Revised structure for the diphenylaminyl radical: The importance of theory in the assignment of electronic transitions in Ph2X (X = CH, N) and PhY (Y = CH2, NH, O)

Article abstract of DOI:10.1021/jp026279i

Density functional theory indicates that the minimum energy structure of the diphenylaminyl radical, Ph₂N, has a "staggered" conformation in which the two phenyl rings are twisted relative to each other by an angle, φ, of 40°. In this conformation, the aromatic rings are oriented so as to maximize interaction with the unpaired electron while minimizing repulsion between the 2- and 2′-hydrogen atoms. This calculated ground state structure of Ph₂N differs from that, which has been accepted for the past 15 years, which had the two rings orthogonal (φ = 90°) with one ring conjugating with the nitrogen's lone pair and the other conjugating with the unpaired electron. This structure was based on unexpected differences between the UV-vis absorption spectra of Ph₂N and the diphenylmethyl radical. However, our calculations indicate that this orthogonal structure lies 3.5 kcal/mol above the global minimum. Further support for the staggered conformation of Ph₂N is provided by the similarities between absorption transition wavelengths determined theoretically and the experimental absorption bands of Ph₂N and other diarylaminyl radicals generated by laser flash photolysis. The long wavelength transition of Ph₂N, resulting in a structure that can be represented as (Ph₂) ⁺N^-, is red-shifted as compared to the related transition from Ph₂CH to (Ph₂)⁺CH^- due to the electronegativity of the N atom. The absorption bands for PhCH₂, PhNH, and PhO in the 300-450 nm region are similar in position, which has been taken to indicate that for isoelectronic species the electronic transition energies should be little affected by heteroatom substitution. Our calculations show, however, that these sets of absorption bands arise from different transitions. Therefore, the experimentally similar 300-450 nm absorption bands for these three radicals are fortuitous and do not reflect some common, unifying traits, a fact that further serves to emphasize the importance of theory in the assignment of bands due to electronic transitions.

Full text of DOI:10.1021/jp026279i

J. Phys. Chem. A 2002, 106, 11719-11725
11719
Revised Structure for the Diphenylaminyl Radical: The Importance of Theory in the
Assignment of Electronic Transitions in Ph2X• (X ) CH, N) and PhY• (Y ) CH2, NH, O)
Gino A. DiLabio,*,† Grzegorz Litwinienko,*,†,‡ Shuquiong Lin,† Derek A. Pratt,§ and
K. U. Ingold†
National Research Council of Canada, 100 Sussex DriVe, Ottawa Ontario, Canada K1A 0R6, and the
Department of Chemistry, Vanderbilt UniVersity, NashVille, Tennessee 37235
ReceiVed: June 10, 2002; In Final Form: September 4, 2002
Density functional theory indicates that the minimum energy structure of the diphenylaminyl radical, Ph2N•,
has a “staggered” conformation in which the two phenyl rings are twisted relative to each other by an angle,
φ, of 40°. In this conformation, the aromatic rings are oriented so as to maximize interaction with the unpaired
electron while minimizing repulsion between the 2- and 2′-hydrogen atoms. This calculated ground state
structure of Ph2N• differs from that, which has been accepted for the past 15 years, which had the two rings
orthogonal (φ ) 90°) with one ring conjugating with the nitrogen’s lone pair and the other conjugating with
the unpaired electron. This structure was based on unexpected differences between the UV-vis absorption
spectra of Ph2N• and the diphenylmethyl radical. However, our calculations indicate that this orthogonal
structure lies 3.5 kcal/mol above the global minimum. Further support for the staggered conformation of
Ph2N• is provided by the similarities between absorption transition wavelengths determined theoretically and
the experimental absorption bands of Ph2N• and other diarylaminyl radicals generated by laser flash photolysis.
The long wavelength transition of Ph2N•, resulting in a structure that can be represented as (Ph2)+N-, is
red-shifted as compared to the related transition from Ph2CH• to (Ph2)+CH- due to the electronegativity of
•
the N atom. The absorption bands for PhCH2 , PhNH•, and PhO• in the 300-450 nm region are similar in
position, which has been taken to indicate that for isoelectronic species the electronic transition energies
should be little affected by heteroatom substitution. Our calculations show, however, that these sets of absorption
bands arise from different transitions. Therefore, the experimentally similar 300-450 nm absorption bands
for these three radicals are fortuitous and do not reflect some common, unifying traits, a fact that further
serves to emphasize the importance of theory in the assignment of bands due to electronic transitions.
Introduction
interactions between the 2- and 2′-hydrogen atoms while
maximizing their conjugative interaction with the unpaired
electron. The rings are twisted in opposite directions from the
nodal plane of the unpaired electron’s orbital (i.e., from the
SOMO’s nodal plane) at angles, ψ, of about (20°. The
“orthogonal” Ph2N• structure proposed by Leyva et al.2 has
φ ) 90° with one ring in the SOMO nodal plane (ψ ) 0°,
maximum conjugation with the unpaired electron) and the other
perpendicular to this nodal plane (ψ ) 90°, maximum conjuga-
tion with the nitrogen’s lone pair of electrons). This structure
was proposed because the UV-vis absorption spectra of Ph2N•
and of the isoelectronic diphenylmethyl radical (Ph2CH•) were
quite different although they had been expected to be rather
similar. Specifically, and as has been known for many years,
Ph2N•3 and ring-substituted diarylaminyls3a,4 have long wave-
length absorptions with λmax in the range of 740-784 nm. An
absorption at such long wavelengths is not present in the
spectrum of Ph2CH•5 (nor, for that matter, in the spectra of
diarylnitroxides).6
We have recently investigated the effects of substituents on
the differences in bond dissociation enthalpies (∆BDEs) for the
N-H bonds in aniline vs 4-substituted anilines, phenothiazine
vs 3,7-disubstituted phenothiazines, and diphenylamine vs 4,4′-
disubstituted diphenylamines using both theoretical calculations
and experimental measurements.1 The calculated ∆BDEs for
both the phenothiazines and the diphenylamines agreed to within
1 kcal/mol with the experimental ∆BDEs determined using the
radical equilibrium electron paramagnetic resonance spectros-
copy technique.1 However, the semiempirical method used for
geometry optimizations gave a minimum energy structure for
diphenylaminyl (Ph2N•) different from that which has been
accepted for the past 15 years. Furthermore, this computed
structure and the accepted structure could not be reconciled by
additional higher level calculations, which were instead found
to support the semiempirical Ph2N• structure. The calculated
structure has the two aromatic rings twisted relative to one
another with a dihedral angle between the ring planes, φ, of
about 40 °. The rings are oriented so as to minimize steric
As Leyva et al.2 noted in 1987, “It would be difficult to obtain
a reliable prediction for the lowest energy structure of diphen-
ylaminyl from theoretical calculations.” Fortunately, this is no
longer true. The excellent agreement between our experimental
and our calculated ∆BDEs for 4,4′-disubstituted diphenylamines
together with our computed optimized Ph2N• geometry led us
to conclude that our φ ) 40°, ψ ) (20° structure is more likely
* To whom correspondence should be addressed: G.A.D.: Gino.DiLabio@
nrc.ca. G.L.: Grzegorz.Litwinienko@nrc.ca.
† National Research Council of Canada.
‡ Permanent address: Warsaw University, Department of Chemistry,
Pasteur 1, 02-093 Warsaw, Poland.
§ Vanderbilt University.
10.1021/jp026279i CCC: $22.00 © 2002 American Chemical Society
Published on Web 11/12/2002

11720 J. Phys. Chem. A, Vol. 106, No. 48, 2002
DiLabio et al.
TABLE 1: Rate Constants, k2, for Abstraction of the Amino
Hydrogen Atom from Diarylamines by tert-Butoxyl Radicals
at Ambient Temperatures and Calculated N-H BDEs
10-8 k2 (M-1 s-1
)
λaq
N-H BDEd
(kcal/mol)
amine
Ph2NH
Mes2NH
(CH2C6H4)2NH
(CHC6H4)2NH
(C6H4)2NH
(nm)a
this work
ref 5
690
400
690
400
610
12 ( 2
3.2 ( 0.3
12 ( 3
11 ( 1b
84.9
83.3
84.1e
79.6
90.3
c
c
c
25 ( 3
1.8 ( 0.4
5.5 ( 1.2
a Acquisition wavelength for kinetic measurements. b Another LFP
study gives k2 in a variety of solvents including CCl4 (14 × 108 M-1
s-1) and benzene (15 × 108 M-1 s-1).7 A less direct competition study
gave k2 ) 23 × 108 M-1 s-1 in benzene.8 c No literature data available.
d Calculated using the MLM2 model described in ref 9. e The calculated
N-H BDE for CH2(C6H4)2NH is 82.1 kcal/mol.
Figure 1. Structures and names of the diarylamines/diarylaminyls
studied in this work.
to be correct than the orthogonal structure.1 Herein, we validate
this conclusion by a combination of density functional theory
(DFT) calculations of structures and absorption spectra for a
number of diarylaminyl radicals combined with experimental
measurements of their absorption spectra, including the spectra
of radicals derived from three previously unexamined amines,
iminodibenzyl, (CH2C6H4)2NH; iminostilbene, (CHC6H4)2NH;
and dimesitylamine, Mes2NH. The aminyl radicals were gener-
ated from their parent amines by 355 nm laser flash photolysis
where k0 represents all first- and pseudo-first-order processes,
which might occur in the absence of amine. Quite apart from
any intrinsic interest in the k2 values for different amines, the
fact that the absorption grows-in rather than appearing instan-
taneously after the laser pulse provides confirmation that the
absorption spectrum that grows-in is due to the aminyl radical
(rather than to some photoexcited species).
t
t
(LFP) in neat di-tert-butyl peroxide, BuOOtBu, or BuOOtBu/
Reaction 2 rate constants for the amines studied in the present
work are listed in Table 1 together with the available, though
very limited, literature data2,7,8 and with calculated N-H BDEs.
A typical grow-in trace, that for the Mes2N• radical, is shown
in Figure 2.
benzene, 2:1 v/v:
tBuOOtBu hν (355 nm)8 2tBuO•
(1)
(2)
tBuO• + Ar2NH f tBuOH + Ar2N•
The absorption spectra of the aminyl radicals are based on
the average change in OD (∆OD) from each of five laser pulses
at each of eight well-separated times in the “plateau” region of
the grow-in traces (after the grow-in kinetics had been deter-
mined using a region of the spectrum where ∆OD following
LFP was substantial). In the plateau region, reaction 2 is >90%
complete and the aminyl radicals produced do not decay on
the time scales of our experiments. Spectra for Ph2N•, Mes2N•,
and (CH2C6H4)2N• are shown in Figure 3 (see also Supporting
Information). The only absorption spectra available in the
literature for comparison are those for Ph2N•2,3b-d and
carbazolyl.2,3d Our spectra (Ph2N• in Figure 3 and (C6H4)2N• in
the Supporting Information) are in good agreement with the
earlier work.
The amines (shown in Figure 1) were selected because their
molecular architecture dictates that the dihedral angle, φ,
between the two aromatic ring planes must be 0°, e.g.,
(C6H4)2N•, slightly greater than 0°, (CH2C6H4)2N•, and much
greater than 0°, Mes2N•.
Results
LFP. In a typical experiment, 3-5 mM amine was dissolved
in carefully deoxygenated neat tBuOOtBu or, mainly for
t
solubility reasons, in BuOOtBu/benzene, 2:1 v/v. These solu-
tions were then subjected to 355 nm nanosecond LFP at ambient
temperatures, and changes in optical density (OD) were
monitored as a function of time at wavelengths ranging from
375 to ca. 800 nm in 10-20 nm intervals. Data were collected
at each wavelength from five laser pulses and then averaged.
Great care was taken in purifying the amines and keeping them
and their solutions out of contact with the air. This was necessary
because even trace “impurities” formed by air oxidation of the
amine (a particularly facile process in the case of Mes2NH) gave
the solutions a strong absorption at the laser wavelength.
Fortunately, none of the pure amines absorbed significantly at
355 nm (at the amine concentrations employed). This is
important because the “clean” formation of an aminyl radical
via reaction 2 requires that most of the laser’s energy, which is
Theoretical Calculations
Minimum energy geometries were calculated for the six
aminyl radicals shown in Figure 1 using the (U)B3LYP11,12
functional with 6-31G(d) basis sets as implemented in the
Gaussian 98 program package.13 In general, these calculations
were straightforward and the optimized wave functions had little
spin contamination (S2 ≈ 0.85). These optimized geometries
are summarized in Table 2, which also includes the calculated
optimum geometry for the diphenylmethyl radical, Ph2CH•, and
for six nonminimum energy Ph2N• structures. All of the
structures are provided in Cartesian coordinates as Supporting
Information. The transition wavelengths and oscillator strengths
for all 12 radicals, computed using time-dependent (TD) DFT
((U)B3LYP/6-31G(d)),14 are also given in Table 2 together with
the experimental absorption maxima measured in this work,
supplemented by literature data. Calculated energy changes as
a function of the dihedral angle between the two aromatic rings
are shown for three initial conformations of Ph2N• and Ph2CH•
in Figure 4.
t
absorbed, be absorbed by the BuOOtBu. In this way, the tert-
butoxyl radicals (tBuO•) are generated only during the laser
pulse, i.e., essentially “instantaneously” (reaction 1). Following
this pulse, the aminyl radical should “grow-in” with pseudo-
first-order kinetics (rate constant, kexptl) and the rate constant
for its formation, k2, can be obtained by monitoring the grow-
in at different amine concentrations:
kexptl ) k0 + k2[Ar2NH]

Revised Structure for the Diphenylaminyl Radical
J. Phys. Chem. A, Vol. 106, No. 48, 2002 11721
t
Figure 2. Grow-in trace for Mes2N• generated by LFP of a 1.6 mM solution of Mes2NH in 2:1 v/v BuOOtBu/benzene. The arrow indicates the
time at which the laser was fired. The solid line indicates the first-order growth fit of the data to obtain kexptl. The inset shows the linear, least-
squares fit of kexptl vs [Mes2NH] used to obtain the pseudo-first-order rate constant, k2, for the formation of Mes2N•.
Discussion
Rate Constants for H-Atom Abstraction from Diaryl-
amines. The noninstantaneous, pseudo-first-order grow-in of
the absorptions following LFP of the six Ar2NH/tBuOOtBu
systems are consistent with the sole occurrence of the chemistry
depicted by reactions 1 and 2. That is, the spectra observed at
times corresponding to the plateau region of the grow-in traces
must be due to the expected Ar2N• radicals. The measured values
of k2 are consistent with calculated N-H BDEs (Table 1) except
for Mes2NH, which, for steric reasons, is significantly less
reactive than Ph2NH rather than being comparable. Carbazole
is also less reactive than Ph2NH. This is because the amino
hydrogen atom in (C6H4)2NH lies in the aromatic plane and
the N-H bond is not, therefore, weakened by resonance
stabilization of the incipient radical center by the aromatic
π-electron system. Iminodibenzyl, (CH2C6H4)2NH, has the same
reactivity as Ph2NH, which is consistent with their rather similar
N-H BDEs, while iminostilbene, (CHC6H4)2NH, has the
weakest N-H bond and is the most reactive amine.
Transition Wavelengths of Diarylaminyl Radicals. The
longest wavelength absorption bands for all of the radicals
shown in Table 2 are calculated to involve primarily (85-100%)
promotion of an electron from the highest doubly occupied
π-molecular orbital (the π-1 MO) to the highest semioccupied
π-MO (π/0). These transitions should therefore be represented
as π/ r π-1
.
The bands at shorter wavelengths are calcu-
15
0
Figure 3. Absorption spectra for aminyl radicals obtained from the
average ∆OD from each of five laser pulses at each of eight well-
separated times in the “plateau” region of the grow-in traces. (a) Ph2N•,
(b) Mes2N•, and (c) (CH2C6H4)2N•.
lated to involve primarily π/ r π-n (n ) 2, 3, etc.) transitions.
0
For Ph2N•, (CH2C6H4)2N•, and CH2(C6H4)2N•, there is excellent
agreement between the calculated π/ r π-1 wavelengths and
0

11722 J. Phys. Chem. A, Vol. 106, No. 48, 2002
DiLabio et al.
TABLE 2: Calculated Minimum Energy Geometries, Transition Wavelength (λmax/nm), and Oscillator Strengths
(f, in Parentheses) for Six Diarylaminyl Radicals Together with the Same Information for the Diphenylmethyl Radical and
for Six Nonminimum Energy Ph2N• Structures and the Experimental λmax Values
calculations
θ(CN•C)d
experiments
radical
(pt group)
φa
ψb
R(C-N•)c
λmaxe (103 f
)
λmax
f
Ph2N• (C2)
40
68
22
0
0
0
+20, -20
+34, -34
+11, -11
0, 0
0, 0
0, 0
+20, -20
136.8
136.4
136.4
136.7
137.7
135.8
143.5q
123.2
126.5
130.3
118.6
105.0
130.5
130.5q
750(44), 439(4), 429(1), 398(37)
1012(53), 501(9), 474(5), 383(26)
724(16), 471(11), 450(7), 441(50)
571(1),h 462(5),h 460(69), 415(6)
954(2), 641(1), 525(79), 409(0)
734(0),k 580(0),l 519(13),m 430(7)n
434(1),r 383(0), 381(1), 335(17)s
735,g 420g
410
Mes2 N• (C2)
(CH2C6H4)2 N• (C2)
CH2(C6H4)2 N• (C2V)
(C6H4)2 N• (C2V)
(CHC6H4)2 N• (C2V)
Ph2CH• (C2)p
700, 520
567,i 540, 510, 480i
620,j 570, 440j
e420o
40
523,t 336t
Ph2N• in constrained geometries
orthogonal (Cs)
orthogonal (C2)
planar (C2V)
90
90
0
0
0
0, 90
+45, -45
0, 0
0, 0
0, 0
+34, -34
140.7, 134.5
120.2
119.7
130.8
118.6u
105.0w
126.5y
911(0), 444(4), 430(1), 364(47)
137.6
136.5
136.7u
137.7w
136.4y
859(45), 438(3), 419(3), 377(2)
709(0), 473(89), 444(16), 438(5)
522(1),V 488(98), 460(29), 449(5)
511(104), 482(47), 465(4), 397(1)
932(50), 447(3), 436(3), 372(20)z
planar (C2V)
planar (C2V)
Mes2N• structurex (C2)
68
a Angle (in degrees) between the planes of the two aromatic rings. b Angles (in degrees) between the aromatic ring planes and the nodal plane
of the N 2p singly occupied orbital. c C-N• bond length (in pm). d CN•C angle (in degrees). e The long wavelength band listed first is the lowest
energy transition for which the main contribution is the π/ r π-1 transition unless otherwise noted. The main contributions to the other absorptions
0
are due to π/0 r π-n (n ) 2, 3, etc.) transitions unless otherwise noted. Mixing involving lower energy π levels increases as the wavelength
decreases. f This work unless otherwise noted. g Literature: 760 and 410 nm;2 770 and 425 nm.3d h The 571 nm transition is due to π/0 r π-3. The
462 nm transition is due to π/ r π-1
.
i Ref 10. j Literature: 610 and 560 nm;2 617 and 560 nm.3d k Due to π/1 r π0. l Due to π/0 r π-2
.
m Due to
o See Figure S1 in Supporting Information. p As determined from a
0
π/ r π-1
.
n Approximately equal contributions from π/ r π-1/π/ r π-3
.
0
1
0
high-resolution spectroscopy study.5 q Replace N• by C•(H). r Approximately equal contributions from π/ r π-1/π/ r π0. s Approximately equal
0
1
contributions from π/ r π-2/π/ r π0 (383 nm), π/ r π-3/π/ r π0 (381 nm), and π/ r π-2/π/ r π0 (335 nm). t Ref 5. u Chosen to be the same
0
2
0
3
0
2
as in CH2(C6H4)2N• but all other structural parameters were optimized. V Transition due to π/0 r π-4 w Chosen to be the same as in (C6H4)2N• but
.
all other structural parameters were optimized. x This structure was generated by replacing the methyl groups with hydrogen atoms in the optimized
Mes2N• structure. No further optimization was performed. y Chosen to be the same as Mes2N•. z Approximately equal contributions from π/0 r
π-2/π/ r π0 (335 nm).
2
we calculate a long wavelength transition with zero intensity,
which agrees with the absence of such a peak in the spectrum
that we obtained. The calculated shorter wavelength transitions
are in reasonable to excellent agreement with experiment (see,
e.g., Ph2CH• 335 nm (calcd) vs 336 nm (exp)).
Although the calculated transition wavelengths generally
agree rather well with experiment, the same cannot be said for
the calculated oscillator strengths and observed band intensities.
The deficiencies in time-resolved DFT-calculated oscillator
strengths have been observed in other systems,16 and it is well-
recognized that they can be misleading in the band assignment
process.16
The optimized structure of Ph2N• has two equivalent aromatic
rings, which are twisted 40° (φ) relative to one another and
(20° (ψ) out of the nodal plane of the singly occupied orbital;
hence, they are not quite maximally conjugated with the
unpaired electron.17
The excellent agreement between the calculated π/ r π-1
0
transition wavelengths and the experimental λmax values for
Ph2N• and those aminyl radicals necessarily having restricted,
nearly planar, or planar geometries, viz., (CH2C6H4)2N• and CH2-
(C6H4)2N•, gives us confidence in our calculated, slightly
nonplanar structure for Ph2N•. However, to explore the geo-
metric effect on π/ r π-1 wavelengths, we also carried out
0
Figure 4. Plots of rotational energy as a function of dihedral angle
calculations on Ph2N• held in various nonminimum energy
for three conformations of (a) Ph2N• and (b) Ph2C•H. The dihedral angle,
structures (see Table 2). Calculation on the “orthogonal”
structure (φ ) 90°, ψ ) 0°, 90°) gave a long wavelength λmax
) 911 nm with a very low oscillator strength, a result that is
inconsistent with experiment. Keeping φ ) 90° but conjugating
both rings equally with the unpaired electron and nitrogen lone
pair by setting ψ ) (45° gave λmax ) 859 nm, a result that is
also inconsistent with experiment.17 Turning to planar structures
(φ ) 0°, ψ ) 0°, 0°) and minimizing steric repulsion between
ψ, of one aromatic ring is fixed at 9 ) 0°, b ) 20°, and [ ) 90°
with respect to the nodal plane while the second ring is rotated.
the experimental λmax values, the differences in wavelengths
being 15, 24, and 4 nm, respectively; see Table 2. For Mes2N•
and (C6H4)2N•, the calculated longest wavelength transitions at
1 012 and 954 nm, respectively, are outside the spectral detection
range of our equipment (limit ca. 800 nm). For (CHC6H4)2N•,

Revised Structure for the Diphenylaminyl Radical
J. Phys. Chem. A, Vol. 106, No. 48, 2002 11723
the 2- and 2′-hydrogen atoms by allowing both the CNC angle
and the C-N bond length to increase yields λmax ) 709 nm,
which is slightly farther away from the experimental value of
735 nm than the value calculated for the optimized structure
(λmax ) 750 nm; see Table 2). This 709 nm structure is fairly
similar to that of (CH2C6H4)2N•, and not surprisingly, this λmax
is close to the calculated (724 nm) and experimental (700 nm)
values found for (CH2C6H4)2N•. When the CNC angle and CN
bond lengths for planar Ph2N• are constrained to equal those
electronic transition energies should be little affected by
heteroatom substitution.2 However, TD UB3LYP/6-311+G(d)
•
calculations on the PhCH2 , PhNH•, and PhO• radicals show
that the bands do not arise from the same transitions, viz.,
/
PhCH2 , 391 (π r π-1/π/ r π0), 365 (π/ r π0/π/ r π-2),
•
2
0
and 324 nm (π/0r π-1/π/ 1r π0) (all in reasonable agreement
0
1
with the experimental values of 448,25a 318,25b and 30525b nm);
PhNH•, 539 (π/ r π-2), 439 (π/ r π-1), and 360 nm (π/ r
0
0
2
π0/π/ r π-3) (in reasonable agreement with the experimental
0
calculated for CH2(C6H4)2N• (λmax ) 567 nm), the π/ r π-1
0
values of 400 and 308 nm);25c PhO•, 1166 (dipole forbidden
π/ r π-1 transition), 533 (π/ r π-2), and 350 nm (π/ r π-3
)
transition wavelength decreases to 522 nm and has a low
oscillator strength and when constrained to the (C6H4)2N•
geometry, this wavelength decreases to 511 nm. Finally, to
explore the magnitude of the expected red-shift induced by the
six methyl groups in Mes2N•, calculations were carried out on
Ph2N• at the Mes2N• geometry (φ ) 68°, ψ ) (34°). This
0
0
0
(in reasonable agreement with the experimental values of 1 124,
625, and 397 nm).26 The very long wavelength, but forbidden,
transition for PhO• is consistent with the expected stability of
Ph+O-. Therefore, the experimentally similar 300-450 nm
•
patterns of absorption bands for PhCH2 , PhNH•, and PhO• are
causes the π/ r π-1 transition to decrease in wavelength from
fortuitous and do not reflect some common, unifying traits.
Rotational Energy Surfaces of the Diphenylaminyl and
Diphenylmethyl Radicals. To explore further the similarities
and differences between Ph2N• and Ph2CH•, the energy changes
involved in rotating one phenyl ring about the Ph-N and Ph-C
bonds have been calculated while keeping the other phenyl ring
at one of three, fixed dihedral angles, ψ, with respect to SOMO’s
nodal plane. These angles were ψ ) 0, 20 (ψ for the minimum
energy structures), and 90°, and the results are shown in Figure
4. For the cases where the dihedral angle for one ring has been
fixed at 20°, both potentials are very flat, which indicates that
both Ph2N• and Ph2CH• will experience large deviations from
their minimum energy structures even at room temperature. The
barriers to complete rotation of this “free” phenyl group are 5
kcal/mol for Ph2N• and 7.5 kcal/mol for Ph2CH•. The lower
barrier in Ph2N• is to be expected because at ψ ) 90° there is
stabilization of this orthogonal ring by conjugative delocalization
with the lone pair of electrons on nitrogen. In the cases where
ψ for one ring is fixed at 90°, the energy cost of rotating the
other ring to ψ ) 90° (which breaks its delocalization of the
unpaired electron) is 15 kcal/mol for both Ph2N• and Ph2CH•.
This energy change is in reasonable agreement with accepted
resonance stabilization enthalpies for PhNH• (12.0 kcal/mol)19
0
1 012 to 932 nm, only 21 nm larger than the calculated value
for the orthogonal structure. Taken in their entirety, the
foregoing results overwhelmingly support a minimum energy
geometry for the Ph2N• radical equal, or certainly close to, that
calculated, viz., φ ) 40°, ψ ) (20°.
The geometry of Ph2N• is essentially identical to that
calculated for Ph2CH• (see Table 2). This result is perfectly
reasonable provided π-aromatic conjugation with the unpaired
electron in Ph2N• is significantly more stabilizing than π-aro-
matic conjugation with the lone pair on the nitrogen. A strong
preference for π-aromatic conjugation with the unpaired electron
is supported by independent evidence. That is, on the basis of
N-H BDEs in PhNH2 and CH3NH2,19 the planar PhNH• radical
can be estimated to be stabilized by 12.0 kcal/mol relative to
CH3NH• and this must be due to delocalization of the unpaired
electron into the aromatic ring. However, the barrier to rotation
about the Ph-N bond in PhNHCH3 is only 7.2 kcal/mol.20,21
Because this barrier must reflect stabilization arising from
conjugation of the nitrogen’s lone pair with the aromatic
π-electrons, it can be seen that conjugation with the lone pair
is much less stabilizing than conjugation with the unpaired
electron. In Ph2N•, the two aromatic rings adopt a conformation,
which balances maximum interaction with the unpaired elec-
tron23 with minimum steric repulsion between the 2- and 2′-
H-atoms.
•
and for PhCH2 (12.2 kcal/mol).19
Experimental Section
The energy-minimized structures of Ph2N• and Ph2CH• differ
only in the expected slightly longer Ph-C than Ph-N bond
and slightly greater CC•HC than CN•C angle. Nevertheless,
unlike Ph2N•, the Ph2CH• radical has no long wavelength
Method of Calculation. In part, this is described under the
Results. Transition wavelengths were calculated using TD (U)-
B3LYP14 with 6-31G(d) basis sets. Additional TD (U)B3LYP/
6-311G** calculations on Ph2N• and Mes2N• produced wave-
lengths that agreed to within about 5 nm with the results
obtained with the smaller basis set. The rotational energy plots
shown in Figure 4 are based on the (U)B3LYP/6-31G(d)
energies of structures that were partially optimized using the
AM127 method.
Materials. Spectrograde benzene (OmniSolv) was used as
received. tBuOOtBu (Aldrich) was passed though neutral
alumina before use. Ph2NH, (C6H4)2NH, and (CH2C6H4)2NH
(Aldrich) were recrystallized from hexane (or hexane/ethyl
acetate), dried under vacuum, and stored under a nitrogen
atmosphere at 4 °C.
Synthesis of Di(2,4,6-trimethylphenyl)nitroxide. Following
a literature procedure,28 2-bromomesitylene (7.66 mL, 0.05 mol)
and magnesium turnings (1.22 g, 0.05 mol) were stirred in a
solvent composed of sodium-dried ether (50 mL) and benzene
(25 mL). A few crystals of I2 were added, and the reactants
were heated to reflux for 24 h. After they were cooled to room
temperature under nitrogen, 2-nitromesitylene (4.13 g, 0.025
π/ r π-1 transition, a spectral difference on which the Ph2N•
0
orthogonal structure was largely based.2 We attribute this
difference in the absorption spectra of Ph2N• and Ph2CH• to
the greater electronegativity of nitrogen as compared to carbon.
This will make an electronic transition from ground state Ph2N•
to a state that can be approximately represented by (Ph2)+N-
more facile,15 i.e., red-shifted, as compared with a transition
from Ph2CH• to (Ph2)+CH-.24 Caution must, therefore, always
be exercised when structural assignments are based on similari-
ties and/or differences in the spectra of isoelectronic species
unless explicit consideration is given to differences in the
electronegativities of the constituent atoms by calculations
similar to those described herein.
To explore this matter further, we have applied theory to study
the absorption bands of PhCH2 , PhNH•, and PhO•. In the 300-
•
450 nm range, the bands for these three radicals are similar in
position (but not intensity) and therefore appear to be consistent
with the prevailing view that for isoelectronic species the

11724 J. Phys. Chem. A, Vol. 106, No. 48, 2002
DiLabio et al.
mol) in dry ether was added dropwise from a syringe. The
solution turned red. Fifteen minutes after the addition was
completed, the reaction solution was poured into an aqueous
saturated solution of NH4Cl containing some ice cubes. The
aqueous layer was extracted with ether (3 × 40 mL), and the
combined organic solution was dried with anhydrous MgSO4
and concentrated to give the crude dimesityl nitroxide as a red
solid. This was thrice recrystallized from MeOH to give 2.5 g
of the desired red crystalline product (mp 138-139 °C, Lit.28
142-143 °C). The purity and identity of the product were
confirmed by thin-layer chromatography (TLC, 15:1 hexane:
EtOAc) and high-resolution mass spectroscopy (M + 1:
observed M/Z ) 269.1783 amu, calcd ) 269.1780 amu).
Supporting Information Available: Kinetic data for the
t
reaction of amines with BuOOtBu. Energies required for the
evaluation of N-H BDEs in the arylamines. The fully and
partially optimized geometries of the compounds listed in Table
2. The spectra obtained for iminostilbene and for carbazolyl.
This material is available free of charge via the Internet at
http://pubs.acs.org.
References and Notes
(1) Pratt, D. A.; DiLabio, G. A.; Valgimigli, L.; Pedulli, G. F.; Ingold,
K. U. J. Am. Chem. Soc. 2002, 124, 11085-11092.
(2) Leyva, E.; Platz, M. S.; Niu, B.; Wirz, J. J. Phys. Chem. 1987, 91,
2293-2298.
(3) Wieland, H. Annalen 1911, 381, 200-216. (b) Lewis, G. N.; Lipkin,
D. J. Am. Chem. Soc. 1942, 64, 2801-2808. (c) Wiersma, D. A.;
Kommandeur, J. Mol. Phys. 1967, 13, 241-251. (d) Shida, T.; Kira, A. J.
Phys. Chem. 1969, 73, 4315-4320. (e) Johnston, L. J.; Redmond, R. W. J.
Phys. Chem. A 1997, 101, 4660-4665.
(4) See, for example (a) Wieland, H. Chem. Ber. 1915, 48, 1078-
1095. (b) Neugebauer, F. A.; Fischer, P. H. H. Chem Ber. 1965, 98, 844-
850.
(5) Bromberg, A.; Meisel, D. J. Phys. Chem. 1985, 89, 2507-2513.
(6) Forrester, A. R.; Hay, J. M.; Thomson, R. H. Organic Chemistry
of Stable Free Radicals; Academic: London, 1968; Chapter 3.
(7) MacFaul, P. A.; Ingold, K. U.; Lusztyk, J. J. Org. Chem. 1996,
61, 1316-1321.
(8) Lucarini, M.; Pedrielli, P.; Pedulli, G. F.; Valgimigli, L.; Gigmes,
D.; Tordo, P. J. Am. Chem. Soc. 1999, 121, 11546-11553.
(9) Dilabio, G. A.; Pratt, D. A.; LoFaro, A. D.; Wright, J. S. J. Phys.
Chem. A 1999, 103, 1653-1661.
(10) Shida, T.; Kira, A. Bull. Chem. Soc. Jpn. 1969, 42, 1197-1201.
(11) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
(12) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789.
(13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgonery, J. A., Jr.;
Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A.
D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi,
M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;
Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick,
D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.;
Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-
Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.
M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.9;
Gaussian, Inc.: Pittsburgh, PA, 1998.
Synthesis of Di(2,4,6-trimethylphenyl)amine. An attempted
synthesis of this compound from dimesityl nitroxide by the
literature procedure28 was complicated by the amine’s extreme
air sensitivity. This very rapidly regenerates the nitroxide and
makes manipulation of the amine very difficult. The dimesityl
nitroxide was therefore reduced directly in the LFP solvent,
tBuOOtBu. (In a control experiment, this peroxide was found
to be stable under the hydrogenation conditions.) Dimesityl
nitroxide (107.3 mg, 0.4 mmol) was dissolved in 80 mL of
t
freshly purified BuOOtBu, and platinum(IV) oxide (11.4 mg,
0.05 mmol) was added, followed by hydrogenation for 2 h at
room temperature. The solution turned from red to colorless in
the first 10 min of hydrogenation. The product solution
1
was transferred to the LFP quartz cuvette under helium. H
NMR (400 MHz, CDCl329): δ 6.81 (s, 4H), 2.26 (s, 6H), 2.00
(s, 12 H).
LFP. Excitation was provided by a Lumonics HY 750 Nd:
YAG laser (third harmonic, 355 nm, 10 ns pulses, 40 mJ/pulse).
The transient signals collected by a Tektronix 7912 AD digitizer
were transferred to a personal computer that controlled the
experiment and provided suitable data processing and storage.
Kinetics. All solutions were deaerated by bubbling with
helium for 5 min prior to laser excitation. For each concentration
of the parent amine, the mean of at least five transient growth
traces of the radical was analyzed by least-squares fitting, on
the basis of pseudo-first-order kinetics, to obtain experimental
rate constants, kexptl. Values of kexptl plotted vs the parent amine
concentration gave straight line fits with R2 greater than 0.96
in all cases. Full kinetic results are provided in the Supporting
Information.
(14) Stratmann, R. E.; Scuseria, G. E.; Frisch, M. J. J. Chem. Phys.
1998, 109, 8218-8224.
(15) This transition can be envisaged as roughly corresponding to the
promotion of an aromatic π-electron into the N-2p SOMO, i.e., to the
formation of a delocalized aromatic radical cation and a localized nitrogen
anion.
(16) See, for example Hirata, S.; Lee, T. J.; Head-Gordon, M. J. Chem.
Phys. 1999, 111, 8904-8912.
Spectra. All samples were deaerated by passing a stream of
helium through the sample before and during the laser experi-
ments. The concentrations of tBuOOtBu, benzene (when present),
and parent amines were adjusted to obtain absorbance not greater
than 0.45 at 355 nm. The concentrations of the parent amines
were [Ph2NH] ) 4.97 mM, [(C6H4)2NH] ) 5.6 mM, [(CH2C6-
H4)2NH] ) 3.3 mM, and [Mes2NH] ) 5.0 mM. Transient
absorption spectra were recorded at 20 °C in a flow system
using a 7 × 7 mm2 quartz flow-through cell connected with a
Teflon line to a sample reservoir. This avoided contamination
byproduct build-up. The flow rate was generally 2 mL/min.
Transient spectra were collected within the plateau region (see
Figure 2) of the kinetic curves.
(17) The possibility that one (or both) of the aromatic rings in Ph2N• is
(are) preferentially conjugated with the lone pair on nitrogen rather than
with the unpaired electron has been considered and rejected on the basis of
substituents effects on the ESR spectra of ring-substituted diphenylaminyls.
See Danen, W. C.; Neugebauer, F. A. Angew. Chem., Int. Ed. Engl. 1975,
14, 783-789.
(18) Note that all structures with φ ) 90° will have equal energy
irrespective of their ψ angles.
(19) See Table 2 in Ingold, K. U.; Wright, J. S. J. Chem. Educ. 2000,
77, 1062-1064.
(20) Lunazzi, L.; Magagnoli, C.; Guerra, M.; Macciantelli, D. Tetra-
hedron Lett. 1979, 3031-3032. (b) Lunazzi, L.; Magagnoli, C.; Macciantelli,
D. J. Chem. Soc., Perkin Trans. 2 1980, 1704-1707.
(21) ∆Gq ) 7.24 ( 0.02 kcal/mol, ∆Hq ) 7.6 ( 0.2 kcal/mol, ∆Sq )
2 ( 1.5 cal/mol/K.20a The inversion barrier for aniline is much lower (1.6
kcal/mol).22
(22) Brand, J. C. D.; Williams, D. R.; Cook, T. J. J. Mol. Spectrosc.
1966, 20, 359-380.
Acknowledgment. G.L. wishes to thank the Foundation for
Polish Science (FNP) for a foreign Postdoctoral Fellowship.
D.A.P. thanks Professor N. A. Porter, Vanderbilt University,
and NSERC Canada for their support. We also thank Prof. M.
S. Platz and the referees for some helpful comments and
suggestions.
(23) This interaction energy will follow a cos2 ψ relation and cos2
20° ) 0.88, i.e., only 12% below the maximum of 1.0 at ψ ) 0°. It is also
worth noting that on the basis of the ESR coupling constants, it has been
calculated that the unpaired electron in Ph2N• is delocalized into the phenyl
groups to the extent of ca. 60%; see Neugebauer, F. A.; Bamberger, S.
Angew. Chem., Int. Ed. Engl. 1971, 10, 71.

Revised Structure for the Diphenylaminyl Radical
J. Phys. Chem. A, Vol. 106, No. 48, 2002 11725
(24) Although the frequency of the long wavelength absorption band
of Ph2N• might be expected to change in more polar solvents (in view of
the dipolar nature of the excited state), no change was detected in 70%
tBuOOtBu/30% CH3CN.
(25) Porter, G.; Ward, B. J. Chim. Phys. 1964, 61, 1517-1522. (b)
Porter, G.; Strachan, E. Spectrochim. Acta 1958, 12, 299-304. (c) Land,
E. J.; Porter, G. Trans. Faraday Soc. 1963, 59, 2027-2037.
(26) Radziszewski, J. G.; Gil, M.; Gorski, A.; Spanget-Larsen, J.; Waluk,
J.; Mro´z, B. J. J. Chem. Phys. 2001, 115, 9733-9738.
(27) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J.
Am. Chem. Soc. 1985, 107, 3902-3909.
(28) Neugebauer, F. A.; Bamberger, S. Chem. Ber. 1974, 107, 2362-
2382.
(29) By reduction in CDCl3 in an NMR tube.