590 I
Molecular Orbital Theory of the Electronic Structure of Molecules. 35. ,&Substituent Effects on the Stabilities of Ethyl and Vinyl Cations. Comparison with Isoelectronic Methyl Boranes. The Relative Importance of Hyperconjugative and Inductive Effects Yitzhak Apeloig,'" Paul v. R. Schleyer,*Ib and John A. PopleIc Contribution from the Departments of Chemistry, Princeton University, Princeton, New Jersey 08540 and Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, and the Institut f u r Organische Chemie der Universitat Erlangen-Nurnberg, 8520 Erlangen, West Germany. Received October 13, 1976
Abstract: The effect of @-substituents,X, on the stabilities of ethyl and vinyl cations is studied by standard ab initio procedures. The ethyl cations are examined in perpendicular (1) and eclipsed (2) conformations. X is varied systematically along the whole series of first short period substituents, Li, BeH, BH2, CH3, NH2, OH, and F. Electropositive substituents are extremely effective in stabilizing ethyl cations, e.g., 88.9 and 27.1 kcal/mol (RHF/4-3 1G) for @-Liand @-BeH,respectively. Hyperconjugative contributions are larger than inductive effects for most substituents. Hyperconjugation between the C-X bond and the empty 2p cationic orbital is stabilizing for electropositive (relative to hydrogen) substituents which thus prefer conformation 1, but destabilizing for electronegative substituents which prefer conformation 2. Very high barriers for rotation around the C-C+ bond were found for P-lithio- and 0-beryllioethyl cations, 49.8 and 22.8 kcal/mol (RHF/4-3 IC), respectively. A linear correlation exists between the rotation barriers in the ethyl cations and the isoelectronic boranes, the cations being 2.3 times more sensitive to substituent effects. The stabilization of substituted vinyl cations parallels that of the perpendicular conformation (1) of ethyl cations.
Carbenium ions contain a positively charged electron-deficient center which renders them particularly sensitive to electronic influences and thus ideal for the study of substituent effects. Numerous experimental2 and t h e ~ r e t i c a l ~studies -~ have been published, but most of those involved alkyl group^,^^^ or highly electronegative groups such as hydroxy5 and halog e n ~ . Stabilization ~-~ of cationic centers by P-carbon-metal bonds is known.10-16Thus, ferrocenyl and other metallocenyl methyl carbenium ions are very stable.Io Many instances are known" in which apparent carbenium ion formation is accelerated by P-carbon-metal bonds. These include reactions such as the protonation of allylmetal compounds (metal = Si, Ge, Sn, Pb, Hg)12 and benzylmercury halides,I3 the cleavage of the aryl-silicon bond of Me3SiCH2C6H4SiMe311 and the solvolysis rates of P-silylalkyl halides.14 Traylor showed that @-Pb(C6H5)3,@ - S I I ( C H ~P-HgC6H5, )~, and similar metalloid substituents stabilize carbenium ions by as much as 6 kcal/ m01.13b315 The remarkable stability of nonacarbonyltricobaltcarbon-substituted carbonium ions was recently reported by Seyferth.16 The importance of hyperconjugation in affecting the energies of @-substituted ethyl cations has raised considerable controversy over the past 40 years.I7 The importance of u-T hyperconjugation in stabilizing P-metal-substituted carbenium ions was pointed out by T r a y l ~ r I and ~ ~ ,other^.^^,^^,^^.^^,^^ ~~ The experimental demonstration that stabilization by the metal is possible only when the carbon-metal bond is coplanar with the axis of the empty cationic p orbital is of particular importance as it appears to rule out significant contribution by the inductive effect.ISaqeHowever, other concepts such as metal participationloa and overlap with the metal's d orbitals20 have also been suggested as possible explanations. The experimental difficultiesI7of separating the inductive and the hyperconjugative effects and of avoiding the influence of solvation can be overcome computationally. Recent ab initio calculation^^-^ show that the preferred conformation of @-substitutedcations is determined largely by the relative hyperconjugative abilities of the bonds at the P-carbon, and that considerable barriers for rotation around the formally single C-C+ bond result.
Examples are 10 kcal/mo16 for H2BCH2CH2+ and 8-1 1 k c a l / m 0 1 ~ * for ~ . ~FCH2CH2+. ~ The only other @-metallosubstituted cation studied by ab initio methods is H3SiCH2CH2+, which is found to be more stable than CH3CH2CH2+.21A few other cations involving group 4 subs t i t u e n t and ~ ~ the ~ ~a-ferrocenyl ~~~ cation23have been studied by semiempirical methods. Qualitative theoretical arguments show that the ability of a C-X bond to hyperconjugate depends on the electronegativity of X and predict that electropositive substituents should be especially effective.6 It is therefore of interest to extend our previous ab initio study of 8-substituted ethyl cations5 to include all of the first short period groups, Li, BeH, BH2, CH3, NH2, OH, and F. We have also investigated the corresponding series of @-substituted vinyl cations. This allows a systematic evaluation of the electronic effects and conformational preferences produced by such 0-substituents. Special attention is drawn to the large effects of electropositive groups, Li, BeH, and BH2. Although these particular substituted cations are not practical experimentally and may in any case rearrange to some other form (bridged or a-substituted), they nevertheless provide a valuable model for P-substitution in carbocations where such rearrangement does not take place. We shall therefore restrict ourselves to geometries in which the P-carbon is constrained to have an unaltered structure (tetrahedral for ethyl and trigonal for vinyl). This paper complements our study of a-substituted cations with the same series of substituent^.^^
Method, Geometrical Models, and Results Calculations were carried out at the restricted Hartree-Fock (RHF) level using the ab initio SCF-MO GAUSSIAN 70 series of programs.25 The minimal STO-3G basis set26aand the split-valence 4-3 1G basis set26b,cwere used. The 4-3 1 G level of theory is preferable for prediction of relative energies and will be used in most of the discussion. Parallel STO-3G results will also be given as this lower level theory can be more readily extended to larger systems. The geometries of the carbenium ions and the corresponding neutral molecules are constructed from the standard models described p r e v i o u ~ l y . For ~ . ~ the ~
Apeloig, Schleyer, Pople
/
Stabilities of Ethyl and Vinyl Cations
5902 Table 1. Total Energies (hartrees) of &Substituted Ethvl Cations R+ and of Molecules RH"
Cation (R+) Substituent (X) H Li Be H BH2 planarb BH2 perpendicularC CH3 H2N planarb NH2 perpendicularc OH F
Neutral molecule (RH) (3)
Eclipsed (2)
Perpendicular (1) RHF/STO-3G
RHF/4-31G
RHF/STO-3G
RHF/4-31G
RHF/STO-3G
RHF/4-31G
-77.405 94' -84.239 70 -91.873 05 -102.366 I @ -102.358 39' - 115.992 94e -131.68648f -131.703 95' -151.213 54' -174.821 33'
-78.192 -85.145 -92.822 -103.416 -103.407 -117.181 -133.109 -133.130 -152.904 -176.869
-77.405 94' -84.15488 -91.835 05 -102.348 69g -102.342 83j -115.98893e -131.696 48g -131.703 101 -151.225 76e -174.836 17e
-78.192 57' -85.066 16 -92.786 07 -103.400 67g -103.394 6 1 j -117.177?6' -133.122 22g -133.131 26J -152.923 04 -176.892 24f
-78.305 -84.992 -92.725 -103.242 -103.243 -116.885 -132.597 -132.596 -152.129 -175.752
-79.1 1484e -85.926 01 -93.701 52
57' 45 39 44-f 84' 67' 92f 64' 80 90
49' 73 23 17h 02k 12e 04h 95k 49' 12'
-104.319 19h -118.092 11" -134.047 95h -153.854 1 I m -177.841 54m
Using standard geometries. See text. The XH2 group and the CCX atoms lie in the same plane. The XH2 group and the CCX atoms define two perpendicular planes. CCOH anti. e From ref 5 and 28. /Conformation la. g Conformation 2a. Conformation 4a. Conformation lb. Conformation 2b. Conformation 4b. Fully minimized, from ref 4a. From ref 32.
ethyl cations, the a- and /3-carbons are constrained to be trigonal and tetrahedral, respectively, and the standard bond lengths (C-C+ = 1.49, C+-H = 1.12 A) are based on the optimized geometry of the unsubstituted ethyl cation.2s In a similar manner, a-and @-carbonsof vinyl cations are taken to be linear and trigonal and standard bond lengths (C=C+ = 1.28, C+-H = 1.1 1 A) from the parent are used.28 For hydroxyl derivatives, the conformation about the C - 0 bond is taken to be CCOH trans unless otherwise specified. For amino derivatives, planar arrangements around nitrogen with bond angles of 120' were used. Although these are not the preferred amino geometries, there are interpretive advantages for this choice as it allows direct comparison of NH2 as a *-donor with BH2 as a ?r-acceptor. The standard bond lengths and angles for lithium, beryllium, and boron derivatives were reported recently.29 Two rotational conformations around the C-C+ bond were calculated for each substituted ethyl cation, perpendicular (1) and eclipsed (2). For X = BH2 and NH2, two conformations resulting from rotation around the C-X bond were calculated for both the perpendicular (la and lb) and the eclipsed (2a and 2b) cations. For most of the substituted vinyl cations, only the single conformation 3 has to be considered. However, for BH2 and NH2, both planar (3a) and perpendicular (3b) confor-
4
mations were examined. The neutral molecules were calculated in their standard staggered conformations (4), and for X = BH2 and NH2, planar (4a) and perpendicular (4b) arrangements of the XH2 group relative to the C-C bond were studied. The calculated total energies for the @-substitutedethyl cations (1 and 2) and the corresponding neutral ethanes at both the RHF/STO-3G and the RHF/4-31G levels are given in Table I. Corresponding results for the &substituted vinyl cations and corresponding ethylenes are listed in Table 11.
Discussion Stabilities of 8-Substituted Ethyl Cations. The calculated energies for the isodesmic reactions30 XCH2CH2' (1) CH3CH3 XCH2CH3 H3CCH2' (1)
+
XCH2CH2+ (2)
-
I
H
H
3b
30
Journal of the American Chemical Society
/
99:18
+
+ CH3CH3
+
H
4b
40
XCH2CH3
+ H3CCH2+
(2)
(Table 111) provide a comparison of the stabilities of the perpendicular (1) and eclipsed (2) &substituted ethyl cations relative to the ethyl cation. A positive energy indicates a greater stabilization by X in the ethyl cation than in the corresponding substituted ethane. From previous experience, it is well known that the energies of such isodesmic reactions are generally well described even at the RHF/STO-3G30.3' and the RHF/43 lG32levels. The estimated error limit for such reactions (not involving small rings) is of the order of 5 k c a l / m 0 1 . ~ ~ ~ ~ The most striking result of Table 111 is the very large stabilization provided by electropositive b-su bsti t uents. B H 2 stabilizes the cation by 12.3 kcal/mol, BeH by 27.1 kcal/mol, and lithium by 88.9 kcal/mol (RHF/4-31G)! The calculated energies for both reactions parallel the electronegativity of the substituent. The ,&substituted ethyl cations are more stable than the ethyl cation when the substituents are less electronegative than hydrogen, but are generally less stable than the ethyl cation when the substituents are more electronegative. The inductive effect of a @-substituentshould be, to a first approximation, independent of the conformation of the cation and thus is assumed to be roughly equal in 1 and in 2. C-X hyperconjugation, on the other hand, is an orientationally
/ August 31, 1977
5903 Table 11. Total Energies (hartrees) of @-SubstitutedVinyl Cations R+ and of Molecules RH‘
@-Substitutedvinyl cations (3) Substituent (XI
RHF/STO-3G
Li Be H BH2 perpendicularc BH2 planard CH3 NH2 perpendicularC NH2 planard OH F
-76.165 406 -83.022 47 -90.645 55 -101.133 54 -101.131 99 - 1 14.768 59’ - 130.465 32 - 130.493 52 - 149.997 07 -173.592 40
H
I’
Substituted ethylenes
R H F/STO-3G
RHF/4-31G -76.977 53’ -83.944 52 -91.614 87 -102.205 21 -102,206 36 -1 15.975 03b -131.917 09 - 13I .93439 -151.702 67 -175.650 71
RHF/4-31G
-77.073 96‘ -83.784 03 -91.508 03 -102.014 19 - 102.025 22 - 1 15.656 68/ -131.369 02 - 131.38476 - 150.908 8 d -174.529 41f
-77.921 88’ -84.747 03 -92.517 16 -103.127 36 -103.140 16 -1 16.902 03g -I 32.858 90 -132.870 16 - 152.664 22g - 176.646 01 g
Fully optimized geometries from ref 5 and 28. The XH2 and the CCX atoms lie From ref 32 and
Using standard geometries unless otherwise noted.
in the same plane. The XH2 group and the CCX atoms define two perpendicular planes. e CCOH anti. f From ref 3 I . L. Radom, P. C. Hariharan, J. A. Pople, and P. v. R. Schleyer, J . Am. Chem. SOC.,95,6531 (1973).
Table 111. Ethyl Stabilization Energies (kcal/mol) for the Perpendicular (1) and Eclipsed (2) @-SubstitutedEthyl Cationsu
Substituent (X)
H Li Be H BH2 planar BH2 perpendicular CH3 N H2 planar NH2 perpendicular OH F
Reaction 1 Electronegativityb
RHF/STO-3G
2.1
RHF/4-31G
0 91.9 29.7 14.2? 9.4c 4.6 -6.9? 4.1c - 10.3 -19.6
1 .o
I .5 2.0 2.0 2.5 3.O 3.0 3.5 4.0
Reaction 2
0 88.9 27.1 12.2c 6.9c 7.4 -9.9c 3.1c - 17.0 -31.0
RHF/STO-3G 0
38.7 5.9 3.3c -0.4? 2. I -0.6
