3082 J . Org. Chem., Vol. 40, No. 21,1975
Jaff6 and Koser
On the Electronic Structure of Phenyl Cation. A CNDO/S Treatment Hans H. Jaff6* Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221
Gerald F. Koser* Department of Chemistry, T h e University of Akron, Akron, Ohio 44325 Received February 25,1975 Calculations (CNDO/S with CI) on 12 electronic states of phenyl cation in the symmetric benzene geometry ~ state by have been performed. The ground singlet state is predicted to be more stable than the lowest u , ? triplet 0.87 eV and more stable than the lowest closed-shell excited singlet state by 1.56 eV. Extension of the calculations to two other geometric configurations revealed that the various electronic states of phenyl cation can be divided into three geometric categories. Those electronic states with a vacant C-1 u orbital prefer a highly distorted geometry in which C-1, C-2, and C-6 are colinear while those states with two electrons in the C-1 u orbital prefer the symmetric benzene geometry. Electronic states with one electron in the C-1 u orbital either prefer an intermediate geometry or show little discrimination between an intermediate geometry and that in which C-1, C-2, and C-6 are colinear. The conformational preferences of the various electronic states of the phenylium ion appear to be related to orbital hybridization a t C-1.
In 1961, Taft suggested that the phenyl cation (I), presumably formed during the thermal hydrolysis of benzenediazonium salts, may actually exist as the a,a-triplet diradical 2 in its ground state.l This proposal was subsequently extended by Abramovitch and his coworkers, who studied the phenylation of various aromatic substrates with benzenediazonium tetrafluoroborate.2 They obtained partial rate factors comparable to those for similar arylations with highly electrophilic radicals such as 2-nitrophenyl (4)
H
1
2
Y
Y
3
4
culations on the 4-aminophenyl cation, however, revealed a profound substituent effect. In this case, the lowest triplet state is predicted to be slightly more stable (0.01 eV) than the lowest singlet state, and it exhibits the v,a configuration. Although their calculations oppose the notion of a facile interconversion between 1 and 2 for the parent cation, the authors issue a caveat regarding the accuracy of their findings since the computations were made without the inclusion of configuration i n t e r a ~ t i o n . ~ More recently, Swain and his coworkers reported INDO calculations with geometry optimization (but without CI) on 1 and were led to the surprising conclusion that C-1, C-2, and C-6 are colinear in the ground singlet state of phenyl cation (see conformation I, Chart I). The calculated en-
Chart Ia
and argued that the phenyl cation must be endowed with radical charactere2To rationalize the ability of aryl cations to sometimes undergo apparent insertion reactions typical of singlet carbenes (see eq 1),3 structure 3 for CsH5+ was 0
CH,Ph
d\
N
< CH,Ph ++$FCHPj A 3 N2+
H
H 1.397
1 also proposed.2a The authors concluded that a dynamic equilibrium between 1, 2, and 3 would “account for all the reported properties of the phenyl cation.’’2a A quantitative assessment of the possible existence of triplet diradical 2 has been published by Evleth and Horow it^,^ who performed INDO calculations on CsH5+ with a symmetric benzene geometry (see conformation I11 below). Their results place the lowest triplet state of phenyl cation 3.5 eV above the ground singlet state. Moreover, the electron configuration of the INDO triplet is such that all of the positive charge and both unpaired electrons reside in the c system. That is, the triplet is of the a,g type and is not the C , K triplet originally proposed by Taft. Similar cal-
1
I1
I11 All C-H bond lengths in each conformation were taken to be 1.084A.
ergy difference for the optimal geometry vs. the symmetric benzene geometry is 4.05 eV (94 kcal mol-l). The linear INDO triplet was found to be 146 kcal mol-l less stable than the linear INDO singlet, but the authors did not indicate whether it was of the o , ~ a,a, , or ?r,a type.5 At this point, it is well to keep in mind that conventional INDO calculations such as those described above (program QCEP 141) cannot be applied indiscriminately to any given electronic state of a molecular species. Molecular orbitals are
J. Org. Chem., Vol. 40, No. 21, 1975
CNDO/S on the Electronic Structure of Phenyl Cation
3083
Table I Phenylium Ion C G H ~(Symmetric + Benzene Geometry) Relative State Energies in eVa Virtual State
SCF
orbitals
0 1.18 0.90 1.84 2.17
->, v
Singlets calculated with Mataga and triplets with Pariser integrals.
h
populated in such a way that only the lowest lying singlet and triplet states will be generated. Thus, in the case of phenyl cation, Evleth and Horowitz found that the singly occupied orbitals of the INDO triplet are u orbital^.^ Furthermore, since conventional INDO calculations cannot predict relative energies of various excited states in a reasonable manner, the conclusion that the low-lying triplet is of the u p type seems doubtful.
W
a
M L
c)
E
0)
.-m
-
I .
0
cc
Results and Discussion No calculations on the electronic states of phenyl cation specifically represented by valence-bond structures 2 and 3 appear to have been performed, and, therefore, the possible coexistence of species 1,2, and 3 remains an open question. In this paper, we report the results of CNDO/S calculations6 with configuration interaction on 12 electronic states of phenyl cation including those represented by structures I, 2, and 3. As described elsewhere, the CNDO/S method has been parameterized for the accurate computation of energy differences between various electronic states of a given molecular species.6 Our computations have two unique features. First, the electrons have been "forced" to reside in either the u or T system of phenyl cation depending on which electronic state is being ~ t u d i e d Second, .~ we report some of the first calculations on closed-shell singlet excited states. Two sets of computations were performed. In the first set, the symmetric benzene geometry (conformation 111) was assumed. In the second set, two other geometries were examined, namely, the geometry of Swain's linear INDO singlet5 (conformation I) and a geometry halfway between that and the symmetric benzene geometry (conformation 11). The results of the first set are summarized in Table I. Configurations are given in terms of the three highest occupied orbitals of phenyl cation (point group Cz0), namely, the a2 and bl T orbitals and the a1 n orbital shown below. The a2 and bl orbitals are not degenerate as they are in benzene, and, for that reason, the 3A2 and 3B1 states of phenyl cation differ in energy. Structures 1, 2, and 3 refer to the az2b12singlet, the a22blal triplet, and the aZ2al2singlet states, respectively.
aL
b,
a,
Our calculations predict that the U,T triplet 2 should be significantly less stable than 1 (0.87 eV), but the energy gap is not nearly so large as that predicted by INDO calcula-
I
n C o n f o r m a t ion
Figure 1. Relative energies of various electronic states of the phenylium ion as a function of molecular geometry.
tions between 1 and the u,a-triplet diradical. Likewise, the closed-shell excited singlet species 3 is predicted to be less stable than 1 by 1.56 eV. By way of comparison, CNDO/2 SCF calculations yield energy differences of 3.47 eV between l and 2 and 7.67 eV between l and 3. Also, the positive charge of the phenylium ion in all of its electronic states is significantly more delocalized than indicated by classical valence-bound structures. The computed electron densities, broken down into u and T contributions, are summarized in Table 11. There is little justification for the assumption that phenyl cation will prefer the symmetric benzene geometry in each of its electronic configurations. Indeed, it seems more likely that each electronic state will exhibit a unique geometry. Accordingly, we have extended our treatment to include conformations I and I1 for all states listed in Table I. Also, we have performed calculations on four *,a* excited states in all three conformations. Excited-state energies were determined by adding CNDO/S excitation energies to appropriate CNDO/2 ground-state energies. The data are displayed in Table I11 and Figure 1. Our CND0/2 computations on the singlet ground state (a22bI2) of phenyl cation are consistent with the finding of Swain and his coworkers that conformation I generates an energy minimum. However, the most intriguing feature of our calculations is the natural division of the electronic states of phenyl cation into three geometric categories. Those species with a vacant u orbital (al) a t C-1 are most stable in conformation I while excited states in which two T electrons have been transferred to the C-1 u orbital are most stable in conformation 111. For example, the singlet ground state (sib?) prefers conformation I over conformation I11 by 5.26 eV, but the closed-shell excited singlet state (aza?) prefers conformation I11 over conformation I by 1.96 eV. Finally, those excited states with one electron in the a1
3084 J.Org. Chem., Vol. 40, No. 21,1975
Jaff6 and Koser Table I1 (Symmetric Benzene Geometry) Electron Distributions
Phenjlium Ion C&+
1Ai (ai a;)
'Ai (a$bi) r
Atom
u
1
2.46 2.99 2.97 3.08 0.90 0.91 0.92 +1.02
2 3 4 7 8 9 Charge
1.30 0.92 1.oo
0.85
+0.01
a
Total
3.77 3.90 3.97 3.93 0.90 0.91 0.92 Cl.03
3.84 3 -17 2.98 3.30 0.91 0.93 0.88
-1 .oo
3B1 ( g b l a l ) a
1 2
3.17 3.05 3.04 3.16 0.90 0.90 0.90 -0.01
3 4 7 8
9 Charge
a
Total
0.62 0.92 0.94 0.67
3.79 3.96 3.98 3.82 0.90 0.90 0 -90 +o .99
+o -99
3.04 3 .lo 3 .ll 3.03 0.90 0.90 0.91 0
Table I11 Phenylium Ion C6&+ Relative State Energies (in eV) for Various Conformations Energy Statea
0 0
. . .
1
I1
1x1
3 -64 4.36 3.91 4.50 4.62 5.50 4.99 5.54 8.78 9.84 10.92
1.32 4 -93 4.40 5.64 4.59 6.28 7.24 4 -63 5.51 7.67 8.40 9.12
5.26 8.78 6.13 9.33 6.16 10.18 10.80 6.26 7.45 6.82 7.58 8.37
nb
1 0 1 0 0 1 1 2 2 2
-
0
States marked x A* involve various mixtures of such promotions. The number of electrons occupying orbital ax. a
0.13 0.71 1.02 0.42
+1.99
Total
a
3.97 3.88 4 .OO 3.72 0.91 0.93 0.88 +o .99
3.59 3.22 3.29 2.87 0.90 0.89 0.93 -0.99
3Az(&?b;ai)
u
Atom
U
l A i (b;aT)
orbital either prefer an intermediate geometry (not necessarily conformation I1 which lies exactly halfway between conformations I and 111) or show little descrimination between conformations I and 11. It seems clear that the driving force behind the conformational preferences of the phenylium ion can be related to the state of hybridization of C-1. Thus, when the C-1 orbital is vacant, it acquires 100% p character (sp hybridization a t carbon), but when the C-1 u orbital contains two electrons, it tends toward maximum s character (sp2 hybridization at carbon). A sin-
U
0.98 0.75 0.75 1.02
+l.oo
Total
T
0.66 0.63 0.44 1.21
4.25 3.85 3.73 4.08 0.90 0.89 0.93 +0.98
+1.99 3B~(a~bia;)
Total
a
4.02 3.86 3.86 4 -06 0.90 0.90 0.91 +1.00
3.77 3.18 3.14 3.08 0.90 0.90 0.90 -0.99
Total
u
0.40 0.66 0.73 0.85
4.17 3.83 3.86 3.94 0.90 0.90 0.90 +1.01
+1.99
glet electron in the C-1 0 orbital distorts the symmetric benzene geometry but not necessarily all the way to conformation I. It is comforting to note the estimation of excitedstate energies by the addition of CNDO/S excitation energies to CND0/2 ground-state energies agrees with chemical intuition. Finally, it can be seen from the data in Table I11 that the triplet diradical2 (a:blal) is clearly not the ground state of phenyl cation. Indeed, both the 3A1 and 3B1 rr rr* triplet excited states are predicted to be of lower energy than 2. Further, the singlet species 3 (ais:) in its most stable conformation is placed 6.82 eV above 1 in its most stable conformation. Hence, we are forced to conclude, within the framework of our calculations, that the aiblal triplet and az2b12singlet states of phenyl cation may not be accessible through the thermal decomposition of benzenediazonium salts, and the rate factors of Abramovitch should probably be explained in some other way.
-
Registry
No.-Phenylium
ion, 17333-73-20.
References and Notes (1) R. W. Taft, J. Am. Chem. SOC.,83,3350 (1961). (2) (a) R. A. Abramovitch and J. G. Saha, Can. J. Chem., 43, 3269 (1965); (b) R. A. Abramovitch, W. A. Hymers. J. B. Rajan, and R. Wilson, Tetrahedron Lett., 1507 (1963); (c) R. A. Abramovitch and F. F. Gadaliah, J. Chem. SOC.S, 497 (1968). (3) T. Cohen and J. Lipowitz, J. Am. Chem. SOC.,86, 2514 (1964). (4) E. M. Evleth and P. M. Horowitz, J. Am. Chem. Soc., 93, 5636 (1971). (5) C. G. Swain, J. E. Sheats. D. G. Gorensteln, and K. G. Habison. J. Am. Chem. SOC.,97, 791 (1975). (6) (a) J. Del Bene and H. H. Jaffe, J. Chem. Phys.. 48, 1807 (1968); (b) R. L. Ellis, G. Kuehnlenz. and H. H. Jaffe. Theor. Chim. Ada, 28, 131 (1972); (c) H. M. Chang, H. H. Jaffe, and C. A. Masmanidis. J. Phys. Chem., in press. (7) For an explanation of methodology, see H. H. Jaffe. H. M. Chang, and C. A. Masmanidis, J. Comput. Phys., 14, 180 (1974).
