How the π conjugation length affects the fluorescence emission efficiency

Article abstract of DOI:10.1021/ja8040493

How the π conjugation length affects the fluorescence emission efficiency is elucidated by examination of the theoretical and experimental relationship between absolute quantum yield (Φ_f) and magnitude (A_π) of the π conjugation lengt

Full text of DOI:10.1021/ja8040493

Published on Web 09/25/2008
How the π Conjugation Length Affects the Fluorescence Emission Efficiency
Yoshihiro Yamaguchi,* Yoshio Matsubara, Takanori Ochi, Tateaki Wakamiya, and Zen-ichi Yoshida*
Department of Chemistry, Kinki UniVersity, 3-4-1 Kowakae, Higashi-Osaka, Osaka, 577-8502, Japan
Received June 8, 2008; E-mail: yamaguch@chem.kindai.ac.jp; yoshida@chem.kindai.ac.jp
Table 1. Photophysical Data of π Conjugated Hydrocarbons in
Recent developments in science and technology utilizing organic
fluorescent materials have resulted in the increasing requirement
for highly efficient fluorophores. For creation of such fluorophores
it should be valuable to find some correlation between the
fluorescent quantum yield and π structure of fluorophores,1 since
no general concept has been established yet. Thus the challenge of
obtaining a novel concept for this issue has been undertaken by
examining any relationship between fluorescent quantum yield and
other photophysical characteristics of the typical π conjugated
hydrocarbons2 shown in Figure 1, the most fundamental fluoro-
phores. Photoreactive hydrocarbons were excluded because of the
reliability of photophysical data: 1. Rod- and star-shaped phenyl-
acetylene architectures (1-7 in Figure 1); rod-shaped: three benzene
ring system (1) to five benzene ring system (3); star-shaped: three
benzene ring system (4) to seven benzene ring system (7). 2. Rod-
shaped oligophenylenes (P-0-P-3 in Figure 1) consisting of two,
three, four, and five benzene rings. 3. Condensed aromatic
hydrocarbons (C-1-C-4 in Figure 1) consisting of two, three, four,
and five benzene rings.
a,b
CHCl3
λem
(nm) log ꢀ (nm)
λabs
τ
(ns)
kr
(s-1
knr
(s-1
Aπ
(Å)
compd
Φf
)
)
1
2
3
4
5
6
7
P-0
P-1
P-2
P-3
0.83 348 4.59 328
0.87 389 4.77 343
0.93 389 5.13 354
0.14 330 4.70 302
5.51 1.51 × 108 3.09 × 107
6.01 1.45 × 108 2.16 × 107
6.27 1.48 × 108 1.12 × 107
1.59
1.90
2.59
5.46 2.56 × 107 1.58 × 108 -1.82
0.18 353 4.93 305 18.78 9.58 × 106 4.37 × 107 -1.52
0.57 391 5.13 315
6.11 9.33 × 107 4.04 × 107
0.28
0.27 449 5.07 349 21.64 1.25 × 107 3.37 × 107 -0.99
0.02 314 4.24 249
0.49 342 4.49 280
0.86 369 4.64 298
0.91 386 4.80 309
4.72 4.24 × 106 2.08 × 108 -3.89
4.38 1.12 × 108 1.16 × 108 -0.04
5.83 1.48 × 108 2.40 × 107
5.46 1.67 × 108 1.65 × 107
1.82
2.31
C-1 0.02 323 3.58 286
C-2 0.13 383 3.85 379
5.33 3.75 × 106 1.84 × 108 -3.89
5.75 2.26 × 107 1.51 × 108 -1.90
C-3 0.26 373 4.60 338 89.30 2.91 × 106 8.29 × 106 -1.05
C-4 0.90 448 4.53 438
6.49 1.39 × 108 1.54 × 107
2.20
a All spectra were measured for 10-6 M solution at 295 K. In the
case of C-3, cyclohexane was used as solvent. b Details of the
photophysical measurements: see Supporting Information.
Figure 2. Schematic diagrams of light absorption (hVa), fluorescence
emission (hVf), radiative (kr) and radiationless (knr) processes, π conjugation
length (Aπ) at the S1 state, and intramolecular electron transfer (ET) of a π
conjugated molecule. The number (0 and 1) in parentheses corresponds to
S0 and S1, respectively.
Figure 1. Structures of π conjugated hydrocarbons used in this study.
The obtained photophysical properties are summarized in Table
1. We examined if any correlation exists between absolute
fluorescent quantum yield (Φf) and λem, λabs, or ꢀ for all hydrocar-
bons shown in Figure 1. However no simple correlation was found.
Hence we have examined correlation between the Φf and
magnitude (Aπ) of the π conjugation length in the excited singlet
state (Figure 2). For this purpose it is necessary to derive Aπ from,
for instance, the radiative (rate constant: kr) and radiationless process
(rate constant: knr).3 Since kr and knr are related to the corresponding
emission quantum yields and lifetime by Φf ) kr × τ and kr + knr
) τ -1, we calculated the values of kr and knr using quantum yield
and lifetime data.4 The obtained kr and knr values are shown in
Table 1. As illustrated in Figure 2, the kr is the rate constant for
the return process of a π electron promoted to the excited singlet
(S1) state to the ground (S0) state of a π conjugated molecule
accompanying fluorescence emission, and the knr is the rate constant
for radiationless process due to internal conversion and intersystem
crossing. As demonstrated in Figure 2, Aπ may be defined as the
distance between dipoles arising from S0 f S1 transition (light
absorption). Thus knr is regarded as the rate constant of radiationless
decay due to the electron transfer (ET) from the negative charge
to the positive charge.
As shown in Table 1, the kr values increase and the knr values
decrease with π conjugation length of the rod-shaped molecules
(P-0-P-3), suggesting that the kr/knr value might be related to π
extension in the S1 state of the π conjugated molecule.
First, we derive Aπ from kr and knr. From Einstein’s equation5
(fundamental relationship of transition probability with absorption
and emission), kr is given by eq 1,
kr ) A1,0
(1)
where A1,0 is the Einstein transition rate constant for spontaneous
emission from the S1 to the S0 state.
9
10.1021/ja8040493 CCC: $40.75
2008 American Chemical Society
J. AM. CHEM. SOC. 2008, 130, 13867–13869 13867

C O M M U N I C A T I O N S
Figure 3. Correlation between fluorescence emission maximum (λem) and
magnitude (Aπ) of π conjugation length in the S1 state of π conjugated
hydrocarbons, P0-P3.
Figure 4. Correlation between absolute fluorescence quantum yield (Φf)
and magnitude (Aπ) of π conjugation length in the S1 state of π conjugated
hydrocarbons. Solid line: theoretical line based on eq 13.
On the other hand, knr is known to follow the energy gap law:
knr is proportional to exp(-Em), where Em is the energy gap between
the S1 and S0 state.6,7 This equation, however, does not contain Aπ
(or related term). As shown in Figure 2, knr can be regarded as the
rate constant for the intramolecular electron-transfer process from
S1 to S0. And so the Hush equation8,9 shown in eq 2 may serve our
purpose, though it does not include the S0 f S1 transition term.
Multiplication of both sides of eq 10 (unitless) by 1 Å gives the
values in units of angstrom. The Aπ values (Å) are summarized in
Table 1. The practical π conjugation length (Aπ*) in the S1 state
could be given by (Aπ + 4.6) (Å) (Supporting Information).3 It is
noted that a linear relationship with a positive slope between Aπ
and λem is observed for the rod-shaped π conjugated systems,
P0-P3 as shown in Figure 3.
Next, we derive the relationship between Φf and Aπ. From Φf
kET ) k0 exp(-ꢀR)
(2)
-1
) kr × τ and kr + knr ) τ
as described before, we get eq 11.
where k0 is the rate constant at R ) 0 and ꢀ is a constant. R is the
distance between negative charge and positive charge.
Φf ) kr ⁄ (knr + kr)
(11)
Hence, knr is considered to be expressed by combining the Hush
Upon dividing the denominator and the numerator in eq 11 by
kr, we obtain eq 12.
and Einstein equations for light absorption5 as shown in eq 3,
knr ) B0,1 exp(-ꢀAπ)
(3)
Φf ) 1 ⁄ ((km ⁄ kr) + 1)
By using simple mathematics based on eqs 9 and 12, we have
eq 13.
(12)
where B0,1 is the Einstein transition probability, the rate of the
molecule going from the S0 to the S1 state by absorption of
radiation.5 Since B0,1 ) B1,0 (rate constant for induced emission
from S1 to S0) and eq 4 (relationship between B1,0 and A1,0) is
known,5 knr is expressed by eq 5,
Φf ) 1 ⁄ (exp(-Aπ) + 1)
(13)
This is the theoretically derived relationship between Φf and Aπ.
Equation 13 gives a sigmoid relationship between Φf and Aπ as
shown by the solid line in Figure 4. The plot (blue color) of Φf
against Aπ for all compounds listed in Table 1 falls on the theoretical
line. Thus we have been able to elucidate how the π conjugation
length affects fluorescence emission efficiency, providing a new
concept for molecular design for highly fluorescent organic
compounds. The approximately linear portion observed between
Φf ) 0.1 and Φf ) 0.9 is particularly useful for this purpose. In
Figure 4 Aπ becomes 0 when Φf is 0.5 (where kr ) knr from Φf )
kr/(kr + knr)). As a tool to predict Φf from a structural model, (ν˜a
- ν˜f)1/2 × a3/2 (ν˜a: wavenumber of absorption maximum, ν˜f:
wavenumber of emission maximum, a: molecular radius) could be
used instead of Aπ (Supporting Information).
B0,1 ) B1,0 ) (c3 ⁄ 8πhν3)A1,0
(4)
where c is the speed of light, h is Planck’s constant, and ν is the
frequency of fluorescence emission maximum.
knr ) (c3 ⁄ 8πhν3)A1,0 exp(-ꢀAπ)
From eqs 1 and 5, we get eq 6.
kr ⁄ knr ) (8πhν3 ⁄ c3) exp(ꢀAπ)
(5)
(6)
Equation 6 is a kr/knr relationship at arbitrary fluorescence quantum
yield (Φf).
If we consider the case of Φf ) 0.5 as the reference standard
s
s
(where, krs ) knr and Aπ ) 0 as described later), we get eq 7.
We have preliminarily examined the correlation between Φf and
Aπ for the following substituted π systems: (1) donor(OMe)/
acceptor(CN)-substituted diphenylacetylene1f (8), (2) donor(OMe)/
acceptor(CN)-substituted pentakis(p-phenylene ethynylene (9), and
(3) donor(OMe)-substituted 51d (10). The new compound 9 was
synthesized by the reactions shown in Scheme 1 (synthetic
procedures, Supporting Information). Their photophysical data are
shown in Table 2.
As shown in Figure 4 (red), it is of particular interest that the
plot of Φf against Aπ for 8, 9, and 10 also falls on the solid line.
The significant increase in Φf and λem occurs by the introduction
of donor/acceptor groups (8 and 9) or donor groups (10).
(kr ⁄ knr) ⁄ (krs ⁄ knrs) ) kr ⁄ knr ) (ν3 ⁄ νs3) exp(ꢀAπ)
(7)
Assuming that ν ≈ νs based on the relationship between ν and
Aπ (Figure 3), eq 7 could be simplified as
kr ⁄ knr ) exp(ꢀAπ)
(8)
Though ꢀ should be experimentally determined, if we assume
that ꢀ is 1 inferring from literature values,8,9 we get eqs 9 and 10.
kr ⁄ knr ) exp(Aπ)
Aπ ) ln(kr ⁄ knr)
(9)
(10)
9
13868 J. AM. CHEM. SOC. VOL. 130, NO. 42, 2008

C O M M U N I C A T I O N S
Scheme 1
a similar emission characteristic to that of a green fluorescent protein
(Topaz, T203Y type, Φf 0.60, λem 527 nm, log ꢀ 4.98) of current
topic,10 has been created based on our concept.
Although it is necessary to establish the generality of this concept
by the experimental examination for various other π systems, this
concept should be valuable for (1) examination of an excited singlet
state structure (for instance, coplanarity of excited-state molecules)
and (2) molecular design of novel materials, in which the excited
singlet state plays an important role, such as highly efficient
fluorophores, electroluminescent materials, photoconducting materi-
als, and nonlinear optical materials.
Acknowledgment. We thank Prof. Jeffrey R. Reimers (the
University of Sydney) for the Hush equation and related data and
Dr. Y. Shimoi (AIST, Japan) for TD-DFT calculations. This work
was supported by the Grant-in-Aid for Creative Scientific Research
(No. 16GS0209) and Scientific Research (No. 16550131) from the
Ministry of Education, Science, Sport, and Culture of Japan.
a
Table 2. Photophysical Data of Substituted π Systems in CHCl3
λem
λabs
(nm) log ꢀ (nm) (ns)
τ
kr
(s-1
knr
(s-1
Aπ
(Å)
compdb
Φf
)
)
8
9
10
0.44 374 4.40 326 5.86 7.51 × 107 9.56 × 107 -0.24
0.88 527 4.72 456 6.29 1.40 × 108 1.91 × 107
1.99
Supporting Information Available: Materials and methods, syn-
thetic procedures, correlation of the (ν˜a - ν˜f)1/2 × a3/2 with Φf and
practical Aπ values. This material is available free of charge via the
Internet at http://pubs.acs.org.
0.40 384 4.65 334 6.47 6.18 × 107 9.28 × 107 -0.41
a All spectra were measured for 10-6
M solution at 295 K.
b Structures of 8, 9, and 10 are as follows.
References
(1) (a) Yamaguchi, Y.; Tanaka, T.; Kobayashi, S.; Wakamiya, T.; Matsubara,
Y.; Yoshida, Z. J. Am. Chem. Soc. 2005, 127, 9332. (b) Yamaguchi, Y.;
Kobayashi, S.; Wakamiya, T.; Matsubara, Y.; Yoshida, Z. Angew. Chem.,
Int. Ed. 2005, 44, 7040. (c) Yamaguchi, Y.; Ochi, T.; Wakamiya, T.;
Matsubara, Y.; Yoshida, Z. Org. Lett. 2006, 8, 717. (d) Yamaguchi, Y.;
Ochi, T.; Miyamura, S.; Tanaka, T.; Kobayashi, S.; Wakamiya, T.;
Matsubara, Y.; Yoshida, Z. J. Am. Chem. Soc. 2006, 128, 4504. (e) Ochi,
T.; Yamaguchi, Y.; Kobayashi, S.; Wakamiya, T.; Matsubara, Y.; Yoshida,
Z. Chem. Lett. 2007, 36, 794. (f) Ochi, T.; Yamaguchi, Y.; Wakamiya, T.;
Matsubara, Y.; Yoshida, Z. Org. Biomol. Chem. 2008, 6, 1222.
(2) The molecular size has been restricted owing to their solubility in CHCl3
as solvent.
(3) Aπ values range from positive values to negative values, because of the
logarithmic values. However the negative sign only means it is smaller
than the positive one. The absolute Aπ value could be given by ln(kr/kd)-
ln(kr/kd) at Φf ) 0. The situation is similar to the case of temperature.
(4) (a) Leventis, N.; Rawashdeh, A. -M. M.; Elder, I. A.; Yang, J.; Dass, A.;
Sotiriou-Leventis, C. Chem. Mater. 2004, 16, 1493. (b) Barltrop, J. A.;
Coyle, J. D. Principles of photochemistry; Wiley: New York, 1978; p 68.
(5) (a) Einstein, A. Physik. Z. 1917, 18, 121. (b) Strickler, S. J.; Berg, R. A.
J. Chem. Phys. 1962, 37, 814. (c) Berks, J. B.; Dyson, D. J. Proc. R. London
Soc., Ser. A 1963, 275, 135. (d) Valeur, B. Molecular Fluorescence; Wiley-
VCH: Weinheim, 2002.
(6) Theory: For example, (a) Lin, S. H. Radiationless Transitions; Academic
Press: New York, 1980. (b) Kober, E. M.; Caspar, J. V.; Lumpkin, R. R.;
Meyer, T. J. J. Phys. Chem. 1986, 90, 3722.
(7) Experimental verification for organic π systems: For example, (a) Siebran,
W. J. Chem. Phys. 1971, 55, 5843. (b) Gillipsie, G. D.; Lim, E. C. Chem.
Phys. Lett. 1979, 63, 193. (c) Griesser, H. S.; Wild, U. P. Chem. Phys.
1980, 52, 117. (d) Murata, S.; Iwanaga, C.; Toda, T.; Kokubun, H. Chem.
Phys. Lett. 1972, 13, 102.
Figure 5. Fluorescence spectrum and color of 9 in CHCl3.
(8) (a) Hush, N. S. Coord. Chem. ReV. 1985, 64, 135. (b) Overing, H.; Paddon-
Rov, M. N.; Heppener, M.; Oliver, A. M.; Cotsaris, E.; Verhaeven, J. W.;
Hush, N. S. J. Am. Chem. Soc. 1987, 109, 3258.
(9) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
(10) (a) Dong, J.; Solntsev, K. M.; Tolbert, L. M. J. Am. Chem. Soc. 2006, 128,
12038. (b) Zimmer, M. Chem. ReV. 2002, 102, 759.
In the donor/acceptor-substituted linear π conjugated systems,
an increase in π conjugation length in the excited singlet state is
considered to bring about the increase in both Φf and λem
.
It should be of great interest that the remarkably intense green
fluorophore 9 (Φf 0.88, λem 527 nm, log ꢀ 4.72) (Figure 5), having
JA8040493
9
J. AM. CHEM. SOC. VOL. 130, NO. 42, 2008 13869