Cyclopropenyl, Azirinyl, and Diazirinyl Cations J. zyx Org. zyxwv Chem., Vol. zyx 39, No. 3, zy 1974 zy 373 INDO Theoretical Studies. V1.I Cyclopropenyl, Azirinyl, and Diazirinyl Cations Charles U. Pittman, Jr.,* Albert Kress,2 Thurman B. Patterson,2 Pamela Walton,2 and Lowell D. Kispert* Department zyxwvutsr of Chemistry, The University of Alabama, University, Alabama 35486 Received July 3, 1973 Geometry-optimizedtheoretical calculations, in the INDO approximation, have been carried out on a series of cyclopropenyl cations including C3H3+ (l), C3F3+ (2), C3(NH&+ (3), and CsHzPh+ (9). The most stable geometries of zyxwvutsrqp 1-3 had D3h symmetry, but a distorted C3 ring with a small quinoid contribution was found for 9. From a study of the n-bond orders, bond lengths, rotational barriers, charge densities, and orbital electron den- sities, it was shown that F and NHz groups conjugate strongly with the ring. However, the resonance interac- tion of the phenyl substituent was weak and this result is compared to experimental results in the literature. Geometry-optimized INDO calculations on CzBH3 (4) and the azirinyl (CzNHz+)and the diazirinyl (CNzH+) cations (5 and 6, respectively) indicated extensive delocalization within the three-membered rings and suggest that these species are aromatic. Calculations on cyclopropenone (7) indicate very little aromatic nature and very little positive charge buildup on the olefinic ring carbons. However, the carbonyl group is very highly PO- larized toward oxygen. On the other hand, protonated cyclopropenone (8) resembles a 2 T aromatic system. Previous studies have indicated that alkyl groups stabi- lize cyclopropenyl cations3 more than do phenyl g r o u ~ s . ~ - ~ This suggested that cyclopropenyl cations, with their closed 2 T aromatic shell, were less susceptible to reso- nance stabilization than traditional open-shell carbonium ions. Without resonance stabilization by the phenyls' K clouds, alkyl groups would be more effective stabilizing groups via their inductive effect. Interest in a wide variety of substituted cyclopropenyl cations has persisted una- bated?-11 and this anomalous stabilizing behavior of the phenyl group has caused extensive d isc~ssion.~-~~~~-~~ Simple Huckel MO theory predicts a delocalization en- ergy of 2/3 for C3H3+. Semiempirical SCF-LCAO-MO cal- culationsl6 of Bairdl? predict AHf values of 263, 268, and 279 kcal/mol for the cyclopropenyl, phenylcyclopropenyl, and diphenylcyclopropenyl cations, respectively. Inter- estingly, Baird calculated out-of-plane rotational barriers of 19 and 15 kcal/mol for the phenyl and diphenylcyclo- propenyl cations, respectively. This is consistent with marked phenyl conjugation. Extended Hackel calcula- tion~,~~ on the other hand, predicted a shallow minimum when all rings were perpendicular to the C3 plane in Ph&+ (ie., 5.3 kcal/mol). An X-ray diffraction study of Ph3C3+C104- indicates only a slight noncoplanarity of the phenyl rings, presumably due to nonbonded ortho hy- drogen repulsions (rings were rotated 7.6, 12.1, and 21.2" with respect to the C3 plane).l8 Brief mention has been made of a CNDO studyls of the trisaminocyclopropenyl cation with predicted 1.36-A C-C bond lengths. This is in good agreement with the 1.363-A C-C length found in the X-ray crystal structure of 1,2,3-trisdimethylaminocyclo- propenium perchlorate.2" No systematic theoretical study of a variety of substi- tuted cyclopropenyl cations has appeared. In view of their high C-C stretching force constantz1 (for C3C13+ 6.32 mdyn/A us. 5.59 mdyn/A for benzene), the high degree of s character in the ring carbon to substituent bonds [J(I3C-H) zyxwvutsrqp = 265 Hz, 53% s for C S H ~ + ] , ~ ~ and their great stability, we undertook theoretical studies of such a series in the INDO approximati~n.~~-~~ In addition to C3H3+, C3F3+, C3(NH2)3+, and C3H2Ph+ we performed calcula- tions on CzBH3 (isoelectronic with C3H3+), cycloprope- none,26 protonated cycl~propenone,~? the azirinyl cation (CzNHz+), and the diazirinyl cation (CNzH+). The azir- inyl cations, for which simple Huckel MO calculations predict a 1.58/3 delocalization energy, have not been ob- served, but they have been implicated in isomerizations of 3-chloro-l-azirines.28 Similarly, the diazirinyl cation should be stable according to simple Huckel theory,29 but extended Huckel calculations predict it to be unstable with respect to distortion to a linear diazomethane cat- i0n.3~ Diazirinyl cations are postulated intermediates in reactions of halodiazirine~.~~?~~ Results The program (CNINDO), QCPE No. 141,33 was modi- fied for use on a Univac 1108.1 Structures were generated using model builder program QCPE No. 135. The geome- tries of all ions (except the phenylcyclopropenyl cation) were completely and systematically optimized with re- spect to all bond lengths and angle^.^^^^^ The optimum geometries of the cyclopropenyl (l), trifluorocyclopropenyl (2), and trisaminocyclopropenyl (3) cations had symmetri- cal equilateral triangular rings with the substituent bond axis on a line bisecting the CCC 60" angle and in the Ca plane (i.e., D3h symmetry). Boracyclopropene (4), the az- irinyl cation (5), and the diazirinyl cation each exhibit Czu symmetry. The bond lengths, angles, and charge den- sities are summarized in Figure 1. Figure 1 also summa- rizes the geometries and charge densities of cycloprope- none (7) ( CzV symmetry), protonated cyclopropenone (8) (C, overall symmetry with local Czu symmetry) and the phenylcyclopropenyl cation (9b). The charge densities are defined as q - Nwhere N = the atomic number. The *-bond orders of 1-9 are given in Table I and the calculated HOMO to LUMO energy gaps are below 85 nm for 1-9. We emphasize that these are Et - E, (eigenvalue differences) rather than El - E, - Jij + 2KLj as given by Pople3'ja for transition energies. The individual orbital q values have been obtained by calculations using several different axis systems.36b This provides a picture of the polarization both of the n and u bonds in 1-9. A few re- sults are noted in Table 11. Discussion Cyclopropenyl Cations 1-3. The only experimental and calculated geometry which may be compared is that of 3 with the X-ray crystal geometry of the trisdimethylamino- cyclopropenyl cation.20 The calculated C-C (1.40) and C-N (1.36) lengths in 3 are comparable to the observed C-C (1.36) and C-N (1.33) lengths. The fact that the ob- served bond lengths are actually slightly shorter than those calculated suggests that the INDO method will not seriously overestimate resonance effects in this series due to any serious underestimation of bond lengths. The ring bond lengths in the triphenylcyclopropenyl cation are