THE JOURNAL OF CHEMICAL PHYSICS 124, 034306 共2006兲
On the photophysics of all-trans polyenes: Hexatriene versus octatetraene
J. Catalána兲 and J. L. G. de Pazb兲
Departamento de Química Física Aplicada, Universidad Autónoma, C-II-203, Cantoblanco,
28049 Madrid, Spain
共Received 26 September 2005; accepted 28 November 2005; published online 19 January 2006兲
The disparate photophysical behavior of trans-1,3,5-hexatriene 共nonfluorescent兲 and
trans-1,3,5,7-octatetraene 共with two fluorescence emissions兲 in the gas phase is explained in terms
of the tendency of their 1Bu excited states to rotate about their terminal carbon-carbon single bonds
in order to adopt a quasiplanar molecular form of lower energy than the 1Bu state in the parent
all-trans structure. The origin of their disparate photophysical behavior is that such a transformation
is subject to a small energy barrier in octatetraene; the barrier produces two minima 共two
fluorescence emissions兲 in the corresponding potential-energy curve. Instead of an energy barrier,
hexatriene gives a 1,3-diene species which falls to the ground state so rapidly that no emission is
produced. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2158992兴
I. INTRODUCTION
Polyene structures are present as chromophores in such
prominent substances as visual pigments,1 the carotenoid antennae of photosynthesis,2,3 and vitamins A 共Ref. 4兲 and D.5
Also, they have played a crucial role in the development of
the theory of color in organic compounds.6 This has fostered
extensive research into their photophysical behavior.
The earliest significant contributions to understanding
the photophysics of polyenes date back to 1930, when
Hausser et al.7–13 not only reported precise absorption and
emission spectra for these substances but also identified such
important patterns in their photophysical behavior as the following: 共a兲 the wavelength and intensity of the first electronic transition in the absorption spectrum increase markedly with increasing chain length, 共b兲 their absorption and
emission exhibit an unexpected energy gap—an inference
which is still the subject of much debate, and 共c兲 solvents
appear to influence their absorption and emission differently.
In 1939, Mulliken14 accounted for the energy gap between the absorption and emission of polyenes previously
identified by Hausser et al.7–13 in terms of a Franck-Condon
argument involving a low-frequency in-plane distortion. In
1952, Förster15 ascribed the gap to a strong change in the
nuclear configuration upon electronic excitation. In 1963,
Birks and Dyson16 hypothesized that the nuclear configurations of the ground and excited states differed considerably.
In 1970, Berlman17 included polyenes in class 5 of his
scheme 共viz., planar compounds in the ground state and nonplanar ones in the excited state兲; accordingly, electronic excitation must produce nonplanar isomeric forms the fluorescent transition of which will be considerably weaker than the
absorption of the corresponding planar trans forms. In 1972,
Hudson and Kohler18 hypothesized that polyenes undergo
inversion of their first two excited electronic states as their
chain is lengthened, so the emitting state is not 1Bu—which
is populated by absorption as the 1Ag → 1Bu transition is
strongly dipole allowed—but rather 2Ag, which cannot be
populated by absorption as the 1Ag → 2Ag transition is dipole
forbidden.
In 1975, however, Cehelnik et al.,19 and Birks and
Birch,20 independently concluded that none of the models
previously used to account for the photophysics of polyenes
was completely satisfactory. In any case, the past 30 years
have seen strong efforts at detecting the 2Ag states in the
model of Hudson and Kohler using multiphoton spectroscopy 共see, for example, the reviews in Refs. 21–25兲.
To our minds, it makes no sense to develop a model for
the photophysics of polyenes ignoring such categorical evidence as the facts that 1,3,5-hexatriene is nonfluorescent,
whereas the next member in the family, 1,3,5,7-octatetraene,
exhibits two fluorescent emissions. Thus, in 1973, Gavin et
al.26 detected no fluorescent emission from 1,3,5-hexatriene
in the gas phase, a conclusion which has been refuted by
none of the many studies conducted in this direction.27–30 In
contrast, in 1978, Gavin et al.31 found octatetraene not only
to be fluorescent but also
共a兲
共b兲
共c兲
Author to whom correspondence should be addressed. Fax: ⫹34
914974785. Electronic mail: [email protected]
b兲
Electronic mail: [email protected]
a兲
0021-9606/2006/124共3兲/034306/11/$23.00
124, 034306-1
To exhibit no energy gap between its absorption and
emission spectra at 295 K in the gas phase. In addition,
both spectra exhibited mirror symmetry, so they concluded that the first absorbing and emitting singlet for
the compound was the 1Bu state.
To possess an emission spectrum at 295 K in solution
much less structured than its absorption spectrum under
identical conditions. Also, the two spectra exhibited an
energy gap but were not mirror images of each other,
so 1Bu all-trans could not be the emitting state.
To possess a radiative emission constant of 6.75⫻ 106
and 4.54⫻ 106 in the gas phase and hexane at 295 K,
respectively 共i.e., a constant that decreases by only
33% from the gas phase to a solvent or, in other words,
from an emitting state to another兲.
© 2006 American Institute of Physics
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034306-2
J. Catalan and J. L. G. de Paz
The controversy raised by the evidence reported by
Gavin et al.31 led Heimbrook et al.32 to state the following in
relation to the emission of octatetraene in a supersonic helium jet—which they ascribed to a 1Bu → 1Ag transition:
“The rough mirror symmetry between the 0-0 emission and
excitation spectra and the short lifetime indicate that the
emission comes exclusively from the 1Bu state, with no significant contribution from the lower-lying 2Ag state.” Leopold et al.33 obtained the 1Ag → 1Bu absorption spectrum in
a cooled jet 共i.e., at a few Kelvins in the gas phase兲 and
found it to be very similar to that recorded by Gavin et al.31
at 295 K. Bouwman et al.34 found a sample of octatetraene at
ambient temperature in the gas phase in equilibrium with the
crystal phase to exhibit strongly structured emission from the
1Bu state in addition to a weak, structureless emission redshifted from the previous one that exhibited an energy gap
with respect to the 1Ag → 1Bu absorption.
In summary, hexatriene emits no fluorescence, so its 1Bu
state, which is that directly populated by absorption, must
rapidly disappear nonradiatively. On the other hand, octatetraene in its 1Bu state, which is also directly populated by
absorption, does emit fluorescence and must produce an also
fluorescent structure. In addition, the new fluorescent structure in octatetraene must be the primary channel of emission
in the condensed phase. In this work, we used timedependent density-functional theory 共TDDFT兲 and the optimized geometries for the molecular structures involved to
derive a theoretical explanation for the previous photophysical evidence based on the 1Bu state, which is that produced
by ultraviolet absorption.
Although the 2Ag electronic state of hexatriene and octatetraene will not be used in this work for the description of
the photopysics of these compounds, it seems convenient to
collect, in the Appendix , the information on the situation of
the 2Ag and 1Bu states in the corresponding energy diagram
for each polyenic systems, and the convenience of the theoretical model we are using.
II. THEORY
All computations were done within the framework of the
density-functional theory 共DFT兲 and the TDDFT, using the
TURBOMOLE software package,35 which was developed by
the Quantum Chemistry Group of the University of
Karlsruhe 共Germany兲. Full geometry optimization of the
ground and excited singlet electronic states was done by using Becke’s three-parameter hybrid functional36,37 共B3兲 with
the Lee, Yang, and Parr38 共LYP兲 expression for the nonlocal
correlation 共B3LYP兲; as implemented in TURBOMOLE.39 We
chose the 6-31G** basis set40 for compatibility with our previous studies in this field. Excited states were examined at
the TDDFT level41 as implemented in TURBOMOLE.42–46 All
structures thus identified were confirmed to be true energy
minima by checking whether they possessed all-real vibrational frequencies. Previous studies had shown this methodology to be accurate with photoexcited molecules;47 also, it
was recently successfully used.48
Potential-energy surfaces and the form produced from
the structure of the 1Bu excited state by torsion of the termi-
J. Chem. Phys. 124, 034306 共2006兲
SCHEME 1. Atom numbering for tHT and ttOT.
nal single bond were constructed from the molecular structures of the reactant and the corresponding product, as well
as from the barriers between them; whether they constituted
true energy minima with all-real frequencies and transition
states with a single imaginary frequency were checked in all
cases.
The 0-0 components of the electronic transitions were
calculated from the fully optimized geometry for each state
involved in the electronic transition, which was corrected for
the zero-point energy as computed from the vibrational frequencies for the compound.
III. RESULTS AND DISCUSSION
This section initially deals with the stability, structure,
and corresponding 0-0 components of the different structurally feasible forms that can be produced by cis-trans isomerization of the double bonds in the formal all-trans structure,
using those normally produced by ultraviolet-visible 共UVvis兲 absorption 共viz., 1Bu all-trans-1,3,5-hexatriene and 1Bu
all-trans-1,3,5,7-octatetraene兲 as references 共see Scheme 1兲.
Then, it addresses the isomeric forms, also in the first excited
singlet state, obtained by torsion of the terminal single bonds
in the 1Bu all-trans structures. Finally, it provides an explanation for the disparate photophysical behavior of the two
compounds that we believe essential with a view to constructing a general model accurately describing the photophysics of this prominent family of compounds.
A. On the isomeric structures of the S0 and S1 states
Hexatriene can adopt two isomeric structures that are
interconvertible via cis-trans isomerism 共viz., the all-trans
structure which we shall designate tHT兲 and one by torsion
of its central double bond 共cHT兲 共see Fig. 1兲. The two types
of structure are planar in both the ground and the first excited
electronic state. Also, they possess C2h and C2v symmetries,
respectively, and constitute true energy minima in both states
as they possess all-real vibrational frequencies. The all-trans
structure is the more stable 共by 1.2 kcal/ mol in the first excited state and by 1.9 kcal/ mol in the ground state兲. Table I
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034306-3
Photophysics of all-trans polyenes
J. Chem. Phys. 124, 034306 共2006兲
the 1Bu excited state in octatetraene 共see Table II兲. Also, the
central double bond in hexatriene becomes a formal single
bond.
It should be noted that the minimum-energy structure of
the ground excited state of cHT is planar; this is consistent
with elaborate computations,54 but contradicts experimental
evidence obtained by electron diffraction at 290 K in the gas
phase, based on which the central double bond forms a dihedral angle of 10.13°.49共b兲 Our calculations suggest that both
the ground state and the first excited electronic state in tcOT
and ccOT are planar.
Table IV lists the rotational constants for the most salient
structures studied in this work. Note the good consistency
between the experimental58 and theoretical values.
B. On the 0-0 components of S0 \ S1 transitions
in polyenes
FIG. 1. Molecular systems under study.
summarizes the structural properties of the isomers.
Octatetraene can adopt three isomeric structures, one alltrans 共ttOT兲, in addition to two reached by torsion of one
central double bond 共tcOT兲 or both 共ccOT兲 共see Fig. 1兲.
These structures are planar and constitute true energy
minima in both the first excited electronic state and the
ground state 共see Table II兲. The all-trans structure is the most
stable in both states. Table III shows the stability of tcOT and
ccOT with respect to the all-trans forms as experimentally
determined by Kohler et al.56 for the ground state and the
2Ag excited state, as well as the theoretical values for the
ground state and the first 1Bu excited state obtained in this
work—all relative to the all-trans forms. The good consistency between the theoretical and experimental data for the
ground state testifies to the goodness of the data computed in
this work. Worth special note is the high agreement 共see
Table III兲 between the relative stability data experimentally
determined by Kohler et al.56 for the 2Ag state in these isomeric structures and the theoretical values for the 1Bu state
calculated here.
The structural changes undergone by the polyene chain
in the electronic transition 1Ag → 1Bu are highly significant;
probably, the most salient outcome is that the polyene
switches from alternate single and double carbon-carbon
bonds in the ground state 共1Ag兲 共Ref. 57兲 to an average bond
order and only one purely double bond 共the terminal bond兲 in
Linear polyenes, whether unsubstituted or bearing terminal alkyl groups, allow the 0-0 components of their first ␲
→ ␲* to be highly precisely measured even in the condensed
phase. This, together with the fact that they are chromophores giving a very strong 1Ag → 1Bu transition involving two states of zero polarity but exhibiting strong solvatochromism, makes them potentially effective polarizability
probes. Recently, we showed 3,20-di共tert-butyl兲-2,2,21,21tetramethyl-all-trans-3,5,7,9,11,13,15,17,19-docosanonaen
共ttbP9兲 to be an ideal probe for determining the polarizability
共SP兲 of its environment;59 in fact, this compound was used to
characterize 100 solvents at 295 K. This is a general property
of polyenes, as shown by the excellent fitting 共n = 10, r
= 0.9988, sd = 0.049 kK兲 between the 0-0 components for octatetraene in pentane, hexane, heptane, hexadecane, chloroform, carbon tetrachloride, methanol, benzene, 1,2dichlorobenzene, and the gas phase at 295 K as measured by
Gavin et al.31 and the corresponding SP values in these
solvents59 共see Fig. 2兲.
Recently, we showed a highly dilute solution of ttbP9 in
2-methylbutane to clearly exhibit the 0-0 component of its
1Ag → 1Bu transition and also that the maximum of the component was shifted to a higher wavelength—with no change
in the transition onset—as the temperature was lowered.
Also, we found a close linear relationship between the wavelength of the 0-0 component and the sample temperature
from 295 to 120 K. In part, these results have been ascribed
to these forms being highly flexible and adopting a planar
structure—which causes a red shift in the 0-0
component—in electronic transitions to more rigid forms. It
is well documented60 that, as a result, polyenes fail to obey
the Mulliken-Rieke rule.61 It is also known from electrondiffraction data that cHT at 290 K in the gas phase behaves
as a nonplanar structure that forms a dihedral angle of 10.13°
involving its central bond;49共b兲 as noted earlier, however, the
theoretical calculations show beyond doubt that it is, in fact,
a planar structure. Liu and Zhou62 suggest that thermal averaging of the low-frequency torsional motions around C–C
single bonds and the central C v C double bond may account
for the loss of planarity in cHT at 290 K in the gas phase.
We believe it is of interest at this point to quote the
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034306-4
J. Chem. Phys. 124, 034306 共2006兲
J. Catalan and J. L. G. de Paz
TABLE I. 共a兲 Optimized geometries for fundamental 共S0兲 and first excited 共1Bu兲 states of tHT. 共b兲 Optimized geometries for fundamental and low excited
states of cHT 共trans-cis-1,3,5-hexatriene兲. The values are in angstroms and degrees.
共a兲
1Bu
S0
a
RC⬘vC1
1
RC1–C2
RC2vC3
RC1–H1
RC2–H2
RC3–H3
RC3–H4
␪ C⬘C1C2
1
␪ C1C2C3
␪ C⬘C1H1
1
␪ C1C2H2
␪ C2C3H3
␪C2C3CH4
b
Expt.
TDDFT
1.368
1.458
1.337
1.104
1.104
1.104
1.104
124.4
121.7
115.6
121.3
120.5
120.5
1.352
1.450
1.343
1.091
1.090
1.087
1.085
124.3
124.5
119.0
116.3
121.5
121.7
c
MP2
1.366
1.458
1.359
1.099
1.097
1.092
1.094
123.6
123.6
119.0
117.0
121.3
122.0
CASSCF
d
CASSCF
1.345
1.469
1.338
e
1.351
1.461
1.345
124.0
124.2
TDDFT
b
1.431
1.412
1.388
1.090
1.091
1.087
1.085
124.2
125.4
117.5
116.7
121.3
121.3
CASSCFd
1.423
1.397
1.395
CASSCF 共RASSCFe兲
1.401共1.413兲
1.404共1.410兲
1.384共1.398兲
124.6共123.8兲
125.8共125.5兲
共b兲
1B1
S0
f
RC⬘vC1
1
RC1–C2
RC2vC3
RC1–H1
RC2–H2
RC3–H3
RC3–H4
␪ C⬘C1C2
1
␪ C1C2C3
␪ C⬘C1H⬘
1
1
␪ C1C2H2
␪ C2C3H3
␪C2C3CH4
g
Expt.
TDDFT
1.362
1.462
1.336
1.090
1.090
1.090
1.090
125.9
122.1
118.0
121.0
124.0
124.0
1.356
1.453
1.343
1.090
1.088
1.088
1.085
127.1
123.6
117.6
117.8
121.5
121.8
MP2
h
1.369
1.460
1.359
1.097
1.095
1.094
1.092
126.1
122.7
117.8
118.7
120.9
121.4
CASSCF
1.360
1.472
1.345
137.4
133.0
i
TDDFT
g
1.437
1.413
1.389
1.089
1.090
1.087
1.085
126.3
124.9
116.4
117.8
121.2
121.3
CASSCF 共RASSCFi兲
1.420共1.445兲
1.409共1.419兲
1.381共1.393兲
136.9共136.7兲
134.0共132.2兲
a
Reference 49.
This work.
c
Reference 50.
d
Reference 51.
e
Complete-active-space self-consistent field CASSCF共6 , 6兲 / 6-31G**, and in parentheses the restricted active-space self-consistent-field RASCCF共32, 13+ 6
+ 9兲关1 , 1兴 / 6-31G* + 3p from Ref. 52 共supplementary materials兲.
f
Experimental values from Ref. 53.
g
This work.
h
Values from Ref. 54.
i
For comparison pruposes, we show CASSCF共6 , 6兲 / 6-31G** and 共in parentheses兲 RASCCF共32, 13+ 6 + 9兲关1 , 1兴 / 6-31G* + 3p values for all the all-cis conformer from Boggio-Pasqua et al. 共Ref. 52, supplementary materials兲.
b
following comment by Kohler in his review of octatetraene
photoisomerization:24 “In the ground state, the barriers to
rotation about the formal double bonds are high enough
共20– 40 kcal/ mol兲 that double bond cis and trans isomers
exist as independent, distinct molecules. The barrier to rotation about formal single bonds is sufficiently low 共ca.
4 kcal/ mol兲 that these species rapidly interconvert in roomtemperature solution although they may be studied as independent species at low temperature.”
We believe that it is torsion of the single bond that allows conjugation in the polyene structure to be partially broken and the spectrum blueshifted on average as the sample
temperature is raised and the structure loses planarity. Similarly, the 0-0 component will be redshifted as these torsional
movements are hindered by the medium. Consequently, we
believe that, for comparison with theoretical calculations, the
experimental data should be obtained from tests conducted in
an appropriate matrix at a low temperature in order to ensure
that a correct UV-vis spectrum is recorded. In this respect,
we should note that Gavin et al.31 found the 0-0 component
of the 1Ag → 1Bu transition of octatetraene in n-hexane at 77
K to lie at 311.5 nm, which coincides exactly with the value
obtained by Granville et al.63 in n-octane at 4.2 K—the
sample was trapped in a matrix in both cases.
Table V shows a representative collection of experimental and theoretical data for the 0-0 component of the 1Ag
→ 1Bu transition in hexatriene and octatetraene. The data for
such components had never before been reported; in fact, the
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034306-5
J. Chem. Phys. 124, 034306 共2006兲
Photophysics of all-trans polyenes
TABLE II. 共a兲 Optimized geometries for fundamental 共S0兲 and first excited 共1Bu兲 states of ttOT. 共b兲 Optimized
geometries at TDDFT level for fundamental 共S0兲 and first excited 共1Bu兲 states of tcOT and ccOT. The values are
in angstroms and degrees.
共a兲
1Bu
S0
Expt.a
RC⬘vC1
1
RC1–C2
RC2vC3
RC3vC4
RC1–H1
RC2–H2
RC3–H3
RC4–H4
RC4–H5
␪ C⬘C1C2
1
␪ C1C2C3
␪ C2C3C4
␪ C⬘C1H1
1
␪ C1C2H2
␪ C2C3H3
␪C3C4CH4
␪C3C4CH5
TDDFTb
CASSAc
1.441
1.356
1.448
1.344
1.091
1.091
1.090
1.087
1.085
124.5
124.2
124.5
116.8
118.9
116.4
121.5
121.7
1.452
1.349
1.456
1.343
1.078
1.078
1.078
1.077
1.075
124.1
124.0
124.3
116.9
1.451
1.327
1.451
1.336
125.3
125.1
124.7
RC⬘vC1
1
RC1–C2
RC2vC3
RC3vC4
RC1–H1
RC2–H2
RC3–H3
RC4–H4
RC4–H5
␪ C⬘C1C2
1
␪ C1C2C3
␪ C2C3C4
␪ C⬘C1H1
1
␪ C1C2H2
␪ C2C3H3
␪C3C4CH4
␪C3C4CH5
1.444
1.356
1.448
1.344
1.089
1.091
1.090
1.087
1.085
123.6
124.3
124.5
118.3
118.9
116.4
121.5
121.7
1.451
1.351
1.457
1.345
116.7
121.6
121.4
TDDFTb
CASSAc
CASSCFd
1.404
1.411
1.418
1.373
1.091
1.091
1.092
1.087
1.085
124.7
124.1
125.4
117.8
117.9
118.5
121.4
121.4
1.391
1.400
1.411
1.374
1.078
1.078
1.078
1.075
1.073
124.6
123.9
125.5
117.7
118.0
116.6
121.5
125.4
1.395
1.401
1.413
1.379
共b兲
ccoT
tcoT
S0
CASSCFd
1Bu
1.406
1.410
1.418
1.372
1.089
1.091
1.091
1.087
1.085
123.8
124.4
125.2
109.1
117.8
116.6
121.4
121.4
S0
1.446
1.359
1.451
1.344
1.087
1.090
1.088
1.088
1.085
126.5
127.3
123.5
116.9
117.5
117.9
121.4
121.8
1Bu
1.407
1.416
1.419
1.373
1.088
1.089
1.090
1.087
1.085
126.6
126.8
124.6
117.7
116.6
117.8
121.4
121.5
a
Reference 49.
This work.
c
Reference 55.
d
Reference 51.
b
reported data for the 1Ag → 1Bu were restricted to the differences between the potential-energy minima for the two states
involved that were not corrected for the respective zero-point
energies. Table V includes the most salient reported theoretical data corrected for zero-point energies as calculated in
this work at the TDDFT level. As can be seen, the TDDFT
data obtained in this work are as precise as those obtained at
the multireference Moller-Plesset 共MRMP兲 level and even
better than those determined at the complete-active-space
second-order perturbation theory 共CASPT2兲 level52—at least
for these two specific compounds.
C. On the Cs structure produced by torsion
of the terminal single bond
Once the all-trans form was found to be the most stable
in the first excited electronic state of hexatriene and octatetraene, and the ability of polyene structures to rotate about
their single bonds explained, we thought it is of interest to
examine the stability of the structures produced by rotation
about the C1⬘ – C2⬘ bond in hexatriene and C2⬘ – C3⬘ in octatetraene. Because the potential interaction between two hydrogen atoms in these structures could make them nonplanar, we
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034306-6
J. Chem. Phys. 124, 034306 共2006兲
J. Catalan and J. L. G. de Paz
TABLE III. Relative stability to the corresponding all-trans polyene, for
1,3,5-hexatriene and 1,3,5,7-octatetraene, shown as the variation of the electronic energy and the Gibbs free energy. We show in parentheses the corresponding experimental values taken from Ref. 56. All data are in kcal/mol.
tHT 共all-trans-1,3,5-hexatriene兲, cHT 共trans-cis-1,3,5-hexatriene兲, ttOT 共alltrans-1,3,5,7-octatetraene兲, tcOT 共trans-trans-cis-1,3,5,7-octatetraene兲, and
ccOT 共trans-cis-cis-1,3,5,7-octatetraene兲.
S1
S0
Compound
⌬E
⌬G
⌬E
⌬G
tHT
cHT
ttOT
tcOT
ccOT
0
1.9
0.0
1.9
4.0
0
1.9
0.0共0.0兲
1.5共1.1兲
4.0共2.4兲
0
1.2
0.0
1.6
3.5
共0.0兲
共1.4兲
共1.9兲
initially assumed a dihedral angle of 150° with respect to the
all-trans configuration. However, the minimum-energy structures were, in fact, all planar 共see Scheme 2兲; also, they had
all-real vibrational frequencies and were 4.05 and
0.59 kcal/ mol more stable than the parent state 共viz, 1Bu in
the all-trans structure in both hexatriene and octatetraene兲.
Once corrected for the zero-point energies, the energies
for the structures cs12HT and cs23OT fell 3.74 and
0.41 kcal/ mol, respectively, below that of 1Bu. It should be
noted that, while the 1Bu structures are nonpolar for symmetry reasons, the forms cs12HT and cs23OT are slightly polar
共with dipole moments of 0.38 and 0.48 D, respectively兲. This
can be specially influential on their photophysical behavior
in the condensed phase.
One interesting question is how easy the structural conversion between 1Bu all-trans—which is directly produced
by the absorption of light—and the resulting Cs form in the
first excited state is. Such a conversion is fairly easy in octatetraene as it is subject to a potential barrier of only
3.50 kcal/ mol as measured from the minimum of the
potential-energy curve at the top of the barrier—as expected,
the corresponding structure of the calculated transition state
possesses a negative vibrational frequency 共see Scheme 3兲,
so the structure is polar 共its dipole moment is 0.10 D兲. Surprisingly, however, the results for HT exclude a structure for
the transition state between 1Bu and the form cs12HT; rather,
rotation about the C1⬘ – C2⬘ bond in the HT structure produces
TABLE IV. Rotational constants for some structures of 1,3,5,7-octatetraene
and 1,3,5-hexatriene. All values are in MHz. Experimental values are taken
from Ref. 58.
ttOT 共S0兲
共S0 expt.
ttOT 共1Bu兲
共S1 expt.
cS23OT共S1兲
ccOT共S1兲
tcOT共S1兲
tHT共S0兲
tHT共1Bu兲
cS12HT共S1兲
cHT共S1兲
FIG. 2. The 0-0 components for octatetraene in pentane, hexane, heptane,
hexadecane, chloroform, carbon tetrachloride, methanol, benzene, 1,2dichlorobenzene, and the gas phase at 295 K as measured by Gavin et al.
共Ref. 31兲 and the corresponding SP values in these solvents 共Ref. 59兲.
a 1,3-diene that rapidly stabilizes by reaching the ground
state of HT. Optimization of the resulting structure 共see
Scheme 3兲 at the closed layer level produces a form with
all-real vibrational frequencies that coincides with the alltrans form of HT—the structure originally undergoing electronic excitation.
TABLE V. Representative collection of experimental and theoretical data
for the 0-0 component of the 1Ag → 1Bu transition in hexatriene and octatetraene. Experimental wavelength values are in nm. Calculated values in this
work at TDDFT level 共see text兲, otherwise the reference is indicated. The *
denotes that the value is corrected by our ZPE calculated at TDDFT level.
MRMP means multi reference Moller-Plesset.
Vapor at RT
Free jet
Free jet
n-hexane 共RT兲
3-Me-pentane 共298 K兲
n-hexane 共77 K兲
n-octane 共4.2 K兲
TDDFT
MRMPd
CASPT2e
1,3,5,7-octatetraene
␭0−0 共in nm兲
Gas phase
281.5a
281.2b
281.3c
Condensed phase
302.0a
301.7
311.5a
311.5
Calculated
325.2
323.1*
291.8*
1,3,5-hexatriene
Gas phase
19649.5
18192± 1242
19809.5
20724± 2000
10520.4
11899.3
9350.3
26636.8
26834.1
12587.6
14940.2
567.5
571± 0.05
558.7
559.3± 0.05
628.3
659.4
643.6
1330.9
1295.2
1601.0
1516.2
551.6
554.9兲
543.4
543.9兲
592.9
624.8
602.2
1267.6
1235.5
1420.3
1376.5
Vapor
Free jet
3-Me-pentane 共293 K兲
3-Me-pentane 共77 K兲
TDDFT
MRMPd
251.3
Condensed phase
265.6
271.4
Calculated
278.3
287.3*
a
d
b
e
Reference 31.
Reference 33.
c
Reference 32.
Reference 51.
Reference 52.
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034306-7
Photophysics of all-trans polyenes
J. Chem. Phys. 124, 034306 共2006兲
SCHEME 2. The most important molecular parameters for ground and first
excited state of cs12HT and cs23OT.
This disparate behavior could have been predicted if the
structures for the 1Bu states in HT and OT had been observed. Interestingly, the length of the C1 – C1⬘ central bond in
HT 共Scheme 4兲, 1.430 Å, virtually coincides with that of a
single bond; it is therefore such a bond that undergoes the
torsion and leads to the above-mentioned 1,3-diene structure.
D. On the photophysics of hexatriene
and octatetraene
As shown for the first time here, the interesting photophysical behavior of both hexatriene 共nonfluorescent兲 and
SCHEME 3. Quenching structure for tHT and transition structure for ttOT
in the first excited state.
octatetraene 共doubly fluorescent兲 can be explained in terms
of the excited state produced by light absorption 共1Bu兲 and
torsion of a single bond in the structure, which quenches
such a state or produces a new, also fluorescent, structure.
Excitation of the most stable form of hexatriene in the
ground electronic state 共viz., the all-trans form兲 produces the
excited state 1Bu, which possesses a single central bond 1.43
Å long 共see Table I兲 that undergoes the torsion and rapidly
gives a 1,3-diene structure where the central bond is 1.444 Å
long, the C2C1C1⬘C2⬘ dihedral angle is 73° and the C3 – C2 and
C2⬘ – C3⬘ double bonds are in orthogonal planes 共see Scheme
3兲. This brings the system to the surface of the ground electronic state 共see Fig. 3兲, thereby quenching the potential fluorescence emission from 1Bu. Also, the absence of torsion in
the form cs12HT precludes the emission of fluorescence, so
hexatriene is nonfluorescent.
Our hypothesis that torsion of the central bond in the
excited electronic state 1Bu in HT is the mechanism by
which the fluorescence of this polyene is quenched is
strongly supported by the fact that 1,2-divinylcyclopentene
共see Scheme 5兲, the central bond which cannot undergo tor-
SCHEME 4. C–C bond length for the 1Bu states in tHT and ttOT.
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034306-8
J. Catalan and J. L. G. de Paz
J. Chem. Phys. 124, 034306 共2006兲
FIG. 3. Potential-energy curves corresponding to the ground and 1Bu state
that describes the photophysical behavior of tHT.
FIG. 4. Potential-energy curves corresponding to the ground and 1Bu state
that describes the photophysical behavior of ttOT.
sion, is strongly fluorescent.64 The evidence reported by
Hudson et al.65 that 3,8-Di共tert-butyl兲-2,2,9,9-tetramethyl3,5,7-decatriene is fluorescent in n-hexane matrices cannot
be held as final as subsequent experiments66 involving the
same samples in 2-methylbuthane, decalin, and squalane matrices excluded fluorescence emission in these compounds.
Octatetraene in the gas phase exhibits two fluorescence
emissions.31,32,34 One, structured, is the mirror image of the
1Ag → 1Bu absorption; the other, structureless, appears at
higher wavelengths. As noted by Bouwman et al.,34 “It is
important to note that both emissions give rise to the same
structured fluorescence excitation spectra and that the corrected excitation spectra are in good agreement with the gasphase absorption spectra in terms of both the wavelengths
and the relative intensities of the 1Ag → 1Bu vibronic bands.”
The theoretical results obtained in this work show that
electronic excitation of the most stable structure of octatetraene 共viz., the all-trans from兲 produces the excited state 1Bu
which overcomes a barrier of 3.5 kcal/ mol to produce the
form cs23OT 共see Fig. 4兲. This results in a potential-energy
curve with two minima corresponding to 1Bu and cs23OT, the
oscillator strengths for which 共1.49 and 1.09, respectively兲
are very large. In this situation, octatetraene can indeed be
expected to produce two fluorescence emissions upon electronic excitation in the gas phase.
However, the facts that the fluorescence from cs23OT is
structureless and occurs at a lower energy remain unexplained. Therefore, their origin can only be the potentialenergy curve for the target electronic state of the transition
from the ground state. In the ground state, Cs23OT is nonplanar, has a C1⬘C2⬘C3⬘C4⬘ dihedral angle of 18° and all-real vibrational frequencies, and lies 3.58 kcal/ mol above the most
stable structure 共the all-trans form兲. Consequently, the tran-
sition from the excited form cs23OT in the gas phase, which
is planar, must lead via a Franck-Condon mechanism to a
more unstable planar structure 共viz., the optimized form
cs23OT兲; this will shift the transition to a lower energy—in
fact, the calculated wavelength for the vertical emission transition is 352 nm. Because the emitting form is planar 共initial
state兲 and the structure of the final state of this transition is
nonplanar, there will be an inevitable loss of vibronic structure in the corresponding fluorescent transition.
If one assumes the transformation of cs23OT 共nonplanar兲
into the all-trans form in the ground electronic state via a
barrier the transition state of which is at only
5.3 kcal/ mol—as measured from the minimum of the curve
to the top of the barrier—then the form cs23OT resulting
from the emission cannot be stored for a long time. Consequently, the excitation spectrum obtained by tuning light in
the zone corresponding to the emission from cs23OT will
SCHEME 5. 1,2-divinylcyclopentene.
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034306-9
J. Chem. Phys. 124, 034306 共2006兲
Photophysics of all-trans polyenes
continue to be that for the 1Ag → 1Bu transition. The
potential-energy curve for the transformation between
cs23OT and the all-trans form is included in Fig. 4 in order to
provide a more comprehensive picture of the photophysics of
octatetraene.
One interesting finding is that, according to Gavin et
al.,31 the radiative constant at 295 K for the new fluorescence
at the higher wavelength is only 33% smaller than that for
the 1Bu → 1Ag fluorescence; also, the oscillator strength,
which is calculated in this work and involved in the emission
from cs23OT, is only 27% smaller than that for the emission
from 1Bu. Again, there is a high consistency between experimental evidence and our theoretical data.
Finally, the octatetraene in the condensed phase seemingly emits from the form cs23OT only can be ascribed to
both the transition state and the form cs23OT being polar,
and 1Bu nonpolar. As a result, stabilization of these two
forms via the solvent effect may result in the 1Bu form produced by electronic excitation being largely reconverted into
cs23OT, which could thus be the origin of the fluorescence
emission in octatetraene.
This hypothesis requires closer scrutiny, however, by
studying photostable polyenes such as linear tetra-tert-butyl
compounds bearing terminal substituents. In fact, we have
recently reported on the photophysics of the corresponding
nonaene 共ttbP9兲 and shown that this polyene only emits from
its 1Bu state in the condensed phase.67
IV. CONCLUSIONS
The photophysics of two compounds with such a highly
controversial fluorescent behavior as hexatriene and octatetraene is explained here on the basis of the behavior of their
1Bu excited electronic state and the production of a 1,3-diene
intermediate that quenches the fluorescence of hexatriene or
a planar isomer responsible for the fluorescence that exhibits
a large Stokes shift and is produced by torsion of the formal
terminal single bond in octatetraene.
This explanation for the photophysical behavior of these
two compounds provides a solid basis for constructing a general model accounting for the behavior of polyenes as their
chain is lengthened.
ACKNOWLEDGMENTS
This paper is dedicated to Professor R. M. Gavin and
Professor Stuart A. Rice for contributing essential evidence
on the polyene spectroscopy that, without their adequate description, any feasible photo-physic model for this family of
compounds might not be acceptable. We thank Professor J.
C. del Valle 共UAM, Spain兲 for reading the manuscript and
his help. The authors acknowledge with thanks DGICYT of
Spain for financial support of this work 共Project No.
BQU2002-02106兲.
APPENDIX: ON THE RELATIVE SITUATION
OF THE 2Ag AND 1Bu EXCITED STATES
The 2Ag state holds a double-excitation character68 and,
owing to this reason, they are not adequately described by
the time-dependent density-functional theory 共TDDFT兲
method used in this work. However, Hsu et al.69 show that
the TDDFT method is a significant improvement for excitation energies of excited states that, when treated by wavefunction-based methods, have appreciable “double-excitation
character.” This point of view is strengthened by the results
obtained for polyenic systems.57,69 Being stated this important fact on TDDFT methodology, we will analyze the relative position of 2Ag and 1Bu states in hexatriene and octatetraene by this method, and compared with the results found in
the bibliography.
The position of an electronic state in an energy diagram
is done by the 0-0 component from the ground electronic
state, and it is evaluated from the energy difference between
the equilibrium geometry of each state, corrected by their
corresponding zero-point energy 共ZPE兲.
1. All-trans hexatriene
Our calculated results at TDDFT level using optimized
geometries show the 0-0 component of 2Ag state for
hexatriene is placed at 5.39 eV, that is, 0.94 eV above the
1Bu state, whose 0-0 component is 4.45 eV at this theoretical
level. Against this ordering of states we have found the recently published results on this compound by Nakayama et
al.,51 using more accurate calculations at multireference
Moller-Plesset 共MRMP兲 with a geometry optimized at
complete-active-space self-consistent-field 共CASSCF兲 level
with double zeta with polarization basis 共MRMP/DZp兲. They
found the 0-0 component of 2Ag state with a value of 4.07
eV and the one for 1Bu state at 4.88 eV, without ZPE correction. Using the corresponding ZPE values obtained in our
work, the corrected values for the 0-0 components become
3.93 and 4.75 eV, respectively. However, the calculated values by Boggio-Pasqua et al.52 at restricted active-space selfconsistent-field 共RASSCF兲, RASSCF共32, 13+ 6 + 9兲关1 , 1兴 / 6
− 31G* + 3p level show the 0-0 component for the 2Ag state
of hexatriene at 4.66 eV, but the one of the 1Bu state becomes
5.64 eV. After the correction by using our ZPE values, the
values become 4.51 and 5.51 eV, respectively. Summarizing,
these advanced methods obtain the first excited state for alltrans hexatriene is clearly 2Ag, being the 1Bu state at an
energy 0.82 or 1 eV higher than that of 2Ag.
A good and difficult experimental work have been undertaken in order to know the situation of the low-lying 2Ag
state in all-trans hexatriene by electron impact,70–72 multiphoton ionization,73,74 or thermal blooming,74,75 thus finding
no sign of the existence of the aforementioned state. Only
Fujii et al.,76 by using a two-photon absorption 共TPA兲 study
by coherent anti-Stokes 共CARS兲 and Stokes-Raman scattering 共CSRS兲 on a pure liquid sample of all-trans hexatriene,
are able to detect a wide absorption band that they assign to
the 2Ag state. They can only obtain its corresponding vertical
transition to this state at the value of 5.20 eV. It is interesting
to note that these authors wrote, at the end of their work,
“This suggests the possibility that in hexatriene the 1Bu state
is the lowest and provided a very efficient pathway of radiationless decay.”
Very recently, Cave et al.77 have developed a theoretical
approximation they call Dressed TDDFT that allows one to
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034306-10
treat within the TDDFT model these doubly excited states,
and they have used it to calculate the vertical transition
1Ag → 2Ag for hexatriene,78 using for the ground state a fully
optimized geometry at B3LYP/ 6-311G共d , p兲 level. They
have found that this transition is shifted 0.98 eV to a lower
energy value. It is clear that a procedure for geometry optimization using this new method for the 2Ag and 1Bu states of
hexatriene is needed in order to know the ordering of these
states in the framework of TDDFT theory.
2. All-trans octatetraene
Our calculated results at TDDFT level optimized geometries show that the 0-0 component of the 2Ag state for octatetraene is placed at 4.58 eV, that is, 0.77 eV above the 1Bu
state, whose 0-0 component is 3.81 eV.
In contrary, the results obtained using a more accurate
level of theory by Serrano-Andres et al.55 shown calculations
at complete-active-space second-order perturbation theory
共CASPT2兲 level, thus obtaining a value for the 0-0 component of the 2Ag state of 3.61 eV and at 4.35 eV for the 1Bu
state, without ZPE correction. Using the corresponding ZPE
values obtained in our work, the corrected values for the 0-0
components become 3.50 and 4.25 eV. Recently, Nakayama
et al.51 obtained theoretical results at MRMP/DZp level, being 3.45 eV for the 0-0 component of the 2Ag state of octatetraene, and 4.02 eV for the 1Bu state. After the correction
using our ZPE values, the data values become 3.34 and 3.92
eV, respectively. In conclusion, again both methods show
clearly 2Ag state for octatetraene as the first excited one,
being the 1Bu state 0.58 or 0.75 eV above 2Ag.
On the experimental situation of 2Ag state in octatetraene, we only can show a recent theoretical work of Hsu et
al.69 where they use a value of 3.97 eV, but it is an estimated
value from the fluorescence spectrum assuming the same
parabolic shapes for the ground- and excited-state surfaces
and assuming the right behavior of the Hudson-Kohler
model.22
In a short summary, it is obvious that the ordering of the
2Ag and 1Bu states for hexatriene and octatetraene is not well
established. Consequently, it is uncertain whether the 2Ag
state is mainly responsible for the photophysics of these systems, as it has been stated in many works.52,79–85 It is clear
that the new experimental work must be focused in obtaining
experimental evidence to allow scientists to propose a photophysical model for this important group of compounds, a
model capable of explaining the photophysical behavior of
hexatriene 共it does not show fluorescence兲, octatetraene 共it
shows two fluorescences兲, and nonaene 共it shows a single
fluorescence assigned with no doubt to the 1Bu state67兲.
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