Dispersed fluorescence spectra of jet-cooled benzophenone ketyl radical: Assignment of the low-frequency vibrational modes

Article abstract of DOI:10.1039/b212696f

We measured the laser-induced fluorescence (LIF) and dispersed fluorescence (DF) spectra of jet-cooled benzophenone ketyl radical (BPK), which was generated by the 248 nm photolysis of α-phenyl benzoin or benzhydrol. The several single vibronic level (SVL) DF spectra of BPK were obtained to analyze the low-frequency vibrational modes. We identified three low-frequency vibrations of 47, 74, and 98 cm^-1 in the ground state, which are assigned to the out-of-phase torsional motion, the in-phase torsional motion and Ph-C-Ph bending motion, respectively, with the aid of the density functional theory (DFT) calculation. The corresponding vibrational frequencies are 60, 65 and 84 cm^-1, respectively, in the excited state. The geometries of BPK in the ground and excited states are discussed based on the experimental results, ab initio calculations, and one-dimensional Franck-Condon simulation.

Full text of DOI:10.1039/b212696f

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Dispersed fluorescence spectra of jet-cooled benzophenone
ketyl radical: Assignment of the low-frequency vibrational modes
Satoshi Hamatani,a Kazuhide Tsuji,a Akio Kawaiab and Kazuhiko Shibuya*a
a
Department of Chemistry, Graduate School of Science and Engineering, Tokyo Institute of
Technology, 2-12-1 Ohokayama, Meguro, Tokyo 152-8551, Japan
PRESTO, Japan Science and Technology Corporation, Kawaguchi, Saitama 332-0012, Japan
b
Received 6th January 2003, Accepted 14th February 2003
First published as an Advance Article on the web 3rd March 2003
We measured the laser-induced fluorescence (LIF) and dispersed fluorescence (DF) spectra of jet-cooled
benzophenone ketyl radical (BPK), which was generated by the 248 nm photolysis of a-phenyl benzoin or
benzhydrol. The several single vibronic level (SVL) DF spectra of BPK were obtained to analyze the low-
frequency vibrational modes. We identified three low-frequency vibrations of 47, 74, and 98 cmꢀ1 in the ground
state, which are assigned to the out-of-phase torsional motion, the in-phase torsional motion and Ph–C–Ph
bending motion, respectively, with the aid of the density functional theory (DFT) calculation. The
corresponding vibrational frequencies are 60, 65 and 84 cmꢀ1, respectively, in the excited state. The geometries
of BPK in the ground and excited states are discussed based on the experimental results, ab initio calculations,
and one-dimensional Franck–Condon simulation.
reaction between BP and 1,4-cyclohexadiene in the supersonic
Introduction
free jet.25 These observed spectra were not sharp enough to
resolve the vibronic structure of BPK because of the conges-
tion of low-frequency van der Waals modes of BPK-1,4-cyclo-
hexadiene clusters. Kawai et al.26 have also investigated
photoreaction of BP in various BP/solvent molecule clusters
and observed emissions of BPK and exciplexes. Recently,
Wada et al. produced the jet-cooled BPK by photolysis of a-
phenyl benzoin and obtained the vibrationally resolved struc-
tures in the laser-induced fluorescence (LIF) and dispersed
fluorescence (DF) spectra for the first time.27 A few low-
frequency vibrations in the first excited state were observed
and assigned on the basis of the vibrational assignments of
BP.28–32 Only one low-frequency vibration was observed in
the ground state due to the limitation of their low spectral
resolution. There is little information about the geometries of
BPK in the ground and excited states; whether the twist angle
between two phenyl rings upon the excitation becomes large or
small?
In this work, we measured several single vibronic level (SVL)
DF spectra of BPK with higher spectral resolution and found
in total three low-frequency vibrations in the ground state,
which are significantly important in the assignment of vibra-
tions in the excited state. The vibrational frequencies of BPK
in the ground state are calculated by means of the DFT
method. Those low-frequency vibrations in the ground and
excited states are assigned by comparison with those of the
DFT calculation. The geometrical change between the ground
and excited states is discussed with the aid of an ab initio
calculation.
Benzophenone ketyl (BPK) radical is an important and
well-known intermediate generated in the photoreduction of
benzophenone (BP). After photoexcitation, BP in the electro-
nically-excited singlet state rapidly undergoes intersystem
crossing with a unity quantum yield, and BP in the lowest tri-
plet state (3np*) abstracts a hydrogen atom from hydrogen
donor molecule, which can be alkane, alkene, alcohol, or
amine, to yield BPK. Many studies on BPK have been carried
out through absorption and emission methods to elucidate the
excited state dynamics and electronic structure in the con-
densed phase.1–22 Flexible molecules such as BPK may be
characterized by large-amplitude low-frequency vibrational
motions. The hyperfine coupling constant derived from the
ESR spectrum of BPK strongly depends on the solvent
employed, which is understood in terms of the flexible internal
motions of OH and two phenyl rings and the conformational
change by the solvents with different dielectric constants.
Recently, Kawai et al. have revealed that the conformation
is also an important factor to control the complex formation
reaction of BPK with amines.23 However, little is known about
the equilibrium orientation of the two phenyl rings along the
torsional coordinate and the frequencies of the low-frequency
torsional vibrations in the ground and excited states. The equi-
librium orientation is controlled by the conjugated p inter-
actions in the phenyl–carbon–phenyl skeleton and the steric
repulsions between ortho-hydrogen atoms belonging to differ-
ent rings and between the hydrogen atom of OH and a phenyl
ring. The overall geometry including the central carbon, OH,
and two phenyl rings depends on the electronic state. The geo-
metry change upon the photo-excitation is richer in diversity in
these flexible molecules than in rigid molecules like benzene.
Supersonic-jet spectroscopy is one of the most powerful
means for studying such low-frequency vibrations of OH and
two phenyl rings. Matsushita et al. studied the hydrogen
abstraction reaction of BP in the gas phase.24 In their subse-
quent work, they reported the fluorescence excitation and dis-
persed emission spectra of BPK generated by the intracluster
Experiment
The experimental setup is essentially the same as described in
detail elsewhere.27,33 a-Phenyl benzoin and benzhydrol (Tokyo
Kasei, EP grade) are used as parent molecules to generate BPK
by photolysis. The Ne carrier gas containing the sample vapor-
ized at ca. 420 K was expanded into a vacuum chamber
through a 400 mm diameter orifice of a pulsed valve (Parker
1370
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DOI: 10.1039/b212696f

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Hannifin, General Valve Ser. 9) operated at 10 Hz. A KrF
excimer laser (Lambda Physik, COMPex 102) was collimated
with a 1000 mm focal length lens and used to photolyze the
sample just after the nozzle. A XeCl excimer laser (Lambda
Physik, COMPex 102) pumped dye laser (Lambda Physik,
SCANMATE) was collimated with another 1000 mm focal
length lens and crossed the supersonic jet beam at 10 mm
downstream from the orifice to probe the jet-cooled photolysis
products by the LIF method. The wavenumbers in the LIF
spectra were calibrated by the opto-galvanic lines of Ne
recorded simultaneously. The LIF signals were measured with
a photomultiplier (Hamamatsu Photonics, R-928) and aver-
aged by a boxcar integrator (Stanford Research Systems,
SR-250). A monochromator (JY, 500M, 1800 gr/mm) was
used for the DF measurements.
a-Phenyl benzoin was synthesized as described in detail else-
where.34 Phenylmagnesium bromide which was prepared by
mixing bromobenzene, magnesium, and iodine was added to
benzil dissolved in anhydrous tetrahydrofuran (THF) solution
at 245 K. The product was separated through a column and
purified by recrystallization in appropriate solvents. The pro-
duction of a-phenyl benzoin was confirmed by the NMR and
IR spectra. a-Phenyl benzoin-d was prepared by deuteration
of the hydroxyl group of a-phenyl benzoin with deuterium
oxide in THF solution. The reagents used in the synthesis were
purchased from Aldrich and Kanto Chemicals.
The MO calculations were performed for the ground and
excited states of BPK using a Gaussian 98 program.35 The
geometries of the ground and excited states were optimized
at the UB3LYP/6-31G(d,p) level of theory, and at the
UCIS/6-31G(d) and 6-31G(d,p) levels, respectively. The vibra-
tional calculations of BPK in the ground state were performed
at the UB3LYP/6-31G(d,p) and 6-311+G(d,p) levels.
Fig. 1 LIF spectra of jet-cooled BPK generated by photolysis of (a)
a-phenyl benzoin and (b) benzhydrol. The symbols of a, b and g denote
the out-of-phase torsional, in-phase torsional and Ph–C–Ph bending
modes, respectively.
main progression (bn0) with an interval of about 65 cmꢀ1 starts
from the 000 band. The other progressions (bn0 g01 and b0n g20)
with the 65 cmꢀ1 interꢀva1l also start from the 18 535 cmꢀ1 band
(g10) and the 18 619 cm band (g02), respectively. The g10 band is
blue-shifted by 84 cmꢀ1 from the 000 band. Another weak pro-
gression starts from the 18 511 cmꢀ1 band (a01), which is blue-
shifted by 60 cmꢀ1 from the 000 band. Three vibrational modes
of 60, 65, and 84 cmꢀ1 make a series of progressions in the
D1–D0 transition of BPK. On the basis of the spectral similar-
ity observed in the LIF spectra of BP28–30 and BPK, the vibra-
tions of 65 and 84 cmꢀ1 have been assigned to the in-phase and
out-of-phase torsional motions, respectively.27 Fig. 2 shows
Results and discussion
LIF spectra
Fig. 1a shows the LIF spectrum of jet-cooled BPK prepared by
the photolysis of a-phenyl benzoin (a-PB), which coincides
with a previously reported one.27 Fig. 1b also shows the LIF
spectrum of jet-cooled BPK prepared by photolysis of benzhy-
drol (BH). It is confirmed that the fluorescent chemical species
is BPK because the same species is generated by the photolysis
of a-PB or BH.
The absorption of the diphenylmethyl radical36 does not
occur in this spectral region because the 000 band of the diphe-
nylmethyl radical prepared by the photolysis of BH is located
at 19 369 cmꢀ1. The 18 451 cmꢀ1 band is concluded to be the 000
band of the D1–D0 transition of BPK. Several progressions
were observed on the higher energy side of the 000 band. The
Fig. 2 (a) Representation of BPK with the position numbers of car-
bon atoms. Two phenyl rings (Ph and Ph0) rotate by y and y0 around
C1–C2 and C1–C02 bonds, respectively, from a hypothetical geometry
that the Ph and Ph0 rings and the C1 atom are on a plane. The Ph0 ring
is defined to be located on the hydrogen atom side on the OH group.
Two arrows indicate the positive rotational direction of y and y0. (b)
Two torsional motions. The in-phase torsional motion corresponds
to conrotatory twisting motion (left), while the out-of-phase torsional
motion corresponds to disrotatory twisting (right). The signs of ‘‘+’’
and ‘‘ꢀ’’ indicate the directions of the phenyl ring motions.
Scheme 1
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these torsional modes of BPK. The in-phase torsional motion
is a conrotatory twisting motion of the two phenyl rings along
the C–C bonds between a center carbon atom and phenyl
rings, while the out-of-phase torsional is another disrotatory
twisting motion.
Dispersed fluorescence (DF) spectra
Wada et al.27 reported the DF spectrum (ca. 40 cmꢀ1 resolu-
tion) obtained by the 000 band excitation of BPK, which
showed only one progression with the vibrational interval of
about 74 cmꢀ1. The 74 cmꢀ1 vibration was assigned to the
in-phase torsional mode. In order to study the low-frequency
vibrations in detail, we measured several SVL-DF spectra of
BPK with a higher resolution of 8 cmꢀ1
.
Fig. 3a shows the DF spectrum obtained by the 000 band
excitation. The spectrum is characterized by three progres-
sions with a vibrational interval of ca. 74 cmꢀ1. The primary
progression starts from the excitation wavenumber, as
reported previously.27 The progression is recognized up to
six quanta with a maximum at two quanta. A peak located
at 47 cmꢀ1 from the excitation wavenumber was observed
for the first time. The second progression starting from the
47 cmꢀ1 band is also recognized. Another progression starts
at 172 cmꢀ1 from the excitation wavenumber. The third pro-
gression seems to start from the position of 98 cmꢀ1, which
is indicated by a dotted line, though the 98 cmꢀ1 peak is
negligibly weak in Fig. 3a. The reason why we set the posi-
tion of 98 cmꢀ1 for the third progression will be discussed
later.
Fig. 3b shows the SVꢀL1-DF spectrum obtained by the 18 516
cmꢀ1 band (000 + 65 cm band, b10) excitation. A progression
with the 74 cmꢀ1 interval starts from the excitation wavenum-
ber. The progression is recognized up to nine quanta with an
intensity minimum at three quanta. The Franck-Condon pat-
tern is different from that observed in the DF spectrum
obtained by the 000 band excitation. These facts indicate that
the vibration of 65 cmꢀ1 in the excited state corresponds to
that of 74 cmꢀ1 in the ground state. On the basis of the
Franck-Condon analysis, this correspondence will be discussed
later. Another weak 74 cmꢀ1 progression starts at 98 cmꢀ1
from the excitation wavenumber, though the 98 cmꢀ1 band
has negligibly weak intensity.
Fig. 3c shows the SVL-DF spectrum obtained by the 18 535
cmꢀ1 band (000 + 84 cmꢀ1 band, g10) excitation. The intense
peak obviously appears at 98 cmꢀ1 from the excitation wave-
number, which corresponds to the negligibly weak 98 cmꢀ1
bands in Figs. 3a and 3b. The 74 cmꢀ1 progression starting
from the 98 cmꢀ1 band in Fig. 3c is similar to those starting
from the excitation wavenumbers in Figs. 3a and 3b. Another
weak 74 cmꢀ1 progression starting from the 196 cmꢀ1 band,
the lower state of which corresponds to two quanta of the 98
cmꢀ1 vibration, is also recognized in Fig. 3c. These facts indi-
cate that the 84 cmꢀ1 vibrational mode in the excited state cor-
responds to that of 98 cmꢀ1 in the ground state. Now we are
sure that there is a vibrational level at 98 cmꢀ1 in the ground
state of BPK, which supports our vibrational assignment of
the 98 cmꢀ1 bands made in Figs. 3a and 3b. Fig. 3c also shows
a relatively weak 74 cmꢀ1 progression starting from the excita-
tion wavenumber, which is quite different in an intensity pat-
tern from the corresponding progression observed in Fig. 3a.
This point will be discussed later.
Fig. 3 Dispersed fluorescence spectra. The signals at the excitation
wavenumbers are very intense due to laser scattering. (a) The 000 band
excitation. (b) The 000 + 65 cmꢀ1 band corresponding to the b10 excita-
tion. (c) The 000 + 84 cmꢀ1 band corresponding to the g10 excitation.
cmꢀ1 vibrations in the excited state correspond to the 74 and
98 cmꢀ1 vibrations in the ground state, respectively.
In order to assign these vibrational modes, the vibrational
frequencies in the ground state were calculated by the DFT
method. Three vibrational modes were calculated to have
low frequencies below 100 cmꢀ1. The values obtained for the
UB3LYP/6-311+G(d,p) level are 48.4, 72.2, and 98.6 cmꢀ1
Three low-frequency vibrational modes
As described above, we found three low-frequency vibrations
of 47, 74, and 98 cmꢀ1 in the ground state. From the analysis
of the SVL-DF spectra, it was also found that the 65 and 84
1372
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Table 1 Vibrational modes and frequencies (cmꢀ1) of BPK
D0
D1
Calc.a
Exp.
Approx.
description
Mode (symbol in text)
Exp.
47
6-31G(d,p)
50.0
6-311+G(d,p)
48.4
Out-of-phase torsion (a)
59.8
In-phase torsion (b)
74
98
72.4
97.6
72.2
98.6
65.4
84.3
Ph–C–Ph bend (g)
a
Scaled by 0.95 and 0.99 for the UB3LYP/6-31G(d,p) and 6-311+G(d,p) levels of theory, respectively.
corresponding to the out-of-phase torsion, the in-phase tor-
sion, and the in-plane Ph–C–Ph bend, respectively, which are
listed in Table 1. Two sets of frequencies calculated on the
UB3LYP/6-31G(d,p) and UB3LYP/6-311+G(d,p) levels of
theory are essentially the same. The experimental frequency
of 74 cmꢀ1, which was previously assigned to the in-phase
torsion, is close to the calculated value of 72.2 cmꢀ1. The
DF spectrum obtained by the 000 band excitation shows a long
main progression with the 74 cmꢀ1 interval, which suggests
that the D1–D0 transition of BPK brings the structural
change along the coordinate of the in-phase torsional motion.
The other two experimental frequencies of 47 and 98 cmꢀ1
coincide well with the calculated values of 48.4 and 98.6
cmꢀ1, respectively. On the basis of the good agreement
between the measured and calculated values, the vibrational
modes of 47 and 98 cmꢀ1 are assigned to the out-of-phase tor-
sion and the Ph–C–Ph bend, respectively. In the previous
report,27 the vibrational energy of the out-of-phase torsion
of BPK was estimated to be higher than that of the in-phase
torsion because of steric hindrance. However, the present
DFT calculation suggests that the frequencies of the out-of-
phase and in-phase torsions are the first and second lowest,
respectively, and the third lowest vibration is the Ph–C–Ph
bend.
Equilibrium geometries
The in-phase torsional motion of 65 cmꢀ1 makes the main long
progression in the LIF spectrum. This observation implies that
the structural change between the ground and excited states
takes place along the coordinate of the in-phase torsional
motion. In order to confirm this interpretation, we calculated
the geometries of BPK in the ground and excited states.
The geometries of BPK were optimized using the UB3LYP/
6-31G(d,p) level in the ground state, and the UCIS/6-31G(d)
and UCIS/6-31G(d,p) levels in the excited state, respectively.
Fig. 4 shows these optimized geometries with geometry para-
meters. The bonds connected to the center carbon atom, C1 ,
As described above, the 65 and 84 cmꢀ1 vibrations in the
excited state correspond to those of 74 and 98 cmꢀ1 in the
ground state, respectively. Thus, the 65 and 84 cmꢀ1 vibrations
in the excited state are assigned to the in-phase torsion and the
Ph–C–Ph bend, respectively. Table 1 summarizes the vibra-
tional modes and frequencies in the ground and excited states
determined in the present work. Wada et al.27 assigned the 84
cmꢀ1 vibration in the excited state as the out-of-phase torsion,
which does not agree with our assignment. They carried out
the vibrational analysis under the assumption that the geome-
tries and normal modes of BPK and BP are similar. It might be
of note that the vibration assigned to the out-of-phase torsion
of BP could be the Ph–C–Ph bend.37
We also produced BPK-d with a deuterated hydroxy group
and measured the LIF spectrum, which coincides with a pre-
viously reported one.27 The observed BPK-d frequencies of
59.4, 65.0 and 84.0 cmꢀ1 in the excited state are essentially
the same as the corresponding BPK-h frequencies of 59.8,
65.4 and 84.3 cmꢀ1. According to our DFT calculation, three
low-frequencies of BPK-h in the ground state (48.4, 72.2 and
98.6 cmꢀ1) correspond to the 48.4, 72.3 and 98.4 cmꢀ1 frequen-
cies of BPK-d, respectively. It implies that three low-frequen-
cies are not affected by the deuteration of the OH group.
These results also support that three low-frequency vibrations
of BPK are due to the out-of-phase torsion, the in-phase
torsion, and the Ph–C–Ph bend.
Fig. 4 Optimized geometries of BPK (a) in the ground D0 state
(UB3LYP/6-31G(d,p)) and (b) in the excited D1 state (UCIS/
6-31G(d) and 6-31G(d,p)). The bonds connected to C1 are almost
sp2-hybridized and the four atoms (C1 , C2 , C02 , O) are in a coplanar
conformation. This plane is called ‘‘C2–C02–O plane’’. Two phenyl
rings (Ph a0nd Ph0) are twisted to the y and y0angles, respectively, from
˚
the ‘‘C2–C 2–O plane’’. Bond length (A) and bond angle (degrees).
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of BPK are almost sp2-hybridized and the four atoms (C1 , C2 ,
C02 , O) are in a coplanar conformation (C2–C02–O plane). The
twist angles, y and y0, of two phenyl rings (Ph and Ph0) from
the C2–C02–O plane are not equal, because of the different
steric repulsions of a hydrogen atom on the OH group against
Ph and Ph0. In the ground state, the twist angles y0 (for the Ph0
ring on the hydrogen atom side of OH) and y (for the Ph ring
on the other side) are calculated to be 31ꢁ and 21ꢁ, respectively.
Upon the electronic excitation to the D1 state, the y0 and y
angles become 40–42ꢁ and 29–31ꢁ, respectively, which are lar-
ger by 8–11ꢁ than the corresponding angles in the ground state.
Wada et al.27 estimated the angle change between the ground
and excited states by means of a one-dimensional Franck-
Condon simulation for the in-phase torsional mode. One-
dimensional oscillators of 74 and 65 cmꢀ1 were used for the
ground and excited states, respectively. Assuming that the
angle changes of Dy and Dy0 are the same, the observed excita-
tion spectrum of BPK was reproduced with Dy (ꢂDy0) ffi 8ꢁ.
This angle change is a little bit smaller than the Dy value
(8–11ꢁ) obtained by our ab initio calculation, though they
might be essentially the same by considering that the compar-
ison is based on a simple excited state calculation and a one-
dimensional Franck-Condon simulation. The one-dimensional
simulation only gives the magnitude of the angle change but
not the direction of the angle change. In our ab initio calcula-
tion, it turns out that the interplanar angles increase with the
excitation. This fact is unusual as the p–p* excitation cases.
In biphenyl, two phenyl rings are twisted to an interplanar
angle of ca. 44ꢁ in the ground state, but adopt a coplanar con-
formation upon the transition to the first excited state.38,39 The
equilibrium orientation of two rings would be determined by a
subtle balance between the steric repulsion of ortho-hydrogen
atoms and the strength in p-electron conjugation covering
the molecule. It is interpreted that the repulsion is a major fac-
tor to determine the nonplanar geometry in the ground state,
while upon the excitation the increased strength in the p-elec-
tron conjugation makes two phenyl rings to be planar. Accord-
ing to ab initio calculation of 3-aminobiphenyl,40 the C–C
bond length and theꢁdihedral angle between the phenyl rings
Fig. 5 Observed (black bars) and calculated (white bars) Franck-
Condon factors for the in-phase torsional mode in SVL-DF spectra
obtained by the excitations of (a) the 000 band, (b) the b01 band
(000 + 65 cmꢀ1) and (c) the b02 band (000 + 130 cmꢀ1). Gray bars repre-
sent the measured signals involving laser scattering.
respectively. The calculated intensity patterns, which are
reproduced with Dy (ꢂDy0) ffi 8ꢁ, are consistent with the
observed ones. It is confirmed that the 65 cmꢀ1 vibration in
the excited state corresponds to the 74 cmꢀ1 vibration in the
ground state, and the 65 and 130 cmꢀ1 bands are the transi-
tions to first and second excited levels for the in-phase tor-
sional mode.
According to the ab initio calculation, the <(C5C1C05) angle
is 131ꢁ and 120ꢁ in the ground and excited states, respectively.
The <(C5C1C05) angle is not equal to the <(C2C1C02) angle
because three bonds of the carbon atom, C02 , in the excited
state are almost coplanar but slightly pyramidal. In contrast
with the twist angle, the <(C5C1C05) angle is smaller in the
excited state than in the ground state. The change in the
<(C5C1C05) angle indicates that the Ph–C–Ph bending mode
(g) is active in the emission and excitation spectra, which coin-
cides with the observation shown in Figs. 1 and 3.
The Ph–C–Ph bending mode has relatively strong intensity
in the LIF spectrum as shown in Fig. 1. On the other hand, this
g mode does not have appreciable intensity in the DF spectrum
obtained by the 000 band excitation. The LIF spectrum was
measured under the unsaturated conditions of laser power.
The mirror image was not observed on the Ph–C–Ph bending
mode in the excitation and emission spectra. The vibrational
normal coordinates in the excited state are thought to be differ-
ent from those in the ground state, which is described as
Duschinsky rotatioꢀn1. In the SVL-DF spectrum obtained by
the g10 (000 + 84 cm band) excitation, the progressions due
to the in-phase torsional mode appear together with the Ph–
C–Ph bending mode, which makes the progression intensity
pattern different from that in the DF spectrum obtained by
the 000 band excitation. If a mode mixing between the in-phase
torsion and the Ph–C–Ph bend does not occur, then the pro-
gression of the in-phase torsion shown in this spectrum has
˚
are 1.492 A and 45.8 , respectively, in the ground state. Upon
˚
excitation the bond length decreases to 1.412 A and the dihe-
dral angle decreases to 5.4ꢁ.
In BPK, the bond lengths between the center carbon and
two phenyl rings (the C1–C2 and C1–C02 lengths) decrease
˚
˚
˚
˚
(from 1.439 A to 1.417 A, and from 1.446 A to 1.407 A, respec-
tively) upon excitation, as shown in Fig. 5. On the contrary,
the twist angles between two phenyl rings (y and y0) increase
(from 21 to 29–31ꢁ, and from 31 to 40–42ꢁ, respectively) upon
excitation. In comparison with the biphenyl molecules, the
BPK radical has a carbon atom existing between two phenyl
rings. The main contribution in the D1–D0 transition of BPK
is found to be composed of the LUMO SOMO transition
(UCIS/6-31G(d,p), 90%). The node of the LUMO exists on
the center carbon C1 and two phenyl rings are more twisted
upon excitation. The p-orbitals on C2 and C02 have opposite
signs and tend to induce hyperconjugation accompanied by
more twisting two phenyl rings. As a result of the hyperconju-
gation, the distance between the two phenyl rings becomes clo-
ser and the C1–C2 and C1–C02 bond lengths become shorter.
The predictions of the ab initio calculation coincide with our
observation.
Vibrational intensity patterns
The Franck-Condon factors in the SVL-DF spectra obtained
by the 000, b01 (000 + 65 cmꢀ1) and b02 (000 + 130 cmꢀ1) band exci-
tations were estimated by means of a one-dimensional Franck-
Condon simulation for the in-phase torsional mode. The
results are shown in Fig. 5. One-dimensional oscillators of 74
and 65 cmꢀ1 were used for the ground and excited states,
1374
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18 L. J. Johnston, D. J. Lougnot and J. C. Scaiano, Chem. Phys.
Lett., 1986, 129, 205.
19 L. J. Johnston, D. J. Lougnot, V. Wintgens and J. C. Scaiano,
J. Am. Chem. Soc., 1988, 110, 518.
20 R. W. Redmond and J. C. Scaiano, Chem. Phys. Lett., 1990,
166, 20.
21 R. W. Redmond, J. C. Scaiano and L. J. Johnston, J. Am. Chem.
Soc., 1990, 112, 398.
22 Y. Kajii, H. Itabashi, K. Shibuya and K. Obi, J. Phys. Chem.,
1992, 96, 7244.
23 A. Kawai, M. Hirakawa, T. Abe, K. Obi and K. Shibuya, J. Phys.
Chem. A, 2001, 105, 9628.
the same intensity pattern as that in the DF spectrum obtained
by the 000 band excitation. This progression, however, has dif-
ferent intensity pattern from that in the DF spectrum obtained
by the 000 band excitation, which is similar to that in the DF
spectrum obtained by the 65 cmꢀ1 band excitation. In addition
to the Duschinsky rotation, mode mixing between the in-phase
torsion and the Ph–C–Ph bend is likely to exist in the excited
state, although it is difficult to analyze it quantitatively at the
present moment.
24 Y. Matsushita, Y. Kajii and K. Obi, J. Phys. Chem., 1992, 96,
4455.
25 Y. Matsushita, Y. Kajii and K. Obi, J. Phys. Chem., 1992, 96,
6566.
Acknowledgements
We would like to thank Professor K. Obi (Japan Women’s
University), Dr Y. Matsushita (Tokyo Institute of Technol-
ogy), and Dr S. Wada (Hiroshima University) for their
valuable discussions. This work was partly supported by a
Grant-in-aid for Scientific Research on Priority Areas (B) of
the Ministry of Education, Science, Sports and Culture (Con-
tract No. 13127202).
26 A. Kawai, S. Noguchi and K. Obi, Chem. Phys. Lett., 2002,
362, 397.
27 S. Wada, Y. Matsushita and K. Obi, J. Phys. Chem. A, 1997, 101,
2423.
28 H. Abe, S. Kamei, N. Mikami and M. Ito, Chem. Phys. Lett.,
1984, 109, 217.
29 S. Kamei, T. Sato, N. Mikami and M. Ito, J. Phys. Chem., 1986,
90, 5615.
30 N. Ohmori, T. Suzuki and M. Ito, J. Phys. Chem., 1988, 92, 1086.
31 K. W. Holtzclaw and D. W. Pratt, J. Chem. Phys., 1986, 84, 4713.
32 J. H. Frederick, E. J. Heller, J. L. Ozment and D. W. Pratt,
J. Chem. Phys., 1988, 88, 2169.
33 S. Hamatani, K. Tsuji, A. Kawai and K. Shibuya, Chem. Phys.
Lett., 2002, 360, 466.
References
1
2
B. J. McClelland, Trans. Faraday Soc., 1961, 57, 1458.
G. Porter and F. Wilkinson, Trans. Faraday Soc., 1961, 57,
1686.
34 T. Ohwada and K. Shudo, J. Am. Chem. Soc., 1988, 110, 1862.
35 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A.
Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr.,
R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D.
Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V.
Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.
Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala,
Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K.
Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B.
Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.
Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham,
C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe,
P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres,
C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople,
GAUSSIAN 98, Revision A.11, Gaussian, Pittsburgh, PA, 1998.
36 T.-Y. D. Lin, C. P. Damo, J. R. Dunlop and T. A. Miller, Chem.
Phys. Lett., 1990, 168, 349.
37 D. V. Vachev and J. H. Frederick, Chem. Phys. Lett., 1996,
249, 476.
38 Y. Takei, T. Yamaguchi, Y. Osamura, K. Fuke and K. Kaya,
J. Phys. Chem., 1988, 92, 577.
39 H.-S. Im and E. R. Bernstein, J. Chem. Phys., 1988, 88, 7337.
40 K. Pirowska, A. Parusel, J. Najbar, P. Kolek and P. Gajdek,
Chem. Phys. Lett., 1999, 310, 537.
3
4
5
A. Beckett and G. Porter, Trans. Faraday Soc., 1963, 59, 2038.
T. Shida and W. H. Hamill, J. Am. Chem. Soc., 1966, 88, 3683.
T. Shida, S. Iwata and M. Imamura, J. Phys. Chem., 1974,
78, 741.
6
7
8
H. Murai, M. Jinguji and K. Obi, J. Phys. Chem., 1976, 80, 429.
K. Obi and H. Yamaguchi, Chem. Phys. Lett., 1978, 54, 448.
M. Hoshino, S. Arai, M. Imamura, K. Ikehara and Y. Hama,
J. Phys. Chem., 1980, 84, 2576.
9
R. Mehnert, O. Brede and W. Helmstreit, Z. Chem., 1975, 15, 448.
10 M. R. Topp, Chem. Phys. Lett., 1976, 39, 423.
11 K. Razinaqvi and U. P. Wild, Chem. Phys. Lett., 1976, 41, 570.
12 J. L. Marignier and B. Hickel, Chem. Phys. Lett., 1982, 86, 95.
13 H. Hiratsuka, T. Yamazaki, M. Takahashi, T. Hikida and Y.
Mori, Chem. Phys. Lett., 1983, 101, 341.
14 T. Minegishi, H. Hiratsuka, Y. Tanizaki and Y. Mori, Bull. Chem.
Soc. Jpn., 1984, 57, 162.
15 H. Hiratsuka, T. Yamazaki, Y. Maekawa, T. Hikida and Y.
Mori, J. Phys. Chem., 1986, 90, 774.
16 S. Baral-Tosh, S. K. Chattopadhyay and P. K. Das, J. Phys.
Chem., 1984, 88, 1404.
17 V. Nagarajan and R. W. Fessenden, Chem. Phys. Lett., 1984,
112, 207.
Phys. Chem. Chem. Phys., 2003, 5, 1370–1375
1375