J . Phys. Chem. 1984, 88, 1513-1517
3eH2
Figure 3. Hidden-line view of surface described in Figure 2.
particular case, it is likely that the problem arises because the surface is quite flat along the RBeH2coordinate in the initial phase of the uphill Be H2 walk. Path D represents a downhill walk from the transition state to the linear product BeH2. This walk might, in principle, have been expected to possibly dissociate to Be H H. However, this is improbable because the algorithm is instructed to move downhill in all directions. Once the neighborhood of the stream bifurcation is reached, the Be H H products lie uphill.
+
+ +
+ +
-
Finally, path E of Figure 1 describes the downhill motion from Be 2H to Be H2, which is, of course, nothing but the 2H Hz recombination reaction. This path does not go through a transition state because, as was the case in walk A, it describes a simple bond formation reaction, not a concerted breaking-formed reaction. At each point on the above reaction paths, the information available includes the electronic energy and the forces and curvatures along and perpendicular to the reaction path. This local information can be used to construct an approximation to the C, potential energy surface (Figures 2 and 3) from which one can obtain a clear picture of the energetics of these reactions. The energetic and structural information needed to characterize the various reactant and transition-state species is summarized in Table 11. In summary, we see that the potential energy surface walking algorithm of ref 7 can reliably use only local force and curvature data to generate reaction paths, find transition states, and locate various product species. The extension of this method to permit more efficient location of reaction path bifurcations and to allow its use within dynamical studies cast in the language of ref 9 is currently under investigation.
+
Be t 2H
1513
+
Acknowledgment. We acknowledge the financial support of the National Science Foundation (Grant No. 8206845) and the donors of the Petroleum Research Fund, administered by the American Chemical Society. Registry No. Be, 7440-41-7;H,, 1333-74-0; BeH,, 7787-52-2
A Theoretical Study of Monosubstituted Allyl Cations M. H. Lien Department of Chemistry, National Chung-Hsing University, Taichung, Taiwan 400, Republic of China
and A. C . Hopkinson* Department of Chemistry, York University, Downsview, Ontario, Canada M3J 1 P3 (Received: August 12, 1983)
Ab initio molecular orbital calculations are reported for trans 1-X-allyl, cis 1-X-allyl, 2-X-allyl, and a-X-cyclopropylcations, where X is H, CHj, “2, OH, F, NC, and CN. Geometries were optimized by using a 3-21G basis set, and single-point calculations were done at the 6-31G* level. The stabilizing effects of the substituents are compared with the effect of the same substituents in the methyl cations. Substituents at the 2-position are found to have little effect on the barrier to rotation of a CH2 group. Substituents at the 1-position raise the barrier to rotation of the CH, group while the barrier to rotation of the CHX group is lower than in the allyl cation.
Introduction Allyl cations were first postulated as reaction intermediates and subsequently were directly observed in strong acid solutions.’ The parent allyl cation is a well-characterized species in the gas phase,24 and recently the 2-hydroxyallyl cation has been shown to be a long-lived species in the gas phase.5 ~
(1) For a review, see N. C. Deno in
~
~~~~~
‘‘Carbonium Ions’’, Vol 11, G.A. Olah
and P.v. R. Schleyer Eds. Wiley-Interscience, New York, 1972, Chapter 18. (2) D. H. Aue and M. T. Bowers in “Gas Phase Ion Chemistry”, Vol. 11, M. T. Bowers Ed., Academic Press, New York, 1979, pp 1-52. (3) F. P. Lowing, Can. J . Chem., 49, 356 (1971); 50, 3973 (1972). (4) M. T. Bowers, L. Shuying, P. Kemper, R. Stradling, H. Webb, D. H. Aue, J. R. Gilbert, and K. R. Jennings, J. Am. Chem. SOC.,102,4830 (1980). (5) M. W. E. M. van Tilborg, R. van Doorn, and N. M. M. Nibbering, J. Am. Chem. Soc., 101, 7617 (1979).
The parent allyl cation is the simplest r-delocalized carbenium ion and consequently has been the subject of many theoretical There have also been two minimal STO-3G basis set studies on substituted allyl cations, one studying the relative energies of 2-substituted allyl cations and the isomeric a-substituted cyclopropyl cations13 and the other studying the effect ( 6 ) D. T. Clark and D. R. Armstrong, J . Chem. SOC.D , 850 (1969). (7) S. D.Peyerimhoff and R. J. Buenker, J. Chem. Phys., 51,2528 (1969). ( 8 ) N. C. Baird, Tetrahedron, 28, 2355 (1972). (9) H. Kollmar and H. 0. Smith, Theor. Chim. Acta, 20, 65 (1971). (10) L. Radom, P. C. Hariharan, J. A. Pople, and P. v. R. Schleyer, J . Am. Chem. SOC.,95, 6531 (1973). (1 1) P. Merlet, S. D. Peyerimhoff, R. J. Buenker, and S . Shih, J . Am. Chem. SOC.,96, 959 (1974). (12) K. Raghavachari, R. A. Whiteside, J. A. Pople, and P. v. R. Schleyer, J. Am. Chem. SOC.,103, 5649 (1981).
0022-365418412088- 15 13$01.SO10 0 1984 American Chemical Society
1514 The Journal of Physical Chemistry, Vol. 88, No. 8, 1984
Lien and Hopkinson
of methyl substituents on the structure, the barriers to rotation, and the stability of the allyl cation.14 The effect of substituents on the stability of carbenium ions has also been examined for methyl cations CH2X+,15ethyl cations C2H4X+,15 a-substituted vinyl cations H2C=CX+,l5 and propargyl cations H2C=C= CXfI6 (X = H, CH,, NH,, OH, and F). We now report an analogous study on the 1-X-allyl and 2-X-allyl cations. Recently there has been considerable e ~ p e r i m e n t a l ' ~and - ~ ~t h e o r e t i ~ a l ~ ~ - ~ ~ interest in carbenium ions containing a destabilizing a-substituent which is both u- and .rr-electronwithdrawing (X = CHO, COOR, and CN). Also, carbenium ions containing an a-isocyano group have been compared with the isomeric cyano-substituted carbenium ion^.^^,^ We have therefore included the cyano and isccyano substituents in this study of monosubstituted allyl cations.
H
20 -
3c
3b
Methods
3d -
Standard closed-shell self-consistent-field ab initio calculations were carried out with a version of the MONSTERGAUSS program.25 Geometry optimizations using gradient optimization procedure^^^^^^ were performed with a 3-21G basis set?8 In all cases the criterion for optimization was that the norm of the gradient vector was less than 5 X lo4 mdyn at convergence, a condition which generally gives bond lengths and angles within 0.0001 A and O.0lo, respectively, of the true optimum value. The 3-21G optimized structures were then used for single-point calculations at the 6-31G* level.2g Throughout the text 3-21G//3-21G means a 3-21G level calculation at the 3-21G optimized geometry and 6-31G*//3-21G means a 6-31G* level calculation at the 3-21G optimized geometry.
Results and Discussion
N
Structural Details. The 3-21G optimized structures for the allyl cations and the isomeric cyclopropyl cations are given in Figure 1. All structural parameters were optimized, but for the sake of clarity bond lengths and bond angles are given only for bonds including two "heavy" atoms. In preliminary studies at the STO-3G level all the substituents were found to lie in the plane defined by the three carbon atoms, and for substituents CH3, NH2, and O H the preferred rotamers were found to have one of the hydrogens on the substituent in this plane. Introduction of a substituent into the 2-position of an allyl cation has little effect on the carbon-carbon bond lengths and produces a small decrease in Lccc (Figure 1, structures 2c-7c). However,
60 -
N
6b -
C
76 7c 7b Figure 1. Geometries of allyl cations and or-cyclopropyl cations as optimized at the 3-21G level. Bond lengths are in angstroms, and bond angles are in degrees.
70
(13) L. Radom, J. A. Pople, and P. v. R. Schleyer, J . Am. Chem. Soc., 95, 8193 (1973). (14) H. Mayr, W. Forner, and P. v. R. Schleyer, J . Am. Chem. Soc., 101, 6032 (1979). (15) Y. Apeloig, P. v. R. Schleyer, and J. A. Pople, J . Am. Chem. Soc., 99, 1291 (1977). (16) M. Dorado, 0. Mo, and M. Yinez, J . Am. Chem. Soc., 102, 947 (19x0) ,---,. (17) P. G. Gassman and J. J. Talky, J. Am. Chem. Soc., 102, 1214 (1980); 102, 4138 (1980). (18) X.Craary and C. C. Geiger, J . Am. Chem. Soc., 104, (1982). (19) G. A. Olah, G. K. S. Prakash, and M. J. Arvanaahi, - J . Am. Chem. Sac., 102, 6640 (1980). (20) A. C. Hopkinson, L. H. Dao, P. Duperrouzel, M. Maleki, and E. Lee-Ruff, J. Chem. SOC.,Chem. Commun., 727 (1983). (21) D. A. Dixon, P. A. Charlier, and P. G. Gassman, J . Am. Chem. Soc., 102, 3957 (1980). (22) M. Paddon-Row, C. Santiago, and K. N. Houk, J . Am. Chem. SOC., 102, 6561 (1980). (23) J . B. Moffat, I n f . J . Quantum. Chem., 19, 771 (1981). (24) A. C. Hopkinson, M. H. Lien, and M. A. McKinney, J . Mol. Struct., Theochem, 105, 37 (1983). (25) Program MONSTERGAUSS, M. R. Pet;rson and R. A. Poirier, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1Al. (26) H. B. Schlegel, Ph.D. Thesis, Queens University, 1975. (27) W. C. Davidon and L. Nazareth, Technical Memos 303 and 306, 1977, Applied Mathematics Division, Argonne National Laboratories, Argonne, IL 60439. (28) J. S. Binkley, J. A. Pople, and W. J. Hehre, J . Am. Chem. Soc., 102, 939 (1980). (29) P. C. Hariharan and J. A Pople, Theor. Chim Acta, 28, 213 (1973).
a substituent in the 1-position results in an increase in the C1-C2 bond length (the largest increase is 0.06 when X = N H ) and a decrease in the C& distance (largest decrease is 0.07 for X = NH2) showing canonical structure 8a" to be an important contributor. The 1-isomer exists in cis (2b-7b) and trans (2a-7a)
a
k,
I
8a
A
A 8a' H
H
H-N
I
+I
\/CNC/H
I
H
I
H
8a"
forms, but the bond lengths for both isomers are similar. The only structural parameter to show appreciable difference is Lee-,
The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 1515
Monosubstituted Allyl Cations TABLE I: Total Energies (hartrees) and Relative Energies (kcal mol-' ) of Allyl and a-Substituted Cyclopropyl Cations la Id
2a 2b 2c 2d 3a 3b
3c 3d 4a 4b
4c 4d
Sa 5b
5c 5d 6a 6b 6c 6d
7a 7b 7c 7d
3-21G//3-21G
b
6-31G*//3-21G
c
-115.542 14 -115.46705 - 154.385 72 - 154.380 90 -154.367 96 - 154.323 85 - 170.346 69 - 170.340 0 8 -170.26761 -170.303 30 -190,017 35 -190.017 98 -189.971 61 - 189.962 I 2 -213.85828 -213.86033 -213.840 87 -213.785 5 3 -206.735 60 -206.734 37 -206.73040 -206.668 79 -206.731 81 -206.729 86 -206.708 89 -206.67295
0.0 47.1 0.0 3.0 11.1 35.8 0.0 4.1 49.6 27.2 0.0 -0.4 28.7 34.7 0.0 -1.3 10.9 45.7 0.0 0.8 3.3 41.9 0.0 1.2 14.4 36.9
-1 16.193 13 -116.131 77 -155.25299 -155.247 71 -155.235 00 - 155.203 78 -171.296 79 - 171.288 62 - 17 1.220 45 -171.257 16 -191.085 04 -191.08276 -191.037 96 -191.035 78 -215.044 96 -215.04359 -215.023 01 -214.981 03 -207.899 27 -207.898 06 -207.895 52 -207.840 34 -207.895 55 -207.891 93 -207.873 52 -207.841 16
0.0 38.5a 0.0 3.3 11.3 30.9 0.0 5.1 47.9 24.5
0.0 1.4 29.6 30.9 0.0 0.9 13.8 40.1 0.0 0.8 2.4 37.0
0.0 2.3 13.8 34.1
a 6-31G**//6-31G* calculations given a relative energy of 37.8 kcal mol-' (K. Raghavachari, R. A. Whiteside, J . A. Pople, and P. v. R. Schleyer,J. Am. Chem. Soc., 1 0 3 , 5 6 4 9 (1981)).
b
Energy relative to
'w.c Energy relative to
-,'
which is considerably larger in the cis isomers due to in-plane steric interactions. In valence-bond terminology the charge on the allyl cation is located only on the terminal carbons, and a a-donating substituent
i
H
I
H\;/C\/
H\,/C\i/H
I
H
I
H
I
H
I
H
should therefore have a powerful stabilizing effect when located at the 1-positionbut be ineffective at the 2-position. The structural effects produced by the 3-21G optimization support this conclusion. An additional method of assessing the interaction between the substituent, X,and the hydrocarbon fragment is to compare the C-X bond lengths in the 1-allyl and 2-allyl cations. The C-X bond lengths in all the 1-substituted allyl cations are all much shorter than in the 2-allyl cations. Comparing the trans isomers with the corresponding 2-allyl cations, A(C-X) for the different substituents is as follows: CH3, 0.046 A; NH2, 0.076 A; OH, 0.077 A; F, 0.050 A; C N 0.029 A; and NC 0.049 A. Hence, using only these structural changes as a criterion, the powerful a-donating a-amino and a-hydroxy groups interact most strongly with the allyl cation and the a-withdrawing cyano group interacts most weakly. Relative Energies. For all substituents at the 6-3 lG*//3-21G level the trans 1-substituted allyl cations (2a-7a) have the lowest energy, with their cis isomers (2b-7b) only 0.8-5.9 kcal mol-' higher (Table I). The 2-substituted allyl cations are considerably higher in energy, with the largest difference being for the ions containing the amino group. This substituent is a o-acceptor and a a-donor, and the latter property results in large stabilizations in a-amino carbenium i o n ~ . ' ~InJ ~the allyl cation the charge is formally located on the terminal carbon atoms, and the amino group is therefore strongly stabilizing a t the 1-position but has little effect at the 2-position. In the cyclopropyl cation much of the charge (+0.262 compared with -0.244 for the other carbons) is localized at the carbon formally carrying the charge, and a a-donor attached to this
Scheme I X
X
I
k
H
9c
H
9b
9c carbon is strongly stabilizing. Of the substituents considered here, the a-amino group is the strongest a-donor and the a-aminocyclopropyl cation is lower in energy than the 2-aminoallyl cation by 23.4 kcal mol-' at the 6-31G*//3-21G level. Previous minimal basis set calculation^^^ have shown the a-aminocyclopropyl cation to be the more stable, and both the a-dimethylamino- and amethylaminocyclopropyl cations are sufficiently stable to have been characterized by NMR.30-32 The hydroxy group also stabilizes the a-cyclopropyl cation by a-donation, but to a lesser extent than the amino group. Consequently, the a-hydroxycyclopropyl and 2-hydroxyallyl cations are of similar energy with the latter lower in energy by 1.3 kcal mol-' at the 6-31G*//3-21G level. Experimentally, the a-methoxycyclopropyl cation appears to be a stable intermediate in substitution reactions in soluti011,3~and there is convincing evidence for the independent existence of both the a-methoxycyclopropyl and 2-methoxyallyl cations in the gas phase.34 Stabilization by Substituents. The stabilizing effect of substituents is often assessed by using isodesmic reactions. Here we have used three different hypothetical reactions to estimate substituent effects in 2-substituted allyl cations (see eq 1, 2, and 3 in Table 11). A positive energy for these equations indicates stabilization of the reactants by the substituent. Equation 1 is analogous to those used previously in assessing the effect of methyl substitution in allyl cations.14 Equation 2 is a similar reaction, but here the substituent is on a secondary carbon in both the reactant and the product and there is the same number of methyl groups on both sides of the equation. The results from reaction 2 are generally lower than those from reaction 1, but there is the same obvious trend, with only the methyl and amino groups being slightly stabilizing and all other substituents being destabilizing. The hydroxy group usually acts as a a-donor in carbenium ions and is strongly stabilizing in a-hydroxy-substituted carbenium ions.l5 In the 2-hydroxyallyl cation, however, there is little adonation, as shown by the relatively long C-0 bond (1.357 8, compared with 1.382 A in (E)-3-hydroxy-2-butene) and the high a-population on the oxygen atom (1.903e, compared with 1.728e in the trans 1-hydroxyallyl cation). Addition of a hydride ion to a 2-substituted allyl cation generates a 1,l-disubstituted ethylene, and eq 3 represents a hydride transfer reaction similar to those used in assessing substituent effects in saturated carbenium ions.14 However, this method of analysis is complicated by the interaction between the substituents in the 1,l-disubstituted ethylenes.35 Despite this problem the energies for reaction 3 are similar to those for reaction 2, except (30) E. Jongejan, W. J. M. van Tilborg, Ch. H. V. Dusseau, H. Steinberg, and Th. J. deBoer, Tetrahedron Len., 2359 (1972). (31) E. Jongejan, H. Steinberg, and Th. J. deBoer, Tetrahedron Lett., 397 (1976). . (32) E. Jongejan, H. Steinberg, and Th. J. deBoer, Recl. Trau. Chim. Paw-Bas. 98. 66 (1979). '(33) J.' R.~vander Vkcht, H. Steinberg, and Th. J. deBoer, Recl. Trau. Chim. Pays-Bas, 96, 313 (1977). (34) M. W. E. M. van Tilborg, R. van Doorn, and N. M. M. Nibbering, J. Am. Chem. Soc., 101, 7617 (1979). (35) M. H. Whangbo, D. J. Mitchell, and S. Wolfe, J . Am. Chem. SOC., 100, 3698 (1978).
1516 The Journal of Physical Chemistry, Vol. 88, No. 8, 1984
Lien and Hopkinson
TABLE 11: Evaluation of Substituent Effects Using 6-31G*//3-21G CalculationsUtb CH,
2"
OH
F
CN
NC
2-allyl cations X
A (2) A
(1)
- 6+
+
CH3CH3
+
CH3CH2CH3
-
X
CH3CH2X
4.5 (4.1)
6.2 (9.6)
-0.4 (0.3)
-11.0 (-10.2)
-17.4 (-18.3)
-14.5 (-12.9)
+
4.1 (2.9)
7.2 (7.3)
-3.4 (-3.5)
-15.5 (-15.2)
-19.9 (-19.5)
-16.4 (-15.4)
1.7 (1.7)
-0.7 (-0.9)
-9.3 (-9.9)
-15.8 (-17.1)
-21.0 (-19.6)
-17.5 (-16.8)
15.8 (15.2)
54.1 (59.1)
29.2 (29.0)
2.8 (0.7)
-17.3 (-15.0)
-0.7 (1.5)
13.2 (13.3)
50.1 (51.9)
24.3 (23.0)
2.4 (-3.3)
-20.2 (-17.7)
-3.0 (-1.4)
12.5 (12.2)
49.0 (55.1)
27.8 (29.4)
1.9 (2.0)
-18.1 (-15.8)
-3.0 (0.3)
11.5 (11.8)
45.3 (47.9)
23.4 (23.5)
1.9 (-2.0)
-20.8 (-18.5)
-5.4 (-3.2)
28.9 (28.9)
87.4 (93.5)
53.4 (52.6)
14.2 (8.7)
-13.0 (-8.5)
15.4 (18.4)
x
4+ trans I-allyl cations
(4)
CH~CH~
cis 1-allyl cations
(6)
-
wX +
9+
+
A '+*
-+
CH~CH~
+
CH~CHXCH~
OH > CH3 r= N C = F.
Summary The trans 1-substituted isomers are the lowest energy allyl cations, and for all substituents except when X = NH2, the 2X-allyl cations are lower in energy than the a-X-cyclopropyl cations. Substituents at the 2-position range from weakly stabilizing (X = CH3 and NH,) to more strongly destabilizing (X = CN). The CH3, NH2, and OH substituents at the 1-position are strongly stabilizing and are roughly half as effective as the same substituents in the methyl cation. The F and -NC groups have little effect on the stability of allyl cations, but the - C N group at the 1-position is more destabilizing than in the methyl cation. In all the allyl cations structural variations tend to be large when the substituent is strongly stabilizing, and the structures of the ions are easily understood in terms of stabilization through adonation. The barriers to rotation about carbon-carbon bonds in the 2-X-allyl cations are similar to those in the parent allyl cation, but when X is NH2 and OH, the perpendicular ions collapse into cyclic ions in which the charge is formally on the heteroatom in a three-membered ring. The 2-aminoallyl cation is higher in energy than both the a-aminocyclopropyl cation and protonated methyleneaziridine, 10, but only derivatives of the lowest energy species, the a-aminocyclopropyl cation, have been observed experimentally. The 2-hydroxyallyl and 2-hydroxycyclopropyl cations are similar in energy and are considerably lower than 0-protonated allene oxide, 11. The experimental observation that both the 1-methoxycyclopropyl and 2-methoxyallyl cations exist independently in the gas phase is consistent with the molecular orbital results. The barriers to rotation in the 1-X-allyl cations are larger for the CH2 group and smaller for the CHX group than in the parent allyl cation. These deviations result from a decrease and an increase, respectively, in delocalization of the charge onto the substituent in the perpendicular cation. Acknowledgment. We thank the Natural Science and Engineering Research Council of Canada for financial support and York University Computer Centre for generous allotments of computer time. Registry No. la, 1724-44-3; Id, 1724-43-2; 2a/2b, 17171-50-5; 2c, 17542-17-5; 2d, 2941 8-02-8; 3a/3b, 62399-27-3; 3c, 51229-07-3; 3d, 88945-61-3; 4a/4b, 57344-16-8; 4c, 51229-08-4; 4d, 88945-62-4; 5a/5b, 64710-13-0; 5c, 51229-09-5; 5d, 51229-12-0; 6a/6b, 88945-63-5; 6c, 88945-64-6; 6d, 88945-65-7; 7a/7b, 88945-66-8; 7c, 88945-67-9; 7d, 88945-68-0.
