Evidence for significant through-space and through-bond electronic coupling in the 1,4-diphenylcyclohexane-1,4-diyl radical cation gained by absorption spectroscopy and DFT calculations

Article abstract of DOI:10.1002/chem.200700820

Photoinduced single-electron-transfer promoted oxidation of 2,5-diphenyl-l,5-hexadiene by using N-methylquinolinium tetrafluoroborate/ biphenyl co-sensitization takes place with the formation of an intense electronic absorption band at 476 nm, which is attributed to the 1,4-diphenylcyclohexane-1,4-diyl radical cation. The absorption maximum (λ_ob) of this transient occurs at a longer wavelength than is expected for either the cumyl radical or the cumyl cation components. Substitution at the para positions of the phenyl groups in this radical cation by CH₃O, CH₃, F, Cl, and Br leads to an increasingly larger redshift of λ_ob. A comparison of the ρ value, which was obtained from a Hammett plot of the electronic transition energies of the radical cations versus σ⁺, with that for the cumyl cation shows that the substituent effects on the transition energies for the 1,4-diarylcyclohexane-1,4-diyl radical cations are approximately one half of the substituent effects on the transition energies of the cumyl cation. The observed substitu_ent-induced redshifts of λ_ob and the reduced sensitivity of λ_ob to substituent changes are in accordance with the proposal that significant through-space and -bond electronic interactions exist between the cumyl radical and the cumyl cation moieties of the 1,4-diphenylcyclohexane-1,4-diyl radical cation. This proposal gains strong support from the results of density functional theory (DFT) calculations. Moreover, the results of time-dependent DFT calculations indicate that the absorption band at 476 nm for the 1,4-diphenylcyclohexane-1,4-diyl radical cation corresponds to a SOMO-3-SOMO transition.

Full text of DOI:10.1002/chem.200700820

FULL PAPER
DOI: 10.1002/chem.200700820
Evidence for Significant Through-Space and Through-Bond Electronic
Coupling in the 1,4-Diphenylcyclohexane-1,4-diyl Radical Cation Gained by
Absorption Spectroscopy and DFT Calculations
Hiroshi Ikeda,*[a] Yosuke Hoshi,[b] Hayato Namai,[b] Futoshi Tanaka,[b]
Joshua L. Goodman,[c] and Kazuhiko Mizuno[a]
Abstract: Photoinduced single-elec-
tron-transfer promoted oxidation of
2,5-diphenyl-1,5-hexadiene by using N-
methylquinolinium tetrafluoroborate/
biphenyl co-sensitization takes place
with the formation of an intense elec-
tronic absorption band at 476 nm,
which is attributed to the 1,4-diphenyl-
cyclohexane-1,4-diyl radical cation. The
absorption maximum (lob) of this tran-
sient occurs at a longer wavelength
than is expected for either the cumyl
radical or the cumyl cation compo-
nents. Substitution at the para positions
of the phenyl groups in this radical
cation by CH3O, CH3, F, Cl, and Br
leads to an increasingly larger redshift
of lob. A comparison of the 1 value,
which was obtained from a Hammett
plot of the electronic transition ener-
gies of the radical cations versus s+,
with that for the cumyl cation shows
that the substituent effects on the tran-
sition energies for the 1,4-diarylcyclo-
hexane-1,4-diyl radical cations are ap-
proximately one half of the substituent
effects on the transition energies of the
cumyl cation. The observed substitu-
ent-induced redshifts of lob and the re-
duced sensitivity of lob to substituent
changes are in accordance with the
proposal that significant through-space
and -bond electronic interactions exist
between the cumyl radical and the
cumyl cation moieties of the 1,4-diphe-
nylcyclohexane-1,4-diyl radical cation.
This proposal gains strong support
from the results of density functional
theory (DFT) calculations. Moreover,
the results of time-dependent DFT cal-
culations indicate that the absorption
band at 476 nm for the 1,4-diphenylcy-
clohexane-1,4-diyl radical cation corre-
sponds to a SOMO-3!SOMO transi-
tion.
Keywords: absorption
functional calculations
·
·
density
electron
transfer
· orbital interactions ·
radical ions
Introduction
Observation of short-lived transients by absorption spectros-
copy is a powerful methodology to elucidate the mecha-
nisms of photoinduced electron-transfer (PET) reactions.[1]
Usually the assignment of structures to the transients is ac-
complished by comparing the observed absorption spectra
with those of intermediates or structurally related intermedi-
ates generated in independent ways. However, the absorp-
tion spectra of bifunctional radical cations,[2–5] which are
generated in a variety of electron-transfer reactions, often
do not correspond to those associated with either of the
component functionalities. In most of these cases, the spec-
tra have dual characteristics that correspond to both the rad-
ical and the cation subunits. There is great interest in radical
cations that have mixed spectral properties of this type be-
cause this phenomenon might lead to new functions of the
radical cations.[6]
[a]Prof. Dr. H. Ikeda, Prof. Dr. K. Mizuno
Department of Applied Chemistry
Graduate School of Engineering
Osaka Prefecture University
Sakai, Osaka 599-8531 (Japan)
Fax : (+81)72-254-9289
E-mail: ikeda@chem.osakafu-u.ac.jp
[b]Dr. Y. Hoshi, Dr. H. Namai, Dr. F. Tanaka
Department of Chemistry Graduate School of Science
Tohoku University (TU), Sendai, Miyagi 980-8578 (Japan)
[c]Prof. Dr. J. L. Goodman
Department of Chemistry, University of Rochester
Rochester, New York 14627 (USA)
Supporting information for this article is available on the WWW
under http://www.chemeurj.org/ or from the author. It contains infor-
mation on the general methods used and descriptions of the prepara-
tion of 1, 11, and 12.
Chem. Eur. J. 2007, 13, 9207 – 9215
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9207

We have previously reported that the PET-induced degen-
erate Cope rearrangement of 2,5-diphenyl-3,3,4,4-tetradeu-
terio-1,5-hexadiene ([D4]1d) occurs by a radical-cation cycli-
zation (RCCY)–diradical cleavage (DRCL) mechanism
(Scheme 1).[7] The key intermediate in this pathway, the 1,4-
685 nm in CFCl4.[13] Moreover, he proposed that a through-
+
C
bond (TB) interaction takes place in 4 and that the ob-
served absorption band corresponds to a singly occupied
molecular orbital (SOMO)!lowest unoccupied molecular
orbital (LUMO) transition. At first sight, it might appear
+
C
that a similar TB interaction could be occurring in 2d and
that a SOMO!LUMO transition might account for the ab-
sorption band at 476 nm for this intermediate. However, the
dramatically shorter wavelength maximum, relative to that
of nonphenyl-substituted 4 +, strongly indicates that another
C
+
C
interaction and transition are involved in 2d
.
In a similar manner, electronic coupling has been suggest-
ed to explain the lob of the chair and boat conformations of
the 1,4-bis(4-methoxyphenyl)-2,3-dimethylcyclohexane-1,4-
+
diyl radical cations (aaC-5a and n,cB-5a +, Scheme 2a)[2]
C
C
Scheme 1. PET-induced degenerate Cope rearrangement of 2,5-diphenyl-
3,3,4,4-tetradeuterio-1,5-hexadiene ([D4]1d). Sens=sensitizer; RCCY=
radical cation cyclization; DRCL=diradical cleavage; BET=back elec-
tron transfer.
diphenylcyclohexane-1,4-diyl radical cation (2d +), was ob-
C
served spectroscopically. By using nanosecond-resolved laser
flash photolysis (LFP) and the N-methylquinolinium tetra-
À
fluoroborate (NMQ+BF4 )/biphenyl (BP) co-sensitization
+
C
technique, the absorption maximum (lob) of 2d was ob-
served at 476 nm[8] in dichloromethane (Figure 1a). Interest-
+
C
Figure 1. Comparison of the absorption spectra of a) 2d in CH2Cl2 at
C
ambient temperatures, b) 3d in cyclohexane at ambient temperature, and
Scheme 2. a: Ar=4-CH3OC6H4.
c) 3d+ in HSO3F at À788C.
+
C
and the 1,4-diarylbutane-1,4-diyl radical cation (8
,
+
C
ingly, the lob of 2d appears at an unusually long wave-
Scheme 2b).[3,4] Takamuku et al. observed an unusually long
wavelength absorption band at lob =505 nm when 4-methox-
ystyrene (6a) and 1,2-bis(4-methoxyphenyl)cyclobutane
length in comparison with those of its chromophoric compo-
C
nents, the cumyl radical (3d , lob =322 nm in cyclohexane,
Figure 1b)[9,10] and the cumyl cation (3d+, lob =322 nm in
(7a) were independently subjected to pulse radiolysis in 1,2-
+
HSO3F, Figure 1c).[11,12]
dichloroethane.[3] These workers assigned the band to 8a
C
Williams reported earlier that the parent cyclohexane-1,4-
and proposed the possibility that an electronic interaction
diyl radical cation (4 +) in its chair conformation has a lob at
was taking place. Steenken et al. also observed an abnormal-
C
+
C
ly long wavelength absorption band at 500 nm for 8a
(Scheme 2c) and its aryl analogues, generated by pulse radi-
olysis of 6a.[4] In addition, a transient with a lob =500 nm
was observed to form in PET reactions of 6a or 7a
(Scheme 2d).[5] Interestingly, this band was assigned to the
cyclic hexatriene radical cation derivative 10a +, formed by
C
intramolecular cycloaddition of 8a +, owing to the fact that
C
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Chem. Eur. J. 2007, 13, 9207 – 9215

Electronic Coupling in 1,4-Radical Cations
FULL PAPER
dihydronaphthalene derivative 9 is the product of this reac-
tion.
Results
The confusion and controversy surrounding the assign-
ment of transients to long wavelength absorption bands and
the characterization of electronic structures of 1,4-radical
cations, especially the aryl-substituted derivatives, led us to
carry out further investigations on the 1,4-diphenylcyclohex-
ane-1,4-diyl radical cation. To gain further insight into the
electronic interactions taking place in this system and the
electronic transition responsible for the absorption band, we
examined the effects of substituents on lob for several p-
Syntheses of 1, 11, and 12: The syntheses of the 4-methoxy-
phenyl, 4-methylphenyl, phenyl, and 4-chlorophenyl deriva-
tives of 2,5-diaryl-1,5-hexadiene 1 have been described pre-
viously.[7a] The 4-fluorophenyl, 4-bromophenyl, and 4-iodo-
phenyl derivatives (1c, 1 f, and 1g) were prepared by Wittig
methylenation of the corresponding 1,4-diaryl-1,4-buta-
diones. The four a,a’-azocumene derivatives 11b–e were
prepared from the corresponding amines (13) through sulfa-
mides (14) by a slight modification of the procedures de-
scribed by Timberlake and co-workers[15,16] (Scheme 4). a-
Methylstyrenes 12a–g were generated by Wittig olefination
of the corresponding acetophenones.
phenyl-substituted derivatives of 2 +, along with those of the
C
+
C
cumyl radical 3 and cumyl cation 3 . These transients were
generated from 2,5-diaryl-1,5-hexadienes (1), a,a’-azocu-
mene derivatives (11), and a-methylstyrene derivatives (12),
respectively (Scheme 3). In addition, we performed theoreti-
Scheme 4. Preparation of a,a’-azocumene derivatives 11b–e from the cor-
responding amines 13. Reagents: i) SO2Cl2, Et3N, CH2Cl2; ii) NaH,
tBuOCl, THF. Ar=4-XC6H4; X=CH3, F, H, and Cl for b, c, d, and e, re-
spectively.
Electron-donating properties of 1: The respective half-wave
oxidation potentials (Eo1 x) determined for 1a–g are +1.27,
=
2
+1.54, +1.92, +1.68, +1.71, +1.76, and +1.62 V versus
SCE in acetonitrile. These values indicate that exothermic
+
C
Scheme 3. Generation of p-phenyl-substituted derivatives of
2
,
the
hole transfer from BP +, which is generated by electron-
C
+
C
cumyl radical 3 , and the cumyl cation 3 from 2,5-diaryl-1,5-hexadienes
(1), a,a’-azocumene derivatives (11), and a-methylstyrene derivatives
(12), respectively. Ar=4-XC6H4; X=CH3O, CH3, F, H, Cl, Br, and I for
a, b, c, d, e, f, and g, respectively.
transfer from BP (Eo1 x =+1.90 V) to the excited state of
=
2
À
NMQ+BF4 , to these dienes will take place to generate the
corresponding radical cations 1 that are the precursors of
the 1,4-diarylcyclohexane-1,4-diyl radical cations 2
+
C
+
C
.
cal calculations on these species by using density functional
Effects of substituents on lob for 2 +: The absorption spectra
C
theory (DFT) and time-dependent (TD) DFT methods. We
+
+
C
C
observed that p-phenyl substitution in 2d with CH3O,
of 2a–g were recorded by independently subjecting solu-
CH3, F, Cl, and Br groups caused an increasingly large red-
tions of the precursor dienes 1a–g in dichloromethane to
shift of lob. A Hammett plot of the relative transition ener-
nanosecond-resolved LFP (308 nm) by using the NMQ+
+
+
À
C
gies, DEob
A
BF4 /BP co-sensitization technique. As was previously ob-
+
C
with negative and positive 1 values. Similar substituent ef-
served for the diphenyl derivative 2d (lob =476 nm), 2a–
fects were observed for DEob of 3+. Interestingly, a compari-
c
and 2e–g have lob values of 522, 496, 473, 499, 509,
+
+
C
C
son of the 1 values for 2 and 3+ indicated that the effects
and 539 nm, respectively.[17] Therefore, the incorporation of
substituents at the para positions of the phenyl groups re-
sults in a redshift of lob. The lone exception to this is the flu-
+
C
+
C
of substituents on DEob
(2 ) are only half of those on
DEob(3+). The observed redshift and smaller effects of sub-
stituents for 2 are successfully reproduced in the results of
+
orine-substituted derivative 2c +. The lob values observed
C
C
+
C
the TD-DFT calculations carried out at the (U)B3LYP/cc-
pVDZ level. A detailed analysis of the molecular orbitals
(MOs), computed by DFT calculations, and a consideration
of orbital interaction theory leads to the reasonable propos-
for 2 are listed in Table 1, together with the relative transi-
tion energies (DEob) based on the absolute transition ener-
+
C
gies (hc/lob) of the phenyl derivative 2d [Eq. (1)].
ꢀ
ꢁ
1
1
al that through-space (TS) and TB interactions take place in
DEob ¼ hc
À
ð1Þ
+
C
lob lobðphenylÞ
the chair conformation of 2d and that a SOMO-3!
SOMO transition is associated with the absorption band at
476 nm.[14] Below, we present detailed results of this study
and a discussion of the mechanistic features involved in TS
As the plot shown in Figure 2 demonstrates, an excellent
+
+
C
C
correlation exists between DEob
(2 ) for 2a–f and Crearyꢁs
+
C
C [18]
and TB electronic couplings in 2d
.
substituent constants, sC . The linear relationship between
Chem. Eur. J. 2007, 13, 9207 – 9215
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www.chemeurj.org
9209

H. Ikeda et al.
+
+
+
C
C
C
Table 1. Substituent constants (sc and s ), absorption maxima (lob), and relative transition energies (DEob) of 2 , 3 , and 3 .
+
2
3+
C
C
3
[b]
[c]
C[a]
sC
X
s+
lob [nm]
DEob [eV]
lob [nm]
DEob [eV]
lob[d] [nm]
DEob [eV]
[e]
a: CH3O
b: CH3
c: F
d: H
e: Cl
f: Br
0.24
0.11
À0.08
0
À0.78
À0.31
À0.07
0
0.11
0.15
0.14
522
496
473
476[i]
499
509
539
À0.230
À0.105
0.017
362[f]
338[g]
324
À0.425
À0.182
À0.024
0
À0.288
À0.444
À0.912
322
0
[h]
0
322[j]
318
0
322[k]
348[l]
364
0.12
À0.120
À0.169
À0.304
0.048
0.14
[m]
g: I
422
C
[a]See ref. [18]. [b]In CH 2Cl2. [c]In cyclohexane. [d]In HSO 3F. [e]The value of lob
A
[g] See ref. [21]. [h] Not detectable. [i] See ref. [8]. [j] See ref. [9]. [k] See ref. [11]. [l] See ref. [22]. [m] Not available.
+
The correlation between DEob for 2a–d and s+ is associat-
C
ed with a 1 value of 0.32. In contrast, a negative 1 value of
+
À1.12 is found for the correlation between 2d–f and s+.[24]
C
The dual phase nature of substituent effects on the transi-
tion energies was also observed in our recent work with
geminally diaryl-substituted trimethylenemethane (TMM)-
type radical cations and diarylethyl cations.[25] In these cases,
Cl and Br substituents acted as electron-donating groups in
governing the electronic transitions.
+
C
Effects of substituents on the lob for 3 and 3 : To gain infor-
+
C
mation about how the effects of substituents on lob for 2
+
C C
Figure 2. Correlation between DEob(2 ) and sC .
A
observed reflect the odd nature of the electron- and charge-
partitioning in the component cumyl moieties, the cumyl
+
C
radical 3 and cation 3 were generated independently from
+
[23]
C
C
DEob
G
11 and 12, respectively (Scheme 3). Azocumenes 11b–e
were subjected to LFP (266 nm) under direct irradiation
conditionsin degassed cyclohexane at ambient tempera-
ture.[10b] Although no clear transient absorption was detected
when 11c was irradiated, LFP of 11b, 11d, and 11e generat-
ed transients with lob at 322, 322,[9] and 318 nm, respectively,
DEobð2CþÞ ꢀ À0:82sC for 2a-fCþ
ð2Þ
A plot of DEob for 2a–f versus the substituent constant s+
consists of two intersecting lines (Figure 3).[24] The finding
C
C
C
which were assigned to 3b , 3d , and 3e , respectively
that DEob
(2 ) correlates with both the sC and s+ parame-
(Table 1). Clearly, no significant effects of substituents on
ters is consistent with the dual radical and cationic nature of
C
lob for 3 were observed.
+
+
+. The two linear relationships between DEob
(2 ) and s
C
C
2
In contrast, substituents have a significant effect on the
lob of 3+. These transients were generated from 12a–g in
HSO3F at À788C by using a slight modification of the proce-
dure described by Sekuur and Kranenburg.[12a] The lob
values for the cumyl cations 3a–g+ formed in this manner
are listed in Table 1. Cations 3a–g+ exhibited intense ab-
sorption bands with the lob at 362,[20] 338,[21] 324, 322,[11]
348,[22] 364, and 422 nm, respectively. As expected, substitu-
ents at the para positions of the phenyl groups in these tran-
sients give rise to redshifts of the lob. The most significant
observation is that the effects of substituent on lob for 3a–f+
are much greater than those on the absorption maxima of
are given by Equation (3) and (4):[23]
DEobð2CþÞ ꢀ 0:32sþ for 2a-dCþ
DEobð2CþÞ ꢀ À1:12sþ for 2d-fCþ
ð3Þ
ð4Þ
2a–f +. This result is best seen by viewing the plot of
C
DEob(3+), based on hc/lob(3d+), versus s+, displayed in
G
Figure 3. As observed for 2a–f +, the Hammett plot for 3a–
f+ is comprised of two intersecting straight lines, expressed
by Equations (5) and (6),[23] which correspond to 1 values of
0.55 and À2.89, respectively.
C
+
Figure 3. Correlation between experimental DEob
DEob(3+) (circles) and s+.
)
(squares) or
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Electronic Coupling in 1,4-Radical Cations
FULL PAPER
DEobð3þÞ ꢀ 0:55sþ for 3a-dþ
DEobð3þÞ ꢀ À2:89sþ for 3d-fþ
ð5Þ
ð6Þ
The differences between the magnitudes of the effects of
+
substituents on lob for 2 and 3+ were evaluated by using
C
+
+
C
Equations (7) and (8). The 1(2 )/1(3 ) ratio is approximate-
+
A
ly 0.6 when comparing 2a–d and 3a–d+ and 0.4 when
C
+
comparing 2d–f and 3d–f+. These findings indicate that
C
the substituent effects on the electronic transition energies
+
C
of 2 are reduced by approximately half compared with
those on the transition energies of 3+ in both the s+ <0 and
s+ >0 regions.
1ð2CþÞ DEobð2CþÞ
+
C
Figure 4. Optimized molecular geometries of 2d obtained by using
¼ 0:6 for 2a-dCþ and 3a-dþ
¼ 0:4 for 2d-fCþ and 3d-fþ
ð7Þ
ð8Þ
ꢀ
UB3LYP/cc-pVDZ, a) top and b) side views, and of 3d+ obtained by
1ð3þÞ DEobð3þÞ
using B3LYP/cc-pVDZ, c) front and d) side views.
1ð2CþÞ DEobð2CþÞ
ꢀ
1ð3þÞ DEobð3þÞ
Discussion
The explanation for the long wavelength absorption band of
+
C
the parent cyclohexane-1,4-diyl radical cation 4 based on a
TB interaction and SOMO!LUMO transition proposed by
Williams[13] cannot easily be applied to the long wavelength
absorption band of 2d +. In fact, phenyl substitution of this
C
+
Figure 5. Electronic transitions of a) 2d and b) 3d+ calculated by using
TD-(U)B3LYP/cc-pVDZ.
C
radical cation (as in 2d +) caused the lob to shift to shorter
C
wavelengths in spite of the extension of the conjugate
system. Thus, another interaction and/or electronic transi-
Table 2. Substituent constants (s+), calculated electronic transition wave-
tion must be taking place in 2d +. We believe that the key
C
lengths (lcal), oscillator strengths (f), and relative transition energies
+
+
(DEcal) for 2 and 3+.
C
to the unusually large wavelength shift of lob for 2d lies in
C
orbital interactions that take place between the cumyl radi-
cal and the cumyl cation components.
+
3+
C
2
[a]
[a]
X
s+
lcal
[nm]
f
DEcal lcal
f
DEcal
[eV]
[eV]
[nm]
+
DFT and TD-DFT calculations on 2 and 3+: To gain an in-
C
a: CH3O À0.78
492 0.14
451 0.12
441 0.10
431 0.10
482 0.12
510 0.11
À0.355
À0.129
À0.067
0.00
330
303
292
288
325
354
0.61 À0.551
0.58 À0.209
0.49 À0.066
0.45 0.00
b: CH3
c: F
À0.31
À0.08
0.00
sight into the factors governing the electronic transitions in
2d +, DFT and TD-DFT calculations were carried out. The
C
d: H
e: Cl
f: Br
results show that 2d and 3d+, as well as the para-substitut-
+
C
0.12
0.14
À0.302
0.56 À0.491
ed counterparts 2a–f and 3a–f+, have typical chair and
+
C
À0.446
0.52 À0.801
planar conformations, respectively, at the (U)B3LYP/cc-
[a]Calculated at the UB3LYP/cc-PVDZ level of theory.
pVDZ level of theory (Figure 4).[14]
The electronic transition wavelengths (lcal) and oscillator
+
+
strengths (f) in the optimized structures of 2a–f and 3a–f+
plots of the data for both 2 and 3+, which consist of two
C
C
were calculated by using TD-(U)B3LYP/cc-pVDZ, as shown
in Figure 5 and Table 2. The TD-DFT calculations success-
intersecting straight lines represented by Equations (9)–(12):
DEcalð2CþÞ ꢀ 0:43sþ for 2a-dCþ
DEcalð2CþÞ ꢀ À2:93sþ for 2d-fCþ
DEcalð3þÞ ꢀ 0:70sþ for 3a-dþ
DEcalð3þÞ ꢀ À5:16sþ for 3d-fþ
ð9Þ
ð10Þ
ð11Þ
ð12Þ
fully reproduced the absorption bands observed in the visi-
ble region for 2 and in the UV region for 3+. The calcula-
+
C
tions suggested that the electronic transitions of 2 and 3+
+
C
+
+
C
C
correspond to a SOMO-X!SOMO (X=1 for 2a , 2c
,
2e , and 2 f and X=3 for 2b and 2d +) and a HOMO-
+
+
+
C
C
C
C
X!LUMO transition (X=1 for 3a+, 3c+, 3e+, and 3 f+
and X=0 for 3b+ and 3d+). Hammett plots of the calculat-
ed relative transition energies of 2 and 3+ versus s+ are
+
C
shown in Figure 6. Excellent correlations are seen in the
These plots and equations closely match those obtained
Chem. Eur. J. 2007, 13, 9207 – 9215
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www.chemeurj.org
9211

A
H. Ikeda et al.
+
+
C
tained as the ratio of DEcal(2 )/DEcal(3 ), is approximately
0.6 for 2 and 3+ [Eqs (13) and (14)]. These findings indi-
cate that the calculations at the (U)B3LYP/cc-pVDZ level
of theory are good enough to accurately describe the elec-
tronic states of the radical cation and cation systems.
+
C
1ð2CþÞ DEcalð2CþÞ
¼ 0:6 for 2a-dCþ and 3a-dþ
¼ 0:6 for 2d-fCþ and 3d-fþ
ð13Þ
ð14Þ
ꢀ
1ð3þÞ DEcalð3þÞ
1ð2CþÞ DEcalð2CþÞ
ꢀ
1ð3þÞ DEcalð3þÞ
MO diagram of 2d +: To elucidate the cause of the redshift
C
+
+
;
C
of the absorption band, we analyzed the MOs of 2d in
C
&
Figure 6. Correlation between computed DEcal
s+.
A
(3+; ) and
*
) or DEcal
detail. A plausible explanation for the computed MOs of
+
2d arises by using two sets of MOs for 3d+ calculated
C
À
with B3LYP/cc-pVDZ and a C C s bond for the cyclohex-
C
ane skeleton (Figure 7). Note that the MOs of 3d are re-
placed by those of 3d+ for simplicity. In the optimized chair
from the experimental data (Figure 3). Furthermore, the re-
sults of the TD-DFT calculations also predict that the mag-
conformation of 2d +, the cumyl radical and the cumyl
C
+
C
À
nitude of the substituent effects in 2 are about half of
cation components are sufficiently close (a C C bond length
those in 3+ [Eqs (7) and (8)]. The ratio of 1
A
+
+
C
between the two benzyl carbon atoms of ca. 2.9 Š) to
enable TS electronic coupling
with each other. The TS interac-
tion is less efficient than the TB
interaction (see below), but
cannot be omitted because an
antiperiplanar approach of the
cumyl cation and the cumyl rad-
ical resulted in a small change
in the MOs in a preliminary cal-
culation. For the TS interaction,
f1 with bonding character and
f2 with antibonding character
are composed of two c1 MOs of
3d+ (or 3d ). Similarly, f5 with
C
bonding character and f6 with
antibonding character are given
by two c3 MOs. Note that the
two p orbitals at the benzylic
+
C
position of 3d and 3d interact
with each other owing to the re-
stricted nature of the chair con-
formation. The TS interaction
between two c2 MOs can be
omitted because the orbital co-
efficients at the benzylic carbon
atoms are negligible. Further-
more, in this system electronic
coupling between the benzyl
radical and the benzyl cation
components through two
s
bonds of the cyclohexane skele-
ton (the so-called TB interac-
tion) plays a crucial role. Be-
cause of the orbital symmetry of
the two benzylic positions, f1
+
C
Figure 7. Conceptual representation that shows the TS and TB interactions in 2d and some important MOs
calculated by using (U)B3LYP/cc-pVDZ.
9212
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Chem. Eur. J. 2007, 13, 9207 – 9215

Electronic Coupling in 1,4-Radical Cations
FULL PAPER
and f5 interact with ss, but f2 and f6 do not. As a result, Y1
with a bonding character and Y3 and Y7 with an antibond-
ing character are produced. MOs of f3 and f4 do not inter-
act with ss for the same reason as described above for c2.
The computed MOs, shown in Figure 7, provide strong
support for an interpretation of the electronic transition
+
C
properties of 2d based on a combination of TS and TB or-
bital interactions. Note that both of these types of interac-
tions cause a large rise in the Y3
with the c1(HOMO-1) level, whereas the TS interaction
alone causes a slight rise in the Y6(SOMO) level compared
with the c3(LUMO) level. In this sense, the TB interaction
(SOMO-3) level compared
ACHTREUNG
AHCTREUNG
ACHTREUNG
is more dominant than the TS interaction. As a result, the
energy gap between Y3 and Y6 becomes smaller than that
between c1 and c3 which govern the respective electronic
+
transitions in 2d and 3d+. Therefore, the surprising red-
C
+
C
shift of the absorption band of 2d compared with that of
+
C
Figure 8. Selected MO diagram that shows the substituent effects in 2
.
3d+ is in reasonable accord with these considerations.
Note that the orbital distributions of the cumyl subunit of
Y3 and Y6 closely resemble those of c1 and c3, respectively
The symbols eA, eB, and E represent the energies of the f1, ss, and Y3-
(SOMO-3) orbitals of 2d +, respectively. d and D represent the incre-
ment in the energy of the c1 (and f1) and Y3(SOMO-3) orbitals of 2a–
and 2e–f +, respectively, induced by substitution of an electron-donat-
ing group.
C
AHCTREUNG
+
C
C
c
(Figure 7). This finding strongly suggests that the absorption
+
C
band at 476 nm for 2d and the absorption band at 322 nm
for 3d+ essentially correspond to the same type of electron-
ic transition. The former is not as a result of the destruction
of forbidden transitions of the benzyl or cumyl radical skele-
tons, which are known to appear weakly at around 450 to
500 nm.
1
2
=
2
E ¼ feA þ eB þ ½ðeAÀeBÞ þ 4h2ABŠ g=2
ð15Þ
ð16Þ
1
E þ D ¼ feA þ d þ eB þ ½ðeA þ dÀeBÞ þ 4h2ABŠ g=2
2
=
2
1
2
1=2
2
=
2
D ¼ fd þ ½ðeA þ dÀeBÞ þ 4hA2 B
Š
À½ðeAÀeBÞ þ 4h2ABŠ g=2
Theory for orbital interactions in 2d +: Because the elec-
C
ð17Þ
tronic transitions associated with the major absorption
+
bands of 2d and 3d+ essentially take place between the
C
When no TB interaction occurs and no resonance integral
between f1 and ss (hAB =0) exists, D is equal to d and a
large energy gap (eAÀeB @0) is present. However, D will de-
crease to 0.5d when there is an effective TB interaction with
a large hAB and a small eAÀeB. Therefore, the ratio D/d
changes from 0.5 to unity, as shown in Equation (18):
same types of MOs, one would expect that the effect of sub-
stituents on these electronic transitions should be of the
same magnitude in both systems. However, the experimental
results and TD-DFT calculations both suggest that the mag-
nitude of the substituent effects on the transition energies of
+
C
2
should be about half of those on the transition energies
of 3+. To reconcile this difference, substitution-induced
0:5 < D=d < 1
ð18Þ
changes in the energies of the MOs were evaluated by using
orbital interaction theory and the simple Hückel method.[26]
The experimentally observed relative energy ratios DEob-
C
(2 )/DEob(3 ) of 0.6 and 0.4 when s <0 and s >0, respec-
+
C
The energy (E) of the Y3
A
+
+
+
+
A
by Equation (15), in which eA, eB, and hAB are the energies
of f1, ss, and the resonance integral between f1 and ss, re-
spectively (Figure 8). Accordingly, the energies E+D of the
tively [Eqs. (7) and (8)], successfully reproduced by TD-
DFT calculations, are close to 0.5 [Eqs. (13) and 14)].[28]
+
C
Thus, TB interactions in 2 must be near the maximum pre-
dicted by orbital interaction theory. In other words, the
+
+
C
C
corresponding derivatives 2a–c and 2e–f can be repre-
sented by Equation (16), in which D is the increment in the
smaller effect of substituents on the transition energies of
+
+
C C
(SOMO-3) for 2a–c and 2e-f when an elec-
energy of Y3
A
+
C
2
compared with those of 3+, in spite of the fact that they
tron-donating group perturbs the MOs, c1, of the cumyl radi-
correspond to the same types of electronic transitions,
strongly suggest that substantial TS and TB interactions
+
C
cal 3d and the cumyl cation 3d with energy d. Note that
although they are generally regarded as electron-withdraw-
ing, Cl and Br are treated as electron-donating groups,
which was shown to be the case in our recent work.[25]
+
C
exist in 2
.
+
+
C
Therefore, D and d correspond to DE(2 ) and DE(3 ), re-
A
spectively. Note that an increase in the energy of d in c1
gives rise to a roughly equal increase in the energy of f1
(Figure 8).[27] Therefore the energy gap D is given by Equa-
tion (17).
Conclusion
The results of this work have demonstrated that the effect
of substituents on the absorption spectra of 2 can be ra-
+
C
Chem. Eur. J. 2007, 13, 9207 – 9215
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
9213

H. Ikeda et al.
excimer laser. The beam diameter at the sample was around 10 mm. The
values of the absorbance at selected times (170–280, 270–380, and 470–
580 ns, and 1.07–1.18, 2.07–2.18, 5.07–5.18, 10.1–10.2, 20.1–20.2, 50.1–50.2,
and 100–101 ms) after excitation were monitored by using a Xe arc lamp
and spectrophotometer. The data collection time was observed by using
an oscilloscope. The delay times of the delay unit were 100, 200, and
400 ns, and 1, 2, 5, 10, 20, 50, and 100 ms. The gate width of the image in-
tensifier was 100 ns. To improve the signal-to-noise ratio, each difference
absorption spectrum was the result of averaging data from at least five
excitation pulses. The monitoring light was directed onto the sample cell
with a fiberglass cable. The transmitted beams were led to an image in-
tensifier coupled to a multichannnel detector controller with a second fi-
berglass cable. This detector was interfaced with a personal computer
that controlled the necessary optical hardware and electronics during
data acquisition, processed the data, and presented the data graphically.
The wavelengths of the spectrophotometer were calibrated at 360.8,
418.5, and 536.4 nm with holmium oxide. The difference absorption spec-
tra span wavelength ranges of approximately 350 to 630 or 500 to
tionalized by considering TS and TB electronic coupling of
the cumyl radical and the cumyl cation components. DFT
calculations[29] and orbital interaction theoretical considera-
tions suggest that TS and TB interactions are operative in
+
C
2d and that Y3
(SOMO-3)!Y6
G
sponsible for the characteristic absorption band in the visi-
ble region. Therefore, the observed redshift of the lob and
the smaller effect of substituents both arise from TS and TB
interactions. This investigation has led to the first theoretical
explanation of the unusually long wavelength absorption
bands observed for aryl-substituted 1,4-radical cations.[30]
They are often called distonic radical cations. However, this
may be a misleading term because its use sometimes implies
the separation of spin and positive charge in a molecule.
There is of course no such separation in a delocalized struc-
ture that results from orbital interactions.
780 nm. See the Supporting Information for transient absorption spectra
+
C
of 2
.
Although we are reluctant to comment on the controversy
C
Spectroscopic observation of 3 : A solution of 11 (3 mm) in cyclohexane
(4 mL) in a quartz cell of 1 cm pathlength was saturated with argon, de-
gassed by using several repeated freeze (À1968C)–pump (10À2 Torr)–
thaw (ambient temperature) cycles, and then sealed at 10À2 Torr. This so-
lution was irradiated at 266 nm through a focusing lens by using a YAG
laser at ambient temperature. The beam diameter at the sample was
+
C
that involves the acyclic radical cation 8 (see the Introduc-
tion), the results of our studies suggest that electronic cou-
pling, probably through TS and TB interactions, rather than
intramolecular cycloadditions is a more likely explanation of
earlier observations. Similar electronic coupling (but proba-
bly involving pseudo-p orbitals[31]) can explain the long
wavelength absorption band of the 1,3-diarylpropane-1,3-
diyl[3a] and 1,3-diarylcyclohexane-1,3-diyl radical cations.[2b]
Our results not only provide a meaningful interpretation of
the interactions in pure radical cations,[32] but they also give
information that assists the design of bifunctional radical
cations as part of the development of conceptually new
chromophores and fluorophores[6,33] in which orbital interac-
tions take place between small subunits. In particular, we re-
cently found a new and general strategy to observe short-
around 5 mm. Data collection was similar to that described for 2 +. The
C
difference absorption spectrum spans a wavelength range of approxi-
mately 250–530 nm.
Spectroscopic observation of 3+: Absorption spectra of 3+ were obtained
by using a slight modification of the procedure reported by Sekuur and
Kranenburg.[12a] A quartz cell that contained HSO3F (2 mL) was quickly
sealed with a rubber septum, saturated with argon by bubbling the gas
through the solution, and cooled to À788C in a 4”4 cm quartz Dewar
flask. A solution of 12 (3–6 mm) in MeOH (5–50 mL) was added to the
quartz cell by using a microsyringe. Absorption spectra of 3+ were re-
corded after stirring for 5 min at À788C. See the Supporting Information
for the transient absorption spectra of 3+.
Quantum chemical calculations: DFT and TD-DFT calculations were
lived biradicals, such as the singlet-excited state of 1,4-di-
performed by using the Gaussian 98 package of programs.[34] Figures 4
1
and 7 were drawn by using WinMOPAC 3.9 software.[35] The cartesian co-
CC
phenylcyclohexane-1,4-diyl ( 2d ), which is a one-electron
+
1
+
C
CC
C
reduced species of 2d (Scheme 5). Biradical 2d was ob-
ordinates for the optimized structures of 2d are given in the Supporting
Information.
Acknowledgements
H.I. and K.M. gratefully acknowledge financial support from a Grant-in-
Aid for Scientific Research on Priority Areas (Nos. 14050008 and
17029058 in Area No. 417) and others (Nos. 09740536, 10640507,
122440173, and 19350025) from the Ministry of Education, Culture,
Sports, Science, and Technology (MEXT) of Japan. H.I. also thanks
Izumi, Iketani, Shorai, and Mazda Science and Technology Foundations
for providing financial support for the work. We also thank Professor
Emeritus T. Miyashi (TU) and Professor M. Ueda (TU) for their insight-
ful and generous suggestions.
1
CC*
Scheme 5. Generation of the excited singlet biradical 2d by back elec-
+
C
tron transfer to 2d in the thermoluminescence experiment.
served at lem =582 nm as thermoluminescence from the ex-
cited state of 2d ( 2d ). This extraordinary long wave-
length emission should also be explained by similar signifi-
1
1
CC
CC*
cant TS and TB electronic coupling between the two cumyl
1
CC* [33]
radical subunits in 2d .
[1]a) J. C. Scaiano, CRC Handbook of Organic Photochemistry, CRC,
Boca Raton, 1989; b) L. J. Johnston, N. P. Schepp, “Kinetics and
Mechanisms for the Reactions of Alkene Radical Cations” in Ad-
vances in Electron Transfer Chemistry, Vol. 5 (Ed.: P. S. Mariano),
JAI Press, London, 1996, pp. 41–102.
Experimental Section
[2]a) H. Ikeda, T. Takasaki, Y. Takahashi, A. Konno, M. Matsumoto, Y.
Hoshi, T. Aoki, T. Suzuki, J. L. Goodman, T. Miyashi, J. Org. Chem.
1999, 64, 1640–1649; b) H. Ikeda, Y. Hoshi, T. Miyashi, Tetrahedron
Lett. 2001, 42, 8485–8488.
À
Spectroscopic observation of 2 +: A solution of 1 (10 mm), NMQ+BF4
C
(1 mm), and BP (0.4m) in aerated CH2Cl2 (2 mL) in a quartz cell of 1 cm
pathlength was irradiated at 308 nm through a focusing lens by using an
9214
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Chem. Eur. J. 2007, 13, 9207 – 9215

Electronic Coupling in 1,4-Radical Cations
FULL PAPER
[3]a) S. Tojo, S. Toki, S. Takamuku, J. Org. Chem. 1991, 56, 6240–6243;
b) S. Tojo, S. Toki, S. Takamuku, Radiat. Phys. Chem. 1992, 40, 95–
99.
[25]H. Namai, H. Ikeda, N. Kato, K. Mizuno, J. Phys. Chem. A 2007,
111 4436–4442.
[26]A. Rauk, Orbital Interaction Theory of Organic Chemistry, Wiley,
[4]O. Brede, F. David, S. Steenken, J. Chem. Soc., Perkin Trans. 2 1995,
23–32.
[5]N. P. Schepp, L. J. Johnston, J. Am. Chem. Soc. 1994, 116, 6895–
6903.
New York, 1994, Chapter 3, pp. 57–93.
+
C
[27]Consequently, the possibility of the f3 or f4!f5 transition of 2d
is ruled out because it cannot explain the observed reduction in the
substituent effects.
[6]H. Namai, H. Ikeda, Y. Hoshi, N. Kato, Y. Morishita, K. Mizuno, J.
Am. Chem. Soc. 2007, 129, 9032–9036.
[7]a) H. Ikeda, T. Minegishi, H. Abe, A. Konno, J. L. Goodman, T.
Miyashi, J. Am. Chem. Soc. 1998, 120, 87–95; b) H. Ikeda, T. Mine-
gishi, Y. Takahashi, T. Miyashi, Tetrahedron Lett. 1996, 37, 4377–
4380; c) T. Miyashi, H. Ikeda, Y. Takahashi, Acc. Chem. Res. 1999,
[28]The orbital interaction analysis assumes that hAB is almost the same
in all cases. One of the reviewers suggested that this may not be
true because the MOs would have a smaller coefficient on C1/C4
when a substituent is attached to the benzene ring. This assumption
may be a cause of the deviation of experimental substituent effects
A
32, 815–824.
(0.5).
+
[29]We also performed calculations on 2++ without any symmetry by
using Hartree–Fock (HF) theory and obtained similar results (a
chair molecular geometry and delocalized electronic structure). One
of the referees commented that this is strong evidence that such a
C
[8]The value of 482 nm for the lob of 2d in dichloromethane, which
was reported in ref. [7], was revised to 476 nm after wavelength cali-
bration of the spectrophotometer. See the Experimental Section.
C
[9]Values for lob(3d ) of 315 (cyclohexane) and 322 nm (cyclohexane)
A
have been reported in refs. [10a]and [10b], respectively.
[10]a) D. R. Boate, J. C. Scaiano, Tetrahedron Lett. 1989, 30, 4633–4636;
b) T. Sumiyoshi, M. Kamachi, Y. Kuwae, W. Schnabel, Bull. Chem.
Soc. Jpn. 1987, 60, 77–81.
structure is indeed the correct one. ESR studies on the parent
+
C
system 4 by Williams and co-workers provide direct evidence for
complete delocalization: a) Q.-X. Guo, X.-Z. Qin, J. T. Wang, F. Wil-
liams, J. Am. Chem. Soc. 1988, 110, 1974–1976; b) F. Williams, Q.-X.
Guo, D. C. Bebout, B. K. Carpenter, J. Am. Chem. Soc. 1989, 111,
4133–4134.
[11]Values for lob
(3d+) of 317 (HSO3F), 325 (CF3CH2OH), and 326 nm
A
(HSO3F–SbF3) have been reported in refs. [12a], [12b], and [12c],
respectively.
[30]Recently, Nelsen, Telo, and co-workers reported that the simple
Koopmans-based model is useful for explaining the absorption spec-
tra of p-phenylene-bridged intervalence radical ions: a) S. F. Nelsen,
M. N. Weaver, J. P. Telo, B. L. Lucht, S. Barlow, J. Org. Chem. 2005,
70, 9326–9333; b) S. F. Nelsen, Y. Luo, M. N. Weaver, J. V. Lockard,
J. I. Zink, J. Org. Chem. 2006, 71, 4286–4295; c) S. F. Nelsen, M. N.
Weaver, D. Yamazaki, K. Komatsu, R. Rathore, T. Bally, J. Phys.
Chem. A 2007, 111, 1667–1676.
[12]a) T. J. Sekuur, P. Kranenburg, Spectrochim. Acta, Part A 1973, 29,
803–805; b) R. A. McClelland, C. Chan, F. Cozens, A. Modro, S.
Steenken, Angew. Chem., 1991, 103, 1389–1391; Angew. Chem. Int.
Ed. Engl. 1991, 30, 1337–1339; c) G. A. Olah, C. U. Pittman, Jr., R.
Waack, M. Doran, J. Am. Chem. Soc. 1966, 88, 1488–1495.
[13]F. Williams, J. Chem. Soc., Faraday Trans. 1994, 90, 1681–1687.
+
C
[14]The chair conformation of
2
is strongly suggested by the stereo-
chemistry of the PET Cope rearrangements of 3,6-diaryl-2,6-octa-
dienes and 2,5-diaryl-3,4-dimethyl-1,5-hexadienes (see ref. [2a]). As
one reviewer suggested, it is important to consider other molecular
[31]For recent studies related to pseudo- p orbitals of 1,3-biradicals, see:
a) D. A. Dougherty, Acc. Chem. Res. 1991, 24, 88–94; b) W. Adam,
W. T. Borden, C. Burda, H. Foster, T. Heidenfelder, M. Heubes,
D. A. Hrovat, F. Kita, S. B. Lewis, D. Scheutzow, J. Wirtz, J. Am.
Chem. Soc. 1998, 120, 593–594; c) M. Abe, W. Adam, W. M. Nau, J.
Am. Chem. Soc. 1998, 120, 11304–11310; d) F. Kita, W, Adam, P.
Jordan, W. M. Nau, J. Wirtz, J. Am. Chem. Soc. 1999, 121, 9265–
9275; e) M. Abe, W. Adam, T. Heidenfelder, W. M. Nau, X. Zhang,
J. Am. Chem. Soc. 2000, 122, 2019–2026; f) M. Abe, W. Adam, M.
Hara, M. Hattori, T. Majima, M. Nojima, K. Tachibana, S. Tojo, J.
Am. Chem. Soc. 2002, 124, 6540–6541; g) M. Abe, W. Adam, W. T.
Borden, M. Hattori, D. A. Hrovat, M. Nojima, K. Nozaki, J. Wirz, J.
Am. Chem. Soc. 2004, 126, 574–582.
[32]a) Advances in Electron Transfer Chemistry (Ed.: P. S. Mariano),
JAI Press, London, 1992; b) Radicals, Ion Radicals, and Triplets: The
Spin BearingIntermediates of Organic Chemistry (Ed.: N. L. Bauld),
Wiley-VCH, New York, 1997.
[33]H. Namai, H. Ikeda, Y. Hoshi, K. Mizuno, 2007, Angew. Chem.
2007, DOI: 10.1002/ange.200702512; Angew. Chem. Int. Ed. 2007,
DOI: 10.1002/anie.200702512.
[34]Gaussian 98, Revision A.11.4, M. J. Frisch, G. W. Trucks, H. B.
Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakr-
zewski, J. A. Montgomery, R. E. Stratmann, J. C. Burant, S. Dap-
prich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O.
Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C.
Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y.
Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Ra-
ghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov,
G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L.
Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Na-
nayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. G. John-
son, W. Chen, M. W. Wong, J. L. Andres, M. Head-Gordon, E. S.
Replogle, J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 1998.
[35]WinMOPAC 3.9, Fujitsu Ltd., Tokyo, 2004.
geometries, especially a twisted boat form. The results of a prelimi-
+
C
nary calculation suggested the twisted boat conformation of 2 has
a similar, but probably less efficient, orbital interaction. To clarify,
we discuss here only the chair form of 2 +, which is optimized as the
C
most stable molecular geometry.
[15]J. W. Timberlake, J. Alender, A. W. Garner, M. L. Hodges, C. Ozm-
eral, S. Szilagyi, J. O. Jacobus, J. Org. Chem. 1981, 46, 2082–2089.
[16]J. W. Timberlake, M. L. Hodges, K. Betterton, Synthesis 1972, 632–
634.
[17]The 4-( N,N-dimethylamino)phenyl, 4-methylthiophenyl, and 4-cya-
nophenyl derivatives of 2,5-diaryl-1,5-hexadiene, prepared from the
corresponding 1,4-diarylbutane-1,4-diones, do not exhibit a clear lob
in the visible region upon LFP under similar conditions. This might
be owing to low efficiencies for the cyclization of the substrate radi-
+
C
cal cations or the low efficiencies for hole transfer from BP to the
substrates.
[18]J. M. Dust, D. R. Arnold, J. Am. Chem. Soc. 1983, 105, 1221–1227,
and references therein.
[19]M. A. OꢁNeill, F. L. Cozens, N. P. Schepp, J. Am. Chem. Soc. 2000,
122, 6017–6027.
[20]A value for lob
(3a+) of 360 nm (CF3CH2OH) has been reported in
G
ref. [12b].
[21]Values for lob
A
have been reported in refs. [12a]and [12b], respectively.
[22]A value for lob
(3e+) of 345 nm (HSO3F) has been reported in
U
ref. [12a].
C
[23]The actual relationships are as follows: DEob
(2 +)=À0.8229sCcÀ0.028
+
+
(r2 =0.9531), DEob
(2 +)=0.3169s+ +0.0124 for 2a–d
C
C
C
for 2a–f
(r2 =0.9679), DEob
(2 +)=À1.1185s+ +0.0006 for 2d–f (r2 =0.9994),
+
C
C
DEob(3+)=0.5547s+ +0.0030
for
3a–d+
(r2 =0.9970),
and
DEob(3+)=À2.8881s+ +0.0063 for 3d–f+ (r2 =0.9911).
[24]The 4-iodophenyl derivatives 2g and 3g+ are exceptions; this is
probably owing to more complex orbital interactions involving an
iodine substituent.
+
C
Received: May 30, 2007
Published online: September 4, 2007
Chem. Eur. J. 2007, 13, 9207 – 9215
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
9215