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The importance of orbital overlap on the structure and stability of organic free radicals
153
Journal of Molecular Structure, 103 (1983) 153-162 THEOCHEM Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE IMPORTANCE OF ORBITAL OVERLAP ON THE STRUCTURE AND STABILITY OF ORGANIC FREE RADICALS * R.F. HUDSON UNIVERSITY CHEMICAL LABORATORY, CANTERBURY, KENT. CT2 7NH.
U.K.
ABSTRACT The electronic energy of free radicals is discussed by using a l-electron treatment for first and second order perturbationswith the inclusion of orbital overlap. In particular the stability of bridged radicals and their tendency to 1.2 rearrangement are discussed in the light of experimental data. The role of orbital energies in determining the conformation of B-substituted radicals is examined quantitatively. Application of the perturbation equations to the relative stability of n and c states leads to a general rule which can be applied also to dissociation energies of molecules leading to conjugated free radicals, in particular radicals of oxygen and nitrogen. Perturbation theory was first applied by Dewar (ref.1) to the structure and reactivity of free radicals in the development of P.M.O. theory, and by Fukui (ref.2) in a quantitative treatment of atom abstractions. By considering the interaction of occupied and unoccupied orbitals of two interacting systems (Fig. 1) one-electron Hiickeltheory leads to the general equation occ AE
=
2
j
unocc
cm-(CCrjCskYrs)2 a-
J
k
-
+
ak
occ
unocc cc CrjCskyrs)2
Cc k
(1)
ak-a j
j
For the interaction of the S.O.M.O. with the frontier orbitals (Fig. 1) AE
q
(C .O)ZC 2y 2 sk rs rJ
t
(C .0)2C 2y 2 sk rs rJ ak - ajo
a. Jo - ak
(2)
where C .O is the coefficient of atom r in the S.O.M.0; of energy a.O, CSk is the J coeffi&t on the terminal atom, s, of the H.O.M.O. and L.U.M.O., and yrs is the appropriate exchange integral for the interaction concerned. This approach has been extended (ref.3,4) to other radical processes, e.g. addition and aromatic substitution, and explains the concept of nucleophilic and electrophilic radicals. This treatment is limited particularly by the neglect of orbital overlap. For example Hickel theory predicts a stabilisation of B,, for the cyclopropenyl *Dedicated to Professor Kenichi Fukui in honour of the award of the 1981 Nobel Prize in Chemistry. 0166-1280/83/$03.00
0 1983 Elsevier Science Publishers B.V.
154
radical (r) whereas Extended Hiickelcalculations (ref.5) show the E form to have a lower energy than the 71in agreement with ab initio calculations (ref.6) and with the limited experimental data (ref.7). This restriction applies to other radical systems and it is the object of this paper to consider the effect of retaining the overlap term on the l-electron perturbation energies. We proceed as follows. The combination of the wavefunctions of 2 orbitals $1 and@s in the lelectron approximation leads to the secular determinant, Ei-E
H ij-ESij
H ij-ESij
Ej-E
where Ei and Ej are energies of 61 and a2 respectively, Hij is the Hamiltonian and Sij the overlap integral.
The energy change AE = 2E-(Ei + Ej) is given by the solution, AE
=
2(Ei + Ej)Sij2 _ 4HijSij + C(Ei - Ej)2 t 4(Hij - EiSij)(Hij-EjSij)lt (3) 2(1 - Sij2)
For the combination of two sub-groups R and S at atoms r and s, the Hamiltonian and overlap integral become
'riCsjHij
and
C .C .S rl so ij
adopting the procedure of Herndon (ref.8). In general equation (3) is solved numerically, but the following limiting' solutions may be employed (ref.g) when
Ei = Ej, A+
= CriSsj(Hij _ EiSij)
and
1 - C,iC,jSij
l + C,iS,jSij and AE”
= -Cri2Csj2(Hij - EiSij)2 and
-C,iCsj(Hij - EiSij)
C m2C .'(Hij - EjSij)2 rl SJ
(4)
(5)
Ei - Ej
Ei - Ej when Ei >> E..
These reduce to the Hickel perturbation equations when Sij = 0, giving first order (AE’)
and second order (AE”)
perturbation energies.
For one and two electron interactions, Hiickeland Extended Hickel P.M.O. treatments give similar results, but for three and four electron interactions the two treatments differ completely, L&Z., From equations (4) and (5). for a 4-electron interaction AE’
=
-4Cri2CSj2CHijSij- EiSij21
(6)
155 and
*Err
=
-2Cri2Csj2E2HijSij- (Ei + Ej)Sij21
(7)
II = 0. whereas in the Hijckeltreatment ,E1 and AE The 3-electron interaction is particularly interesting, i.e.
d and
N
C,iS,j(Hij
AE”
N
-
EiSij) /(I
_
XriCsj’ij)
Cri2Csj2[2(Hij - EiSij)2 -
(8) (Hij - EjSij)21
(9)
Ei - Ej These equations lead to the following important conclusions which may be called the overlap rule (ref.3) and the energy rule (ref.10). (a) As the overlap integral, Sij, increases the perturbation energy decreases to a minimum and then increases to become positive at some limiting value, The magnitude of the energy minimum decreases as the energy (Sij)lim.* difference (Ei - Ej) increases. (b) As the energy difference (Ei - Ej) increases the perturbation energy changes from negative to positive at some critical value (Ei - Ej)lim . Thus in contrast to one electron and'two electron interactions which are always stabilising and four electron interactionswhich are always destabilising, three-electron interactions, always present in free radicals, may be stabilising or destabilising depending on the electronic structure of &he radical. As pointed out previously (ref.3). radicals such as HS2*, HO; and RsN6 are strongly stabilised since the magnitude of Sij is significantly less than (Sij)lim.. Epiotis (ref.10) has pointed out that when the radical centre is joined to an atom of high electronegativity (in particular F, Cl, OR), this energy becomes positive, according to the energy rule, and carbon centred radicals deviate from the planar configuration. Since Walsh's rules (ref.11) also predict a
deviation
from planar to pyramidal it appears that several factors are involved and a unique rule cannot be assumed for the three-electron destabilisation (tide
infm).
We now proceed to apply the rules to other systems of interest, in particular bridged radicals and 1.2 rearrangements. Bridged radicals (ref.12) The rotational barrier in B-substituted radicals, and the stabilisation of the eclipsed form by bridging, may be discussed first by considering hyperconjugation involving u and u* orbitals (ref.l3), and then where appropriate the combination of the S.O.M.O. with the non-bonding electrons on the substituent (Fig. 2(a)). As far as hyperconjugation goes, the S.O.M.O.-o interaction should be greater than the S.O.M.O.-a* interaction because the orbital energies of the first pair
166
SOMO Lj, 1 #-
i-w
Fig. 1.
k-i-k
00
00
c-~-~-~ @ 8 X
”
n
0
(a)
0
Fig. 2.
a@ a’ (b)
are normally similar whereas U* energies are high (ref.14). Thus electron donat ing (electropositive)groups, e.g. RsSn, RsSe, RsSi, increase the orbital coeffin cient (Csj) on the s-carbon atom, thus increasing the three electron stabilisation (with Sij =
0.2 << 0.33).
Conversely, electron attracting substituents decrease the stabilisation (since u and.o* energies decrease (ref.l4)), in spite of a compensating increase in the S.O.M.O.-o* perturbation. Thus first row substituents, e.g. F, OR, have small rotation barriers with minima at the gauche form (ref.15). Considering the combination of the S.O.M.O. and n(p,) orbitals on a substituent, X, the energy is negative when Eiz
Ej, but as the group X migrates to the
a-carbon atom, Sij increases (Fig. 2(b)), thus increasing the energy, AE. other words bridged
~adicaZs
are
msyrmetrica2
In
as found experimentally for the
6-chloroethyl radical (ref.16). In addition to the overlap restriction, the energy restriction controls the stability of the bridge (equation 9).
To examine this quantitatively, the
Hamiltonian is given by the Wolfsberg-Helmholtzapproximation in the usual way, i.e.
157
H
ij
=
k = 1.75
0.5k(Ei t Ej)Sij
The present case issimplified since C,i = Crj = 1.0 and then equation (9) becomes AE
=
C2(0.5k(Ei + Ej) - E.)' - (O.Sk(Ei t Ej) - E.)']Sij'
(10)
Ei - Lj and
AE = 0
when 3
=
2fl-
E. J
(fl- 1)k
(n-
(11)
1)k t 2
With Ei = 10 e.V., i.e. the ionisation potential of the methyl radical as appropriate for a carbon centred radical, values of Ei/E.ican be obtained for a range of a-substituted radicals (Table 1). TABLE 1 Relative stabilities of bridged free radicals.
I.P.(a)(e.V.) s
(b) ij
S
I
Br
Cl
0
F
10.5
10.5
11.5
12.8
13.5
17.5
0.072
-AE(k.cal.mole-') 6.76(')
0.076
0.081
0.067
7.54(')
2.97
0.22
-0.72
lb0
nb
Conformation
b
b
b
-log k(d)
-
5
8
0.083
0.088 -1.3 nb
-
(a) values for the isolated atoms (b) Slater overlap integrals (c) Treated as a first order perturbation (equation (8)) (d) Rate values given by P.S. Skell (ref.12). These data show that the decrease in stability of the bridged radical predicted by equation (10) with increase in lone-pair ionisation potential is observed experimentally with a change from stabilisation for a B-chlorine atom to de-stabilisationfor a a-oxygen substituent. The estimated stabilisation energies, AE, also correlate well with the decomposition rates estimated by Skell (ref.12) from the observed half-lives, and with the calculated values of Rossi and Wood (ref.15). 1.2 Radical rearrangements (ref.32) It is well known that hydrogen atoms and alkyl groups do not undergo the 1.2 rearrangements in free radicals (ref.17) which are so comnon in carbonium
158 ions. This has been explained in general terms (ref.18) by the occupation of the high energy anti-bonding orbital. It
is not clear however from this
explanation why other radicals with a singly occupied anti-bonding orbital, e.g. nitroxyl, peroxy, should be strongly.stabilisedelectronically, This dichotomy is resolved by the two rules given above.
Accordingly,
migration of an alkyl group leads to an increase in overlap Sij (Fig.
2) given
approximately by ~.Sij for a given internuclear distance. With Sij N 0.25 for a C-CT-bond, this gives a group integral of 0.35 which is greater than (Sij)lim .
.
This leads to a high activation energy. Phenyl groups and halogen atoms (with the exception of fluorine) and thiol groups migrate intramolecularly(ref.19). There is some doubt concerning the
migration of alkoxy groups, but since rearrangement competes with disproportionation, recombination and other radical processes, low activation energies are essential. Why then does a chlorine atom migrate intramolecularlywhereas a methyl group does not although C-C and C-Cl dissociation energies are similar? Assuming a symmetrical transition state, the following orbital combinations using p, and p, atomic orbitals on the migrating group X have to be considered (Fig. 3).
00
00
00
-c
063
&a3 @ 0 X
&x6
I-
3 (4 electrons)
(2 elecbons)
(2 electrons)
( 1 electron)
Fig.
3.
The transformationleading to orbitals I and IJ is accompanied by an increase in energy for the reasons already discussed (see equation 9). repulsion represented by III
The four electron
is zero, since the orbital combination is symmetry
forbidden, whereas the stabilising two-electron combination of II*and n(C1) orbitals is symmetry allowed. This leads to a decrease in energy which allows the 1.2 migration to proceed with a low activation energy. A similar explanation may be given for the 1,2 migration of aryl groups, but it is noted that the rearrangementof the B-phenylethyl radical is a high energy process (ref.20).
159 Radical addition to multiple bonds may be treated similarly. This involves the perturbation of the S.O.M.O. by n and n* orbitals (Fig. 4).
630 -C
@@
c-c
6@ 0
00
0 X
Fig.
4.
X
9
3
A consideration of V and VI shows that the radical approaches one (carbon) atom of the multiple bond rather than the centre of the n-bond. This reduces the value of Sij (in V) to a value close to the optimum value (ca. 0.1 to 0.2 when Ei =
Ej), and develops positive overlap with the n* orbital (VI). A further
increase in S ij is produced by an increase in the angle of approach (C-C-X > 98) which provides a basis for the well known rule of em-addition in radical cyclisations (ref.21). Further, it is evident that nucleophilic radicals
must
adopt this configuration since Sij = 0 for the S.O.M.O. - n* combination at the centre of the n-bond. For these reasons radicals do not form n- complexes, although transient species are possible with highly electrophilic free radicals. The relative stability of IIand c radicals The ground states of conjugated carbon radicals are uniformly IIalthough 2.6~tert butyl benzyl radicals adopt the high energy 1 form for steric reasons (ref.22). When heteroatoms with lone-pairs are attached to r-systems a wide range of molecular states is possible, e.g. for the acyloxy radical (ref.23), 2A2(n)s
2A~(z).
2B2(~)
with C2v sy mmetry and 2A"(n) and 2A1(~) with C, synrsetry.
It is now widely accepted that, as a result of ab initio calculations (ref. 23.24) and on the basis of limited experimental data (ref.25) the ground state of RC02* is a I:radical (as required for a low temperature fragmentation). On the other hand the phenoxy radical is n with a resonance energy (17 k.cal.mole-'). Nitrogen radicals are similarly complex. Thus the aminyl radical *NH2 has the n configuration (ref.27), ca. 1.5 e.V. lower than the lowest c state. The amidyl radical, R*COaMe is also known to have a lower energy n state (ref.28), whereas recent work of Skell (ref.29) has suggested that succinyl radicals can be prepared in n and 1 states with the former lower in energy.
160 As no general treatment of the problem appears to have been made, we shall enquire into the electronic factors which stabilise one state relative to another. This can be approached by the following qualitative perturbation argument Consider the r-systems corresponding to IIand z states, for example for the combination of an oxygen atom with a a-system. This involves the combination of the S.O.M.O. with ITand II*orbitals (71state) and of a doubly occupied n-orbital of oxygen with the n and II*orbitals (c state) as in Fig. 5.
\
/ I \
Eo f
/ \
,
\
J-C,
\
\-2s1 \
\
\
/
/
'r ',
K
=#
/
\
/
‘r
I
ti
‘Et VIJ
Ftg. 5. The r-electron energy of the n state is given by AEn
=
- 2E2 +
-Ed
where
E3
Er
=
-2e2 +
93
and of the c state by AE, =
-2~~ - 2~~ t
where
2~s
Thus AE, - AE,,= ~3 - ~1 =
Er
Csk2(H.. 'J - EoSij)2 Eo - EI
1
=
'2E2 t
2~s '12
C:kz[HI'. 1J _ EoSiJ
(12)
E* - E0
For the combination of a p, orbital of oxygen with the T and
n*
orbitals of
benzene (to give the phenoxy radical) it is clear that E* - E, >> El and Csk = CSk*' stabilised.
COtISeqUently E3
>>
~1
and AEa >> AET, i.e. the
n
State
is strongly
With the substitution of strongly electronegative groups, e.g. by the substitution of C=O for C=C, the energies of n and n* orbitals decrease, and C *>c Consequently E3 - ~1 decreases, so that for a large effect AEn > sk sk' BEE. This leads to the conclusion that etectron attracting substituenta in a conjugated
free
m&cat
favour
the c state
over the II state.
Similar considerations apply to the o-system where hyperconjugation (ref. 13) stabilises the x state and 4-electron repulsion destabilises the n state, reinforcing the above conclusion. In addition, in the acyloxy radical 3-
161 electron stabilisation involving a lone pair on oxygen (VII)
also stabilises
the c state. A similar argument can be applied to dissociation leading to conjugated radicals. Thus although diphenyl peroxides are unknown, stable triazinyl peroxides have recently been reported (ref.30). This change in stability is explained as follows. Dissociation of hypothetical diphenyl peroxide produces initially the c radical since the molecule is n-conjugated,which immediately transforms to the stable n ground state, viz.
r-conjugated
z
iT
The initial stage leads to no change in r-stabilisationenergy, and in the second stage the energy change is given by AE, - AE~ (see
equation 12).
The triazine n-system is strongly electron attracting, i.e. the energies of n and II*orbitals (El and E* of Fig. 5) are lower than the corresponding energies for a phenyl group. This leads to a decrease in AE, - AE~ and hence an increase in the dissociation energy. This stabilisation by electron withdrawing groups is clearly an important factor in dissociations where the atoms forming the breaking bond have a lone-pair of electrons, and has been well established for diary1 hydrazines (ref.31). REFERENCES M.J.S. Dewar, J. Amer. Chem. Sot., 74 (1952) 3353 K. Fukui, H. Kato and T. Yonezawa, Bull. Chem. Sot. Jap., 33 (1960) 1198; 35 (1962) 1475 R.F. Hudson, Angew Chem. Internat. Edit. 12 (1973) 36 I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, London, 1976, chapter 5 K. Yates, HiickelMolecular Orbital Theory, Academic Press, New York, 1978, 176 N.C. Baird, J. Org. Chem., 40 (1976) 624 K. Schreiner and A. Berndt, Angew Chem. Internat. Edit, 15 (1976) 698 W.C. Herndon, Chem. Rev., 72 (1972) 157 These equations have been derived by A. Imamura, Mol. Physics 15 (1968) 225, using perturbation theory. There appears to be an anomaly since the first order perturbation for Ei = Ej is given as f C,iC,j(Hij - EiSij), which
10
gives AE = 0 for a 4-electron interaction. When Ei # Ej,perturbation theory gives equation 7 F. Bernardi, N.D. Epiotis, W. Cherry, H.B. Schlegel, M-H. Whangbo and S. Wolfe, J. Amer. Chem. Sot., 98 (1976) 469
162 A.D. Walsh, J. Chem. Sot., 1953, 2296 ;9;3 Skeil and K.J. Shea, Free Radicals, Wiley, New York, J.K. Kochi (Ed) II R. Hiffmann, L. Radom, J.A. Pople, P.R. Schleyer, W.J. Hehre and L. Salem, J. Amer. Chem. Sot., 94 (1972) 6221 J.P. Lowe, J. Amer. Chem. Sot., 99 (1977) 5557 A.R. Rossi and D.E. Wood, J. Amer. Chem. Sot., 98 (1976) 3452 and references therein D.J. Edge and J.K. Kochi, Tet. Letters, 1972, 2427; J.H. Hargis and P.B. Shevlin, J. Chem. Sot. Chem. Commun., 1973, 179 J.W. Wilt, Free Radicals, Wiley, New York, J.K. Kochi (Ed) I, 1973, 340 H.E. Zimmerman and A. Zweig, J. Amer. Chem. Sot., 83 (1961) 1196 P.S. Skell, Chem. Sot. Special Publications, 19 (1965) 131; P.S. Skell and K.J. Shea, Free Radicals, Wiley, New York, J.K. Kochi (Ed) II, 1973, 809 L.H. Slaugh, J. Amer. Chem. Sec., 81 (1959) 2262 A.L.J. Beckwith, Tetrahedron, 37 (1981) 3073; J.E. Baldwin, J. Chem. Sot. Chem. Commun., 1976, 734 K. Schreiner and A. Berndt, Angew Chem., 86 (1974) 131 0. Kikuchi, A. Hiyama, H. Yoshida and K. Susuki, Bull. Chem. Sot. Jap., 51 (1978) 11 T. Koenig, K.A. Wielesek and J.S. Huntington, Tet. Letters, 26 (1974) 2283. See however N.J. Karch, E.T. Koh, B.L. Whitsel and J.M. McBride, J. Amer. Chem. Sot., 97 (1975) 6729 M.B. Yim, 0. Kikuchi and D.E. Wood, J. Amer. Chem. Sot., 100 (1978) 1869; J.M. McBride and R.A. Merrill, ibid., 102 (1980) 1723; P.S. Skell and D.D. May, ibid., 103 (1981) 967 T.J. Stone and W.A. Waters, J. Chem. Sot., 1964, 213 J.W.C. Johns, D.A. Ramsay and S.C. Ross, Can. J. Phys., 54 (1976) 1804 W.C. Danen and R.W. Gellert, J. Amer. Chem. Sot., 94 (1972) 6853; J. Lessard,D. Griller and K.U. Ingold, ibid., 102 (1980) 3262; C. Brown and A.J. Lawson, Tet. Letters, 1975, 191 P.S. Skell and J.C. Day, J. Amer. Chem. Sot., 100 (1978) 1951; Accounts Chem. Res., 11 (1978) 381; Y. Apeloig and R. Schreiber, J. Amer. Chem. sot., 102 (1980) 6144 A.G. Davies and R. Sutcliffe, J. Chem. Sot. Perk. II, 1981, 1512 R;I. Walter, J. Amer. Chem. Sot., 88 (1966) 1923, 1930 J. Fossey and J-Y. Nedelec, Tetrahedron, 37 (1981) 2967
Journal of Molecular Structure, 103 (1983) 153-162 THEOCHEM Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE IMPORTANCE OF ORBITAL OVERLAP ON THE STRUCTURE AND STABILITY OF ORGANIC FREE RADICALS * R.F. HUDSON UNIVERSITY CHEMICAL LABORATORY, CANTERBURY, KENT. CT2 7NH.
U.K.
ABSTRACT The electronic energy of free radicals is discussed by using a l-electron treatment for first and second order perturbationswith the inclusion of orbital overlap. In particular the stability of bridged radicals and their tendency to 1.2 rearrangement are discussed in the light of experimental data. The role of orbital energies in determining the conformation of B-substituted radicals is examined quantitatively. Application of the perturbation equations to the relative stability of n and c states leads to a general rule which can be applied also to dissociation energies of molecules leading to conjugated free radicals, in particular radicals of oxygen and nitrogen. Perturbation theory was first applied by Dewar (ref.1) to the structure and reactivity of free radicals in the development of P.M.O. theory, and by Fukui (ref.2) in a quantitative treatment of atom abstractions. By considering the interaction of occupied and unoccupied orbitals of two interacting systems (Fig. 1) one-electron Hiickeltheory leads to the general equation occ AE
=
2
j
unocc
cm-(CCrjCskYrs)2 a-
J
k
-
+
ak
occ
unocc cc CrjCskyrs)2
Cc k
(1)
ak-a j
j
For the interaction of the S.O.M.O. with the frontier orbitals (Fig. 1) AE
q
(C .O)ZC 2y 2 sk rs rJ
t
(C .0)2C 2y 2 sk rs rJ ak - ajo
a. Jo - ak
(2)
where C .O is the coefficient of atom r in the S.O.M.0; of energy a.O, CSk is the J coeffi&t on the terminal atom, s, of the H.O.M.O. and L.U.M.O., and yrs is the appropriate exchange integral for the interaction concerned. This approach has been extended (ref.3,4) to other radical processes, e.g. addition and aromatic substitution, and explains the concept of nucleophilic and electrophilic radicals. This treatment is limited particularly by the neglect of orbital overlap. For example Hickel theory predicts a stabilisation of B,, for the cyclopropenyl *Dedicated to Professor Kenichi Fukui in honour of the award of the 1981 Nobel Prize in Chemistry. 0166-1280/83/$03.00
0 1983 Elsevier Science Publishers B.V.
154
radical (r) whereas Extended Hiickelcalculations (ref.5) show the E form to have a lower energy than the 71in agreement with ab initio calculations (ref.6) and with the limited experimental data (ref.7). This restriction applies to other radical systems and it is the object of this paper to consider the effect of retaining the overlap term on the l-electron perturbation energies. We proceed as follows. The combination of the wavefunctions of 2 orbitals $1 and@s in the lelectron approximation leads to the secular determinant, Ei-E
H ij-ESij
H ij-ESij
Ej-E
where Ei and Ej are energies of 61 and a2 respectively, Hij is the Hamiltonian and Sij the overlap integral.
The energy change AE = 2E-(Ei + Ej) is given by the solution, AE
=
2(Ei + Ej)Sij2 _ 4HijSij + C(Ei - Ej)2 t 4(Hij - EiSij)(Hij-EjSij)lt (3) 2(1 - Sij2)
For the combination of two sub-groups R and S at atoms r and s, the Hamiltonian and overlap integral become
'riCsjHij
and
C .C .S rl so ij
adopting the procedure of Herndon (ref.8). In general equation (3) is solved numerically, but the following limiting' solutions may be employed (ref.g) when
Ei = Ej, A+
= CriSsj(Hij _ EiSij)
and
1 - C,iC,jSij
l + C,iS,jSij and AE”
= -Cri2Csj2(Hij - EiSij)2 and
-C,iCsj(Hij - EiSij)
C m2C .'(Hij - EjSij)2 rl SJ
(4)
(5)
Ei - Ej
Ei - Ej when Ei >> E..
These reduce to the Hickel perturbation equations when Sij = 0, giving first order (AE’)
and second order (AE”)
perturbation energies.
For one and two electron interactions, Hiickeland Extended Hickel P.M.O. treatments give similar results, but for three and four electron interactions the two treatments differ completely, L&Z., From equations (4) and (5). for a 4-electron interaction AE’
=
-4Cri2CSj2CHijSij- EiSij21
(6)
155 and
*Err
=
-2Cri2Csj2E2HijSij- (Ei + Ej)Sij21
(7)
II = 0. whereas in the Hijckeltreatment ,E1 and AE The 3-electron interaction is particularly interesting, i.e.
d and
N
C,iS,j(Hij
AE”
N
-
EiSij) /(I
_
XriCsj’ij)
Cri2Csj2[2(Hij - EiSij)2 -
(8) (Hij - EjSij)21
(9)
Ei - Ej These equations lead to the following important conclusions which may be called the overlap rule (ref.3) and the energy rule (ref.10). (a) As the overlap integral, Sij, increases the perturbation energy decreases to a minimum and then increases to become positive at some limiting value, The magnitude of the energy minimum decreases as the energy (Sij)lim.* difference (Ei - Ej) increases. (b) As the energy difference (Ei - Ej) increases the perturbation energy changes from negative to positive at some critical value (Ei - Ej)lim . Thus in contrast to one electron and'two electron interactions which are always stabilising and four electron interactionswhich are always destabilising, three-electron interactions, always present in free radicals, may be stabilising or destabilising depending on the electronic structure of &he radical. As pointed out previously (ref.3). radicals such as HS2*, HO; and RsN6 are strongly stabilised since the magnitude of Sij is significantly less than (Sij)lim.. Epiotis (ref.10) has pointed out that when the radical centre is joined to an atom of high electronegativity (in particular F, Cl, OR), this energy becomes positive, according to the energy rule, and carbon centred radicals deviate from the planar configuration. Since Walsh's rules (ref.11) also predict a
deviation
from planar to pyramidal it appears that several factors are involved and a unique rule cannot be assumed for the three-electron destabilisation (tide
infm).
We now proceed to apply the rules to other systems of interest, in particular bridged radicals and 1.2 rearrangements. Bridged radicals (ref.12) The rotational barrier in B-substituted radicals, and the stabilisation of the eclipsed form by bridging, may be discussed first by considering hyperconjugation involving u and u* orbitals (ref.l3), and then where appropriate the combination of the S.O.M.O. with the non-bonding electrons on the substituent (Fig. 2(a)). As far as hyperconjugation goes, the S.O.M.O.-o interaction should be greater than the S.O.M.O.-a* interaction because the orbital energies of the first pair
166
SOMO Lj, 1 #-
i-w
Fig. 1.
k-i-k
00
00
c-~-~-~ @ 8 X
”
n
0
(a)
0
Fig. 2.
a@ a’ (b)
are normally similar whereas U* energies are high (ref.14). Thus electron donat ing (electropositive)groups, e.g. RsSn, RsSe, RsSi, increase the orbital coeffin cient (Csj) on the s-carbon atom, thus increasing the three electron stabilisation (with Sij =
0.2 << 0.33).
Conversely, electron attracting substituents decrease the stabilisation (since u and.o* energies decrease (ref.l4)), in spite of a compensating increase in the S.O.M.O.-o* perturbation. Thus first row substituents, e.g. F, OR, have small rotation barriers with minima at the gauche form (ref.15). Considering the combination of the S.O.M.O. and n(p,) orbitals on a substituent, X, the energy is negative when Eiz
Ej, but as the group X migrates to the
a-carbon atom, Sij increases (Fig. 2(b)), thus increasing the energy, AE. other words bridged
~adicaZs
are
msyrmetrica2
In
as found experimentally for the
6-chloroethyl radical (ref.16). In addition to the overlap restriction, the energy restriction controls the stability of the bridge (equation 9).
To examine this quantitatively, the
Hamiltonian is given by the Wolfsberg-Helmholtzapproximation in the usual way, i.e.
157
H
ij
=
k = 1.75
0.5k(Ei t Ej)Sij
The present case issimplified since C,i = Crj = 1.0 and then equation (9) becomes AE
=
C2(0.5k(Ei + Ej) - E.)' - (O.Sk(Ei t Ej) - E.)']Sij'
(10)
Ei - Lj and
AE = 0
when 3
=
2fl-
E. J
(fl- 1)k
(n-
(11)
1)k t 2
With Ei = 10 e.V., i.e. the ionisation potential of the methyl radical as appropriate for a carbon centred radical, values of Ei/E.ican be obtained for a range of a-substituted radicals (Table 1). TABLE 1 Relative stabilities of bridged free radicals.
I.P.(a)(e.V.) s
(b) ij
S
I
Br
Cl
0
F
10.5
10.5
11.5
12.8
13.5
17.5
0.072
-AE(k.cal.mole-') 6.76(')
0.076
0.081
0.067
7.54(')
2.97
0.22
-0.72
lb0
nb
Conformation
b
b
b
-log k(d)
-
5
8
0.083
0.088 -1.3 nb
-
(a) values for the isolated atoms (b) Slater overlap integrals (c) Treated as a first order perturbation (equation (8)) (d) Rate values given by P.S. Skell (ref.12). These data show that the decrease in stability of the bridged radical predicted by equation (10) with increase in lone-pair ionisation potential is observed experimentally with a change from stabilisation for a B-chlorine atom to de-stabilisationfor a a-oxygen substituent. The estimated stabilisation energies, AE, also correlate well with the decomposition rates estimated by Skell (ref.12) from the observed half-lives, and with the calculated values of Rossi and Wood (ref.15). 1.2 Radical rearrangements (ref.32) It is well known that hydrogen atoms and alkyl groups do not undergo the 1.2 rearrangements in free radicals (ref.17) which are so comnon in carbonium
158 ions. This has been explained in general terms (ref.18) by the occupation of the high energy anti-bonding orbital. It
is not clear however from this
explanation why other radicals with a singly occupied anti-bonding orbital, e.g. nitroxyl, peroxy, should be strongly.stabilisedelectronically, This dichotomy is resolved by the two rules given above.
Accordingly,
migration of an alkyl group leads to an increase in overlap Sij (Fig.
2) given
approximately by ~.Sij for a given internuclear distance. With Sij N 0.25 for a C-CT-bond, this gives a group integral of 0.35 which is greater than (Sij)lim .
.
This leads to a high activation energy. Phenyl groups and halogen atoms (with the exception of fluorine) and thiol groups migrate intramolecularly(ref.19). There is some doubt concerning the
migration of alkoxy groups, but since rearrangement competes with disproportionation, recombination and other radical processes, low activation energies are essential. Why then does a chlorine atom migrate intramolecularlywhereas a methyl group does not although C-C and C-Cl dissociation energies are similar? Assuming a symmetrical transition state, the following orbital combinations using p, and p, atomic orbitals on the migrating group X have to be considered (Fig. 3).
00
00
00
-c
063
&a3 @ 0 X
&x6
I-
3 (4 electrons)
(2 elecbons)
(2 electrons)
( 1 electron)
Fig.
3.
The transformationleading to orbitals I and IJ is accompanied by an increase in energy for the reasons already discussed (see equation 9). repulsion represented by III
The four electron
is zero, since the orbital combination is symmetry
forbidden, whereas the stabilising two-electron combination of II*and n(C1) orbitals is symmetry allowed. This leads to a decrease in energy which allows the 1.2 migration to proceed with a low activation energy. A similar explanation may be given for the 1,2 migration of aryl groups, but it is noted that the rearrangementof the B-phenylethyl radical is a high energy process (ref.20).
159 Radical addition to multiple bonds may be treated similarly. This involves the perturbation of the S.O.M.O. by n and n* orbitals (Fig. 4).
630 -C
@@
c-c
6@ 0
00
0 X
Fig.
4.
X
9
3
A consideration of V and VI shows that the radical approaches one (carbon) atom of the multiple bond rather than the centre of the n-bond. This reduces the value of Sij (in V) to a value close to the optimum value (ca. 0.1 to 0.2 when Ei =
Ej), and develops positive overlap with the n* orbital (VI). A further
increase in S ij is produced by an increase in the angle of approach (C-C-X > 98) which provides a basis for the well known rule of em-addition in radical cyclisations (ref.21). Further, it is evident that nucleophilic radicals
must
adopt this configuration since Sij = 0 for the S.O.M.O. - n* combination at the centre of the n-bond. For these reasons radicals do not form n- complexes, although transient species are possible with highly electrophilic free radicals. The relative stability of IIand c radicals The ground states of conjugated carbon radicals are uniformly IIalthough 2.6~tert butyl benzyl radicals adopt the high energy 1 form for steric reasons (ref.22). When heteroatoms with lone-pairs are attached to r-systems a wide range of molecular states is possible, e.g. for the acyloxy radical (ref.23), 2A2(n)s
2A~(z).
2B2(~)
with C2v sy mmetry and 2A"(n) and 2A1(~) with C, synrsetry.
It is now widely accepted that, as a result of ab initio calculations (ref. 23.24) and on the basis of limited experimental data (ref.25) the ground state of RC02* is a I:radical (as required for a low temperature fragmentation). On the other hand the phenoxy radical is n with a resonance energy (17 k.cal.mole-'). Nitrogen radicals are similarly complex. Thus the aminyl radical *NH2 has the n configuration (ref.27), ca. 1.5 e.V. lower than the lowest c state. The amidyl radical, R*COaMe is also known to have a lower energy n state (ref.28), whereas recent work of Skell (ref.29) has suggested that succinyl radicals can be prepared in n and 1 states with the former lower in energy.
160 As no general treatment of the problem appears to have been made, we shall enquire into the electronic factors which stabilise one state relative to another. This can be approached by the following qualitative perturbation argument Consider the r-systems corresponding to IIand z states, for example for the combination of an oxygen atom with a a-system. This involves the combination of the S.O.M.O. with ITand II*orbitals (71state) and of a doubly occupied n-orbital of oxygen with the n and II*orbitals (c state) as in Fig. 5.
\
/ I \
Eo f
/ \
,
\
J-C,
\
\-2s1 \
\
\
/
/
'r ',
K
=#
/
\
/
‘r
I
ti
‘Et VIJ
Ftg. 5. The r-electron energy of the n state is given by AEn
=
- 2E2 +
-Ed
where
E3
Er
=
-2e2 +
93
and of the c state by AE, =
-2~~ - 2~~ t
where
2~s
Thus AE, - AE,,= ~3 - ~1 =
Er
Csk2(H.. 'J - EoSij)2 Eo - EI
1
=
'2E2 t
2~s '12
C:kz[HI'. 1J _ EoSiJ
(12)
E* - E0
For the combination of a p, orbital of oxygen with the T and
n*
orbitals of
benzene (to give the phenoxy radical) it is clear that E* - E, >> El and Csk = CSk*' stabilised.
COtISeqUently E3
>>
~1
and AEa >> AET, i.e. the
n
State
is strongly
With the substitution of strongly electronegative groups, e.g. by the substitution of C=O for C=C, the energies of n and n* orbitals decrease, and C *>c Consequently E3 - ~1 decreases, so that for a large effect AEn > sk sk' BEE. This leads to the conclusion that etectron attracting substituenta in a conjugated
free
m&cat
favour
the c state
over the II state.
Similar considerations apply to the o-system where hyperconjugation (ref. 13) stabilises the x state and 4-electron repulsion destabilises the n state, reinforcing the above conclusion. In addition, in the acyloxy radical 3-
161 electron stabilisation involving a lone pair on oxygen (VII)
also stabilises
the c state. A similar argument can be applied to dissociation leading to conjugated radicals. Thus although diphenyl peroxides are unknown, stable triazinyl peroxides have recently been reported (ref.30). This change in stability is explained as follows. Dissociation of hypothetical diphenyl peroxide produces initially the c radical since the molecule is n-conjugated,which immediately transforms to the stable n ground state, viz.
r-conjugated
z
iT
The initial stage leads to no change in r-stabilisationenergy, and in the second stage the energy change is given by AE, - AE~ (see
equation 12).
The triazine n-system is strongly electron attracting, i.e. the energies of n and II*orbitals (El and E* of Fig. 5) are lower than the corresponding energies for a phenyl group. This leads to a decrease in AE, - AE~ and hence an increase in the dissociation energy. This stabilisation by electron withdrawing groups is clearly an important factor in dissociations where the atoms forming the breaking bond have a lone-pair of electrons, and has been well established for diary1 hydrazines (ref.31). REFERENCES M.J.S. Dewar, J. Amer. Chem. Sot., 74 (1952) 3353 K. Fukui, H. Kato and T. Yonezawa, Bull. Chem. Sot. Jap., 33 (1960) 1198; 35 (1962) 1475 R.F. Hudson, Angew Chem. Internat. Edit. 12 (1973) 36 I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, London, 1976, chapter 5 K. Yates, HiickelMolecular Orbital Theory, Academic Press, New York, 1978, 176 N.C. Baird, J. Org. Chem., 40 (1976) 624 K. Schreiner and A. Berndt, Angew Chem. Internat. Edit, 15 (1976) 698 W.C. Herndon, Chem. Rev., 72 (1972) 157 These equations have been derived by A. Imamura, Mol. Physics 15 (1968) 225, using perturbation theory. There appears to be an anomaly since the first order perturbation for Ei = Ej is given as f C,iC,j(Hij - EiSij), which
10
gives AE = 0 for a 4-electron interaction. When Ei # Ej,perturbation theory gives equation 7 F. Bernardi, N.D. Epiotis, W. Cherry, H.B. Schlegel, M-H. Whangbo and S. Wolfe, J. Amer. Chem. Sot., 98 (1976) 469
162 A.D. Walsh, J. Chem. Sot., 1953, 2296 ;9;3 Skeil and K.J. Shea, Free Radicals, Wiley, New York, J.K. Kochi (Ed) II R. Hiffmann, L. Radom, J.A. Pople, P.R. Schleyer, W.J. Hehre and L. Salem, J. Amer. Chem. Sot., 94 (1972) 6221 J.P. Lowe, J. Amer. Chem. Sot., 99 (1977) 5557 A.R. Rossi and D.E. Wood, J. Amer. Chem. Sot., 98 (1976) 3452 and references therein D.J. Edge and J.K. Kochi, Tet. Letters, 1972, 2427; J.H. Hargis and P.B. Shevlin, J. Chem. Sot. Chem. Commun., 1973, 179 J.W. Wilt, Free Radicals, Wiley, New York, J.K. Kochi (Ed) I, 1973, 340 H.E. Zimmerman and A. Zweig, J. Amer. Chem. Sot., 83 (1961) 1196 P.S. Skell, Chem. Sot. Special Publications, 19 (1965) 131; P.S. Skell and K.J. Shea, Free Radicals, Wiley, New York, J.K. Kochi (Ed) II, 1973, 809 L.H. Slaugh, J. Amer. Chem. Sec., 81 (1959) 2262 A.L.J. Beckwith, Tetrahedron, 37 (1981) 3073; J.E. Baldwin, J. Chem. Sot. Chem. Commun., 1976, 734 K. Schreiner and A. Berndt, Angew Chem., 86 (1974) 131 0. Kikuchi, A. Hiyama, H. Yoshida and K. Susuki, Bull. Chem. Sot. Jap., 51 (1978) 11 T. Koenig, K.A. Wielesek and J.S. Huntington, Tet. Letters, 26 (1974) 2283. See however N.J. Karch, E.T. Koh, B.L. Whitsel and J.M. McBride, J. Amer. Chem. Sot., 97 (1975) 6729 M.B. Yim, 0. Kikuchi and D.E. Wood, J. Amer. Chem. Sot., 100 (1978) 1869; J.M. McBride and R.A. Merrill, ibid., 102 (1980) 1723; P.S. Skell and D.D. May, ibid., 103 (1981) 967 T.J. Stone and W.A. Waters, J. Chem. Sot., 1964, 213 J.W.C. Johns, D.A. Ramsay and S.C. Ross, Can. J. Phys., 54 (1976) 1804 W.C. Danen and R.W. Gellert, J. Amer. Chem. Sot., 94 (1972) 6853; J. Lessard,D. Griller and K.U. Ingold, ibid., 102 (1980) 3262; C. Brown and A.J. Lawson, Tet. Letters, 1975, 191 P.S. Skell and J.C. Day, J. Amer. Chem. Sot., 100 (1978) 1951; Accounts Chem. Res., 11 (1978) 381; Y. Apeloig and R. Schreiber, J. Amer. Chem. sot., 102 (1980) 6144 A.G. Davies and R. Sutcliffe, J. Chem. Sot. Perk. II, 1981, 1512 R;I. Walter, J. Amer. Chem. Sot., 88 (1966) 1923, 1930 J. Fossey and J-Y. Nedelec, Tetrahedron, 37 (1981) 2967