Broadening the Horizon of the Bell–Evans–Polanyi Principle towards Optically Triggered Structure Planarization

Article abstract of DOI:10.1002/anie.202015274

Finding a relationship between kinetics and thermodynamics may be difficult. However, semi-empirical rules exist to compensate for this shortcoming, among which the Bell–Evans–Polanyi (B-E-P) principle is an example for reactions involving bond breakage a

Full text of DOI:10.1002/anie.202015274

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How to cite: Angew. Chem. Int. Ed. 2021, 60, 7205–7212
International Edition: doi.org/10.1002/anie.202015274
German Edition: doi.org/10.1002/ange.202015274
Luminescent Molecules Hot Paper
Broadening the Horizon of the Bell–Evans–Polanyi Principle towards
Optically Triggered Structure Planarization
+
+
+
Yi Chen , Kai-Hsin Chang , Fan-Yi Meng , Sheng-Ming Tseng, and Pi-Tai Chou*
Abstract: Finding a relationship between kinetics and thermo-
dynamics may be difficult. However, semi-empirical rules exist
to compensate for this shortcoming, among which the Bell–
Evans–Polanyi (B-E-P) principle is an example for reactions
involving bond breakage and reformation. We expand the
B-E-P principle to a new territory by probing photoinduced
where E is the intercept, and a is a value characteristic of the
transition state along the reaction coordinate, which should
0
be in the range of 0 ꢀ a < 1. These lead to the conclusion that
a decrease in the reaction barrier should increase the reaction
exothermicity. While the B-E-P principle has been applied to
[9–14]
a number of reactions involving bond rearrangement,
the
structure planarization (PISP) of
a
series of dibenz-
fundamental issue of whether the reaction parameters, e.g.,
transition-state structure and reactive frequency, meet the
criteria is often overlooked.
[
b,f]azepine derivatives incorporating bent-to-planar and ro-
tation motion. The latter involves twisting of the partial double
bond character, thereby inducing a barrier that is substituent
dependent at the para N-phenyl position. The transition-state
structure and frequency data satisfy and broaden the B-E-P
principle to PISP reactions without bond rearrangement.
Together with dual emissions during PISP, this makes possible
harnessing of the kinetics/thermodynamics relationship and
hence ratiometric luminescence properties for excited-state
structural transformations.
In yet another instance, upon excitation, changes in the
electron density distribution are induced, where structure
relaxation becomes a ubiquitous phenomenon. Interestingly,
despite wide studies on photoinduced structural transforma-
[15–23]
tion,
probing the kinetics/thermodynamics relationship is
very rare. One example is the study on the structural profile
for the dinuclear platinum(II) complexes in the triplet
manifold, where the B-E-P principle was qualitatively
[
22]
cited. In this study, we aim to expand the B-E-P principle
Introduction
to a new class of photoinduced structure planarization
[24–26]
(
PISP),
open up this new research direction, we designed and
synthesized series of seven-membered heterocyclic
with no rearrangement of chemical bonds. To
In chemistry, discovering the correlation between kinetics
and thermodynamics is of paramount importance but is not
feasible in general. Nevertheless, theories, rules or principles
exist to describe the correlation between the kinetics and
a
p-conjugated molecules based on the dibenzo[b,f]azepine
(DBA) core, forming N-phenyl DBA derivatives denoted
PDBAs (Figure 1a). This platform is reminiscent of hetero-
[1–5]
thermodynamics of certain reactions.
One elegant exam-
ple is Marcus electron transfer theory in the weak electronic
pine systems, nonplanar seven-membered rings such as
[
3,6]
[27–32]
coupling region,
where the relationship between the
oxepins and thiepins,
where dibenz[b,f]oxepin exhibited
kinetics and thermodynamics relevant to internal and exter-
nal reorganization can be formulated. As for reactions
involving bond breakage and reformation, finding the rela-
tionship is very difficult or perhaps impossible in most
instances. In this regard, one long-standing chemical theory
is the Bell–Evans–Polanyi (B-E-P) principle. In an AÀB +
C ! A + BÀC bond breakage-formation reaction, the B-E-P
principle states that if the position and frequency of the
transition state along the reaction coordinate are approxi-
mately the same within a family of derivatives, then the
a large Stokes-shifted emission that was proposed to result
from structural planarization. Chemically, this process
is driven by a gain in aromaticity in the excited state, which
[27,33–36]
is known as Bairdꢀs rule.
In comparison, PDBAs
offer the obvious advantage that their N substitution provides
a versatile chemical handle for fine-tuning the reaction
dynamics.
Comprehensive spectroscopic and dynamic analyses were
used to establish a mechanism of the excited-state structural
R* ! P* transformation of PDBAs, which incorporates
planarization of the core azepine accompanied by rotation
(f) of the N-phenyl moiety. The synergy of these two motions
induces a barrier that can be simply envisaged as in Figure 1b
[
7,8]
activation energy, DE , of the reaction is proportional to the
a
[
7]
enthalpy of the reaction, DH, expressed as
DE ¼ E þ aDH
ð1Þ
a
0
(vide infra). We then discovered such a transformation
possessing similar transition-state structure and reactive
frequency along the PISP pathway, satisfying the kinetics/
thermodynamics relationship declared by the B-E-P princi-
ple. This, together with the ratiometric dual emission during
PISP, leads to bright prospects in harnessing excited-state
structure planarization.
[
+]
[+]
[+]
[
*] Dr. Y. Chen, Dr. K.-H. Chang, Dr. F.-Y. Meng, S.-M. Tseng,
Prof. Dr. P.-T. Chou
Department of Chemistry, National (Taiwan) University
Taipei, 10617 (Taiwan, R.O.C.)
E-mail: chop@ntu.edu.tw
+
[
] These authors contributed equally to this work.
Supporting information and the ORCID identification number(s) for
the author(s) of this article can be found under:
https://doi.org/10.1002/anie.202015274.
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by the angle between the C(6)-C(7)-C(9) plane and the C(1)-
C(6)-C(14) plane) of 21–288 and Vs2 (defined by the angle
between the C(1)-N-C(14) plane and the C(1)-C(6)-C(14)
plane) of 47–578. Moreover, the bending angle V (angle
a
between the C(1)-C(3)-C(4) plane and the C(14)-C(12)-
C(11)) of PDBAwas recorded as 1268, while that of DBAwas
substantially greater at 1448, and the angle V (the angle
b
between the C(7)-C(8)-N plane and the line along N-C(15))
was 1078 and 1348 for PDBA and DBA, respectively. This
difference can be attributed to the steric interactions between
the N-substituted phenyl group and the dibenzazepine core.
When the substituent was varied from an electron-donating
group (-OMe) to an electron-withdrawing group (-CN), the
bending angle V increased from 1198 to 1288, and the angle
a
Vb ranged from 928 to 1178. The NÀC(15) bond length
provides more direct evidence of this, as it decreases in the
order of PDBA-OMe (1.421 Š) > PDBA-Me (1.404 Š) >
PDBA (1.399 Š) > PDBA-COMe (1.391 Š) > PDBA-CN
(1.385 Š) (Figure 2), presumably due to charge transfer from
the N-phenyl nitrogen to the para substituent. The results thus
indicate that both the nature of the azepine bending structure
and the substituent substantially influence the conformation
and molecular characteristics.
Photophysical properties. Figure 3 shows the absorption
(in terms of the extinction coefficient, e) and emission spectra
of DBA (the control group) and the PDBAs in cyclohexane.
The maxima of the lowest lying (S !S ) absorption bands of
Figure 1. a) Chemical structures and brief synthetic pathways to the
target molecules. The red circle arrow represents an increase in the
electron-donating strength. b) Illustration of the structural transforma-
tion for PDBAs in the excited state, where R*, T* and P* denote the
starting structure, transition state and final structure, respectively, in
the excited state.
0
1
DBA and all PDBAs appear at approximately 350 nm and
show small absorptivity. For example, the absorption molar
extinction coefficient, e, of DBA at 350 nm was measured to
À1
À1
be 820 Æ 30 M cm (Table 1; Supporting Information, Fig-
ure S2). The N-phenyl-derivatized PDBAs show even weaker
lowest lying absorption bands, with extinction coefficients of
À1
À1
Results and Discussion
approximately 300–700 M cm at their maxima. This trend
can be rationalized by the large separation between the
electron densities of the HOMO and LUMO (vide infra),
which are mainly located on the para-substituted N-phenyl
moiety and the dibenzo- moiety, respectively, i.e., by the
Synthesis and characterization. Figure 1a depicts the
series of N-substituted DBA derivatives probed in this study.
Details of the synthetic route and characterization are
presented in the Supporting Information. As shown in
single-crystal X-ray diffraction analyses (Figure 2; Supporting
[38]
charge-transfer properties. This conclusion is also support-
ed by the resulting solvatochromism of the initially prepared
bent-structure emission (Figure S5).
[37]
Information, Table S1),
all the PDBAs exhibit bent
dibenzo[b,f]azepine structures with bay angles Vs1 (defined
Figure 2. Single-crystal structures of the studied molecules from two perspectives.
7
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Figure 3. Steady-state absorption (dashed lines) and photoluminescence (solid lines) spectra of a) DBA, b) PDBA-OMe, c) PDBA-Me, d) PDBA,
e) PDBA-COMe, f) PDBA-CN and g) MDBA in cyclohexane (l =300 nm), and of h) PDBAs in solid film.
ex
Table 1: Experimental and calculated optical characteristics for the target molecules in cyclohexane at
room temperature.
vibronic spectral feature, suggests
that DBA undergoes planarization
in the excited state to restore the
aromaticity.
[
a]
[b]
[c]
Name
Absorption S !S
Emission S !S
Q.Y. [%]
t [ps]
0
1
1
0
[
a]
[a]
labs [nm]
l
f
l
l
f
calc
[a]
em
[a]
calc
[a]
À1
À1 [a]
(
e [M cm ])
[nm]
[nm]
[nm]
All the PDBAs exhibit absorp-
DBA
MDBA
360
406 0.0326 666
386 0.0380 556
425 0.0001 498
733 0.0115
636 0.0264
621 0.0001
0.05
0.35
0.50
0.05
0.03
0.03
0.03
600 at 600 nm tion profiles similar to that of DBA.
(
821)
In sharp contrast, however, depend-
ing on the substituent, they exhibit
349
1209)
356
1100 at 550 nm
(
diverse emission characteristics
very distinct from those of DBA
PDBA-OMe
PDBA-Me
PDBA
1600 at 460 nm
(
305)
(
Figure 3). Compared to the vibron-
351
401 0.0001 482
548 0.0020
698 0.0150
517 0.0062
696 0.0153
480 0.0185
658 0.0164
470 0.0285
658 0.0184
167 at 440 nm
183 at 660 nm
ic progressive 600 nm emission of
(
395)
648
388 0.0005 462
642
366 0.0020 451
628
348
56 at 440 nm DBA, the emission of PDBA-OMe
184 at 650 nm is drastically blue-shifted to 500 nm
(
397)
PDBA-COMe
PDBA-CN
ꢁ360
472)
ꢁ343
735)
29 at 410 nm
225 at 660 nm
20 at 420 nm
200 at 650 nm
in cyclohexane, which is mirrored
by the lowest lying absorption spec-
trum. Moreover, unlike the solvent
polarity independence of the
(
357 0.0026 434
626
(
[
a] Experimental lowest lying absorption (labs), emission wavelengths (lem), calculated lowest lying
absorption or emission wavelengths (lcalc), molar extinction coefficient (e), oscillator strengths (f).
b] Emission quantum yield (Q.Y.). The measurement was performed by using excitation at 370 nm for
DBA and MDBA, and at 287 nm for PDBA-OMe, PDBA-Me, PDBA, PDBA-COMe, and PDBA-CN.
6
00 nm emission band of DBA,
the PDBA-OMe emission exhibits
pronounced solvatochromism, as it
is redshifted from 500 nm in cyclo-
[
[
c] Decay time constants (t).
hexane to 550 nm in THF (Fig-
ure S5). These results demonstrate
DBA was previously reported to be nonemissive at room
the normal emission with charge-transfer behavior of PDBA-
OMe. Dual fluorescence emission bands were observed for
the rest PDBAs (Figure 3). In terms of the peak wavelength
and solvent polarity dependence, the short emission wave-
[
39]
temperature. However, in this study, DBA was found to
exhibit a weak orange-red, vibronic progressive emission with
a maximum at approximately 600 nm in various solvents
(
Figure 3a; Figure S5). This emission feature was previously
length band (the F band) shows spectral features and charge-
1
unrecognized, perhaps due to its anomalously large Stokes
transfer trends similar to those of the band of PDBA-OMe,
À1
shift of > ꢁ 10000 cm in the red region. Such a large Stokes-
while the long wavelength red emission band (the F band) is
2
shifted emission even in nonpolar solvents, together with the
nearly solvent polarity independent and hence similar to the
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red DBA emission band. Importantly, in solid thin film form,
time-correlated single-photon counting (for TCSPC, see the
Supporting Information) results show single exponential
decay dynamics with a lifetime of 576 ps (Figure 4a). We
then performed a fluorescence upconversion experiment by
monitoring at 500 nm, which is supposed to be in the region of
all the PDBAs exhibit only an F band (Figures S6 and S7).
1
The observation of the F band only for PDBA-OMe and
1
dual emission for the other PDBAs suggests that the
electronic properties of the para substituent play a key role
in fine-tuning the barrier and hence altering the structural
relaxation dynamics. When the para substituent is switched
from an electron-donating group to an electron-withdrawing
group, the F /F emission intensity ratio appears to increase in
F emission where the steady-state intensity is obscured due
1
to its fast relaxation to F . The results shown in the inset of
2
Figure 4a reveal a fast decay time constant of 3.9 ps. The fast
structural planarization of DBA can be attributed to the lack
of steric hindrance during PISP. For PDBA-OMe, which
2
1
the order of PDBA-OMe < PDBA-Me < PDBA < PDBA-
COMe < PDBA-CN. The presence of only the F band for
exhibits solely F emission, the time-resolved studies reveal
1
1
PDBA-OMe implies that the reaction barrier and/or ener-
getics are high, prohibiting PISP. Conversely, the control
compound, DBA with no N-phenyl ring to induce steric
hindrance shows the opposite case of a negligible barrier for
PISP, giving solely F2 emission. Chemically, introducing
a bulky group homogenously distributed through the space
so that the azepine will be always hindered during planariza-
tion would be intriguing. Accordingly, the azepine may be
locked at a specific bending angle rather than undergoing
a planar configuration. To prove this viewpoint, we synthe-
sized N-methyl-substituted DBA, namely, MDBA (Fig-
ure 1b), in which the methyl group induces a steric hindrance
that is independent of its rotation. As shown in Figure 3g,
MDBA exhibits a 550 nm emission band that is between F1
a single exponential decay time of as long as 1.6 ns (Fig-
ure 4b). The results imply prohibition of structural relaxation
for PDBA-OMe within its lifespan in the excited state.
We next probed those PDBAs showing dual emission.
Figure 4c depicts the kinetic profiles for the F1 and F2
emission bands of PDBA, while the time-resolved profiles
for the other PDBAs are displayed in Figure S17. All
pertinent kinetic data are listed in Table S11. Using PDBA
as an example, upon monitoring the F band emission at, e.g.,
1
440 nm, the time-resolved measurements reveal a single
exponential decay time constant of 56 Æ 8.0 ps. This time
constant, within the experimental error, matches the rise
component of 58 Æ 8 ps of the F2 emission monitored at
660 nm (Figure 4c; Table S11). Similarly, PDBA-Me, PDBA-
COMe and PDBA-CN all show good correlations in which
(
ꢁ 440 nm) and F ( ꢁ 600 nm) band, affirming the proposal.
2
Time-resolved emission spectroscopy. For DBA, when
the decay time constants of their F band are the same as the
1
monitoring the F emission in the range of 600 to 650 nm, the
rise time constants of their F band (Figure S17).
2
2
Figure 4. Emission kinetic profiles of a) DBA, b) PDBA-OMe and c) PDBA in cyclohexane. The monitored emission wavelength is shown in the
inset. Inset of (a) presents fast decay dynamics monitored at 500 nm measured within 20 ps. d) Temporal spectral evolution of PDBA and its 2D
plot (inset) in cyclohexane at 298 K. e) Temperature-dependent relaxation kinetics of PDBA monitored at the F band (460 nm) from 258 K to
1
À1
2
98 K in methylcyclohexane. Inset: plot of lnkobs v.s. 1K ; l : 287 nm.
ex
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The data listed in Table S11 provide strong evidence that
(S ) structures with the corresponding frontier molecular
0
the rate constant of the structural transformation, k , which is
orbital contours for the HOMO and LUMO of DBA, PDBA-
OMe, PDBA and PDBA-CN are depicted in Figure 5. Similar
structure/frontier orbital properties were obtained for
PDBA-Me and PDBA-COMe (Figure S26). Similar to the
X-ray crystal structures, the ground-state optimized struc-
tures, defined as R (Figure 5), for DBA and the PDBAs all
exhibit a bent structure for the core dibenz[b,f]azepine moiety
t
deduced from k = 1/tdecay of the F bands increases in the
t
1
1
0
À1
10 À1
order of PDBA-Me (0.60 ” 10 s ) < PDBA (1.79 ” 10 s )
10
À1
<
PDBA-COMe (4.17 ” 10 s )
s ). Realizing that PDBAs all possess an N-phenyl
<
PDBA-CN (5.56 ”
1
0
À1
1
0
group, the kinetic trend cannot be rationalized simply by the
differences in the steric hindrance imposed by the N-phenyl
group. Alternatively, the increase in the reaction rate
correlates well with the electron-withdrawing ability of the
substituents, which deceases in the order of -CN > -COMe >
with a bending angle V of 126–1438. Frontier orbital analyses
a
of DBA and PDBAs in the R form indicate that the lowest
lying excited state for DBA and PDBAs mainly involves
a HOMO ! LUMO transition, which is solely attributed to
the p ! p* character (Figure 5). For DBA, HOMO is on the
dibenzo[b,f]azepine moiety, while LUMO is located at the
dibenzo- moiety. For PDBAs, HOMO is mainly on the outer
N-phenyl ring, while LUMO is located at the dibenzo- moiety.
In addition, the natural transition orbitals (NTOs) were also
applied to analyze the S !S transition, which were in line
-
H > -Me. This trend also fits with the strongest electron-
donating group, -OMe, in PDBA-OMe, where the barrier
appears to be too high to undergo structural relaxation during
the lifespan of the F1 emission (1.6 ns). Using PDBA as
a prototype, we then scanned the time-resolved emission
wavelength throughout the entire visible region and plotted
the emission temporal evolution in cyclohexane. The results
shown in Figure 4d clearly indicate that the decrease in the F1
emission band is accompanied by an increase in the F2
emission at 600 nm, affirming the R*!P*, i.e., precursor !
successor, type of structural transformation.
0
1
with the results from the frontier molecular orbital contours
[40,41]
(Figure S27).
The spatially charge-separated HOMO and
LUMO result in the weak transition dipole and hence small
absorption extinction coefficient, consistent with the exper-
imental observations.
The temperature-dependent kinetic study for PDBA
depicted in Figure 4e clearly show that as the temperature
decreases, the decay time constant of the emission monitored
Upon optimizing the S1 state of DBA, a substantial
difference is that the bending angle V changes from 1438 in R
a
at the F band (e.g., 450 nm) increases. Assuming that the
decay of the F1 emission is dominated by the structural
to nearly planar (1808). The results indicate that the original
structure of DBA (R) cannot maintain the proximal bending
angle but spontaneously relaxes to a planar configuration
with a negligible barrier. In contrast, all PDBAs appear to
encounter an appreciable barrier along the structural relax-
ation pathway and localize at a bent structure R* position
under free geometry optimization (Figure 5). For this case,
the N-phenyl group is expected to be the key factor in
introducing a barrier along the potential energy surface (PES)
of the structural transformation. We also analyzed the
changes in aromaticity after PISP for all PDBAs by using
the harmonic oscillator model of aromaticity (for HOMA, see
1
relaxation rate k , the plot of ln k (= 1/tobs)) versus 1/T(K)
t
t
gives a straight line (see inset of Figure 4e), and the slope
À1
renders a value of 2.49 kcalmol for the activation energy
DE (exp.) (exp. stands for experimental data to distinguish it
a
from the DE (calc.) obtained from calculations (vide infra)).
a
A similar approach provides DE (calc.) values of 3.23 kcal
a
À1
À1
À1
mol , 2.16 kcalmol and 1.86 kcalmol for PDBA-Me,
PDBA-COMe and PDBA-CN, respectively (Table 2; Fig-
ures S31 and S32).
General theoretical approach. To rationalize the above
structure-reaction relationship, computational studies were
carried out (Supporting Information). The calculated absorp-
tion and emission data are listed in Table 1, the gaps in terms
of wavelength are compatible with the onset of both the
steady-state absorption and emission spectra. In particular,
the calculated oscillator strength (f) for the lowest lying
transition is small, supporting the experimentally observed
[32,41]
the Supporting Information).
The results clearly indicate
that PDBAs with 4n p electrons possess a bent-shaped
azepine core in the ground state and undergo a structural
planarization process in the excited state (Figure S28), obey-
[33]
ing Bairdꢀs rule.
B-E-P principle extended to PISP of PDBAs. The
reaction PES was then plotted as a function of bending angle
À1
À1
small extinction coefficient of < 1000 M cm for the S !
V and the angle f that represents the rotation of the N-
0
a
S peak wavelength (vide supra). The optimized ground state
phenyl group, generating the 3D plots shown in Figure 5 for
PDBAs (Figures S26 and S30a,b). In the ground state, all the
PDBAs show a global minimum, which increases the
1
Table 2: Experimentally obtained frequency factor n, DE (exp.), calcu-
potential energy en route to planarization. In the S state,
1
a
lated energy barrier DE (calc.) and calculated energy difference (DEP*-R*
)
the plot of the PES along V and f shows an appreciable
a
a
for the R* ! P* structural transformation of PDBAs.
barrier DE (calc.); i.e., a saddle point is calculated for all
a
Name
Excited state (S ) planarization
PDBAs along the corresponding structural transition path-
way from R* to P*. These data, together with the calculated
difference in energy between the reactant and product in the
excited state, DEP*-R*, and experimental data of the barrier
1
À1
[a]
[a]
[a]
n [s
]
DE (exp.) DE (calc.) DEP*-R*
a
a
PDBA-OMe
PDBA-Me
PDBA
–
–
9.15
5.67
4.55
3.41
3.22
2.61
1
1
1
1
2
2
2
2
1.52(Æ0.31)”10
3.23
2.49
2.16
1.86
À1.49
À2.85
À3.69
À4.10
1.17(Æ0.16)”10
DE (exp.) derived from the temperature-dependent kinetics,
a
PDBA-COMe 1.23(Æ0.46)”10
are listed in Table 2. Note that DE (calc.) for PDBA-OMe
a
PDBA-CN
1.31(Æ0.17)”10
À1
was calculated to be as large as 9.15 kcalmol , prohibiting
[
a] Units kcal/mol.
structural relaxation of R* in the excited state.
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Figure 5. Optimized structures and corresponding frontier molecular orbital contours of a) DBA, b) PDBA-OMe, c) PDBA, and d) PDBA-CN in the
S and S states. The R conformer represents the optimized conformer in the ground state. R* represents the local minimum of the bent
0
1
conformer, and P* is the global minimum of the planar conformer in the S state after structural transformation. e) The bending angle V and
1
a
rotation angle f (see text for definition) for PDBA. Optimized conformations and potential energy surfaces of f) PDBA-OMe, g) PDBA and
h) PDBA-CN in the S and S states.
0
1
Figure 6 shows the plots of DE (exp.) and DE (calc.)
tion (1). Assuming that the difference in DPV (P: pressure, V:
a
a
(
kinetics) versus DEP*-R* (thermodynamics). Evidently,
volume) is negligible in the intramolecular structural trans-
DE (exp.) and DE (calc.) show the same trend that decreasing
formation, we take data of DE (calc.) versus DE
(Fig-
a
a
a
P*-R*
the electron-donating ability of the substituent on the phenyl
ring decreases the barrier, which decreases in the order of
ure 6, upper plot) and fit them with Equation (2).
DE
a
ðcalc:Þ ¼ E
0
þ aDEP*ÀR
*
ð2Þ
-
OMe > -Me > -H > -COMe > -CN. Moreover, both plots of
DE (exp.) and DE (calc.) versus DE (Figure 6) reveal
a
a
P*-R*
À1
straight lines, showing a consistent trend that lowering DEa
gives a more negative value of DEP*-R*. This result is
The best linear fit gives E and a of 6.89 kcalmol and
0
0.89, respectively. Additionally, we also fit the experimentally
[
7,8]
reminiscent of the B-E-P principle
expressed in Equa-
resolved DE (exp.) as a function of DE
(Figure 6, lower
a
P*-R*
À1
plot), rendering E0 and a of 3.98 kcalmol
and 0.51,
respectively. Despite the difference in values, both results
fulfil the criterion of 0 ꢀ a < 1 for the B-E-P principle.
Fundamentally, the B-E-P principle relies on a stringent
condition in that the structure of the transition state and its
frequency along the reaction coordinate have to be similar
among the family of target PDBAs. We then mark out the
coordinates of the transition state in terms of V , f and DE in
a
a
the 3D plot shown in Figure 7, where the energy barrier DEa,
bending angle V and rotation angle f have been previously
a
defined and the PES is taken from the plots shown in
Figure 5 f–h (Figure S30) for PDBAs along the steepest slope
from T* to R*. The energy of R* for all PDBAs is set to zero.
In Figure 7, except for PDBA-OMe, DE (exp.) is applied for
a
all PDBAs to reflect the real experiment. According to
Figure 7, the bending angle V and rotation angle f in the
a
studied PDBAs are all located around 151–1528 and 40–508.
From the viewpoint of bending angle V and rotation angle f,
the structures of the transition state are thus more or less the
Figure 6. Dependence of the energy barrier on the energy difference
between R* and P*. Plot of DE (calc.) (blue *) and DE (exp.) (orange
a
a
a
!
) versus DEP*-R* and fit from Equation (2).
same for all PDBAs.
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The above discussion can be visualized by plotting the
NÀC(15) bond distance as a function of the Hammett
[42]
constant (s )
ure S34a.
of the added substituent, shown in Fig-
The results show that when the electron-
p
[
43,44]
donating ability of the substituent increases (smaller s ), the
p
NÀC(15) double bond character also increases. As a result,
the NÀC(15) bond distances are calculated to decrease in the
order of PDBA-CN > PDBA-COMe > PDBA > PDBA-Me
>
PDBA-OMe (Table S20), which follows the trend of s in
p
the order of -CN (0.66) > PDBA-COMe (0.50) > PDBA
(
0.00) > PDBA-Me (À0.17) > PDBA-OMe (À0.27). PDBA-
OMe has the shortest NÀC(15) bond, which is explained by its
substituent having the strongest donating ability and hence
the strongest charge transfer among all the PDBAs. A greater
double bond character of the NÀC(15) bond makes twisting of
the N-phenyl moiety more difficult, consistent with PDBA-
OMe having the largest DEa.
Figure 7. Computed PDBA bending angle V from R* to T* and then
a
Conclusion
to P*. The coordinates of T* are marked by (V , f, DE (exp.)) except
a
a
for PDBA-OMe, where DE (calc.) is applied.
a
In summary, the PISP of dibenzazepine (DBA) and its N-
phenyl derivatives (i.e., the PDBA family) has been studied
in a comprehensive manner. The results indicate a slower
relaxation rate upon increasing the electron-donating ability
of the substituent, giving substituent-dependent F /F ratio-
metric emission. The relationship between the reaction
barrier and thermodynamics can be well described by the
Bell–Evans–Polanyi principle and is rationalized by the
twisting of the N-phenyl group during the planarization to
avoid the steric effect. While the occurrence of excited-state
charge transfer from the N-phenyl group to the dibenzazepine
core gives the NÀC(15) bond a partial double bond character,
the twisting of the N-phenyl moiety along the NÀC(15) bond
Experimentally, we can also obtain the frequency factor
n from the Arrhenius-type kinetics, expressed as
2
1
DE
a
ðexp:Þ
RT
ln kðTÞ ¼ ln uÀ
ð3Þ
by extrapolation of the fitted lnk(T) versus 1/T (see PDBA in
Figure 4e). The deduced frequencies listed in Table 2 clearly
12
À1
indicate that n lies within a narrow interval of 1.17 ” 10 s –
1
2
À1
1
.52 ” 10
s
for all PDBAs. Therefore, both transition-state
structure and frequency factor for the PDBA family meet the
criteria set by the B-E-P principle, rationalizing the linear
induces a barrier, and the barrier height thus depends on the
electron-donating/withdrawing properties on the para sub-
stituent on the N-phenyl group. On reaching the transition
state, the downhill PES to P* is driven by a stabilization in
aromaticity, which is subject to similar frequencies along the
reaction coordinate for the PDBA family. The correlation
thus broadens the horizon of the Bell–Evans–Polanyi princi-
ple towards optically triggered structure planarization.
relationship between DE (exp.) and DEP*-R* for the PDBA
a
family. Similar trends should be obtained upon using the
calculated DE (calc.). This result thus extends the B-E-P
a
principle to a structural relaxation/planarization that virtually
does not involve any bond breakage or reformation.
Origin of the substituent-induced barrier. Finally, insights
into the origin of the barrier and the substituent effect are
discussed. During structural relaxation, the interplay between
the bent-to-planar motion of the core and the twisting of the
N-phenyl group must be strong, creating steric hindrance Acknowledgements
during PISP. This, together with the charge-transfer property
from N-phenyl to the core dibenz[b,f]azepine moiety in the
R* state (Figure 5), suggests that the properties of the
NÀC(15) bond, which is the twisting axis of the N-phenyl
P. -T.C. thanks the Ministry of Science and Technology,
Taiwan, for financial support.
ring, play a key role in controlling the barrier of the reaction
(
Figure 1b). The calculated NÀC(15) bond lengths for R* are Conflict of interest
in the range of 1.348 Š to 1.379 Š for all PDBAs, indicating
that NÀC (15) has a partial double bond character. This can be
The authors declare no conflict of interest.
rationalized by the excited-state N-phenyl (donor) ! dibenz-
[
b,f]azepine (acceptor) charge transfer that increases the
Keywords: azepine · Bell–Evans–Polanyi principle ·
dual emission · excited-state aromaticity ·
photoinduced structural planarization
NÀC(15) bond order. Increasing the electron-donating ability
of the para substituent of the N-phenyl moiety enhances the
charge transfer and hence increases the NÀC(15) double bond
character.
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Manuscript received: November 18, 2020
Accepted manuscript online: December 30, 2020
Version of record online: February 24, 2021
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