Kohler, Lischka
1 Structure and Stability of
C,H5+, C4Hg+, et al.
3479
Theoretical Investigations on Carbocations. Structure and Stability of C3H5+, C4Hg+ (2-Butyl Cation), C5H5+, C6H7+ (Protonated Benzene), and C7H11+ (2-Norbornyl Cation)? Hans-Joachim Kohler and Hans Lischka* Contribution from the Arbeitsgruppe Quantenchemie. Sektion Chemie, Karl Marx Universitat, DDR-701 Leipzig, German Democratic Republic, and Institut fur Theoretische Chemie und Strahienchemie der Universitat Wien, A-1090 Wien, Austria. Received December 4, 1978
Abstract: The title molecules have been investigated by ab initio methods including electron correlation and by the semiempirical M I N D 0 / 3 method. Electron correlation energies of the C3Hs+ system have been calculated explicitly by CEPA. In the other cases a complete CEPA calculation is no longer feasible and correlation effects have been estimated on the basis of pairenergy values. Experimental proton affinities of allene and propyne can be reproduced within experimental accuracy. In contrast, the calculated proton affinity of cyclopropene deviates significantly from the experimental value if, as it has been done in the literature, the cyclopropyl cation is assumed to be the protonated species. I n order to resolve this discrepancy we have investigated the C3Hs+ energy hypersurface and looked for reasonable alternatives. As a solution of this problem we suggest that protonated cyclopropene has not been formed at all, but that ring opening has occurred yielding the 2-propenyl cation. An unusually large stabilization effect by polarization functions and by electron correlation has been observed for the square pyramidal form of CsHs+ in relation to the planar cyclopentadienyl cation. This behavior is explained in terms of chemical bonding. In agreement with other theoretical investigations the u complex of protonated benzene is found more stable than the K complex. The energy difference is estimated to lie between 1 and 6 kcal/mol, significantly less than obtained from double { SCF calculations. For the norbornyl cation system the classical structure is found less stable than the nonclassical one by about 8- I3 kcal/mol. However, the edge-protonated stucture is nearly as stable as the nonclassical one. For an interpretation of experimental gas-phase data both of these structures should be considered.
I. Introduction In the last decade experimental and theoretical evidence has increased strongly in the field of carbocation chemistry.' Experimental investigations may be divided into those which deal with solutions* (usually in superacid media) and into gas-phase experiments mainly performed by means of mass spectrometry3 or ion cyclotron resonance4 (ICR). Although especially the latter methods give very accurate thermodynamic data, one does not obtain direct information about the molecular structure. Thus, quantum mechanical calculations may be very useful: for many problems the molecules involved a r e small enough to allow a b initio calculations with sufficient accuracy. Since the theoretical calculations usually are performed for isolated molecules experimental gas-phase data are especially well suited for comparison. Only very few attempts have been made to include solvation effects into quantum chemical calculation^.^ A comparison of calculations for isolated molecules with experimental data from solution is much more difficult because one still does not know enough about solvation effects. Basis-set effects and electron-correlation contributions to stability differences between open and cyclic cation structures a r e now well understood and documented.6-8 In previous publication^^.^ we have investigated the possibilities of combining a b initio and semiempirical ( M I N D 0 / 3 ) methods. Now we want to apply the experience we have obtained in these investigations to other cases for which open questions still exist. W e shall also try to estimate correlation energy effects on the stability of larger molecules for which direct calculations are out of the question. 11. Methods of Calculation, Basis Sets and Geometries
A t the a b initio level we start from an SCF calculation and compute electron correlation effects by the C E P A - P N O Dedicated
to
Professor 0. E. Polansky on the occasion of his 60th birthday.
0002-7863/79/1501-3479$01 .OO/O
scheme.I0.' I The P N O s are computed from localized orbitalsI2 and only the valence-shell correlation energy is calculated. As in ref 8 b we take advantage of the fact that the interpair interactions between nonneighbor localized bonds are relatively small. Thus, they a r e computed a t the IEPA level only. However, only the overall sum is given in the following tables under the heading of C E P A . I n a previous work (ref 8b, Table IX) we have collected a large number of pair energy values from our calculations on carbocations and classified them with respect to the chemical bonds involved. One finds, in agreement with previous experience,13 that the pair energy values for a certain type of bond are very well transferable from one molecule to another. For the systems investigated in ref 8 b we could reproduce the correlation energy contributions to AE within 2-5 kcal/mol. Of course, we cannot guarantee such an accuracy in each case, but we think that the so estimated electron correlation effects provide a reliable basis for the calculation of the true stabilities of carbocations in cases where a n explicit computation of correlation energies is no longer possible. I n addition, the M I N D 0 / 3 methodi4 and, in a few cases, the M N D O methodiSare used. Since we apply the same methods as in ref 8 and 9 we do not give more details here. T h e thermodynamic quantities like A H o and AGO were computed from AE values given by CEPA and from zero-point energies and temperature dependence obtained from M I N D 0 / 3 results.I6 T h e calculations were performed within the rigid rotator/harmonic oscillator approximation. The way we combine a b initio and semiempirical data is a reasonable compromise in deducing thermodynamic d a t a and has been applied successfully in a previous p ~ b l i c a t i o n . ~ T h e following basis sets are used for the calculations on carbocations: 7s3p on carbon and 3s on hydrogen (basis set no. I ) ; 7s3pld on carbon and 3s on hydrogen (basis set no. 2); 7s3p I d on carbon and 3s 1p on hydrogen (basis set no. 3). Basis sets 1 and 3 are identical with the basis sets 1 and 2 in ref 8b in which the contraction scheme and orbital exponents are also 0 I979 American Chemical Society
Journal of the American Chemical Society
3480
1 101:13 1 June 20, 1979
Table I. MIND0/3 Results: Heats of Formation (AHf), Zero-Point Energies (eo), and Temperature Dependence of the Enthalpy and Free
Energy (kcal/mol)" molecule or cation
AHf
EO 6
HrO- Ho0 ( T = 298.16 K )
2-propenyl ( I I ) corner-protonated cyclopropene, eclipsed (VI Ib) bridged protonated cyclopropene ( V I l l ) bridged protonated trans-2-butene (IX) cyclopentadienyl, nonplanar singlet cation (XIb) cyclopentadienyl, square-based pyramidal form (XII) cyclohexadienyl (protonated benzene, open form) (XI1 I) 2-norborny1, classical (XV) edge-protonated nortricyclene ( X V I J ) H-bridged norbornene, exo form (XVIII) H-bridged norbornene, endo form (XIX) 2-norborny1, nonclassical asymmetric form (XX)
34.96 41.88 59.29 28.43 -2.95 188.61 221.98 21 3.52 236. I I 245.03 170.59 255.30 269.7 I 201.80 214.17 2 16.90 2 18.78 220.33 210.43
36.46 (33.79) 35.82 (33.31) 36.67 (34.21) 63.58 (61.12) 8.84 (9.18) 14.35 43.37 41.55 42.56 42.80 76.00 51.01 5 I .73 70.23 104.77 105.13 104.60 104.62 104.96
3.12 (-14.58)" 3.10 (-14.39)r 2.70 3.56 2.40 (-12.27)c 2.51 (-12.53)" 3.21 3.66 (-15.90)c 3.33 2.94 4.42 3.62 3.21 3.98 4.47 4.07 4.28 4.24 4.44
ProPYne allene cyclopropene benzene hydrogen sulfide sul fhydronium allyl ( I )
[' All molecules and cations are minima on the M I N D 0 / 3 potential hypersurfaces. The values given in parentheses are the experimental zero-point energies.22'. Temperature dependence of the free energy ( C r 0 - HoO). T = 298.16 K (kcal/mol). H
i
=c:-
Table 11. A b Initio Results (au) for Propyne, Allene, and C yclopropene
molecule
basis set no. 1
propyne 115.731 35 allene 115.727 52 cyclopro- 1 15.662 70 pene
1
i
/&\ /C=C-H
H HH
C
HH
\f
Vlll Figure 1. The C ~ H Ssystem. +
given. For the calculations on H2S and H3S+ we use a ( I ls7p2d/Ssl p) Huzinaga basis set contracted to [752/31]. Most of the geometries for our ab initio calculations were
-ESCF
basis set no. 2
basis set no. 3
115.775 55 115.769 81 1 15.728 68
115.787 00 115.782 33 1 15.740 92
-ECEPA
basis set no. 2
116.155 27 116.151 99 1 16.1 I7 78
taken from STO-3G results in the literature (see, e.g., ref 17). In cases where these data were not available we performed the geometry optimization (STO-3G basis) with the gradient program developed by Pulay.' T h e geometries are available on request.
*
111. Results and Discussion
A. C3H5+. The C3H5+ system has been investigated in detail a t the SCF level by Radom et aI.l9 Furthermore, M I N D 0 / 3 calculations for the interconversion of the allyl cation/cyclopropyl cation have been reported.20 Experimental evidence has been obtained from I C R measurements of the protonation reaction of propyne, allene, and cyclopropene.2' Since we shall finally give a different interpretation of the I C R experiment concerning the protonation of cyclopropene we have also investigated in detail the other two reactions and a number of C3H5+ isomers. From the numerical agreement of our results with experiment in cases for which no discrepancies arise we want to draw conclusions for the controversial case as well. I n Figure 1 the C3H5+ structures investigated in this work are presented. Table I shows the pertinent M I N D 0 / 3 information (for all molecules treated in this paper) for the computation of AH values from A E C E P Afor the structures representing local minima on the M I N D 0 / 3 energy hypersurface. I n Tables I 1 and I11 we present our results for propyne, allene, and cyclopropene. T h e computed stabilities obtained from a 63 1 G * basis and our C E P A results give good agreement with experiment. Only the M I N D 0 1 3 result for allene is unsatisfactory. In Chart I our data for the protonation of propyne and allene by H3S+ are compared with experimental values. In connection with these protonation reactions we also optimized the py-
Kohler, Lischka
/
Structure and Stability of
C3H5+, C4H9+,et
al.
348 1
Table 111. Relative Stabilities of Allene and Cyclopropene with Respect to Propyne
AESCF' basis set no. 2 6-31G*b
basis set molecule
no. 1
ProPyne
allene
cyclopropene
(' I a u
0
0
2.4 43. I
3.6 29.4
= 627.73.kcal/mol.
('On the basis of
EO
basis set no.
0 1.7 25.4
2.9 28.9
1.4 23.0
0 0.7 22.8
AH"MINDOI~AH0exptie 0
0
6.9 24.3
1.2 21.8
Reference 6. SCF energy calculated with basis no. 3; correlation energy calculated with basis no. 2. See text. e Reference 23.
-ESCF"
hydrogen sulfideh aulfhydronium, pyramidalC aulfhydronium, planard inversion barrier
398.666 22 398.948 6 I 398.897 0 2 32.4 (32')
-ECEPA" 398.845 69 399.129 86 399.081 2 4 30.5
Basis set; see section II.b Experimental geometry: r ( S - H ) = 1.328 A, 3rHSH = 92.9'. Calculated geometry: r(S-H)sc~= 1.357 A; r ( S - H ) c t p ~= 1.363 A; Q H S H S ~ =F 96.2'; QHSHCEPA= 94.5'. Calculated geometry: r(S-H)sc~= 1.324 A; T(S-H)CEPA = 1.342 A. l' Reference 24.
('
ramidal and planar structure of H3S+ a t the C E P A level (see also Table IV). The inversion barrier a t the S C F level agrees well with the results of Dixon and M a r y n i ~ k . *As ~ in the case of PH3,25 the inversion barrier is modified only slightly by electron correlation effects. W e obtain agreement between experimental and calculated values of proton affinities within the experimental error. The calculated AGO values for reactions 4 and 5 in Chart I differ from the experimental ones by 2-3 kcal/mol. On the other hand, we compute a value of 177 kcal/mol for the proton affinity of cyclopropene with respect to the cyclopropyl cation. This value differs by about 17 kcal/mol from the experimental one (194 kcal/mol) given in ref 21. Such a large discrepancy leads us to the supposition that the interpretation of the I C R experiment was incorrect. O u r opinion is strengthened by the fact that equilibrium could not be obtained under the experimental conditions. In looking for Chart I '
( I ) H3S+=H2S+Hi = 177.3
l E c ~ =p 178.4 ~ PAcJlcd" = 174.2 PA,,p = 172.0 f Z h 173.9 i 2 c
+ H+
( 2 ) CH?C+=CH2 = CH3C=CH ~ E S C=F 187.0 1ECEP.A = I8I . I PAc,[cd'J = 176.9 PAcypI,''174.0 f 3 ( 3 ) CHjC+=CHz = HrC=C=CH2
+ H+
-1E'SCF = 189.9
- 1 E c ~ p=~182.5 PAcJlcda= 177.6 PAexptld = 174.0 f 3 (4) CH3CzCH + H3Sf = CHjC+=CH*
+ H2S
1 E s C F = -1.0 - 1 E C E P A = -2.7 l H o c a l c d= -2.7 A C ' c a l c d = -4.2 l C o c r p t i d= -2. I f 0.1
H?C=C=CH>
+
+
H3S+ = CH3C+=CH2 H2S = -1.3 l E C t P A = -4.1 l H o c d i c d = -3.4 lGocalcd = - 5 . 1 AGOexp,1d = -2.0 f 0.1 ' H 0 2 9 y 16 - Ho0 for H+ = I .48 kcal/mol. Reference 263. lESCF
26b.
AHocaicdd
and HTO - HoO from Table I.
molecule or cation
(5)
AECEPA'
0
Table IV. A b Initio Energies ( a u ) for H2S and H$S+ and Calculated Inversion Barrier (kcal/mol) for H?S+
-1ESCF
3
0
* Reference 21.
