co-workerdl have shown that bis(phosphine) nickelacycles prefer a reductive elimination decomposition pathway whereas three-coordinate monophosphine nickelacycles predominantly undergo p-elimination. Also, chelated diphosphines are known to retard the rate of the homo-Diels- Alder reaction by effectively competing with NBD for binding to the metal.lb Questions as to thermodynamic versus kinetic control at the individual steps have not been thoroughly investigated, but experimental studies suggest the formation of the deltacyclane product is irreversible under the reaction conditions. As a preliminary step toward modeling the regio- and stereochemistry of this reaction, we have undertaken a study of proposed organonickel intermediates employing density functional theory (DFT) methods.12 A number of articles evaluating the use of DFT methods for organometallic calculations have already appeared in the 1 i t e r a t ~ r e . lDFT ~ has the advantage over traditional ab initio methods in that electron correlation is specifically treated and the computational demand is significantly less for large systems. In this paper we examine the predicted geometries and relative energies of the various ground-state complexes in order to gain some insight into the mechanistic pathway. The effects of the level of theory and integration mesh size on relative energies, dipole moments, and Mulliken atomic charges are also presented.
Computational Details Local density calculations were performed with the program DMOLI4 using the Hedin-LundqvisuJanak-Moruzzi- Williams (JMW) parametri~ation'~ of the correlation energy of the
homogeneous electron gas. Double-numericalplus polarization (DNP)basis sets were used for all atoms. This basis set uses approximately two atomic orbitals for each occupied orbital in the free atom together with polarization functions and is comparable in quality to the standard Gaussian 6-31G** basis set. Geometry optimizations employed the BFGS quasiNewton-Raphson minimizer in Cartesian space and have a maximum allowed gradient of 0.001. No symmetry constraints were imposed on the structures. The mesh size used for evaluation of the integrals in geometry optimizations was the "MEDIUM mesh defined in the program. In most cases, the (10)Evans, J . A.; Kemmitt, R. D. W.; Kimura, B. Y.; Russell, D. R. J. Chem. SOC.,Chem. Commun. 1972,509. (11)(a) Grubbs, R. H.: Miyashita, A. J . Am. Chem. SOC.1978,100, 7416. (b) Grubbs, R. H.; Miyashita, A.; Liu, M.-I. M.; Burk, P. L. J . Am. Chem. SOC.1977,99,3863. (12)(a) Anzelm, J.;Labanowski, J. K. Density Functional Methods in Chemistry;Springer-Verlag: New York, 1991. (b) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: h'ew York, 1989. (13)(a)Norrby, P.-0.; Kolb, H. C.; Sharpless, K. B. Organometallics 1994,13, 344. (b) Branchadell, V.;Deng, L.; Ziegler, T. Organometallics 1994,13, 3115. (c) Woo, T. K.; Fan, L.; Ziegler, T. Orgunometallics 1994,13, 2252. (d) Stanton, R. V.; Merz, K. M., J r . J . Chem. Phys. 1994,100,434.(e) Sosa, C.; Andzelm, J.;Elkin, B. C.; Wimmer, E.; Dobbs, K. D.; Dixon, D. A. J . Phys. Chem. 1992,96,6630.(0 Fan, L.; Ziegler, T. J . Chem. Phys. 1991,94,6057. (g) Ziegler, T. Chem. Reu. 1991,91,651 and references therein. (14)(a)DMOL, Version 3.2;Biosym Technologies, Inc.: San Diego, CA, 1993. (b) Delley, B. J . Chem. Phys. 1990,92,508. (15)(a) Hedin, L.; Lundqvist, B. I. J . Phys. C 1971,4 , 2064. (b) Hedin, L.; Lundqvist, B. I.; Lundqvist, S. Solid State Commun. 1971, 9,537. (c) Janak, J. F.; Moruzzi, V. L.; Williams, A. R. Phys. Rev. B 1976,12,1257.
Gugelchuk and Wisner
1836 Organometallics, Vol. 14, No. 4, 1995
5
2
1
Figure 2. Optimized geometries for complexes 1 and 2.
Figure 4. Optimized geometries for nickel bis(phosphine) complexes 5 and 6. Table 1. Selected Bond Distance for Complexes 1-6
3
4
Figure 3. Optimized geometries for complexes 3 and 4.
"FINE" mesh was necessary to complete the optimizations. Nonlocal density corrections (gradient and self-consistent types)were calculated for the optimized geometries using the Becke (B88)functional for exchange16and the Lee-Yang-Parr (LYP) functional for correlation17with both the MEDIUM and FINE meshes. All other parameters were left at the default values contained in the DMOL program.
Results and Discussion Geometries. The calculated structures of the complexes shown in Figure 1 can only be compared to similar metal complexesgCJoJ8 due to a lack of structural data on the specific compounds. However, it is known that the combined sources of error in LDA-calculated structures typically give rise to a level of accuracy of 0.01-0.02 A for main group bond lengths, 0.03 A for metal-ligand distances, and 1-2" for bond angles.12b In particular, carbon-carbon and metal-ligand distances are generally too short whereas carbon-hydrogen bond lengths are too long. Figures 2-4 show the LDA-optimized geometries of complexes 1-6, and selected geometric parameters are summarized in Tables 1 and 2. The numbering scheme is given in Table 2. Overall, the predicted structures are in good agreement with available experimental data. Taking the midpoint of the C=C double bonds as the point of attachment to the Ni atom, the coordination sphere of complex 1 is tetrahedral as expected with fourcoordinate Ni(0) complexes. There is some distortion due to the small bite angle (74")of the chelating NBD. The independent Ni-C, bond lengths of the NBD ligand exhibit significant asymmetry in that the carbons syn to the phosphine are more loosely bound to the metal (16) Becke, A. D. J. Chem. Phys. 1988,88,2547. (17) Lee, C.; Yang, W.; Parr,R. G. Phys. Reo. B 1988,37, 785. (18) Eyring, M. W.; Radonovich, L. J. Orgunometullics 1985,4,1841.
bond
1
2
3
4
5
6
Ni-C2 Ni-C3 Ni-C5 Ni-C6 Ni-C8 Ni-C9 c2-c3 C5-C6 C8-C9 c4-c5 c3-c4 c I -c2 CI-C6 c4-c7 c I -c7 Ni-PI0 c3-c5 C2-C6 C8-C3 C8-CS c9-c3 c9-c5 X I -Ni X2-Ni X3-Ni Ni-PI I
2.10 2.06 2.05 2.09 2.00 2.01 1.39 1.39 1.40 1.53 1.53 1.53 1.54 1.53 1.54 2.15 2.36 2.37 2.98 3.52 3.51 3.04 I .96 I .95 1.88
2.64 1.97 1.94 2.60 2.04 1.98 1.52
2.05 2.04 2.51 1.95 1.94 2.53 1.39 1.52 1.53 1.55 1.54 1.52 1.54 1.53 1.53 2.14 2.52 2.32 3.50 2.48 3.14 1.53 I .92
2.70 1.87 3.28 3.46 1.90 2.86 1.51 1.52 1.51 1.54 1.52 1.53 1.50 1.53
2.78 1.95 3.30 3.48 1.94 2.89
1.95 2.88 2.88 1.95 2.98 2.96 1.54
1.51
1.51
2.12 2.35
2.10 2.38 1.51 2.65 2.54 2.95 1.52
1.54 1.54 1.54 1.53 1.53 1.51 1.52 2.12 2.32 2.16 1.53 2.44 2.43 1.53
2.12
2.12
1.51
1.39 1.52 1.53 1.52 1.53 1.53 1.50 2.13 2.14 1.51 4.00 3.23 3.73 2.81
1.51
2.58 2.53 2.88 1.52
1.51
1.52 1.52 1.53 1.53 1.52 1.51
1.53
1.55
1.88
XI = centroid of C2-C3 double bond, X2 = centroid of C5-C6 double bond, and X3 = centroid of C8-C9 double bond. All values given in angstroms. "
than the corresponding anti carbons (A % 0.035 A). This is reminiscent of the trans influence seen in square planar complexes. Approximate C2" symmetry is observed for the NBD ligand. Strong back-donation from the metal is reflected in the lengthening of the C=C double bonds (1.39A) of the complex compared to free NBD (1.333A).19 The allylic C-C single-bond distances (1.53-1.54 A) are slightly longer than those found in free NBD (1.522A). This is consistent with crystallographic data of known metal-NBD complexes and is thought to reflect a perturbation of the o framework upon complexation.l8 The coordinated ethylene is symmetrically bound and shows the normal C=C bond lengthening. In comparison to the NBD ligand, the NiC, distances of the ethylene ligand are much shorter (average A 0.08 A). Complex 2 has a distorted square planar geometry about the nickel(I1) center. The rigid bidentate nortricyclene ligand has a bite angle of 66", otherwise the bond angles of the nickelacyclobutane moiety are close (19)(a) Wilcox, C. F., Jr.; Winstein, S.; McMillan, W. G. J. Am. Chem. SOC.1960,82,5450. (b) Yokozeki, A.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1971,44,2356.
.
Organometallics, Vol. 14, No. 4, 1995 1837
Density Functional Study of Diels-Alder Intermediates
Table 2. Selected Bond Anglee for Complexes 1-6
angle C2-Ni-C3 C5-Ni-C6 C8-Ni-C9 C2 -Ni -C6 C3-Ni-C5 C2-Ni-C5 C3-Ni-C6 C3-Ni-C8 C5-Ni-C9 C3-Ni-C9 C5-Ni-C8 Ni-C2-C3 Ni-C3-C2 Ni-C5-C6 Ni-C6-C5 Ni-C2-C1 Ni-C6-C I Ni-C3-C4 Ni-C5 -C4 Ni-C8-C9 XI-Ni-X2 XI-Ni-PI0 X2-Ni-PI0 X3-Nl-C3 Xl-Ni-C6
4
3
2
1 1
2
3
4
5
6
39 39 41 69 70 83 83 94 97 119 121 69 72 72 69 95 95 94 95 70 74 I15 114 107 75
35 35 40 34 66 60 60 172 91 142 108 48 97 97 48 121 I22 93 94 72
40 37 37 71 66 82 81 123 35 86 66 70 71 51 92 94 97 101 83 93
32 26 29 25 45 47 42 86 28 72 50 42 I06 84 70 145 102 126 67 113
31 26 29 25 45 46 42 86 28 72 50 42 107 84 71 I45 I04 123 68 I13
30 30 30 67 47 65 65 30 30 49 49 111
39 40 I10 94 94 101
102 74
111
161
75
angle Ni-C9-C8 c 1-c2-c3 C I -C6-C5 c2-c3-c4 C4-C5-C6 C2-CI-C6 c3-c4-c5 C5-C9-C8 C3-C8-C9 C3-Ni-PI0 C5 -Ni-PI0 C6-Ni-C8 C6-Ni-Pl0 C8-Ni-P10 C3-Ni-PI C8-Ni-PI PIO-Ni-P1 C2-Ni-PI0 C2-Ni-P1 C6-Ni-P1 XI-Ni-X3 X2-Ni-X3 X3-Ni-PI0 X3-Ni-C5 Xl-Ni-C8
6
5 1
2
3
4
5
6
69 I06 I06 I06 106 101 101 98 100 133 I32 160 96
50 104 I07 108 98 98 109 108 64 I04 141 80 174 94
38 I07 I07 97 97 60
96
93
116
38 I08 I06 96 96 60 102 113 86 I69 I25 74 131 84 92 171 98 148 77 98
76 I 04 104 I02 102 90 98 I05
101
67 108 108 98 98 60 89 94 69 92 153 I13 I20 91
I
100
I13 85 I75 131 74 I34 90
I 1
I I I
I45
104
97 100
78 163 87 142 I17 98 98 I63 96
124 I27 101 110
108
104 IO0 138
" X I = centroid of C2-C3 double bond, X2 = centroid of C5-C6 double bond, X3 = centroid of C8-C9 double bond. All angles given in degrees.
to 90". A stronger trans influence for ethylene over phosphine is apparent with the Ni-C, bond trans to ethylene being longer by 0.03 A than its counterpart cis t o ethylene and is consistent with the known ordering of trans directors.20 The individual Ni-C, bond lengths vary widely (A = 0.06 A), which results in a slip distortion of the ethylene ligand such that the midpoint of the C=C bond lies well out of the plane defined by Ni and the other ligands. Also, the alkene conformation has a 20" twist from perpendicular with respect to the square plane, most likely t o reduce steric interactions within the complex. There is a close contact (2.14 A) between the C5 hydrogen of the nortricyclene and one of the C9 hydrogens in the optimized structure. All other features appear normal. A distorted square planar geometry is also found about the Ni(I1) center in the n-homoallylic complex 3. There is clear departure from local C, symmetry in the norbornenyl moiety, the most prominent being that the C2-Cl-C6 bond angle (98") is much more acute than the C3-C4-C5 angle (109"). Concerning the predicted Ni-C bond distances of the n-homoallylic system (1.95 and 2.04-2.05 A), the Ni-C6 bond is significantly shorter and most likely a result of the trans influence in combination with the geometrical constraints of the ligand. It is clear that the C6 carbon retains substantial sp2 character. The dihedral angle Hl-Cl-C6-H6 (6.6") is comparable to that found in the NBD complex (20) Crabtree, R. H. The Organometallic Chemistry ofthe Transition Metals, 2nd ed.; John Wiley & Sons, Inc.: New York, 1994; p 6.
(average 2.4") but very different from that expected for sp3 character, as seen in the H4-C4-C5-H5 angle (61.4"). Due to the tridentate nature of the ligand, the nickelacyclopentane ring resulting from insertion of the ethylene fragment adopts an envelope conformation with the nickel atom being the out-of-plane atom. This gives rise to an eclipsed conformation about the C5C9 bond. Complexes 4 and S differ with respect to coordination number. Both complexes exhibit square planar geometry about the nickel(I1) atom. The only significant differences were found in the Ni-C bond distances which are shorter in the 14-electron complex compared t o the 16electron complex. Most notable is the lengthening of the Ni-C3 single bond by 0.08 8, upon coordination of the second phosphine (cf. Table 1). In contrast t o complex 3, the larger six-ring metallocycles adopt a staggered conformation about the C5-C9 bond. However, this conformation produces very close contacts between the exo-C8 and the C4 bridgehead hydrogens (2.06-2.15 A). The calculated structure of complex 6 has nearly perfect C, symmetry. Coordination around the metal is slightly distorted from a square planar arrangement. Bond angles about the nickelacyclobutane moiety are identical to those in complex 2. Relative Energies. While the local density approximation has been quite successful in predicting molecular structures, nonlocal exchangelcorrelation corrections to the total energy are crucial for the quantitative prediction of reaction energetics. LDA
Gugelchuk and Wisner
1838 Organometallics, Vol. 14, No. 4, 1995 Table 3. Comparison of Relative Energies as Functions of Theory Level and Mesh Size" levelhesh JMWN JMWF JMW-B88eN JMW-B88e/F LYPe-B88eN LYPe-B88e/F JMW-B88mN JMW-B88m/F LYPm-B88m/M LYPm-B88m/F
1 +PH3 2+PH3 3 + P H 3 4+PH3 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
27.6 27.6 26.2 26.0 -26.9 26.6 18.7 13.0 23.3 18.5
10.3 10.2 18.1
18.1 14.5 16.0 14.9 9.3 16.0 -15.0
12.0 11.9 13.9 13.8 10.4 13.3 -12.6 5.7 1.8
5
6
-23.0 -23.2 10.6 10.4 -0.1 2.2
-38.9 -39.1 -4.0 -4.2 -10.8 -12.4 -28.8 -74.2 -22.6 -41.1
-72.0 -14.2 -35.6
JMW = Hedin-LundqvidJanak-Moruzzi- Williams local correlation. B88e = Becke nonlocal exchange gradient correction. B88m = Becke nonlocal exchange self-consistent correction. LYPe = Lee-Yang-Parr nonlocal correlation gradient correction. LYPm = Lee-Yang-Parr nonlocal correlation self-consistent correction. M = medium mesh. F = fine mesh. Relative energies are given in kcal/mol.
reaction energies are grossly overestimated, whereas nonlocal corrections provide reaction energies that approach the average error of Hartree-Fock methods ( x 7 kcal/mol).12bSince the magnitude of the exchange energy is significantly larger than that of the correlation energy, the usual practice is to treat corrections to the local exchange and correlation energies separately. These nonlocal corrections can be applied by a perturbative approach in which LDA densities are used to evaluate the gradient terms or by a selfconsistent approach in which nonlocal densities are generated. The self-consistent method gives lower calculated total energies compared t o the perturbative method, but the difference is reported to be less than 1 kcal/mol for small molecules.12cAnother variable to be considered is the effect of the integration mesh size on the total energy. To gain a better understanding of how these factors influence the predicted reaction energies and the electronic structures (as reflected in the dipole moments and Mulliken charges), we carried out a systematic examination of the calculated single-point energies using the LDA-optimized geometries of complexes 1-6. Calculated total energies for each complex are provided in the supplementary material. The resulting relative energies are summarized in Table 3. In general, local density and nonlocal perturbative energies are rather insensitive to the size of the integration mesh. The average energy difference due to mesh size was less than 1 kcal/mol. However, there were substantial differences in the nonlocal energies obtained by the self-consistent approach upon changing from a MEDIUM to a FINE mesh. Using the FINE integration mesh, the calculated energies were on the order of 30 and 50 kcal/mol lower for the 112- and 130-electron systems, respectively. The magnitude of this energy difference was greater as the number of electrons increased. Obviously, the greater numerical precision of the FINE mesh plays an important role in calculating the self-consistent nonlocal energies of these transition metal complexes. Of note, there is virtually no difference in the predicted total energies of the PH3 molecule (18 electrons) with respect to mesh size (cf. Table 4). In two cases, SCF convergence with the B88 functional could not be achieved using the MEDIUM mesh even after several attempts with decreased charge and spin density mixing coefficients and performing charge smearing at the Fermi level.
Table 4. LYPm-BSSm/F Mulliken Charges and Dipole Moments for Complexes 1-6 atom
c1 c2 c3 c4 c5 C6 c7 C8
c9 Ni P10 P11 P (D)
1
2
3
4
5
6
-0.397 -0.373 -0.3 10 -0.399 -0.330 -0.364 -0.642 -0.647 -0.625 -0.039 -0.3 10
-0.289 -0.270 -0.531 -0.304 -0.48 I -0.279 -0.661 -0.594 -0.634 -0.065 -0.2 18
-0.359 -0.345 -0.345 -0.398 -0.270 -0.441 -0.617 -0.782 -0.606 -0.05 1 -0.278
-0.302 -0.281 -0.541 -0.332 -0.304 -0.294 -0.634 -0.714 -0.598 -0.029 -0.291
1.063
1.895
1.712
-0.3 16 -0.207 -0.560 -0.319 -0.298 -0.308 -0.622 -0.750 -0.594 -0.210 -0.210 -0.235 2.660
-0.277 -0.49 I -0.317 -0.350 -0.309 -0.499 -0.633 -0.604 -0.586 -0.209 -0.250 -0.226 2.178
1.382
When we compared the energetic results based on the nonlocal method used at a given mesh size, the SCF nonlocal energies of the organonickel complexes were significantly lower (in the range of 30-180 kcal/mol) than those obtained by the perturbative approach. This is much larger than the 1 kcal/mol typically cited for small systems. For PH3, the SCF nonlocal energies were also lower by 3-5 kcal/mol. In addition, with a FINE mesh these differences were much larger for the 130-electron complexes (172-184 kcal/mol) than the 112-electron species (27-32 kcal/mol). There was no apparent trend in the relative magnitude of the differences with a MEDIUM integration mesh. A closer look at possible explanations, particularly with regard to errors due to truncation in the numerical analysis and the implementation of the LYP functional in the DMOL program,21is warranted. We also find the total calculated charge densities are about an order of magnitude less accurate for the nickel complexes compared to the simple phosphine. To illustrate, the MEDIUM mesh at the LYP-B88/SCF level generated 44 680 integration points for complex 1 and a model charge density of 111.999 771 electrons (error: 3 x The FINE mesh generated 88 350 integration points and a slightly more accurate charge density of 111.999 910 electrons In the phosphine case, either mesh (error: 9 x size gave an error in the calculated charge density of about 3 x There were only modest changes in the Mulliken atomic charges and dipole moments of the complexes as a result of changing the theory level or mesh size. A summary of the calculated charges and dipole moments for all complexes at the LYPm-B88m/F level is given in Table 4. A complete tabulation of these properties as a function of level is given in the supplementary material. For each complex, the nonlocal SCF methods (FINE mesh) gave the lowest dipole moments. In a relative sense, the predicted charge densities at the nickel atom are consistent with conventional descriptions of metalligand bonding. Complex 1, with three strongly backbonding n-alkene ligands, has only a slight excess of electron density at the metal, whereas the metal in complexes 2 and 3 (only one n-alkene ligand) is more electron-rich. The bidphosphine) complexes 6 and 6 have much more electron-rich nickel environments. All nonlocal calculations gave more or less the same qualitative energy orderings among the various species (summarized in Figure 5). In the SCF approach, the (21)Release notes to this version of DMOL caution that the LYP functional has not been properly tested.
Density Functional Study of Diels-Alder Intermediates
Organometallics, Vol. 14,No. 4, 1995 1839
-2+PH3 -3+PH3 1 3 0 4 . PH3 - 10
E 3d w
-
+pH3 -12 ( q 6
0 1 + PH3
2 (-13) -4+PH3
L2
-36 (-72) -5 -41 (-74)6
-
SCF method
Gradient method
Figure 5. Summary of LYP-B88/Frelative energies for all organonickel species. The corresponding JWM-B88/F energies are given in parentheses.
addition of nonlocal correlation corrections had a large influence on the relative energies compared to using nonlocal exchange corrections alone, but was of minor importance in the perturbative approach. The calculations indicate that commonly proposed intermediates 2 and 3 are formed endothermically from complex 1. A more energetically favorable path would be the direct formation of 5 or 6. The entropy change would be expected to be negative in all these transformations due to losses of rotational and/or translational degrees of freedom. It has been estimated that, for bimolecular complexations, the A S term is less than or equal to -36 caVmol K.22 This would still suggest that the direct formation of 5 or 6 from 1 phosphine is energetically accessible. We are currently examining the influence of substituents on the stabilities of these intermediates, particularly in the case of 5 and 6,as these would be the final intermediates before the irreversible reductive elimination step. Detemination of substituent effects is necessary to provide further insight into the control of regiochemistry. Experimental studies have revealed a dominant electronic influence on the regiochemical o ~ t c o m e .With ~ regard to stereoselectivity, it is obvious that, for steric reasons, the exo orientation of an olefin substituent would be more favorable in any of the complexes. Preliminary molecular mechanics calculations using a modified MM2 force field23have indicated that complexes 3, 4, and 5 give good quantitative
+
(22) Page, M. I. In Enzyme Mechanisms; Page, M. I., Williams, A., Eds.; The Royal Society of Chemistry: Burlington House, London, 1987; p 6.
agreement with the observed exo stereoselectivity, but more detailad studies are needed to test their viability as predictive models for this chemistry.
Conclusions We have presented the results of a DFT study on some possible intermediates in the nickel-catalyzed homoDiels-Alder reaction. It would be preferable to compare the relevant transition-state energies, and we are currently carring out this investigation. Reports on DFT transition-state calculations are relatively few at present, and more studies are needed to test the reliability of the method. Work is also in progress on determining the influence of substituents on the relative energies of these intermediates using a combined electronic structure/molecular mechanics approach and will be reported in due course.
Acknowledgment. We are grateful to the Natural Sciences and Engineering Research Council (NSERC) Canada for financial support. We also thank Professor Mark Lautens for helpful discussions. SupplementaryMaterial Available: Tables of calculated total energies, Mulliken charges, and dipole moments as functions of level of theory and mesh size for complexes 1-6 (4 pages). Ordering information is given on any current masthead page. OM940900M (23) Gugelchuk, M. M.; Houk, K. N. J . A m . Chem. SOC.1994, 116, 330.
