1612
J . Phys. Chem. 1991, 95, 1612-1618
than in 2-fluoroethanol. The zero-point effect lowers the energy difference between the cis-syn and cis-anti structures by 0.32 kcal/mol, which gives a hydrogen-bond strength of 3.2 kcal/mol. The cis-trans energy difference for the syn conformers decreases to 4.1 kcal/mol. The strength of the hydrogen bond is significantly higher in the enol than in the alcohol, 3.2 kcal/mol in the former and 1.9 kcal/mol in the latter. This difference is also reflected in the relative hydrogen-bond lengths, 2.37 8, in cis-syn-CHF+H(OH) and 2.52 8, in GG-CH2FCH20H. The former is 0.30 8,shorter whereas than the sum of H and F van der Waals radii (2.67 the latter is only 0.15 8, shorter. The stronger hydrogen bond in the enol can be attributed principally to its more favorable planar, five-membered ring geometry for intramolecular bonding.23 Vibrational Spectra. There are several notable features in the calculated vibrational spectra for 2-fluoroethanol. The 0 - H stretches shift from 4158 cm-' in the hydrogen-bonded GG structure to 4176 cm-' in the G T structure to 4183 cm-l in the 'IT structure. Such red shifts in the 0 - H stretches have previously been observed in other hydrogen-bonded systems.24 The hydrogen-bonding also raises the torsion frequency about the C - 0 bond from 244 and 241 cm-' for the G T and TT structures to 330 cm-' for the GG structure. Thus, the hydrogen bond helps to lock in the position of the bridging hydrogen. The torsional frequency about the C-C bond, 166 cm-l for GG or TT and 139 cm-' for TT, is only weakly affected by hydrogen-bonding. The value for the torsion about the C-C bond in the GG form is in good agreement with the assigned experimental valueZSof 152 f I O cm-I, especially since we have not scaled26 the calculated values to account for anharmonicity or correlation effects. The frequencies of the 0 - H stretches show some surprising trends in the 2-fluoroacetaldehyde enols. The 0 - H stretch in the (22) Bondi, A. J. Phys. Chem. 1964, 68, 441. (23) There appear to be no special electronic properties in the enol that might favor hydrogen-bonding, e.g., CHF=CH(OH) -CHFCH=O+H. The Mulliken charges on the F atoms, and on the 0 and H atoms of the OH groups, are nearly identical in CH2FCH20Hand CHF=CHOH and are virtually independent of geometry: qF,qo, qH (e) = -0.37, -0.64,0.38 (GG); -0.36, -0.63,0.38 ('IT);-0.36, -0.63,0.37 (GT); -0.35, -0.60,0.40 (cis-syn); -0.33, -0.58, 0.39 (cis-anti):-0.33, -0.60, 0.38 (trans-syn). (24) Pine, A. S.; Lafferty, W. J. J . Chem. Phys. 1983, 78, 2154. (25) Buckton, K. S.; Azrak. R. G.J . Chem. Phys. 1970, 52, 5652. (26) Dixon, D. A. J . Phys. Chem. 1988, 92, 86.
-
cis-syn structure with the hydrogen bond is 4142 cm-I. There is a significant blue shift to a frequency of 4198 cm-' in the cis-anti form, consistent with the results for 2-fluoroethanol. The trans isomer, however, shows a similar behavior, even though there is no hydrogen bond. The 0-H stretch is at 4156 cm-' in the trans-syn structure and at 4204 cm-I in the trans-anti structure. The rotated trans-anti structure shows a blue shift of only I O cm-' from the trans-syn frequency. Obviously, the trends in 0 - H stretching frequencies are not necessarily diagnostic of hydrogen-bonding. The lowest lying frequencies for the enols also exhibit informative trends. The three lowest frequencies in the cis-syn structure are at 260,419, and 591 cm-I and can be assigned to an in-plane bend, torsion about the OH bond and an out-of-plane bend, respectively. The cis-anti structure has these frequencies at 15 1, 263, and 580 cm-I, which are assigned to torsion about the 0 - H bond, an in-plane bend, and an out-of-plane bend, respectively. Thus, the 0 - H torsion, as expected, is more restricted in the cis-syn structure where there is a hydrogen bond. The other two frequencies show little change on rotation. In the trans-syn isomer, the 0 - H torsion frequency falls between the corresponding frequencies of the two cis conformers at 288 cm-l. The in-plane and out-of-plane bends are at 348 and 402 cm-I, respectively. The rotated trans-anti structure has the 0 - H torsion at a lower frequency of 209 cm-1 and the two bends at 351 and 371 cm-I. The trans-anti structure is a transition state with an imaginary frequency of 1831 cm-l for the 0 - H torsion and the in-plane and out-of-plane bends at 342 and 373 cm-l, respectively. Dipole Moments. The calculated dipole moment of 1.56 D for the hydrogen-bonded GG conformer of CH2FCH20H is in excellent agreement with the experimental value of 1.51 f 0.02 D.25 This agreement is consistent with the dominance of the hydrogen-bonded structure. The calculated dipole moment of the TT structure is 1.97 D and of the GT structure is 3.03 D. The calculated dipole moment of cis-syn-CHF=CH(OH) is only 0.89 D, compared with 3.35 D for the cis-anti conformer, which again is indicative of hydrogen-bonding in the cis-syn isomer. Even the dipole moment of the trans-syn isomer (1.84 D) is considerably larger than the cis-syn value. The rotated trans-anti conformer has a dipole moment of 2.07 D, and the trans-anti planar transition state has a dipole moment of 2.25 D. Registry No. (Z)-FCH=CH(OH), 371-62-0.
Theoretical Study of Stable Carbocations and Their Interactions with Anions Hiroshi Fujimoto,* Satoshi Denno, and Yasuhisa Jinbu Division of Molecular Engineering, Kyoto University, Kyoto 606, Japan (Received: August 2, 1990)
The relative stabilities of ion-pair and biradical (or covalent) electron configurations are studied with respect to a simple system, CH3--C3H3+,in a C3, symmetrical structure with a view of clarifying the basic feature of hydrocarbon ion pairs. As a possible source of stabilizing cations, the effect of hyperconjugation is analyzed on cyclopropenium ions by representing the interaction between the ring and the substituent groups in terms of paired interacting orbitals. The ability of carbon atoms in cyclopropeniumand tropylium ions for electron acceptance is also discussed by projecting out the reactive unoccupied orbitals each of which has the maximum amplitude on the 2p, atomic orbital of one of the carbon atoms in the threemembered or seven-membered ring. A tropylium ion with an interesting reactivity trend is suggested. Other factors that should stabilize hydrocarbon ion pairs are discussed.
Introduction The formation and cleavage of chemical bonds in organic reactions have long been discussed in terms of two mechanisms, Le., ionic and radical or heterolytic and homo1ytic.I The changes in
bonds are thought generally to take place along with a change in electron distribution. Recently, the possibility of an electrontransfer mechanism has been suggested.2 In that, transfer of an electron between the reagent and the reactant precedes the for-
( I ) See, for example: Lowly, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry; Harper: New York, I98 1.
(2).See, for example: Eberson, L. Electron Transfer Reactions in Organic Chemistry; Springer: Berlin, 1987.
0022-3654/91/2095-1612$02.50/0
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Stable Carbocations c
(4u %*I
-e-e-e-e-
+,
-e&?-
-&€+
-e-e-
“ ‘ 0 ’h amn
cation
crmbn
arion
C“+, Figure 1. Schematic illustration of electron configurations.
govern the stability of an ion-pair structure, we first employ a familiar way of describing the interactions by the molecular orbitals (MOs) of the cation and the MOs of the anion.I4 We begin with the electron configuration denoted by (Do illustrated in Figure 1. This should have the largest contribution to the wave function that represents a pure ion-pair structure, R1--R2+. Other important electron configurations are (Di-.,,+/ in which an electron is transferred from the occupied M O (i = 1, 2, ..., m) of the anion to the unoccupied M O cp,,+/ ( I = 1, 2, ...,N - n) of the cation. The highest occupied (HO) M O of the anion and the lowest unoccupied (LU) MO of the cation will be of particular importance. Each electron configuration is represented by the Slater determinant of the fragment MOs or a linear combination of determinants. For instance, we have
00
mation and breaking of bonds. However, it is easy neither to find out a clear evidence of an electron-transfer mechanism experimentally nor to provide theoretically quantitative arguments on the possibility of that mechanism in organic systems: except for a study on the process involving the Grignard r e a g e r ~ t . ~ It was reported recently that highly conjugated hydrocarbons, i.e., Agranat’s cation, tris[ 1-(5-isopropyl-3,8-dimethylazulenyl)]cyclopropenium ion,s and Kuhn’s anion, tris(7H-dibenzo[c,g]fluorenylidenemethy1)methide ion: gave a hydrocarbon i-Pr
Me
Kuhn’s anion
Agranat’s cation
salt.7 A similar salt was found also for the tricyclopropylcyclopropenium ion and Kuhn’s anion.* Systematic studies of carbon-carbon bond formation have been initiated by Okamoto et al. and by Arnett by synthesizing very stable carbocations and carbanions of conjugated hydrocarbon^.'^^ They observed an equilibrium between hydrocarbon molecules and their fragment ions and also an equilibrium between an ion pair and a radical pair that were transformed mutually by the transfer of an elect r ~ n . ~ .The ’ ~ existence of hydrocarbons that gave ionic salts in solid and ion pairs in solution was also depicted.’ These findings are important in understandirfg chemical bondings in molecules and in organic reactions. An attempt was made to study theoretically such systems from a thermodynamical viewpoint.” In this paper, we report the result of analysis on the electronic structure of some model hydrocarbon ions and their interactions.
Method Electron-donating and -accepting interactions between molecules have been discussed most frequently in terms of the frontier orbitals.12J3 With a view of getting insight into the factors that (3) Pross, A. Acc. Chem. Res. 1983, 16, 363. (4) Nagase, S.;Uchibori, Y. Tetrahedron Lett. 1982, 23, 2585. (5) Agranat, 1.; Aharon-Shalom, E. J. Org. Chem. 1976, 41, 2379. (6) Kuhn, R.; Rewicki, D. Angew. Chem. 1976, 79, 648. (7) Okamoto, K.; Kitagawa, T.; Takeuchi, K.; Komatsu, K.; Takahashi, K. J . Chem. Soc., Chem. Commun. 1985, 173. (8) Okamoto, K.; Kitagawa, T., Takeuchi, K.; Komatsu, K.; Miyabo, A. J . Chem. Soc., Chem. Commun. 1988, 923. (9) Troughton, E. B.; Molter, K. E.; Arnett, E. M. J. Am. Chem. SOC. 1984, 106, 6726. (IO) Arnett, E. M.; Molter, K. E.; Marchot, E. C.; Donovan, W. H.;Smith, P. J . Am. Chem. SOC.1987, 109, 3788. ( I 1) (a) Marcus, R. A. J. Chem. Phys. 1956,24,966. (b) Marcus, R. A. Ann. Rev. Phys. Chem. 1964, 155, 15.
1613
*i-n+/
= 1/
-
~ ~ ~ + l ~ l ~ . ~ d i ~ n + / . ~ . ~ m ~ m ~ l P l . . ~ ~ ~ R . . ~ ~
I+!$1 ~ ~ . ~ i ~ n + ~ ~ . 4 *m* *$~ mk p~ k1* *p * ~~ n ~(1 n )I J
where 4iand cpn+[ indicate the ith occupied MO of Rl- and Ith unoccupied M O of R2+. A basic aspect of chemical interactions between an electron donor and an electron acceptor is interpreted most clearly by this description.1s In the previous studies of reactions involving electron transfer between a reagent and a reactant, no quantitative or semiquantitative argument was provided.16 In the present study, we calculate the energy of electron configurations, Hps (p = 0, i n I, ...), and the interactions between two configurations p and q, (Hp,q- Sp,qHo,o),defined in eqs 2 and 3 by applying the
-+
Lowdin orbital transformation^^^ and the corresponding orbital formalism,ls since the MOs 4 of the anion are not orthogonal to the MOs cp of the cation.19 In eq 2, H is the Hamiltonian of the composite system of RI- and R2+. Our primary purpose is not to obtain quantitative results on this simplified model but to see some trends. Hence, we emplgyed the minimal STO-3G basis set for calculations in the present study.*O The H O M O and LUMO are usually delocalized over the constituent AOs in sizable species. To discuss the factors that should control the stabilities of cations and anions, we next introduce the orbitals that specify the local activity of atoms or some structural units in large molecular systems.21 By dividing an interacting system into two fragments, we transform their MOs simultaneously within each fragment species so that the interfragment part of the density matrix of the composite system has nonzero values only between the paired fragment orbitals.22 We utilize this method to analyze the conjugation between the substituent groups and a cation ring by means of a few pairs of interacting fragment orbitals. We also try to compare the abilities of a structural unit or a functional group for electron donation (12) Fukui, K. Theory of Orientation and Stereoselection; Springer-Verlag: West Berlin, 1975. (13) Fleming, I. Frontier Orbitals and Organic Chemical Reactions; Wiley: London, 1976. (14) Fukui, K.; Fujimoto, H. Bull. Chem. SOC.Jpn. 1968, 41, 1989. (15) Mulliken, R. S.;Person, W. B. Molecular Complexes; Wiley: New York, 1969. (16) See ref 3. Other electron configurations can be included in a similar manner, if necessary. (17) LBwdin, P.-0.J . Chem. Phys. 1950, 18, 365. (18) Amos, A. T.; Hall, G. G. Proc. R . SOC.London, A 1961, 263,483. (19) Fujimoto, H.; Kosugi, N. Bull. Chem. SOC.Jpn. 1977, 50, 2209. (20) Binkley, J . S.;Whiteside, R. A,; Krishnan, R.; Seeger, R.; DeFrees, J.; Schlegel, H. B.; Topiol, S.;Kahn, L. R.; Pople, J. A. QCPE 1981, 13, No. 406. (IMS Computer Center Library Program No. 372, 482.) (21) Fujimoto, H. Acc. Chem. Res. 1987, 20, 448. (22) (a) Fukui, K.; Koga, N.; Fujimoto, H. J . Am. Chem. Soc. 1981, 103, 196. (b) Fujimoto, H.; Koga, N.; Hataue, I. J. Phys. Chem. 1984,88, 3539. (c) Fujimoto. H.; Koga, N.; Fukui, K. J . Am. Chem. Soc. 1981, 103, 7452. (d) Fuj.i.moto. H.; Yamasaki, T.; Mizutani, H.; Koga, N. Ibid. 1985, 107, 6157. (e) Fujimoto, H.; Yamasaki, T. Ibid. 1986, 108, 578.
1614 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Fujimoto et al.
TABLE I: Energy Difference end Interactions between Electron Configurations in the CH3--C&+ System at R = 2.6 A (in au) occupied unoccupied MOs of CpHp+ MOs of CH; 4e 4e 5a 5e 5e energy le 0.234 0.236 0.5 18 0.543 0.539 -. difference" le 0.236 0.234 0.5 18 0.539 0.543 3a -0.029 -0.029 0.258 0.286 0.286 matrix elements le 0 -0.0 162 0 -0.0003 0 le -0.0162 0 0 0 -0.0003 3a 0 0 -0.0000 0 0 "The configuration @o was taken as the reference, Hi-.i,i-, - Ho,o. a.u. 0.2
or acceptance in different molecular species in the following manner. A certain orbital function 6, that characterizes the interaction of a functional unit is projected onto the occupied or unoccupied orbital space of sizable species to give the orbital that has the maximum amplitude on that reference function. For instance, the unoccupied orbital that is localized in that unit,,,,$ ,' is given by a linear combination of the unoccupied MOs, $m+j (j = I , 2, ...,M - m), and the ability of the structural unit for electron is evaluated by a sum of the orbital energies, acceptance, A,,
0.1
9
tm+j:
c
m 6r
=
M-m
C di,r$i + jC =I M-m
d'unoc(6r)
v)
dm+j,rdm+j
i= I
=
C
'I I
r
(4)
5 0 2.2
2.6
M-m dm+j,r$m+j/(
EI
dm+j,r?I'*
(5)
3.0
a
R
0
J=
H
-0.1
The reactivity of a functional unit in different molecules or at different positions in a molecule can be compared in a unified manner.23 By applying these methods, we examine the possibility of yielding hydrocarbon ion pairs and look for ions of interesting properties.
Results and Discussion Electron Configurations. We investigate first how the ion pairs are stabilized to form stable salts of hydrocarbon ions. To get insight into the factors that should contribute to the stabilization of the ion-pair structure relative to the covalent structure, we employ a model of a cation-anion pair extremely simplified by removing all the substituents as illustraged in Figure 2. Possible effects of substituent groups will be discussed later. It has been reported that a covalent hydrocarbon is observed in solution, but it is converted to the corresponding salt in a solid state.' Thus, we begin with a C,, symmetrical structure. The electron configuration denoted by a0 involves two interaction terms, Le., the Coulomb attraction between the charges and exchange repulsion between the occupied MOs of two ions. Figure 2 illustrates that the repulsion is not significant at a large value of R, but it increases rapidly when R gets smaller than 2.6 A. The energy of interaction in Oo [Ho,o- E(CH
