Rotationally resolved electronic spectra of trans trans-octatetraene and its derivatives

Article abstract of DOI:10.1021/jp9838285

Described herein are the rotationally resolved one-photon fluorescence excitation spectra of several vibronic bands in the S₁ ← S₀ electronic transitions of three linear polyenes in the gas phase, 1,3,5,7-octatetraene (OT), 1,3,5,7-nonatetraene (NT), and 2,4,6,8-decatetraene (DT). Several of the spectra are significantly perturbed by an apparent centrifugal distortion in the S₁ state of OT, owing to the high frequency of rotations parallel to a and the low frequency of an in-plane bending mode (v₄₈), by Coriolis coupling in the S₁ state of NT, involving v₄₈ and a nearby methyl torsional level, and by torsion-rotation coupling in the S₁ states of NT and DT, owing to a significant reduction in the excited-state torsional barrier(s) compared to the ground state. Nonetheless, the inertial parameters of eight different S₀ and S₁ vibronic levels have been determined, from which it is concluded that the carriers of the spectra are in all cases the transjrans isomers. The important role of V48 as a promoting mode for S₁ - S₂ vibronic coupling, the source of the S₁ - S₀ oscillator strength, is confirmed. Finally, the measured differences in the rotational constants of the S₀ and S₁ states (e.g., ΔA = 2532, ΔB = -11.7, and ΔC = -11.0 MHz for the vibronic origin of OT) provide new information about the changes in geometry that occur when the photon is absorbed.

Full text of DOI:10.1021/jp9838285

J. Phys. Chem. A 1999, 103, 2337-2347
2337
Rotationally Resolved Electronic Spectra of trans,trans-Octatetraene and Its Derivatives
J. F. Pfanstiel and D. W. Pratt*
Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260
†
B. A. Tounge and R. L. Christensen
Department of Chemistry, Bowdoin College, Brunswick, Maine 04011
ReceiVed: September 23, 1998; In Final Form: December 18, 1998
Described herein are the rotationally resolved one-photon fluorescence excitation spectra of several vibronic
bands in the S r S electronic transitions of three linear polyenes in the gas phase, 1,3,5,7-octatetraene
OT), 1,3,5,7-nonatetraene (NT), and 2,4,6,8-decatetraene (DT). Several of the spectra are significantly perturbed
by an apparent centrifugal distortion in the S state of OT, owing to the high frequency of rotations parallel
to a and the low frequency of an in-plane bending mode (ν48), by Coriolis coupling in the S
involving ν48 and a nearby methyl torsional level, and by torsion-rotation coupling in the S
1
0
(
1
1
state of NT,
states of NT
1
and DT, owing to a significant reduction in the excited-state torsional barrier(s) compared to the ground
state. Nonetheless, the inertial parameters of eight different S and S vibronic levels have been determined,
from which it is concluded that the carriers of the spectra are in all cases the trans,trans isomers. The important
role of ν48 as a promoting mode for S -S vibronic coupling, the source of the S r S oscillator strength,
is confirmed. Finally, the measured differences in the rotational constants of the S and S states (e.g., ∆A )
532, ∆B ) -11.7, and ∆C ) -11.0 MHz for the vibronic origin of OT) provide new information about the
changes in geometry that occur when the photon is absorbed.
0
1
1
2
1
0
0
1
2
Introduction
its one- and two-photon S1 r S0 fluorescence excitation spectra.
A detailed comparison of these spectra led to the conclusion
that the carrier is the trans,trans isomer, the most stable form.
This conclusion was supported by a more recent study of the
fluorescence excitation spectra of two additional “linear”
tetraenes, nontetraene and decatetraene, in which one or both
terminal hydrogen atoms in octatetraene are replaced by methyl
Polyenes (CnHn+2), molecules with alternating single and
double bonds between covalently attached carbon atoms, are
an important class of molecules with many interesting proper-
1
ties. Among these is geometrical isomerism, by far the most
significant property of polyenes in biological systems. Each 180°
turn at either a single or a double bond gives a different
configuration, resulting in a large number of possible structures,
especially when n is large. Thus, octatetraene (n ) 8) has 20
distinguishable isomers, although three or four consecutive cis
configurations result in steric crowding that may prevent their
6
,7
groups.
Rotationally resolved electronic spectroscopy is a powerful
method for establishing the identity of gas-phase chromophores.
The patterns of energy levels observed in this experiment are
sensitive both to the size and shape of the molecule and to how
3
formation. The net count in C8H10 is 15, excluding cis
configurations, and 18, excluding cis configurations.
8
4
2
these change when a photon is absorbed. Here, we demonstrate
the utility of this approach in a study of the high-resolution
one-photon fluorescence excitation spectra of octatetraene,
nonatetraene, and decatetraene in the collision-free environment
of a molecular beam. The results provide an unambiguous
identification of the isomers responsible for the above-mentioned
spectra as the trans,trans forms. The spectra also give new
insight into the remarkable photochemical and photophysical
properties of the polyenes and provide new experimental
Given this fact, the existence of a controversy concerning
the correct assignment of the electronic spectrum of octatetraene
3
1
is not surprising. Heimbrook et al. observed S2 f S0 (1 Bu f
1
1
Ag) emission from the gas-phase molecule and recorded its
strongly allowed S2 r S0 fluorescence excitation spectrum.
However, they were not able to detect the dipole forbidden S1
1
1
T S0 (2 Ag T 1 Ag) transition under isolated molecule
4
conditions. Later, Buma et al. obtained the two-color REMPI
spectrum of the 2 Ag state in the gas phase and assigned their
1
1
benchmarks for evaluating theoretical descriptions of their 2 Ag
states.
spectrum to a “cis, trans” isomer. They argued that only a
noncentrosymmetric isomer would have a large enough oscil-
lator strength to be detected under their experimental conditions.
Then, Petek et al.5 succeeded in observing the S1 f S0
fluorescence of octatetraene in a supersonic jet and recording
Experimental Section
Octatetraene (OT) was prepared by dehydrating 1,4,6-
octatrien-3-ol at 80 °C using pyridinium p-toluenesulfonate
(
Aldrich) following the procedure developed by Yoshida and
*
Corresponding author. Email: pratt+@pitt.edu.
9
†
Tasumi. The 1,4-octatrien-3-ol was produced by mixing 2,4-
hexadienal with vinylmagnesium bromide (Alfa). The dehydra-
Present address: Department of Chemistry, Yale University, New
Haven, CT 06511.
1
0.1021/jp9838285 CCC: $18.00 © 1999 American Chemical Society
Published on Web 02/10/1999

2338 J. Phys. Chem. A, Vol. 103, No. 14, 1999
Pfanstiel et al.
tion produces trans,trans-OT of >99% isomeric purity as
determined by an analysis of the S2 r S0 spectrum in a free
5
jet. The OT crystals were stored at -80 °C to preserve their
isomeric purity. Nonatetraene (NT) and decatetraene (DT) were
synthesized from Wittig reactions, using hexadienal and allyltri-
phenylphosphonium bromide (Fluka) for the former and hexa-
dienal and crotyltriphenylphosphonium bromide (Fluka) for the
latter.
Supersonic jet spectra were obtained using a standard low-
resolution apparatus. Typically, the polyenes (OT at room
temperature, NT and DT with mild heating) were seeded into
80 psig He and expanded through a pulsed 1 mm nozzle
(
General Valve, series 9). The resulting free jet was crossed
3+
with a frequency-doubled Quanta-Ray Nd :YAG-pumped dye
laser beam about 1 cm downstream of the nozzle. When tuned
to a particular vibronic band in the absorption spectrum, the
laser produced S1 f S0 fluorescence, which was collected by a
single lens system, detected by a photomultiplier tube and SRS
boxcar integrator, and acquired by a MASSCOMP data acquisi-
tion system.
High-resolution spectra were obtained using a CW molecular
beam spectrometer equipped with an intracavity-doubled Spectra-
10
Physics ring dye laser, described in detail elsewhere. As above,
OT at room temperature (or NT and DT with mild heating)
was continuously expanded through a 90 µm nozzle in 40-60
psig He, skimmed once, and excited ∼15 cm downstream of
the nozzle by the laser. Fluorescence was collected using
spatially selective optics, detected by a photomultiplier tube and
photon-counting system, and processed by the data acquisition
system. Relative frequency calibrations of the spectra were
performed using a near-confocal interferometer. Approximately
Figure 1. Low-resolution one-photon fluorescence excitation spectra
of (a) octatetraene, (b) nonatetraene, and (c) decatetraene in a supersonic
jet. The three spectra are aligned so that their vibronic origins coincide.
Different horizontal energy scales are used in each spectrum.
1
0 × 100 mg of each sample was available for the experiments,
been assigned as the vibronic origin of the S1 r S0 transition
of trans,trans-NT. Most (but not all) of the remaining bands in
the low-resolution spectrum exhibit similar splittings.
so special care was taken to optimize the performance of the
apparatus prior to each run.
The first strong band in the excitation spectrum of DT (Figure
1c) is a triplet (bands DT-1, 2, and 3). Band DT-1 is at 29 014.0
cm . This band has been assigned as the vibronic origin of
Results and Interpretation
-
1
Figure 1 shows the low-resolution one-photon fluorescence
excitation spectra of OT, NT, and DT recorded in a supersonic
the S1 r S0 transition of trans,trans-DT, whose true origin lies
-1
-1 6,7
5
0.9 cm to the red at 28 963.1 cm . The three components
4
-7
jet. These are similar in every respect to the published spectra.
The first strong band in the excitation spectrum of OT (Figure
-1
of the triplet are separated by 3.09 and 3.16 cm . These have
been assigned as the 0a1 r 0a1, 1g r 1g, and (1e1 + 1e3) r
-
1
1
a) is at 29 024.9 cm (band OT-1). This band has been
(1e1 + 1e3) tunneling components of two equivalent methyl
0
assigned as the 0 band of the S1 r S0 transition of an OT
groups. Further to the blue in the spectra of all three molecules
are several additional vibronic bands that have not been
examined at high resolution. Their assignments are discussed
0
4
having a cis linkage by Buma et al. and as the vibronic origin
5
of trans,trans-OT by Petek et al. Their assignment places the
0
0
-1
4
-7
0
band at 76.2 cm to the red of band OT-1, at 28 948.7
elsewhere.
-1
5
cm , observed only in two-photon excitation experiments. The
frequency of 76.2 cm has been assigned to ν48, a bu in-plane
Figure 2 shows the rotationally resolved one-photon fluores-
-
1
-1
cence excitation spectrum of the band at 29 024.9 cm in OT,
bending mode in the S1 state. Also prominent in the spectrum
11
band OT-1. The spectrum is that of a near-prolate symmetric
0
0
-1
of OT is a band at 0 + 411.9 cm (band OT-2), which has
top (κ ) -0.999) and, despite its overall appearance, is an a-type
been assigned to ν48 + ν16, where ν16 is a totally symmetric
-1
band. Band OT-2, at 29 360.6 cm , is qualitatively similar.
(ag) in-plane bending mode.
The reason for the unusual appearance of these two bands is
that the pseudolinear OT has, in its S0 state, a large A constant
(∼20 GHz) relative to its B and C constants (∼500 MHz). The
moment of inertia about the long axis is very small relative to
those perpendicular to it. Thus, OT is very nearly a symmetric
top. Even a very small percentage change in the A constant on
electronic excitation produces large shifts in the individual Ka
subbands, as shown in Figure 3. These shifts are approximately
The first strong band in the excitation spectrum of NT (Figure
1
2
b) is a doublet (bands NT-1 and NT-2). Band NT-1 lies at
8 950.8 cm and has been assigned as the true origin of the
-
1
7
S1 r S0 transition of trans,trans-NT. According to Petek et
7
al., the doubling of the origin is produced by the hindered
internal rotation of the attached methyl group. Thus, the two
components are 0a1 r 0a1 and 1e r 1e tunneling doublets,
-
1
2
with the latter (band NT-2) shifted to the blue by 3.34 cm
proportional to Ka , destroying the sharp, centrally located
with respect to the former (band NT-1). At 60.1 cm- further
1
Q-branch structure that is normally observed in a-type bands.
Similar effects have been observed in the rotationally resolved
to the blue of band NT-1 lies a second doublet (bands NT-3
and NT-4), also split (by 3.37 cm ) by the tunneling motion
of the methyl group. Band NT-3 lies at 29 010.9 cm and has
-
1
12
S1 r S0 spectra of trans,trans-diphenylbutadiene (DPB) and
-
1
13
trans-stilbene (tS).

trans,trans-Octatetraene and Its Derivatives
J. Phys. Chem. A, Vol. 103, No. 14, 1999 2339
TABLE 1: Inertial Parameters of trans,trans-Octatetraene in
the Zero-Point Vibrational Level of Its Ground Electronic
1
State (1 A
g
)
experiment
expta std errorb HF(6-31G*) CASSCFc
18192
theory
A′′ (MHz)
B′′ (MHz)
C′′ (MHz)
κ′′
1242
0.05
0.04
19831
573.2
557.1
-0.999
0.0
19738
568.0
552.2
-0.998
0.0
571.04(0.1)
554.96(0.1)
-0.999
∆
I′′ (amu Å2) -2.14
1.91
a
Results from a fit of 205 combination-differences that appear in
-
1
0
0
the rotationally resolved spectra of the two bands at 29 024.9 cm (0
-
1
-1
0
-1
+
76.2 cm ) and 29 360.6 cm (00 + 411.9 cm ). Numbers in
parentheses represent estimates of the systematic uncertainties in the
experiment. b Estimated errors from the diagonal elements of the
correlation matrix. c Reference 16.
TABLE 2: Inertial Parameters of trans,trans-Octatetraene in
Two Vibrational Levels of Its First Excited Electronic State
1
(
2 A
g
)
0
0
+ 76.2 cm-1
0
0
-1
0
0 + 411.9 cm
theoretical
Figure 2. High-resolution one-photon fluorescence excitation spectrum
expta
std errorb
expta
std errorb CASSCFc
1 0
of band OT-1 in the S r S transition of octatetraene, at 29 024.9
-
1
A′ (MHz)
B′ (MHz)
C′ (MHz)
DJ′ (Hz)
DJK′ (Hz)
DK′ (MHz)
d1′ (Hz)
d2′ (Hz)
κ′
20724
559.29(0.1) 0.01
543.96(0.1) 0.01
16.6
2310
10.35
3.9
2000
20435
559.30(0.1) 0.01
543.93(0.1) 0.01
2000
19649
555.8
540.5
cm , in a molecular beam. The top trace shows the experimental
spectrum, the next trace shows the computed spectrum (simulated using
the constants in Tables 1 and 2), and the bottom two traces show a
comparison of a portion of the experimental and computed spectra, to
illustrate the quality of the fit. The line width of single rovibronic
features in the experimental spectrum in 15 MHz; this line width is
not included in the simulation in the bottom trace. The rotational
temperature of the fit is 8 K.
0.4
51
0.01
0.1
0.2
44
2
583
13.68
25
289
0.05
2
1.8
5
2
-0.998
-0.998
0.80
192
7.2
-0.998
0.0
∆
I′ (amu Å2)d 1.08
0.01
0.01
assignt
rms (OMC)
353
11.0
a
Numbers in parentheses represent estimates of the systematic
uncertainties in the experiment. Band origins were not determined owing
to the lack of a calibrated I
2
spectrum in this region. b Estimated errors
c
from the diagonal elements of the correlation matrix. Reference 16.
d
Neglecting distortion parameters.
compared to the observed Doppler width of about 15 MHz.
Adding centrifugal distortion terms to the S0 Hamiltonian did
not significantly improve the quality of the fit. Hence, the ZPL
of the ground state is a rigid rotor.
Also listed in Table 1 are two sets of theoretical rotational
constants for the trans,trans isomer of OT. The first set was
calculated from a Hartree-Fock (HF) geometry, optimized using
1
5
the 6-31G* basis set. It gives A′′ ) 19 831, B′′ ) 573, and
C′′ ) 557 MHz. The second set was calculated from a geometry
1
6
obtained by Serrano-Andr e´ s et al. using the complete active-
space self-consistent-field (CASSCF) method. It gives very
similar values: A′′ ) 19 738, B′′ ) 568, and C′′ ) 552 MHz.
The experimental A′′ rotational constant (18 192 MHz) could
not be determined accurately from the spectra owing to their
Figure 3. Deconvolution of the spectrum in Figure 2, showing the
contributions from individual K
blue of successive subbands, determined by ∆(A-B)K
rotor limit. These shifts are increased further by the addition of the
a
subbands. Note the large shift to the
2
17
a
in the rigid-
near-symmetric-top nature. However, the experimental values
of B′′ (571 MHz) and C′′ (555 MHz) are known to high
precision. Moreover, there is near-perfect agreement between
these values and the two sets of theoretical values. We therefore
conclude that the carrier responsible for the two obserVed bands
4
K
D K
a
1
distortion term to the S Hamiltonian.
The parameters obtained from fits of these two spectra to
14
distortable rotor Hamiltonians (S-reduction) are listed in Tables
and 2. Bands OT-1 and OT-2 exhibit the same ground-state
5
1
is trans,trans-OT, in agreement with Petek et al.
rotational constants within experimental error. Thus, they both
originate in the same vibronic level, presumably the zero-point
vibrational level (ZPL) of the S0 state. The ground-state
parameters listed in Table 1 are the results of a fit of 205
combination differences obtained from the two spectra. The
calculated energy differences reproduce the experimental values
to within a standard deviation of 4.5 MHz. This may be
We also have calculated the rotational constants of eight
additional OT isomers, each possessing at least one cis linkage,
using the 6-31G* basis set. All exhibit significantly smaller A′′
values and significantly larger B′′ and C′′ values, as expected.
For example, the tcttt isomer has A′′ ) 8019, B′′ ) 758, and
18
C′′ ) 693 MHz. Thus, there can be little doubt that the carrier
of these bands is the trans,trans structure.

2340 J. Phys. Chem. A, Vol. 103, No. 14, 1999
Pfanstiel et al.
Four bands in the S1 r S0 spectrum of NT have been recorded
at high resolution. These include both components of the doublet
-
1
located at 28 950.8 and 28 954.1 cm (bands NT-1 and NT-2)
and both components of the doublet located at 29 010.9 and
-
1
2
9 014.3 cm (bands NT-3 and NT-4). These are shown in
Figures 4-6. The red and blue members of these doublets have
been assigned to torsional levels having a and e symmetry,
7
respectively. Consistent with this interpretation, bands NT-1
and NT-3 were found to exhibit a-type contours, like the two
recorded bands of OT. Thus, similar strategies could be used
for their analysis. First, we fit the two bands independently,
using rigid rotor Hamiltonians for all four states. Again, we
found near-prolate symmetric top behavior, with large A and
small and nearly equal B and C values. We also found that the
two sets of ground-state constants are identical within experi-
mental error, showing that the two bands originate in the same
vibronic level, presumably the ZPL of the S0 state. Then we
used the combination-difference method to determine more
accurate values of the rotational constants of this level. The
results are listed in Table 3. Examination of these data shows
that, in its ground state, NT is very nearly a planar symmetric
top (κ ) -0.999) to which a single methyl group is attached
Figure 4. High-resolution one-photon fluorescence excitation spectrum
of band NT-1 in the S r S transition of nonatetraene, at 28 950.8
cm , in a molecular beam. See the captions to Figures 2 and 3 for
more details. The rotational temperature of the fit is 4 K.
1
0
-
1
2
(∆I ) -3.3 amu Å ). The data also show that the S0 ZPL of
NT is rigid; adding centrifugal distortion terms did not
significantly improve the quality of the fit.
The excited-state parameters of the two bands listed in Table
2
were determined separately by fixing the S0 rotational
As a substituted polyene, NT also can exhibit the property
of geometrical isomerism, leading to several possible structures.
So again, it is important to compare our results with theory to
ascertain which isomer is responsible for the observed spectra.
Two such comparisons are shown in Table 3, one using the
rotational constants calculated by the HF (6-31G*) method and
a second using the constants calculated by the CASSCF method,
both sets referring to the trans,trans structure. (The second set
of constants was determined by adding a methyl group to the
optimized geometry of trans,trans-OT obtained by Serrano-
Andr e´ s et al. ) Again, we find excellent agreement between
experiment and theory, showing that the carrier responsible for
these two bands is trans,trans-NT.
The two S1 vibrational levels reached in bands NT-1 and
NT-3 have significantly different properties. As can be seen
from Figure 4, the high-resolution spectrum of band NT-1
constants at the experimental values shown in Table 1 and
varying the S1 rotational constants to obtain least-squares fits.
These calculations showed that both excited-state vibrational
levels are nonrigid, requiring the full Watson Hamiltonian for
their analysis. For the band at 0 + 76.2 cm (band OT-1), we
fit 353 transitions with a standard deviation of 11.0 MHz. For
14
0
0
-1
0
0
-1
the band at 0 + 411.9 cm (band OT-2), we fit 192
transitions with a standard deviation of 7.2 MHz. Both deviations
are less than the observed widths of single rovibronic lines in
the two spectra. The complete set of quartic centrifugal distortion
1
6
1
4
terms is listed in Table 2. However, only DK′ significantly
improves the fit. The effect of this term is to shift the parallel-
type Ka subbands even further to the blue, by DK′Ka (cf., Figure
4
3). No other perturbations were observed in these two rotation-
ally resolved spectra of OT.
Figure 5. High-resolution one-photon fluorescence excitation spectrum of band NT-2 in the S
in a molecular beam and an approximate deconvolution of its K subband structure (cf. Figure 3). Note that the K
, where D is the coefficient of the linear angular momentum operator parallel to the
1
r S
0
transition of nonatetraene, at 28 954.1 cm-1,
> 0 transitions are split into two
a
a
subbands. This splitting is approximately proportional to D
a axis.
a
K
a
a

trans,trans-Octatetraene and Its Derivatives
J. Phys. Chem. A, Vol. 103, No. 14, 1999 2341
Figure 6. High-resolution one-photon fluorescence excitation spectra of bands NT-3 and NT-4 in the S
molecular beam and an approximate deconvolution of their K subband structures (cf. Figures 3 and 5). The origin of band NT-3 is at 29 010.9
subbands are not monotonic in nature. See text for proposed explanation.
1 0
r S transition of nonatetraene in a
a
-
1
cm . Note that the shifts of the K
a
TABLE 3: Inertial Parameters of trans,trans-Nonatetraene
TABLE 4: Inertial Parameters of trans,trans-Nonatetraene
in the 0a
1
Torsional Component of the Zero-Point Level of
in the 0a Torsional Component of the Zero-Point Level of
1
1
1
Its Ground Electronic State (“1 A
g
”)
g
Its First Excited Electronic State (“2 A ”)
experiment
theory
experiment
theory
expta
std errorb HF(6-31G*) CASSCFc
expta
std errorb
CASSCFc
A′′ (MHz)
B′′ (MHz)
C′′ (MHz)
κ′′
16302
2500
0.04
0.04
16579
391.5
383.3
-0.999
-3.08
16090
390.0
381.9
-0.999
-3.76
A′ (MHz)
B′ (MHz)
C′ (MHz)
16759
2500
0.01
0.01
3
0.6
0.05
5
15796
381.9
374.0
390.42(0.1)
382.25(0.1)
-0.999
384.05(0.1)
375.82(0.1)
-21
4.4
0.73
18
-2
-0.999
-1.35
207
D
D
D
J
′ (Hz)
JK′ (kHz)
′ (Hz)
I′′ (amu Å2) -3.3
∆
4.8
K
a
Results from a fit of 192 combination-differences that appear in
the rotationally resolved spectra of the two red components of the
d1′ (Hz)
d2′ (Hz)
κ′
∆I′ (amu Å )
assignt
2
0
0
0
0
-1
doublets in the 0 and 0 + 60.1 cm bands, located at 28 950.8 and
-0.999
-3.76
-1
2 d
29 010.9 cm , respectively. Numbers in parentheses represent estimates
0.04
b
of the systematic uncertainties in the experiment. Estimated errors
from the diagonal elements of the correlation matrix. Estimated by
addition of a methyl group to the OT geometry obtained by Serrano-
Andr e´ s et al. (ref 16).
c
rms (OMC)
a
5.3
Numbers in parentheses represent estimates of the systematic
uncertainties in the experiment. Band origin was not determined owing
to the lack of a calibrated I
2
spectrum in this region. b Estimated errors
c
exhibits the same large, monotonic shifts of its Ka subbands
that were observed in bands OT-1 and OT-2 of trans,trans-
OT, signaling a large change in the A rotational constant on S1
excitation. However, a fit of band NT-1 to the distortable rotor
from the diagonal elements of the correlation matrix. Estimated by
addition of a methyl group to the OT geometry obtained by Serrano-
Andr e´ s et al. (ref 16). d Neglecting distortion parameters.
This effect is so dramatic that the Ka ) 1 and 2 subbands exhibit
nearly identical shifts from the origin.
Hamiltonian (using the ground-state constants listed in Table
4
3) revealed no significant additional shifts due to the DK′Ka
The most likely explanation of this effect is Coriolis
distortion term, similar to those observed in OT. The S1
vibrational level reached in band NT-1 is rigid. Its inertial
parameters are listed in Table 4. These parameters include the
quartic distortion terms, but these are relatively small and give
only a slight improvement to the fit. We conclude from this
observation that this level is the ZPL of the S1 state, as suggested
by Petek et al.7
19
coupling. The S1 vibrational level reached in band NT-3, at
0
0
-1
0
+ 60.1 cm , is believed to be the analogue of the S1 level
in band OT-1 of octatetraene, a bu bending mode. According
to Petek et al., it is nearly degenerate with the 3a1 methyl
torsional level built upon the electronic origin of NT, at a
7
0
0
-1
(
calculated) frequency of 0 + 63.2 cm . Therefore, it is
reasonable to suppose that the two zero-order levels are coupled
by a Coriolis interaction, leading to the observed perturbations
in the spectrum, especially since these perturbations appear to
The situation is different in band NT-3. Figure 6 shows its
rotationally resolved spectrum (as well as that of band NT-4,
vide infra). Transitions observed in this spectrum have been
successfully assigned, as demonstrated by their use in the
combination-difference calculations. However, these assign-
ments showed that the observed Ka structure in band NT-3 does
not conform to expectations for either a rigid rotor or a
distortable rotor. In particular, as shown in Figure 6, the shift
be larger for odd K . (A first-order treatment of the Coriolis
interaction in symmetric top molecules leads to terms in the
rotational Hamiltonian that are linear in K . ) A more complete
analysis of this behavior is in progress.
We turn next to the results for bands 2 and 4 of trans,trans-
NT. These bands also are perturbed but for a different reason.
The rotationally resolved spectrum of band NT-2, the blue
member of the doublet located at 28 954.1 cm , is shown in
Figure 5. Our analysis of this spectrum reveals that each Ka
a
17
a
2
of the Ka subbands is not monotonic, proportional to either Ka
or Ka4 or some combination thereof. Instead, the shifts of
particular subbands appear to be larger for odd values of Ka.
-1

2342 J. Phys. Chem. A, Vol. 103, No. 14, 1999
Pfanstiel et al.
subband with Ka g 1 is split into two components, with the
center of gravity of the two components shifting to the red with
increasing |Ka|. Qualitatively similar behavior is exhibited by
the Ka subbands in the rotationally resolved spectrum of the
TABLE 5: Inertial Parameters of trans,trans-Nonatetraene
in the 1e Torsional Components of the Zero-Point Levels of
Its Ground and First Excited Electronic States
1
1
S
0
(“1 A
g
”)
1 g
S (“2 A ”)
-1
blue member of the doublet located at 29 014.3 cm , band NT-
expta
std errorb
exptc
std errorb
4
, as shown in Figure 6.
The origin of these perturbations is the torsion-rotation
A (MHz)
B (MHz)
C (MHz)
16102
390.23(0.1)
382.07(0.1)
2.3
0.02
0.02
15419
2.5
383.85(0.1)
375.70(0.1)
200.3
15428.5
-99.42
-0.999
-4.2
0.03
0.03
0.05
0.2
interaction.17 Recall that bands NT-2 and NT-4 have been
assigned to transitions that connect the 1e methyl torsional
component of the ZPL of the S0 state with the corresponding
components of two different vibrational levels of the S1 state.
As discussed in detail elsewhere,20 the torsion-rotation interac-
tion affects a and e torsional levels differently. The a torsional
levels are affected only in second order, leading to modified
values of their rotational constants, whereas the e torsional levels
are affected both in first and in second order, leading to splittings
that depend on Ka as well as modified rotational constants. The
observation of such splittings in the high-resolution spectra of
bands NT-2 and NT-4 thus confirms their assignment as 1e-
D
D
D
κ
x
(MHz)
(MHz)
(MHz)
z
3
0.19
0.62
z
0.06
-0.999
-3.56
I′ (amu Å2)d
∆
0.08
0.4
a
Results from a fit of 423 combination-differences that appear in
the rotationally resolved spectra of the two blue components of the
0
0
0
0
-
1
doublets that appear in the 0 and 0 + 60.1 cm bands, located at
-1
2
8 954.1 and 29 014.3 cm , respectively, using the torsion-rotation
Hamiltonian (eq 1). Numbers in parentheses represent estimates of the
systematic uncertainties in the experiment. Band origin was not
2
determined owing to the lack of a calibrated I spectrum in this region.
b
Estimated errors from the diagonal elements of the correlation matrix.
1
e bands.
c
Results from a fit of 159 assigned transitions in the spectrum of band
NT-2, the blue component of the doublet of the 0 band, located at
We now use the observed splittings to obtain information
0
0
about the barriers to internal rotation of the methyl group in
the S0 and S1 states of trans,trans-NT. The effective Hamiltonian
is
-
1
2
8 954.1 cm . The ground-state parameters were fixed to the values
shown in this table. The standard deviation of this fit is 7.03 MHz.
d
Neglecting internal rotation parameters.
rotation interaction.20 These perturbations cause a splitting of
the nearly degenerate rotational levels differing only in Kc, which
are exactly degenerate in the symmetric top limit. Increases in
these splittings relative to the resolution of the experiment
provide increased accuracies of the determinations of the A
constants of the affected vibrational levels.
Hˆ ) Hˆ + Hˆ + Hˆ
TR
(1)
T
R
where
2
Hˆ ) Fp + V (1 - cos 3φ)/2
(2)
T
3
2
a
2
b
2
Hˆ ) AP + BP + CP
c
(3)
(4)
Considering next the first-order torsion-rotation constants
in Table 5, we find Dx′′ ) 0 and Dz′′ ) 0.19 MHz for the e
component of the S0 state and Dx′ ) 200 and Dz′ ) 15 430
MHz for the e component of the S1 state. The first-order term
Dz′ is very large, as large as the A′ rotational constant itself,
requiring the inclusion in eq 4 of a third-order correction term
(which is neglected in the subsequent analysis). These data show
that there is a large decrease in the methyl internal rotation
barrier in the S1 state. Combining the data in the usual way20
and using as well the observed tunneling splittings in the low-
R
Hˆ TR ) D P + D P
b b
a
a
and the rest of the terms have their usual meaning.20 We first
fit the high-resolution spectra of bands NT-2 and NT-4 using
eq 1 to model the rotational energy level patterns in the e
torsional components of the connected vibrational levels of the
two electronic states. This led to two sets of ground-state
constants that were found to be identical within experimental
error. Then we used the combination-difference method to
extract more accurate values of the inertial parameters of the e
subtorsional level of the ZPL of the S1 state from the spectrum
of band NT-2. A similar refinement of the fit of band NT-4
was not attempted owing to the presence of additional Coriolis
perturbations in this spectrum.
7
-1
resolution spectrum, we find V3(S0) g 900 cm , and V3(S1)
-
1
) 42.8 and V6(S1) ) -29.4 cm . (The V6 term was added to
eq 2 to improve the fit.) These values are in good agreement
with those determined by Petek et al. Thus, the observed
7
tunneling splittings are almost entirely attributable to a low
torsional barrier in the S1 state.
Table 5 lists the values of the parameters that were derived
using this procedure. Considering first the rotational constants
of the a and e torsional components of the ZPL of the S0 state,
we see from a comparison of the values in Tables 3 and 5 that
they are nearly the same within experimental error, showing
that the second-order contribution of the torsional-rotation
interaction is small in the ground state. Making the same
comparison for the S1 state (Tables 4 and 5), we see again that
the C′ rotational constants are the same but that the A′ and B′
rotational constants are significantly different, showing that the
second-order contributions of the torsion-rotation interaction
are large in this case, especially for motions about a and b. In
this connection, it is interesting to note that the errors in the
determinations of the A rotational constants of the e components
of the ZPL’s of the S0 and S1 states are very small, despite the
near-symmetric-top nature of the spectra. This significant
improvement in the accuracy of the experiment can be traced
to a mixing of Ka, Kc states in the affected levels by the torsion-
Finally, we turn to DT. Figure 7 shows the high-resolution
spectra of two members (DT-1 and DT-2) of the triplet observed
in the DT S1 r S0 spectrum located at 29 014.0 and 29 017.1
-1
cm . (DT-3 was not recorded owing to its low intensity.) Given
the results for OT and NT, it is reasonable to expect (as did
6
,7
Petek et al. ) that bands DT-1, 2, and 3 are the tunneling
-
1
“triplet” of the vibronic origin of DT, 50.9 cm above the true
origin of the S1 r S0 transition. Examination of Figure 7 shows
that these two observed bands conform qualitatively to this
expectation. Both are a-type bands. Band DT-1 appears to be a
0a1 r 0a1 transition, unperturbed by torsion-rotation coupling,
and band DT-2 appears to be a significantly perturbed 1g r 1g
transition. Apparently, the species responsible for these bands
is trans,trans-DT. Unfortunately, both bands are too weak to
permit detailed analysis at this time. This is probably a result
of several factors. Addition of the second methyl group has
restored the center of inversion that makes the S1 r S0 transition
forbidden in the C2h point group. In addition, its intensity is

trans,trans-Octatetraene and Its Derivatives
J. Phys. Chem. A, Vol. 103, No. 14, 1999 2343
1 0
Figure 7. High-resolution one-photon fluorescence excitation spectra of bands DT-1 and DT-2 in the S r S transition of decatetraene in a
-
1
molecular beam. The two bands are centered at 29 014.0 and 29 017.1 cm , respectively.
now spread over three torsional levels having different nuclear
spin symmetries. And perhaps most importantly, the vapor
pressure decreases as one goes from OT to DT, resulting in
progressively lower concentrations in the molecular beam.
Owing to the instability of these compounds, this cannot be
compensated for by heating.
are the most sensitive to its three-dimensional structure. This
information is contained in its principal moments of inertia Ia,
Ib, and Ic, which are related to its rotational constants A, B, and
C by
h
Ia )
, etc.
(5)
2
The inability to observed the blue member of the triplet, DT-
8
π A
3, may indicate the existence of a coupling between the two
methyl rotors, despite their large separation. In the absence of
such coupling, consideration of nuclear spin statistics suggests
that the relative intensities of bands DT-1 and DT-3 should be
the same. However, in the presence of such coupling, the
normally degenerate members of an e torsional level, associated
with clockwise and counterclockwise rotations of the first methyl
group, would have different energies, depending on the sense
of rotation of the second methyl group. A splitting would result,
and to the displacements of each of its component atomic masses
from the relevant axes by
2
2
Ia ) m (b + c ), etc.
(6)
∑i
i
i
i
Thus, the fact that OT has a large A constant is a consequence
of its small moment of inertia Ia; the displacements of each of
the C and H atoms from the a axis (bi and ci) are all relatively
small (I). In contrast, OT has relatively small B and C constants
leading to a further diminution of the intensities of the affected
band, DT-3 in this case. As shown elsewhere,21 the bands of
two coupled rotors also would be expected to exhibit significant
torsion-rotation interactions, especially for rotors that are
hindered by only small barriers.
Discussion
1
1
Eight vibronic bands in the 2 Ag-1 Ag electronic transitions
of OT, NT, and DT have been recorded at high resolution. Given
the thermal instability of the compounds, their near-symmetric-
top nature, and the existence of several perturbations, the
analyses of these spectra posed significant challenges. Neverthe-
less, five of the bands have been fully assigned and three have
been partially analyzed, providing valuable new information
about these polyenes in their ground and first electronically
excited states.
because the displacements of many of the atoms from the b
and c axes are relatively large.
Three rotational constants are clearly insufficient to determine
the complete structure of OT and its derivatives, making
necessary a comparison with theory in order to establish the
identity of the species responsible for the spectra. Fortunately,
this comparison leads to an unambiguous result. OT has 20
distinguishable isomers, 15 including cis configurations.2
Paramount among our findings are the rotational constants
1
of OT and NT in their ground electronic (1 Ag) states (Tables
1
, 3, and 5). Alone among all known spectroscopic parameters
3
of an isolated molecule in the gas phase, its rotational constants

2344 J. Phys. Chem. A, Vol. 103, No. 14, 1999
Pfanstiel et al.
TABLE 6: Modeling the Geometry of
lengths and C-C-C angles close to 120°. The specific values
1
trans,trans-Octatetraene in Its Ground (1 A
g
) and
of these parameters were chosen to most closely match those
1
Electronically Excited (2 A
g
) States
16
of the CASSCF geometry of the ground state, also listed in
1
1
S
0
(1 A
g
)
S
1
(2 A
g
)
Table 6. We ignore the small calculated decrease in the
difference between “single” and “double” bond lengths as one
moves toward the center of the structure, and the small
differences in the bond angles. Despite these facts, model 1 has
the rotational constants A′′ ) 19 574, B′′ ) 571, and C′′ ) 554
MHz, in reasonable agreement with the experimental results.
Next, we distorted the molecule along one or more of the
chosen coordinates to model its possible behavior on excitation
parametera
model 1 CASSCFb model 2 model 3 CASSCFb
r
r
r
r
∠
1
2
3
4
(C
(C
(C
(C
1
2
3
4
-C
-C
-C
-C
1
2
3
2
3
4
5
)
)
)
)
1.340
1.460
1.340
1.460
124.0
124.0
124.0
19,574
570.5
554.4
1.343
1.456
1.349
1.452
124.3
124.0
124.1
19,738
568.0
552.2
1.460
1.340
1.460
1.340
124.0
124.0
124.0
1.460
1.340
1.460
1.340
125.2
125.2
125.2
1.438
1.376
1.437
1.392
124.5
124.3
124.1
19,649
555.8
540.5
1
2
3
(C
(C
(C
-C
-C
-C
2
3
4
-C
-C
-C
3
4
5
)
)
)
∠
∠
1
6,24,25
A (MHz)
B (MHz)
C (MHz)
19,711 20,146
to the S1 state. According to theory,
teristic of the S1 r S0 transition in the polyenes is bond-order
reversal”. Thus, as shown in Table 6, the CASSCF calculation16
the primary charac-
562.6
547.0
555.9
540.9
“
a
Bond lengths in angstroms and bond angles in degrees. A C-H
predicts that single bonds shorten and double bonds lengthen
on S1 excitation, whereas the C-C-C angles remain essentially
unchanged. Model 2 was chosen to mimic this behavior. Here,
we find that decreasing r2 and r4 from 1.460 to 1.340 Å increases
A, B, and C, owing to decreases in the displacements of all
atoms from all three inertial axes. Increasing r1 and r3 from
1
bond length of 1.078 Å and H-C-C angles of / (360 - ∠ C-C-C)°
were used in all calculations. CASSCF/ANO results (ref 16).
2
b
However, only the trans,trans form (I) has calculated B′′ and
C′′ rotational constants that agree with those measured in this
work. For NT, the best agreement between experiment and
theory also is obtained for the trans,trans isomer. Here, we find
from our fit of band NT-2 the values A′′ ) 16 102 ( 2.3, B′′ )
1
.340 to 1.460 Å has the opposite effect. But the magnitudes
of the observed changes in A-C are different in the two cases,
since OT (in its ground state) has fewer C-C single bonds than
double ones. Thus, when we simultaneously increased r1 and
r3 while decreasing r2 and r4, we found that A increases while
B and C decrease. The primary reason for the increase in A is
that a decrease in r4 moves all atoms closer to the a axis.
The model 2 structure, with r1 ) r3 ) 1.460 Å, r2 ) r4 )
3
90.2 ( 0.1, and C′′ ) 382.1 ( 0.1 MHz, whereas theory
1
6
(
CASSCF) gives the values A′′ ) 16 090, B′′ ) 390.0, and
C′′ ) 381.9 MHz. Thus, we confirm the conclusions of Petek
5
-7
et al.
The carriers observed in their spectra of OT, NT, and
DT are primarily the trans,trans forms. These data also show
that modern ab initio theory gives an accurate description of
the structures of the isolated molecules in their ground electronic
states.
1
-
.340 Å, and θ ) 124°, has ∆A ) 137, ∆B ) -7.9, and ∆C )
7.4 MHz. To improve the agreement with experiment, we also
explored the effect of changes in the C-C-C bond angles.
Increasing these angles increases A, since the displacements of
the atoms with respect to a decrease, and decreases B and C,
since the displacements with respect to b and c increase. Our
model 3 structure, which has all C-C-C angles set to 125.2°,
has ∆A ) 572, ∆B ) -14.6, and ∆C ) -13.5 MHz. The
calculated ∆A value is still in rather poor agreement with the
observed one. Nonetheless, it is large and positive, as observed.
Now, the patterns of energy levels observed in the high-
resolution spectra also are sensitive to the size and shape of the
molecules in their electronically excited states and therefore to
the changes in structure that occur when the photon is absorbed.
We find (Tables 2, 4, and 5) that excitation of all three molecules
1
to their S1 (2 Ag) states results in large increases in A and small
decreases in B and C. This shows that the molecular dimensions
perpendicular to a decrease significantly while those perpen-
dicular to b and c increase slightly, compared to the ground
state. Despite uncertainties in the A′ constants themselves, the
changes in the rotational constants, ∆A()A′ - A′′), ∆B, and
Thus, it appears that S excitation of the typical polyene results
1
in significant changes in the bond angles as well as the bond
lengths. Studies of isotopically labeled species and/or further
refinements of theory will be necessary to confirm this finding.
Another dramatic consequence of the change in electronic
structure on S1 r S0 excitation is the large decrease in the
methyl group internal rotation barriers in NT and DT. We find
∆C, are all known to high precision ((0.1 MHz). These are
0
-1
2
532, -11.7, and -11.0 MHz for the 0 + 76.2 cm band of
0
0
-1
OT; 2243, -11.7, and -11.1 MHz for the 0 + 411.9 cm
0
0
0
-1
-1
V3(S0) g 900 cm ; V3(S1) ) 42.8 and V6(S1) ) -29.4 cm
band of OT; and 457, -6.3, and -6.5 MHz for the 0 band of
7
in NT. Petek et al. find comparable values for NT and DT
from their analyses of the low-resolution spectra. Now it is
known that the ground states of propene and other molecules
having CH3-CHdX functionalities prefer methyl group con-
formations that have a C-H bond syn or eclipsed with the
double bond, as shown below (II). The barrier to rotation is on
NT, respectively. The magnitudes of the changes are smaller
in NT. Ab initio theory16 predicts the values ∆A ) -88.8, ∆B
)
-12.3, and ∆C ) -11.7 MHz for trans,trans-OT. The
agreement between the observed and calculated values of ∆B
and ∆C is very good. However, the difference between the
observed and calculated ∆A values is very large, much too large
to be attributed to the vibrational contributions of an in-plane
22
bending motion and/or possible inadequacies of the distortable
rotor Hamiltonian. In all cases, we find ∆A > 0, whereas theory
23
predicts ∆A < 0. This shows that modern ab initio descriptions
of the structures of the excited electronic states of isolated
polyenes are still inadequate.
Intrigued by this result, we have performed some simple
calculations to explore the connections between different model
OT geometries and their rotational constants. The properties of
the model structures are listed in Table 6. For the ground state
-
1
the order of 700 cm . The origin of this barrier can be traced
to repulsive interactions between the occupied methyl group
2
6
orbitals of π symmetry and the π orbitals of CdX. However,
the situation is different in ππ* excited states. Here, the
staggered conformation (III) is preferred because the dominant
interaction is an attractive one, owing to overlap of the singly
(
model 1), we chose r1(C1-C2) ) r3 ) 1.340 Å, r2 ) r4 )
.460 Å, and ∠ 1 ) ∠ 2 ) ∠ 3 (C-C-C) ) 124.0°, thereby
capturing the essence of its structure, alternating C-C bond
1

trans,trans-Octatetraene and Its Derivatives
J. Phys. Chem. A, Vol. 103, No. 14, 1999 2345
2
6
at 335.7 cm-1 in the S1 state, close to the ground-state values.
However, significant changes in both the nature and the
frequencies of these modes could occur on S1 excitation.
The values of the quartic distortion terms derived from the
fits of bands OT-1 and OT-2 provide new information about
the identity of these modes. The largest distortion term by far
is DK′, which is at least 3 orders of magnitude larger than DJ′
and DJK′, and much larger than in other “typical” large
molecules. Thus, if the source of this nonrigid behavior were a
genuine centrifugal effect, we would conclude that the largest
force produced by rotation is for rotation about the a axis, when
Ka is large. That rotation of OT about its (near) symmetric top
axis could lead to distortions of the molecule in directions
perpendicular to the axis of rotation is reasonable. But the DK′
value of NT in the ZPL of its S1 state, where similar effects
might be expected, is relatively small, DK′ ) 0.73 MHz (Table
occupied π*CdC orbital and the vacant π*CH orbital. Thus,
3
the magnitude (and sign) of the methyl group internal rotation
barrier is a sensitive probe of the π-orbital bond order in the
adjacent CdC bond(s).2
Theory (HF/6-31G*)18 predicts that the stable conformation
of NT in its ground electronic state is the eclipsed form II,
consistent with the existence of a double bond between C7 and
C8 and with its measured torsional barrier in the S0 state.
However, this barrier drops precipitously on excitation to the
S1 state. This shows that there is a large decrease in the π bond
order in the adjacent CdC bond in the S1 state. Thus, the small
torsional barrier in the S1 state of NT also provides compelling
evidence for bond order reversal in the S1 r S0 transitions of
these linear polyenes. The C7dC8 bond in trans,trans-NT must
be nearly a single bond in the S1 state.
0,27
It is interesting to note that the methyl group internal rotation
barrier in the S1 state of trans,trans-NT (V3 ) 42.8, V6 ) -29.4
cm ) is comparable to that of the ethyl radical, in its ground
4
). Further, only g vibrational modes can be involved in
3
1
centrifugal distortion. Therefore, it is likely that the large DK′
values for bands OT-1 and OT-2 of octatetraene are not truly
centrifugal in origin but instead are due to Coriolis coupling
involving ν48 and an out-of-plane vibration. This vibration must
be of au symmetry to couple about the a axis. As suggested by
-
1
-1
28
29
state (V3 e 50 cm ). As is well-known, Hudson and Kohler
were the first to show that the S1 state of most linear polyenes
is a mixture of singly and doubly excited Ag configurations
rather than the singly excited Bu (HOMO-LUMO) configura-
tion predicted by simple MO theory. Theoretical calculations
by Schulten et al.24 confirmed this conclusion. One chemical
consequence of this finding is bond-order reversal. A second
consequence is two “separated but paired” electrons, mostly
localized on the terminal carbon atoms in the S1 state. The ethyl
radical also has a largely localized (unpaired) electron, in a
π-type orbital adjacent to the CH3 group. Thus, the fact that
the internal rotation barriers in these two species are similar
suggests that, in accord with theory, the S1 state of trans,trans-
NT also has “single” π electrons localized on C1 and C8. The
measured barrier is a very sensitive probe of the interaction of
these electrons with attached methyl groups.
3
1
Watson, this mechanism also would explain why ∆A for OT
is unexpectedly large.
The approximate Hamiltonian for the K rotational energies
is31
2
ν + AK 2iAúK
4
8
E(K) )
(7)
2
[-2iAúK
]
ν25 + AK
Expanding yields
2
2
2
4 4 4
2
4A ú K
16A ú K
E(K) ) ν + AK +
-
+ ... (8)
48
3
ν - ν
4
8
25
(ν - ν )
48 25
The rotationally resolved spectra presented in this work also
provide compelling evidence for the model proposed by Petek
Here, ν25 is the frequency of an au out-of-plane bending mode,
-1 30
calculated to be 60 cm . If we take ∆A ) 2 GHz, A ) 20
5
-7
et al.
to explain the source of S1 r S0 oscillator strength in
-1
GHz, and ν48-ν25 ) 16 cm , we find from eq 8 the Coriolis
trans,trans-OT, NT, and DT. This information comes from our
analysis of the two bands of OT, in which it was found that the
two excited-state vibrational levels have unusually large values
of the centrifugal distortion term DK′ (10.4 MHz in band OT-1
and 13.7 MHz in band OT-2; Table 2). Both levels exhibit small,
parameter ú ) 0.77, a not unreasonable result. Therefore, we
conclude that the large value of DK′ in band OT-1 is most likely
a consequence of Coriolis effects involving ν48 and ν25. A similar
explanation would account for the large DK′ value in band OT-
2
, in which ν48 +ν16 interact with ν25 + ν16. We further conclude
2
positive inertial defects (1.08 and 0.80 amu Å , respectively),
that such couplings also could account for the large ∆A values
whereas the ZPL of the S0 state exhibits a small, negative ∆I
of these two bands. And finally, we confirm the suggestion of
2
value (-2.14 amu Å ). Both in-plane and out-of-plane vibrations
5
Petek et al.; band OT-1 terminates in the analogue of the
17
contribute to the inertial defects of planar molecules. Usually,
in-plane vibrations make a positive contribution and out-of-plane
vibrations make a negative contribution. We believe, therefore,
that out-of-plane vibrations dominate in the ZPL of the S0 state,
given its observed negative inertial defect. Further, since the
sign of ∆I changes on excitation of trans,trans-OT to both of
the two examined S1 vibrational levels, we also believe that
these two levels involve significant in-plane motions.
“
overall” bu in-plane bending mode (ν48) in the S1 state.
This spectroscopic finding has significant implications for
the properties of the isolated molecule. As shown by Petek et
5
al., the origin in the two-photon excitation spectrum of
-
1
octatetraene is ∼76 cm lower in energy than the origin of
the one-photon spectrum. We have shown that the latter band
originates in the ZPL of the S state of the trans,trans form, is
0
3
2,33
an a-type spectrum,
and terminates in a vibronic level of
-
1
C8H10 has 48 (nondegenerate) vibrational modes, 33 in-plane
the S1 state that has bu symmetry, lying ∼76 cm above the
9
0
0
-1
(
ag and bu) and 15 out-of-plane (au and bg). Six in-plane modes
ZPL. Thus, this band (OT-1 at 0 + 76.2 cm ) is the “false”
-
1
have frequencies less than 600 cm in the ground state. These
are all C-C-C bending modes: ν15 (ag) at 543, ν16 (ag) at 332,
ν17 (ag) at 222, ν46 (bu) at 566, ν47 (bu) at 390, and ν48 (bu) at
6 cm . (The quoted frequencies are scaled MP2/6-31G*
values. ) Given the frequency displacements in the spectra (76
origin of the S1 r S0 transition of trans,trans-OT. It gains its
1
intensity via Herzberg-Teller coupling with the S2 (1 Bu) state,
via the bu promoting mode, which is the origin of most of the
remaining vibrational activity in the spectrum. As also shown
by Petek et al., the complete lack of overlap between vibronic
-
1
5
8
30
5
-
1
and 412 cm ), the observed levels are likely the excited-state
bands in the one- and two-photon spectra proves that the one-
photon (g f u) and two-photon (g f g) selection rules are
strictly obeyed, thus excluding a cis form of OT as the carrier
of the spectrum.
analogues of two of these modes or linear combinations of them
5
(
owing to possible Duschinsky rotations). Petek et al. have
assigned them as ν48 and ν48 + ν16, placing ν48 at 76.2 and ν16

2346 J. Phys. Chem. A, Vol. 103, No. 14, 1999
Pfanstiel et al.
It is interesting to note that the CASSCF geometry of the
and other experimental parameters derived in this work will
serve as benchmarks for future theoretical studies of the
structural and dynamical properties of linear polyenes.
11
2
Bu state of trans,trans-OT has rotational constants of A )
1
6,18
0 148, B ) 559, and C ) 544 MHz.
The calculated values
1
of B and C for the 1 Bu state are nearly the same as those for
the 2 Ag state. However, the calculated value of A for the 1 Bu
1
1
Acknowledgment. The entire scientific community was
saddened by the loss of Bryan Kohler. He was a good friend.
Additionally, he inspired all of us with his infectious enthusiasm
for science and the challenges it presents. One of those
challenges was posed by the results described herein; while they
disagreed with his own work, no one was more interested in
discussing them. Therefore, we are most pleased to dedicate
this work to his memory, acknowledging in this small way
Bryan’s immense contributions to science and to the lives of
those fortunate enough to work with him. We are grateful to
Bryan and to B. Champagne, H. Petek, A. Stolow, X.-Q. Tan,
and J. Watson for many helpful conversations about this work.
T. Korter assisted with some of the calculations. J. Watson
provided the model described in eqs 7 and 8. This research has
been supported by NSF (CHE-9224398, CHE-9617208) and by
a grant from the Pittsburgh Supercomputing Center. Acknowl-
edgment is also made to the donors of the Petroleum Research
Fund, administered by the ACS, for partial support of this
research.
state is significantly larger than the corresponding value for the
Ag state. Thus, if the degree of mixing of the two states via
1
2
the bu promoting mode is large, this may account for at least
some of the discrepancy between the observed and calculated
1
values of ∆A for the 2 Ag state.
Making such arguments quantitative is a challenging task.
3
4
3
5-37
In early work, Kohler and co-workers
invoked vibronic
1
1
coupling between the ground 1 Ag and excited 2 Ag states to
explain the increase in frequency of the Franck-Condon active,
totally symmetric CdC stretch that was observed on excitation
of 2,10-dimethylundecapentaene and 2,12-dimethyltrideca-
3
8
hexaene. Later, Orlandi and Zerbetto showed that, whereas
vibronic couplings between states of the same parity are strong
and are caused predominantly by C-C stretching modes, the
couplings between states of opposite parity are comparatively
weak and involve mainly C-C-C bending modes. More
recently, Buma and Zerbetto39 used CI methods to investigate
vibronic intensity patterns in the spectrum of trans,trans-OT.
They found that the low-frequency bu mode (ν48) is most active
1
1
References and Notes
in coupling the two Ag and 1 Bu states. They also confirmed
that the intensity of the false origin in the one-photon excitation
spectrum of trans,trans-OT is comparable to that of the true
origin in an OT containing a cis linkage, as previously discussed
(1) For reviews, see the following. Hudson, B. S.; Kohler, B. E.;
Schulten, K. Excited States; Lim, E. C., Ed.; Academic Press: New York,
1
982; Vol. 6, p 1. Kohler, B. E. Chem. ReV. 1993, 93, 41.
5
(2) Yeh, C.-Y. J. Chem. Phys. 1996, 105, 9706.
by Petek et al. Future modeling of this effect should focus on
(
3) Heimbrook, L. A.; Kohler, B. E.; Levy, I. J. J. Chem. Phys. 1984,
1, 1592.
(4) Buma, W. J.; Kohler, B. E.; Shaler, T. A. J. Chem. Phys. 1992,
96, 399.
trans,trans-NT, in which both the true and false origins are
observed (cf., Figure 1). Quantitative estimates of the vibronic
coupling matrix elements are needed to account for the large
variations in time scales that have been observed in the excited-
8
(5) Petek, H.; Bell, A. J.; Choi, Y. S.; Yoshihara, K.; Tounge, B. A.;
Christensen, R. L. J. Chem. Phys. 1993, 98, 3777.
40
state relaxation behavior of several polyenes.
(
6) Petek, H.; Bell, A. J.; Yoshihara, K.; Christensen, R. L. J. Chem.
Phys. 1991, 95, 4739.
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(
Conclusions
Christensen, R. L. J. Chem. Phys. 1995, 102, 4726. Slightly different values
of the tunneling splittings of nonatetraene were determined from analysis
of the high-resolution spectra. See Figures 4-6.
Rotationally resolved electronic spectra of several vibronic
bands in the S1 r S0 transitions of octatetraene (OT), nonatet-
raene (NT), and decatetraene (DT) in the gas phase have been
observed and analyzed. These analyses show that (1) the first
strong band in the one-photon spectrum of OT originates in
(
(
8) Pratt, D. W. Annu. ReV. Phys. Chem. 1998, 49, 481.
9) Yoshida, H.; Tasumi, M. J. Chem. Phys. 1988, 89, 2803.
(10) Majewski, W. A.; Pfanstiel, J. F.; Plusquellic, D. F.; Pratt, D. W.
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&
Sons: New York, 1995; p 101.
11) Previously published, without analysis. Mukamel, S. Principles of
1
the zero-point vibrational level (ZPL) of the ground (1 Ag) state
(
of the trans,trans isomer and terminates in the ν48 vibrational
Nonlinear Optical Spectroscopy; Oxford, U.K., 1995.
(12) Pfanstiel, J. F.; Champagne, B. B.; Majewski, W. A.; Plusquellic,
D. F.; Pratt, D. W. Science 1989, 245, 736.
1
-1
level of the excited (2 Ag) state, which lies ∼76 cm above
its ZPL, (2) the one-photon spectrum, strictly forbidden by parity
selection rules, gains its intensity via Herzberg-Teller coupling
(
13) Champagne, B. B.; Pfanstiel, J. F.; Plusquellic, D. F.; Pratt, D. W.;
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15) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.;
1
with the S2 (1 Bu) state, via the ν48 (bu) promoting mode, (3)
(
the S1 state of trans,trans-OT has a different equilibrium
geometry from that of the S0 state, exhibiting significant changes
in the C-C-C bond angles as well as the C-C bond lengths,
as required by bond-order reversal models of the S1 state, (4)
the first two strong bands in the one-photon spectrum of NT
1
(
Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.
A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
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Pittsburgh, PA, 1992.
1
originate in the ZPL of the ground ("1 Ag′′) state of the
trans,trans isomer and terminate in the ZPL and ν48 vibrational
(16) Serrano-Andr e´ s, L.; Lindh, R.; Roos, B. O.; Merch a´ n, M. J. Phys.
1
-1
levels of the excited ("2 Ag") state, which lies ∼60 cm above
its ZPL (the two bands are, respectively, the true and false
origins of the S1 r S0 transition, the former being no longer
strictly forbidden), and (5) the methyl group internal rotation
barrier in trans,trans-NT, large in the S0 state, decreases
significantly on excitation to the S1 state, further validating the
bond reversal model. The observed spectra of DT are consistent
with its assignment to the trans,trans structure. All of these
conclusions agree with the earlier assignments and interpreta-
tions of Petek et al.5 The excited-state rotational constants
Chem. 1993, 97, 9360.
(17) Gordy, W.; Cook, R. L. MicrowaVe Molecular Spectra, 3rd ed.;
Wiley-Interscience: New York, 1984.
(18) Pfanstiel, J. F. Ph.D. Thesis, University of Pittsburgh, 1994.
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(20) Tan, X.-Q.; Majewski, W. A.; Plusquellic, D. F.; Pratt, D. W. J.
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(
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22) The vibrational contributions of ν48 to the rotational constants of
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(
-7

trans,trans-Octatetraene and Its Derivatives
J. Phys. Chem. A, Vol. 103, No. 14, 1999 2347
+
3 MHz from the HF/6-31G* calculations (ref 18). Thus, ∆A, although
(31) Watson, J. K. G. Private communication.
(32) In this connection, it is interesting to note that we find no evidence
having the right order of magnitude, has the wrong sign to explain this
discrepancy.
for an “off-axis” orientation of the S r S transition moment in any of
1
0
(23) Negative ∆A values have been found in DPB (ref 12) and tS (ref
our spectra, such as has been observed for some linear conjugated polyenes
as guests in the channels of urea crystals by Hudson and co-workers (ref
33). However, we cannot rule out the possible existence of such a tilt; it
could be as large as 15°.
1
3), but in these cases the observed changes appear to be associated primarily
with increases in the lengths of the C-C bonds in the phenyl rings that are
most perpendicular to a.
(24) Schulten, K.; Ohmine, I.; Karplus, M. J. Chem. Phys. 1976, 64,
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4
1
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7
4
2
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(
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(
Unpublished results. Sears, T. J. Unpublished results.
(
(
29) Hudson, B. S.; Kohler, B. E. Chem. Phys. Lett. 1972, 14, 299.
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