J. Phys. Chem. 1988, 92, 881-886
881
Structures and Energles of Isomeric C5Ht+ and CgHt+ Dicationd’ Koop Lammertsma*t and Paul von R a g d Schleyer*$ Department of Chemistry, University of Alabama at Birmingham, Birmingham, Alabama 35294, and Institut fur Organische Chemie der Friedrich- Alexander- Universitiit Erlangen- Niirnberg, Henkestrasse 42, 0-8520 Erlangen, Federal Republic of Germany (Received: March 5, 1987)
The geometries of various C5H:+ and C6b2+isomers with acetylene, cumulene, vinyl, propargyl, and three- and four-membered ring structures were optimized by ab initio molecular orbital theory employing the 3-21G basis set. Comparison of the Hartree-Fock (for C6H42+)and MP2/6-31G1 (for C,H:+) relative energies shows clearly that there is no common minimum energy CH , :+ structure of the CH3-C,,-H2+ type as has been suggested from mass spectroscopic investigations. Thus, both 25 ( n = 4) and 26 ( n = 5 ) are quite high in energy relative to most other isomers examined. In addition, the cumulene dications, H2C(C,)CH2+ ( n = 3 and 4), which favor anti-van’t Hoff geometries (lla and 124, are less stable than structures with cyclopropenium ion moieties. The vinylidenecyclopropenium dication ( 1 5 ) and the triafulvene dication (Ma) are the lowest energy C5H>+ and C6Hd2+dications investigated; heats of formation of 630 5 (15a) and 617 & 5 kcal/mol (Ha) are estimated.
*
Introduction Carbodications are well-known experimentally both in the gas phase2 and in stable ion media.3 The solution studies generally involve larger species stabilized by methyl, phenyl, or other substituents3 Mass spectrometric experiments provide abundant but somewhat limited information, i.e., the molecular composition and energies, but only general indications of structure. For example, the analysis of metastable decompositions is said to provide clues to the linear or cyclic nature of certain dicatiom2” Electron impact investigations on a large number of aliphatic and aromatic hydrocarbons reveal the C,H62+and C,H22+ series of dications generally to be observed with high abundance; C,H42+ions also are prominent.2 It has been suggested that these dications may have common structures with linear carbon chains, e.g., 1 for C,H:+, 2 for H c,+:, and 3 for c,,H62+2” (Chart I). More recent innovations in mass spectrometric techniques (e.g., “charge stripping”) allow the generation of nearly every doubly charged hydrocarbon oin!’ This increases the significance of such species greatly. Until recently, relatively few theoretical studies have been devoted to doubly charged hydrocarbons.6 In general, these have been concerned only with specific systems. As part of a systematic investigation of carbodications, we now extend our earlier work on CH,2+ ( n = 1-4),7a CH62+9 7b.c C2H2 2+3 7d C2H42+,7e C2H62+,kf,6 C 2H62+,7c C4H22+,7h C4H42+,60*P97i and C6H62+,7jto C5H42+and C6H42+ isomers. Formal removal of two electrons from the cumulenes, C,H4, to give the dications, C,H42+(2) should result in reversal of the familiar van’t Hoff ~tereochemistry.~g~* Thus, ethylene (4) and H2C=C=C=CH2(5) are planar ( D a ) ,but their dications prefer perpendicular (DM)geometries, 67hand 7.7‘ Such “anti-van’t Hoff ~tereochemistry”~ should also be exhibited by the cyclopropenium ion terminated systems, 8 and 9. The principle has been demonstrated previously in the set of isoelectronic neutral molecules, 10, akin to 8,9 and in the C4Hd2+isomers (8, n = l);609P,7ifurther examples are presented here. We also consider other acyclic and cyclic C5H42+structures in a search for the global energy minima of these carbodications. Methods
Ab initio molecular orbital calculations were performed with the GAUSSIAN 76 and in part with the GAUSSIAN 80 and 82 series of programs1° using the gradient geometry optimization” and standard bases sets.12 Singlets were calculated by the restricted Hartree-Fock (RHF) a p p r o ~ i m a t i o n ’and ~ ~ triplets by the un-
restricted version (UHF).13bAll C5Hd2+and C6H42t:geometries were fully optimized by using in all cases first the minimal
(1) Part 9 of a series on carbodications. For part 8 see: Lammertsma, K.; Pople, J. A.; Schleyer, P. v. R. J . Am. Chem. SOC.1986, 108, 7. (2) For reviews see: (a) Ast, T. Adu. Mass Spectrosc. 1980,8A, 555. (b) Koch, W.; Macquin, F.; Stahl, D.; Schwarz, H. Chimia 1985, 39, 376. (c) See also: Guihaus, M.; Kingston, R. G.; Brenton, A. G.; Beynon, J. H. Org. Mass Spectrom. 1985, 20, 424. (d) 22. Beynon, J. H.; Caprioli, R. M.; Baitinger, W. E.; Amy, J. W. Org. Mass Spectrom. 1970, 3, 903. (3) For reviews see: (a) Olah, G. A,; Prakash, G. K. S.; Sommer, J. Superacids; Wiley-Interscience: New York, 1985; Chapter 3.4.1 1 (b) Prakash, G. K. S.; Rawdah, T. N.; Olah, G. A. Angew. Chem. Int. Ed. Engl. 1983, 22, 390. (c) Pagni, R. M. Tetrahedron 1984, 40, 4161. See also: (d) Prakash, G. K. S.; Krishnamurthy, V. V.; Herges, R.; Bau, R.; Yuan, H.; Olah, G. A.; Fessner, W.-D.; Prinzbach, H. J. Am. Chem. SOC.1986, 108, 836. (e) Schotz, K.; Clark, T.; Schaller, H.; Schleyer, P. v. R. J. Org. Chem. 1984,49,733. ( f ) Lammertsma, K. J. Am. Chem. SOC.1981,102, 3257. (9) Schleyer, P. v. R. Prepr. Diu. Pet. Chem. Am. Chem. SOC.1983, 28,413. (h) Schleyer, P. v. R. In Advances in Mass Spectrometry 1985; Part A: Todd, J. F. J., Ed.; Wiley: New York, 1986; p 287. (4) (a) Rabrenovic, M.; Beynon, J. H. Int. J. Mass Spectrom. Ion Processes 1983, 54, 87. (5) (a) Rabrenovic, M.; Proctor, C. J.; Ast, T.; Herbert, C. G.; Brenton, A. G.; Beynon, J. H. J. Phys. Chem. 1983, 87, 3305. (b) Kingston, E. E.; Brenton, A. G.; Beynon, J. H.; Flammang, R.; Maquestiau, A. Int. J. Mass Spectrom. Ion Processes 1984,62,317. (c) RabrenowiC, M.; Beynon, J. H. Ibid. 1983, 54, 79. (d) Ast, T.; Beynon, J. H.; Cooks, R. G. Org. Mass Spectrom. 1981,16,92. (e) Appling, J. R.; Musier, K. M.; Moran, T. F.Ibid. 1984, 19, 412. (f) Appling, J. R.; Jones, B. E.; Abbey, L. E.; Bostwick, D. E.; Moran, T. F. Ibid. 1983,18, 282. (g) Jones, B. E.; Abbey, L. E.; Chatham, H. L.; Hanner, A. W.; Telehefsky, L. A.; Burgess, E. M.; Moran, T. F . Ibid. 1982, 17, 10. (h) Mathur, B. P.; Burgess, E. M.; Bostwick, D. E.; Moran, T. F. Ibid. 1981, 16,92. (i) Shields, G. C.; Moran, T. F. Theor. Chim. Acta 1986, 69, 147. (6) (a) Klumpp, G. W.; Fleischhauer, J.; Schleker, W. R e d . Trau. Chim. Pays-Bas 1982, 101, 208. (b) Appling, J. R.; Moran, T. F. Chem. Phys. Lett. 1985, 118, 188. (c) Burdick, G. W.; Shields, G. C.; Appling, J. R.; Moran, T. F. Int. J. Mass Spectrom. Ion Processes 1985,64, 315. (d) Craig, D. P.; Radom, L.; Schaefer 111, H. F. Aust. J. Chem. 1978, 31, 261. (e) Radom, L.; Scheafer 111, H. F.J. Am. Chem. SOC.1977, 99, 7522. (0 Moriarty, R. M.; John, L. S.; Luxon, B. A. Tetrahedron Lett. 1983, 1139. (9) Clark, T.; Weiss, R. J . Org. Chem. 1980, 45, 1790. (h) Clark, T, Schleyer, P. v. R. N o w . J . Chim. 1978, 2,665. (i) Sevin, A.; Devaquet, A. Ibid. 1977, I , 367. (j) Siegbahn, P. E. M. Chem. Phys. 1982, 66, 443. (k) Dewar, M. J. S.; Reynolds, C. H. J. Mol. Szruct. THEOCHEM 1986, 136, 209. (1) Olah, G. A.; Simonetta, G. A. Ibid. 1982, 104, 330. (m) Dewar, M. J. S.; Holloway, M. K.J . Am. Chem. SOC.1984, 106,6619. (n) Bentley, T. W.; Wellington, C. A. Org. Mass Spectrom. 1981,16, 523. ( 0 ) Krogh-Jespersen, K.; Schleyer, P. v. R.; Pople, J. A.; Cremer, D. J. Am. Chem. SOC.1978, 100, 4301. (p) Krogh-Jespersen, K.; Cremer, D.; Dill, J. D.; Pople, J. A.; Schleyer, P. v. R. Ibid. 1981, 103, 2589. (9)Hess, B. A.; Ewig, C. S.; Schaad, L. J. J . Org. Chem. 1985, 50, 5869. (r) Olah, G. A.; Simonetta, M. J. Am. Chem. SOC. 1982, 104, 330. (s) Cuthberson, A. I.; Glidewell, C. J. Mol. Srruct. THEOCHEM 1982, 87, 71.
0022-3654/88/2092-0881%01.50/0 0 1988 American Chemical Society
882 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
Lammertsma and Schleyer
TABLE I: Total (in au) and Relative (in kcal/mol) Energies of C f i 2 + Isomers
struct lla l l b (T)' 15a 15b 17a 17b 19a 19b 22
MNDO' 602.1 (0.0) 623.0 (20.9) 627.9 (25.8) 633.9 (31.8) 678.0 (75.9) 688.2 (86.1) 633.7 (31.6) 634.2 (32.1)
22d
640.4 (38.3) 644.6 (42.5)
25 (T)'
MIND0/3" 561.3 (0.0) 581.7 (20.4) 562.7 (1.4) 575.0 (13.7) 581.8 (20.5) 621.8 (60.5)
3-21G//3-21G -189.69930 (0.0) -189.67085 (17.9) -189.67253 (16.8) -189.59861 (63.2) -189.660 15 (24.6)
597.0 (35.7) 606.9 (45.6)' 591.3 (30.0) -189.63648 (39.4)
NIMAGb 4-31G//4-31G [O] -190.50892 (0.0) [O] -190.48303 (16.2) [O] -190.485 59 (14.6) -190.46408 (28.1) [l] -190.411 92 (60.9) -190.349 75 (99.9) [O] -190.47204 (23.1) -190.471 36 (23.6) -190.433 30 (47.5) -190.43299 (47.6) [O] -190.447 16 (38.8)
6-31Gb//3-21G -190.76931 (0.0) -190.75001 (12.1) -190.77866 (-5.9) -190.75787 (7.2)' -190.73062 (24.3)
MP2/6-31G*// 3-2 1G -191.32379 (0.0) -191.25673 (42.1) -191.338 76 (-9.4)
ZPE 42.6 42.4 42.6
-191.31970 (2.6)
40.7
-190.76908 (0.1) -190.768 70 (0.5)'
-191.32560 (-1~1) 43.2
-190.76870 (32.6)
-191.250 17 (46.2)
41.9
'Heats of formation in kcal/mol. bNumber of imaginary frequencies. CTriplet. dPlanar form (C2"). eHF/6-31G*//HF/4-31G values. TABLE II: Total (in au) and Relative (in kcal/mol) Energies of CgH42+Isomers
struct
MNDO'
MIND0/3"
STO-3G//STO-3G
4-31G//STO-3G
3-21G//3-21G
6-31G*//3-21G
12a 12b 12b (T) 16a 16b 18a 18b 21a 21b 23b 26
599.6 (0.0) 604.5 (4.9)
558.7 (0.0) 569.7 (11.0)
-228.640 61 (0.0) -228.61048 (18.9)
557.8 565.1 554.9 560.8 570.7 578.6 583.5 556.9
-228.32290 (0.0) -228.287 24 (22.4) -228.286 50 (22.8) -228.314 14 (5.5) -228.30088 (13.8) -228.319 82 (1.9) -228.315 79 (4.5) -228.29223 (19.2) -228.289 13 (21.2) -228.27940 (27.3) -228.265 26 (36.2)
-227.36085 (0.0) -227.32668 (21.4)
616.1 (16.5) 618.7 (19.1) 632.2 (32.6) 632.7 (33.1) 628.0 (28.4) 629.5 (29.9) 630.8 (31.2) 623.3 (23.7)
-225.886 32 -225.85980 -225.847 55 -225.91064 -225.900 21 -225.944 67 -225.941 92 -225.886 69 -225.884 12 -225.875 87 -225.831 56
-227.350 55 (6.5) -227.33707 (14.9) -227.352 18 (5.4) -227.347 98 (8.1) -227.328 99 (20.0)
-228.66634 -228.653 89 -228.70485 -228.699 79 -228.647 34
-227.313 93 (29.4) -227.30444 (35.4)
-228.631 01 (6.0) -228.581 79 (36.9)
(-0.9) (6.4) (-3.8) (2.1) (12.0) (19.9) (24.8) (-1.8)
(-16.1) (-8.3) (-40.3) (-37.1) (-4.2)
'Heats of formation are given in kcal/mol. bNonplanar (see text). Planar form (C,) has E = -225.87528 au (STO-3G) and -228.278 36 au (4-3 1G).
geometry of 23 satisfactorily; the Ubestnvalue is given. In the early stage of this study, all 4-31GlZCenergies were obtained on and STO-3G(C6H42+)optimized structures. 4-3 1G (C5H4*+) Single-point 6-3 lG*lZdcalculations on the 3-21G (and some 4-31G) optimized geometries were used to explore the effects of polarization functions. In addition, the effect of electron correlation corrections was investigated for C5H42+with Mdler-Plesset theory to the second level with valence electrons only (denoted MP2-FC/6-31G*//HF/3-21G). The 3-21G frequency analysis for some C5H42+isomers showed l l a , llb, 15a, 19a, and 25 to be minima on the potential energy surface, and 17a to be a transition structure with one imaginary frequency. The Mulliken population analyses14 employed the STO-3G wave functions.
STO-3GlZafollowed by the split valence 3-21GlZbbasis set for most isomers. We were unable to obtain the 3-21G optimized (7) (a) Pople, J. A.; Tidor, B.; Schleyer, P. v. R. Chem. Phys. Lett. 1982, 88, 533. (b) Lammertsma, K.; Barzaghi, M.; Olah, G. A.; Pople, J. A.; Schleyer, P. v. R.; Simonetta, M. J . Am. Chem. SOC.1983, 105, 5258. (c) Lammertsma, K.; Olah, G. A.; Barzpghi, M.;Simonetta, M. Ibid. 1982, 104, 6851. (d) Pople, J. A.; Frisch, M. J.; Raghavachari, K.; Schleyer, P. v. R. J . Comput. Chem. 1982, 3, 468. (e) Lammertsma, K.; Barzaghi, M.; Olah, G. A.; Pople, J. A.; Kos, A. J.; Schleyer, P. v. R. J. Am. Chem. SOC.1983, 105, 5252. (0 Lammertsma, K. Ibid. 1984, 106, 4619. (g) Schleyer, P. v. R.; Kos, A. J.; Pople, J. A.; Balaban, A. T. Ibid. 1982, 104, 3771. (h) Lammertsma, K.; Pople, J. A.; Schleyer, P. v. R. Ibid. 1986, 108, 7. (i) Chandrasekhar, J.; Schleyer, P. v. R.; Krogh-Jespersen, K. J . Comput. Chem. 1981,2,356. 0) Lammertsma, K.; Schleyer, P. v. R. J. Am. Chem. Soc. 1983, 105, 1049.
(8) (a) Van't Hoff, J. H. La Chimie dam PEspace; Bazendyk Rotterdam, 1875 The Arrangemenl of Atoms in Space, 2nd ed., Longmans, Green and Co.: New York, 1989; pp 103-105. Also see: Snelders H. A. M. In Van't Hoff Le Bel Centennial; Ramsey, 0 . B., Ed.; ACS Symposium Series, Vol. 12; American Chemical Society: Washington, DC, 1975; Chapter 5, p 66. (b) Hoffmann, R. Tetrahedron 1966, 22, 521. (9) Krogh-Jespersen, K.; Cremer, D.; Poppinger, D.; Pople, J. A.; Schleyer, P. v. R.; Chandrasekhar, J. J . Am. Chem. SOC.1979, 101,4843. (10) Binkley, J. S.; Whiteside, R. A.; Hariharan, P. C.; Seeger, R.; Pople, J. A.; Hehre, W. J.; Newton, M. D. QCPE 1978, 11, 368. Binkley, J. S.; Whiteside, R. A,; Krishnan, R.; Seeger, R.; DeFrees. D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. QCPE 1981, 13, 406. Van Kampen, P. N.; Smits, G. F.; De Leeuw, F. A. A. M.; Altona, C. QCPE 1982, 14, 437. Binkley, J. S.; Frish, M.; Raghavachari, K.; DeFrees, D.; Schlegel, H. B.; Whitcside, R.; Fluder, E.; Seeger, R.; Pople, J. A. GAUSSIAN 82, Release H; Carnegie-Mellon University. (11) Schlegel, H. B.; Wolfe, S.; Bernardi, F. J . Chem. Phys. 1975, 63, 3632. (12) (a) The STO-3G basis: Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (b) The 3-21G basis: Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. Gordon, M. S.; Binkley, J. S.; Pople, J. A. Ibid. 1982, 104, 2797. (c) The 4-31G basis: Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (d) The 6-31G* basis: Hariharan, D. C.; Pople, J. A. Theor. Chim. Acta 1971, 28, 213; Mol. Phys. 1974, 27, 209. (e) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (13) (a) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (b) Pople, J. A.; Newbet, R. K. J . Chem. Phys. 1954, 22, 571. (14) Mulliken, R. S . J. Chem. Phys. 1955, 23, 1833.
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 883
Geometries of C5H42+and c6H42+ Dications SCHEME I: Predictions of Qualitative Molecular Orbital Theory on Neutral Cumulenes (van't Hoff Stereochemistry Preferred) and the Corresponding Dications (Anti-van? Hoff Stereochemishy~~'
CHART II
y
Preferred)
H
Neutral Species
1%
13b
14b
14s .H
1Sb Planar.Dzh
n
-
Perpendicular, DZd
even Ground state
n = odd
Rotational transition state
(closed shell)
(open shell)
Rotational transition
Ground State
state (open shell)
(closed shell)
16b
1Be
Dications
AZ+
A
\ /
\
E
H
Planar,DZh
n
-
E
c;
c=(c)n-z=c /
=
-cg+
(c)n-z
1?a
17b
A Perpandicular
1Ba even Rotational transition
n = odd
Ground state
state (closed shell)
(closed shell)
Ground state
Rotational transition state
(closed shell)
(open shell)
Dewar's semiempirical MNDO programls8 and Bischof s openshell M I N D 0 / 3 versionlSbserved for preliminary scans on many C5H42+isomers as well as providing starting geometries for ab initio geometry optimizations. Absolute and relative energies are summarized in Tables I and Table 11, respectively. The 3-21G and some 4-31G optimized bond distances for the C5H2+ and C6H42+dications are given in the structures.
Results and Discussion The calculational results for the various C5H42+and c6H42+ isomers are first considered together in terms of similar structural types. Cumulene Dications. According to stereochemical rules deduced by van't Hoff in l 875,8 cumulenes with an even number of double bonds and an odd number of carbon atoms, e.g., allene and pentatetraene, prefer perpendicular ( D M ) arrangements (derivatives substituted at both terminals are chiral), while cumulenes with an odd number of double bonds and an even number of carbons, e.g., ethylene and butatriene, prefer planar (D2h) structures (qw-disubstituted derivatives exhibit cis-trans isomerism). Removal of two electrons to give a cumulene dication reverses the van? Hoff ~tereochemistry:~&~ perpendicular neutral species become planar dications, and vice versa. Scheme I summarizes the expectations of qualitative molecular orbital theory, assuming linear carbon skeletons. For dications, 2, with an even number of carbon atoms, the 2n-2% electrons are best divided over the two orthogonal systems in perpendicular, DZd,geometries. The resulting singlets are stabilized by double allylic conjugation and by hyperconjugation with the terminal CH2 groups. These DM forms are more stable than the planar DZhsinglets, where the two positive charges are delocalized in only a single .rr system, an arrangement which is unfavorable electrostatically. Still, planar singlets should be preferred over planar triplets, which would have an odd number of electrons in each T system. In contrast, singlet dications with an odd number of carbon atoms, 2, favor planar DZhgeometries. The positive charges can then be divided between the two orthogonal systems. Triplet (or open-shell singlet) states should be ( 1 5 ) (a) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899. (b) Bischof, P. Ibid. 1976, 90, 6844.
preferred for the less favorable perpendicular C,,H42+( n = odd) geometries. Thus,dications 2, with an odd number of carbon atoms, CH:+, CJHZ+,CC5H:+ (Il), etc. have planar singlet ground states while perpendicular singlets are predicted for C2H2+ (6),C4H4*+(7), C6H42+(I&), etc. Theoretical studies show CH:+ to be planar rather than tetrahedral.6j.7a Both C2H42+and linear C4H:+ favor perpendicular arrangements (6 and 7) with calculated rotational barriers of 28.5 (MP3/6-31G**//6-31 *)7e and 26.0 kcal/mol (6-31G*),7' respectively.16 Similarly, we now find the perpendicular C6H42+structure 1% to be the most stable linear C6Hd2+ isomer with a rotational barrier (for the singlets) of 18.9 kcal/mol (6-31G*). While the triplet state of 12b is only 0.4 kcal/mol higher in energy at UHF/4-31G//STO-3G than the singlet, the UHF method is known to overestimate the stability of states with higher multiplicity. Hence, the actual difference favoring the singlet is probably about 20 kcal/mol or more.17 Thus,the triplet state for the perpendicular C5H:+ isomer llb is calculated to be 12.1 kcal/mol (6-31G*) less stable than the planar form, lla, but this value increases to 42.1 kcal/mol with inclusion of electron correlation (MP2-FC/6-3 1G *). Dications with Three-Membered Rings. Cyclopropenium ion based structures are inherently ~ t a b l e . ~ P * ~Because j * ' ~ the van't Hoff cumulene rule does not change if a terminal CH2 group is (1 6) For comparison, the rotational banier of methane (tetrahedral-planar energy difference) is 141 kcal/mol (MP2/6-31 l+G**//6-31 I+G**, Schleyer, P. v. R., unpublished calculations), cf. ref 12e. (a) Collins, J. B.; Dill, J. D.; Jemmis, E. D.; Apeloig, Y.; Schleyer, P. v. R.; Seeger, R.; Pople, J. A. J. Am. Chem. Soc. 1976,98,5419. (b) Krogh-Jespersen,M.-B.;Chandrasekhar,J.; Wilrtwein, E X . ; Collins, J. B.; Schleyer, P. v. R. Ibid. 19%0,102,2263. The rotational bamer for substituted neutral cumulenes with one double bond (ethylene) is 66 kcal/mol: Douglas, J. E.; Rabinovitch, B. S.; Looney, F. S. J. Chem. Phys. 1954,23,315; and with three double bonds ca. 30 kcal/mol: Roth, W. R.; Exner, H.-D. Chem. Be?. 1976, 109, 1158; and Bertsch, K.; Karich, G.; Jochims, C. Ibid. 1977,110, 3304; these values compare well with MIND0/3 rotational barriers; Bingham, R. C.; Dewar M. J. S.; Lo, D. H. J . Am. Chem. SOC.1975, 97, 1294. Also instructive is the rotational barrier of allene, cf.: Seger, R.; Krishnan, R.; Pople, J. A.; Schleyer, P. v. R. J . Am. Chem. Soc. 1977,99,7103. Rauk, A,; Bouma, W. J.; Radom, L. Ibid.1985, 107, 3780 and references cited. (17) Harrison, J. F. Acc. Chem. Res. 1974, 7, 370. Bender, J. F.; Schaefer 111, J. F.; Franceschetti,D. R.; Allen, L. C. J. Am. Chem. Soc. 1972,94,6888. (18) (a) Radom, L.; Hariharan, P. C.; Pople, J. A.; Schleyer, P. v. R. J . Am. Chem. Soc. 1973, 95, 6531. (b) Ibid. 1976.98, 10. (c) Raghavachari, K.; Whiteside, R. A.; Pople, J. A.; Schleyer, P. v. R. Ibid. 1981, 103, 5649. (d) Budzelaar, P. H. M.; Kos, A. J.; Clark, T.; Schleyer, P. v. R. Organometallics 1986, 4, 429. (e) Budzelaar, P. H. M.; Schleyer, P. v. R. J. Am. Chem. SOC.1986, 108, 3967.
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The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
replaced by a cyclopropene ring, structures 8 and 9,which result from replacement of terminal “CH2+” groups in 2 by cyclopropenium ion moieties, also should prefer anti-van’t Hoff geometries. The model BBC ring compounds lo? isoelectronic with dications 8, are illustrative. The smallest dication in this set, C3H,2+ (8 (n = 0 ) the protonated cyclopropenium cation), has been calculated to prefer a geometry with a planar tetracoordinate carbon (13a)over 13b,6g (Chart 11). (The isoelectronic diboracycl~propane~ is similar, but alternative structures are more stable in both instances.) The next higher homologue, C4H42+ 8 (n = l),” is isoelectronic with the BBC-ring analogue 10 ( n = l).9 Both prefer perpendicular geometries. The planar C5H42+ isomer 15a and perpendicular C6Hd2+form 16a are more stable than their 90’ rotated forms, 15b and 16b (see Tables I and 11). The rotational barriers for 13a-l3b, 14a-l4b,15a-l5b,and 16a-16b are 25.4,@ 8.5,’’ 13.2, and 7.8 kcal/mol (all at 6-31G*), respectively. The barriers are smaller than those for the linear cumulene dications 2,due to the very effective 2a-aromatic stabilizationIs of one of the positive charges in the cyclopropenium ring. What happens when a second three-membered ring is introduced? Oxidation of spiropentadiene to the dication results in a planar preference: 17a (DZhsymmetry imposed) is calculated to be 39 kcal/mol (4-31G) more stable than the triplet perpendicular conformation 17b (DZdsymmetry imposed). The spiro atom in 17a is another example of a molecule predicted to have a planar tetracoordinate arbo on.^*^^^,^^^^ As discussed below, its energy relative to the most stable C5Hd2+isomers is quite low. The next higher homologue of 17,the bicyclopropenylidene dication, 9 (n = 0),prefers the perpendicular arrangement, 18a. As anticipated, the rotational barrier Ma-18b is small, 3.2 kcal/mol (6-3 lG*). Both positive charges enjoy aromatic stabilization in the two separate cyclopropenium rings. Double hyperconjugation in perpendicular 18a is not nearly as important as in perpendicular C2H42+.7eSmall differences in the central C-C bond distance, Ad = 0.016 8, and Mulliken overlap populations, A = 0.092 (3-21G), are found in the two forms 18a and 18b. Tetramino-substituted bicyclopropenylidene dication, also formulated as the triafulvalene dication, has been found experimentally by several groups to be quite ~ t a b 1 e . I ~Planar DZh structures have been a s s ~ m e d ,but ~ ~the ~ , substituents ~ are strong a-electron donors. Other Vinyl and Propargyl Cation Derivatives. Dications 15 and 16 can also considered to be classical vinyl and propargyl cation derivatives, respectively, with one of the hydrogens replaced by a cyclopropenium ring. Additional C5H42+and C6Hd2+isomers can be derived by similar substitution at another carbon. Thus, while 19 (Chart 111) has a normally less favorable primary vinyl cation center, it benefits from the greater separation of the formal charges. Bridged vinyl cation derivatives, 20,which would combine these features, also are possible. The alternative propargyl (allenyl) cation structures are 21a and 21b. Isomer 15a is favored over 19a by 8.3 kcal/mol (MP2/6-31G*). The preference of 15a is due to the strong hyperconjugative stabilization of the formally empty C, p-orbital in the plane both with the terminal CH2group and with one of the Walsh orbitals of the three-membered ring. The very small rotational barrier (19a-1%, only 0.3 kcal/mol (6-31G*/4-31G)) indicates a minimal interaction between the vinyl and cyclopropenyl u and a systems. This is substantiated by the C-C Mulliken overlap populations between these moieties of only 0.004 and 0.020 (STO-3G), respectively. Interestingly, M I N D 0 / 3 calculations starting with 19a and 19b resulted in the H-bridged structures 2Oa and 2Ob, respectively. This semiempirical method indicates 20a to be 4.5 kcal/mol less stable than 15a;the rotational barrier, 20a-20b, is 3.7 kcal/mol. Could the bridged structures, 20 be more stable than classical forms, 19? While M I N D 0 / 3 shows the parent bridged vinyl (19) (a) Yoshida, Z.-I.; Konishi, H.; Sawada, %-I.; Ogoshi, H. Chem. Commun. 1977, 250. (b) Gompper, R.; Bartmann, E. Angew. Chem. 1978, 90, 490. (c) Wolf, H.; Weiss, R. Chem. Ber. 1980, 113, 1746.
Lammertsma and Schleyer CHART 111
19b
19a
H,I+&--,~C1.352 -H 1.245
H
P
1,361 +
1 .
/
