- Email: [email protected]
Optical dephasing and electron-phonon interaction in β-carotene solutions
a __
-_ BB
ELSEYIER
JOURNAL
OF
LUMINESCENCE Journal of Luminescence 76&77 (1998) 604-607
Optical dephasing and electron-phonon in p-carotene solutions
interaction
Abstract Fluorescence spectra of p-carotene in are compared with a model calculation. weighted by coupling constant, p(r~) x energy E,, = 210cm-’ and temperature
ethanol measured in a temperature range from liquid to solid phases of solvent assuming a linear electronPphonon interaction with a phonon density of states cae -“’ “+,. We obtain a peak phonon energy CO,,= 28 cm I, a lattice relaxation dependences of amplitude of the energy modulation and inhomogeneous width.
The ratio ELR/wp z 8 shows that the electron -phonon tem. (‘ 1998 Elsevier Science B.V. All rights reserved. Kq~uwds:
Optical dephasing; Electron--phonon
interaction
interaction; p-carotene
I. Introduction The optical dephasing of dye molecules in solution has been extensively investigated by various experimental methods and it is shown that the dephasing occurs on the time scale of femtoseconds. The energy modulation of the electronic states, which causes the dephasing, has been analyzed by models which take into account non-Markovian nature of the energy modulation [l-5]. However, reports on temperature dependence of the energy modulation are limited [6,7]. In this paper, fluorescence spectra of p-carotene in ethanol measured in a temperature range 16-240K are compared with a model calculation assuming a linear electronphonon coupling between the dye and surrounding
author. *Corresponding [email protected].
Fax:
81 117179304:
is near the strong coupling regime in this sys-
e-mail:
00X-2313/98/$19.00 (’ 1998 Elsevier Science B.V. All rights reserved PII SOO22-23 13(97)00258-5
solvent molecules. In the case of b-carotene molecule in solution. the decay time of the fluorescence from the first optically allowed S2 excited state is about 0.2~s [S,S]. Due to the short decay time, stationary fluorescence spectrum of p-carotene shifts in energy when the excitation photon energy is varied even in the liquid phase of solvent as a result of selective excitation within the inhomogeneously distributed transition energy [7]. Thus, b-carotene in solution is a suitable system for investigation of the energy modulation and inhomogeneous broadening in solutions by measurements of stationary fluorescence spectra.
2. Experimental The p-carotene is dissolved in ethanol with a concentration of about IO-” M. The sample in a glass cell is cooled in a cryostat by a continuous
J. Wutanahe et al.
Jourr~ul of Luminescmcc
flow of nitrogen or helium gas. In the preparation of sample in solid phase of solvent, the cooling rate of the sample is about 5 K/min. For measurements of emission spectra of p-carotene, a cw-Ar ion laser or a dye laser pumped by a nitrogen laser (3 Hz) is employed as an exciting source. The excitation energy is varied in the spectral range from the peak to the low-energy side of vibronic C-O absorption band in the first optically allowed So-S2 transition so as not to excite O-l or O-2 vibronic bands. The emitted light from the sample is introduced to a double monochromator and detected by a photomultiplier. Its output is analyzed by a photon counter or a digital oscilloscope.
3. Model We assume that there are only two relevant electronic states in a dye molecule and that the electronic states are coupled linearly with normal modes of surrounding atoms. These modes are often called as phonon mode even in disordered system [9]. The Hamiltonians of the system in the subspace of the ground and excited electronic states are given by H, = &o,h:hk, H, = H, + i: + V. where I/ = &(u~x~(~; + hk). Here, h: and bl, are the creation and annihilation operators for the lith phonon mode with energy (rjk, respectively, CQis the linear electron-phonon coupling constant and c is the electronic excitation energy. We consider the slow modulation regime where the modulation amplitude D of the transition enD = Vs’m = v~‘&x:01~(2nk + I) ergy. where nl, = 1, [exp(cc,lt’li,sT) - 11. is much larger than the rate of energy modulation. The slow modulation nature of the energy modulation in this system has been discussed in several reports [4,5,7]. Then the fluorescence spectrum is given by [lo] I 1,(V,,. ffjz) = to:A,(c!,,)
eC2:“F(tu,,
tu2; t)dt,
(1)
i I,, where PJ, and ~1)~are the excitation and emitted photon energies, respectively, A,(tu,) is the absorption spectrum, A,.(c!,,) x 10, exp[ - ((0, - 1:)‘i2D~],
(2)
76& 77 (199X) 604
605
607
and F(to,. ~1~; t) is the transient trum given by
fluorescence
spec-
F(tu,.toz: t) x (l;W’ (t)) exp[ - (~0~ - E(t))‘.‘W(t)‘].
(3)
In the time integral of Eq. (l), we set to 2 (dephasing time) in order to obtain only a broad fluorescence component of emission spectrum. The peak energy E(t) and the width l+‘(t) of the transient fluorescence spectrum in Eq. (3) are expressed using lattice relaxation energy EI.K = &~f(fj~ and spectral intensity .I(c~I) of V(t) which is defined by J(U)) = &JL , e”‘“( V(t)V(O)) dt [lo]. Taking into account inhomogeneous broadening, the spectra of I,:(to,, (rj2) and A,(cgJ,) are convoluted over the inhomogeneous distribution of the transition energy C, where we assume a Gaussian distribution with width (HWHM) of IV,.
4. Results and discussion We show the typical fluorescence spectra of pcarotene in ethanol at 100 K in Fig. 1b Fig. 1d for three different excitation energies which are indicated by arrows and the absorption spectrum in Fig. la. The fluorescence spectra show a clear structure due to O--O and 0 -1 vibronic transitions. The three sharp lines. located at 1004. 1158 and 1525cm. ’ from the laser line, are the first-order Raman scattering lines of v3. \lZ and Y, vibrational modes of p-carotene. respectively. The peak energy of 0-O fluorescence band shifts when the excitation energy is varied from the peak to the low-energy side of the O-O absorption band. The fluorescence width (HWHM) of 0 -0 band slightly \,aries from 300 to 230 cm- ’ as decreasing the excitation energy and it is smaller than that of absorption. 340 cm ‘. The shift and the fact that the fluorescence width is smaller than the absorption width are considered as a result of the selective excitation by an excitation light within the inhomogeneously distributed transition energy. The excitation energy dependence of Huorescence spectrum measured in a temperature range 16-240 K shows almost the same feature as that of spectra at lOOK. In Fig. 2, we show fluorescence
J. Watuncrhe et 01. I Journul ~f’Luminescence
606
u
,I 19000
18000
20000
21000
Wavenumber ( cm-‘) Fig. I. (a) Absorption spectrum of p-carotene in ethanol at IOOK. (b)_(d) Fluorescence spectra measured at 100 K excited by 4965 A(b). 5017 A(c) and 5 I45 A(d) lines of a cw-Ar ion laser. The arrows show the excitation laser energies. (0-O). (O-I) denote the vibrational bands in the absorption and fluorescence spectra. Solid lines are the curves of (a) absorption and (bHd) fluorescence spectra obtained by numerical calculations with parameter values discussed in the text.
. .
I
I
* .
00
18 Wavenumber
(cm-‘)
Fig. 2. Fluorescence spectra of p-carotene in ethanol for various temperatures. The arrows show the excitation laser energies. Solid lines are the curves of fluorescence spectra obtained by numerical calculations with parameter values discussed in the text.
76& 77 (1998) 604-607
spectra measured at several temperatures excited near the O-0 absorption energy. As seen in the figure, the fluorescence width gradually increases with increasing temperature. In the following. we analyze experimental results in terms of the model described in Section 3. We assume the shape of phonon density of state weighted by the electron-phonon coupling constant as /I = &JIY~~((~-, - (uk) N (~e-‘y’(9p. which was applied to analyze time-dependent fluorescence Stokes shift and optical Kerr effect measurements in liquids [3]. We calculate fluorescence and absorption spectra with fluorescence decay rate 2;* = 24 cm- ’ [S.S] and experimental values of width (Fig. 3) and peak energy of absorption spectrum. In addition, we take into account O-l fluorescence band with relative intensity ratios between I’~, 1t2 and \13 modes which are obtained from Ramanscattering lines. From the fitting of numerical calculation with observed spectra in a temperature range 16-240 K, the parameter values are determined as which are incop = 28 cm _ ’ and ELR = 210cm-‘, dependent of temperature, and D = 130 cm-’ for OK. In Fig. 1, the calculated fluorescence and absorption spectra for 100K are shown by solid curves. Here D = 180cm- ’ and W, = 260cm- ‘. The absorption spectrum and excitation energy dependence of O-O fluorescence band are well reproduced by the calculated spectra. In Fig. 2, the calculated fluorescence spectra for each temperature are shown by solid curves. Here D = 130,180. 230 and 270cm-‘, W, = 210,260, 400 and 530cm-’ for 16, 100, 177 and 240 K. respectively. The calculated spectra reproduce well the broadening of 0-O fluorescence band with increasing temperature. The temperature dependences of the modulation amplitude D and the inhomogeneous width W, are shown in Fig. 3. The inhomogeneous width increases rapidly with increasing temperature above the freezing point of ethanol (159K). On the other hand, the modulation amplitude gradually increases with temperature. Since the temperature dependence of the fluorescence spectrum is well reproduced by the calculation assuming the temperature independent p(tu) with constant (‘J,,. it is suggested that the phonon structure of the
n n absorption width .
0 0
n
I
0
(HWHM)
I
I
100
dependencies
at low-energy
of
(K) the
Solid line is the temperature
width
References
absorption
side of the O&Oabsorption
squares) and the cnhomogeneous
I
200
Temperature Fig. 3. Temperature
i
[I-carotene solution in liquid and solid phases of solvent. Summarizing, fluorescence spectra of /I-carotene in ethanol in a temperature range from liquid to solid phases of solvent are analyzed by a linear electrons-phonon coupling model. The result shows that the electron-phonon interaction is near the strong coupling regime, which is consistent with the slow modulation nature of the energy modulation in this system. This work has been supported in part by a Grant-in-Aid for Scientific Research from The Ministry of Education. Science. Sports and Culture.
width
band (closed
[‘I
dependence of modulation
tude D. T, indicates the freezing point of ethanol.
7, =
ampli-
M.S.
Pshenichmko\.
K. Duppcn.
D.A.
Wlcrma.
Phys.
Rc\,. Lett. 74 (1995) 674.
W, (open diamonds).
III
J.Y. Bigot. M.T.
Portella.
A. Migus. C.V. Shank.
159 K.
PI
R.W. Schoenlein. C.J. Hardeen.
Phys. Ret. Lett. 66 11991) 113X
M. Cho. S.J. Rosenthal.
N.F.
Scherer. L.1). Ziegler. GR.
Fleming. .I. Chem. Phys. 96 (19921 5037.
electron--phonon interaction is essentially the same within a temperature range from liquid to solid phases of ethanol. The ratio E,Jco, 2 8 determined in the present work indicates that the electronphonon interaction is near the strong-coupling regime in this system, which is consistent with the assumption of slow modulation nature of the energy modulation. Thus, the linear electron-phonon coupling model with a large value of ELRj~op is a good approximation for describing the nonMarkovian nature of the energy modulation in
[41 .I. Sue. S. Mukamel. .I. Chem. Phys. XX (IYXXI 651. 151 .I. Watanabe. S. Kinoshita. T. Kushida. .I. Chem. Ph\\.
X7
(19X7) 4471.
161 E.T.J. Nibbering. Phgh. 93
( 1990)
[71 J. Watanabe.
( 1997) PI
K.
Duppcn.
D.A.
Wler\ma.
.I (‘hem.
5477.
H. Yano. J. Nakahara.
.I. Phyh. Sot. .lapan 66
X53.
H. Kandorl.
H. Sasahe. M. Mimuro,.l.
Am. Chem. Sot. I I6
(19941 ‘671.
191 S. Kinoshita. Y. Fujimura and
Y. Kanematsu,
In: J.H.
Ltn. ,A.A. Villaeys.
(Eds.). Advances in Multiphonon
Spectroscopy.
vol. Y. World
Scientific.
Processes Singapore,
1905. p. I.
[1()1 Y. Kayanuma.
J. Phqs. Sot. Japan 57
I IYXXI
32.
-_ BB
ELSEYIER
JOURNAL
OF
LUMINESCENCE Journal of Luminescence 76&77 (1998) 604-607
Optical dephasing and electron-phonon in p-carotene solutions
interaction
Abstract Fluorescence spectra of p-carotene in are compared with a model calculation. weighted by coupling constant, p(r~) x energy E,, = 210cm-’ and temperature
ethanol measured in a temperature range from liquid to solid phases of solvent assuming a linear electronPphonon interaction with a phonon density of states cae -“’ “+,. We obtain a peak phonon energy CO,,= 28 cm I, a lattice relaxation dependences of amplitude of the energy modulation and inhomogeneous width.
The ratio ELR/wp z 8 shows that the electron -phonon tem. (‘ 1998 Elsevier Science B.V. All rights reserved. Kq~uwds:
Optical dephasing; Electron--phonon
interaction
interaction; p-carotene
I. Introduction The optical dephasing of dye molecules in solution has been extensively investigated by various experimental methods and it is shown that the dephasing occurs on the time scale of femtoseconds. The energy modulation of the electronic states, which causes the dephasing, has been analyzed by models which take into account non-Markovian nature of the energy modulation [l-5]. However, reports on temperature dependence of the energy modulation are limited [6,7]. In this paper, fluorescence spectra of p-carotene in ethanol measured in a temperature range 16-240K are compared with a model calculation assuming a linear electronphonon coupling between the dye and surrounding
author. *Corresponding [email protected].
Fax:
81 117179304:
is near the strong coupling regime in this sys-
e-mail:
00X-2313/98/$19.00 (’ 1998 Elsevier Science B.V. All rights reserved PII SOO22-23 13(97)00258-5
solvent molecules. In the case of b-carotene molecule in solution. the decay time of the fluorescence from the first optically allowed S2 excited state is about 0.2~s [S,S]. Due to the short decay time, stationary fluorescence spectrum of p-carotene shifts in energy when the excitation photon energy is varied even in the liquid phase of solvent as a result of selective excitation within the inhomogeneously distributed transition energy [7]. Thus, b-carotene in solution is a suitable system for investigation of the energy modulation and inhomogeneous broadening in solutions by measurements of stationary fluorescence spectra.
2. Experimental The p-carotene is dissolved in ethanol with a concentration of about IO-” M. The sample in a glass cell is cooled in a cryostat by a continuous
J. Wutanahe et al.
Jourr~ul of Luminescmcc
flow of nitrogen or helium gas. In the preparation of sample in solid phase of solvent, the cooling rate of the sample is about 5 K/min. For measurements of emission spectra of p-carotene, a cw-Ar ion laser or a dye laser pumped by a nitrogen laser (3 Hz) is employed as an exciting source. The excitation energy is varied in the spectral range from the peak to the low-energy side of vibronic C-O absorption band in the first optically allowed So-S2 transition so as not to excite O-l or O-2 vibronic bands. The emitted light from the sample is introduced to a double monochromator and detected by a photomultiplier. Its output is analyzed by a photon counter or a digital oscilloscope.
3. Model We assume that there are only two relevant electronic states in a dye molecule and that the electronic states are coupled linearly with normal modes of surrounding atoms. These modes are often called as phonon mode even in disordered system [9]. The Hamiltonians of the system in the subspace of the ground and excited electronic states are given by H, = &o,h:hk, H, = H, + i: + V. where I/ = &(u~x~(~; + hk). Here, h: and bl, are the creation and annihilation operators for the lith phonon mode with energy (rjk, respectively, CQis the linear electron-phonon coupling constant and c is the electronic excitation energy. We consider the slow modulation regime where the modulation amplitude D of the transition enD = Vs’m = v~‘&x:01~(2nk + I) ergy. where nl, = 1, [exp(cc,lt’li,sT) - 11. is much larger than the rate of energy modulation. The slow modulation nature of the energy modulation in this system has been discussed in several reports [4,5,7]. Then the fluorescence spectrum is given by [lo] I 1,(V,,. ffjz) = to:A,(c!,,)
eC2:“F(tu,,
tu2; t)dt,
(1)
i I,, where PJ, and ~1)~are the excitation and emitted photon energies, respectively, A,(tu,) is the absorption spectrum, A,.(c!,,) x 10, exp[ - ((0, - 1:)‘i2D~],
(2)
76& 77 (199X) 604
605
607
and F(to,. ~1~; t) is the transient trum given by
fluorescence
spec-
F(tu,.toz: t) x (l;W’ (t)) exp[ - (~0~ - E(t))‘.‘W(t)‘].
(3)
In the time integral of Eq. (l), we set to 2 (dephasing time) in order to obtain only a broad fluorescence component of emission spectrum. The peak energy E(t) and the width l+‘(t) of the transient fluorescence spectrum in Eq. (3) are expressed using lattice relaxation energy EI.K = &~f(fj~ and spectral intensity .I(c~I) of V(t) which is defined by J(U)) = &JL , e”‘“( V(t)V(O)) dt [lo]. Taking into account inhomogeneous broadening, the spectra of I,:(to,, (rj2) and A,(cgJ,) are convoluted over the inhomogeneous distribution of the transition energy C, where we assume a Gaussian distribution with width (HWHM) of IV,.
4. Results and discussion We show the typical fluorescence spectra of pcarotene in ethanol at 100 K in Fig. 1b Fig. 1d for three different excitation energies which are indicated by arrows and the absorption spectrum in Fig. la. The fluorescence spectra show a clear structure due to O--O and 0 -1 vibronic transitions. The three sharp lines. located at 1004. 1158 and 1525cm. ’ from the laser line, are the first-order Raman scattering lines of v3. \lZ and Y, vibrational modes of p-carotene. respectively. The peak energy of 0-O fluorescence band shifts when the excitation energy is varied from the peak to the low-energy side of the O-O absorption band. The fluorescence width (HWHM) of 0 -0 band slightly \,aries from 300 to 230 cm- ’ as decreasing the excitation energy and it is smaller than that of absorption. 340 cm ‘. The shift and the fact that the fluorescence width is smaller than the absorption width are considered as a result of the selective excitation by an excitation light within the inhomogeneously distributed transition energy. The excitation energy dependence of Huorescence spectrum measured in a temperature range 16-240 K shows almost the same feature as that of spectra at lOOK. In Fig. 2, we show fluorescence
J. Watuncrhe et 01. I Journul ~f’Luminescence
606
u
,I 19000
18000
20000
21000
Wavenumber ( cm-‘) Fig. I. (a) Absorption spectrum of p-carotene in ethanol at IOOK. (b)_(d) Fluorescence spectra measured at 100 K excited by 4965 A(b). 5017 A(c) and 5 I45 A(d) lines of a cw-Ar ion laser. The arrows show the excitation laser energies. (0-O). (O-I) denote the vibrational bands in the absorption and fluorescence spectra. Solid lines are the curves of (a) absorption and (bHd) fluorescence spectra obtained by numerical calculations with parameter values discussed in the text.
. .
I
I
* .
00
18 Wavenumber
(cm-‘)
Fig. 2. Fluorescence spectra of p-carotene in ethanol for various temperatures. The arrows show the excitation laser energies. Solid lines are the curves of fluorescence spectra obtained by numerical calculations with parameter values discussed in the text.
76& 77 (1998) 604-607
spectra measured at several temperatures excited near the O-0 absorption energy. As seen in the figure, the fluorescence width gradually increases with increasing temperature. In the following. we analyze experimental results in terms of the model described in Section 3. We assume the shape of phonon density of state weighted by the electron-phonon coupling constant as /I = &JIY~~((~-, - (uk) N (~e-‘y’(9p. which was applied to analyze time-dependent fluorescence Stokes shift and optical Kerr effect measurements in liquids [3]. We calculate fluorescence and absorption spectra with fluorescence decay rate 2;* = 24 cm- ’ [S.S] and experimental values of width (Fig. 3) and peak energy of absorption spectrum. In addition, we take into account O-l fluorescence band with relative intensity ratios between I’~, 1t2 and \13 modes which are obtained from Ramanscattering lines. From the fitting of numerical calculation with observed spectra in a temperature range 16-240 K, the parameter values are determined as which are incop = 28 cm _ ’ and ELR = 210cm-‘, dependent of temperature, and D = 130 cm-’ for OK. In Fig. 1, the calculated fluorescence and absorption spectra for 100K are shown by solid curves. Here D = 180cm- ’ and W, = 260cm- ‘. The absorption spectrum and excitation energy dependence of O-O fluorescence band are well reproduced by the calculated spectra. In Fig. 2, the calculated fluorescence spectra for each temperature are shown by solid curves. Here D = 130,180. 230 and 270cm-‘, W, = 210,260, 400 and 530cm-’ for 16, 100, 177 and 240 K. respectively. The calculated spectra reproduce well the broadening of 0-O fluorescence band with increasing temperature. The temperature dependences of the modulation amplitude D and the inhomogeneous width W, are shown in Fig. 3. The inhomogeneous width increases rapidly with increasing temperature above the freezing point of ethanol (159K). On the other hand, the modulation amplitude gradually increases with temperature. Since the temperature dependence of the fluorescence spectrum is well reproduced by the calculation assuming the temperature independent p(tu) with constant (‘J,,. it is suggested that the phonon structure of the
n n absorption width .
0 0
n
I
0
(HWHM)
I
I
100
dependencies
at low-energy
of
(K) the
Solid line is the temperature
width
References
absorption
side of the O&Oabsorption
squares) and the cnhomogeneous
I
200
Temperature Fig. 3. Temperature
i
[I-carotene solution in liquid and solid phases of solvent. Summarizing, fluorescence spectra of /I-carotene in ethanol in a temperature range from liquid to solid phases of solvent are analyzed by a linear electrons-phonon coupling model. The result shows that the electron-phonon interaction is near the strong coupling regime, which is consistent with the slow modulation nature of the energy modulation in this system. This work has been supported in part by a Grant-in-Aid for Scientific Research from The Ministry of Education. Science. Sports and Culture.
width
band (closed
[‘I
dependence of modulation
tude D. T, indicates the freezing point of ethanol.
7, =
ampli-
M.S.
Pshenichmko\.
K. Duppcn.
D.A.
Wlcrma.
Phys.
Rc\,. Lett. 74 (1995) 674.
W, (open diamonds).
III
J.Y. Bigot. M.T.
Portella.
A. Migus. C.V. Shank.
159 K.
PI
R.W. Schoenlein. C.J. Hardeen.
Phys. Ret. Lett. 66 11991) 113X
M. Cho. S.J. Rosenthal.
N.F.
Scherer. L.1). Ziegler. GR.
Fleming. .I. Chem. Phys. 96 (19921 5037.
electron--phonon interaction is essentially the same within a temperature range from liquid to solid phases of ethanol. The ratio E,Jco, 2 8 determined in the present work indicates that the electronphonon interaction is near the strong-coupling regime in this system, which is consistent with the assumption of slow modulation nature of the energy modulation. Thus, the linear electron-phonon coupling model with a large value of ELRj~op is a good approximation for describing the nonMarkovian nature of the energy modulation in
[41 .I. Sue. S. Mukamel. .I. Chem. Phys. XX (IYXXI 651. 151 .I. Watanabe. S. Kinoshita. T. Kushida. .I. Chem. Ph\\.
X7
(19X7) 4471.
161 E.T.J. Nibbering. Phgh. 93
( 1990)
[71 J. Watanabe.
( 1997) PI
K.
Duppcn.
D.A.
Wler\ma.
.I (‘hem.
5477.
H. Yano. J. Nakahara.
.I. Phyh. Sot. .lapan 66
X53.
H. Kandorl.
H. Sasahe. M. Mimuro,.l.
Am. Chem. Sot. I I6
(19941 ‘671.
191 S. Kinoshita. Y. Fujimura and
Y. Kanematsu,
In: J.H.
Ltn. ,A.A. Villaeys.
(Eds.). Advances in Multiphonon
Spectroscopy.
vol. Y. World
Scientific.
Processes Singapore,
1905. p. I.
[1()1 Y. Kayanuma.
J. Phqs. Sot. Japan 57
I IYXXI
32.