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Intramolecular charge transfer and locally excited states of the fullerene-linked quarter-thiophenes dyad
Chemical Physics Letters 413 (2005) 110–117 www.elsevier.com/locate/cplett
Intramolecular charge transfer and locally excited states of the fullerene-linked quarter-thiophenes dyad Mengtao Sun
a,b,*
, Yuehui Chen a, Peng Song
a,1
, Fengcai Ma
a
a
b
Department of Physics, Liaoning University, Shenyang 110036, China Department of Chemical Physics, Lund University, Box 124, Lund SE221 00, Sweden Received 8 May 2005; in final form 17 July 2005 Available online 8 August 2005
Abstract The ground and the excited state properties of the fullerene-linked quarter-thiophenes dyad were studied theoretically with the quantum chemistry method. To reveal the excited state properties of them in the vertical absorption process, the energies and densities of the HOMO and LUMO, the intramolecular charge transfer (ICT), locally excited (LE) are studied with transition density matrix, charge difference density and the off-resonant and resonant non-linear polarizabilities. The conclusion is drawn that there are also some intramolecular charge transfer (ICT) excited states, which result from large data of off-resonant and the resonant nonlinear polarizabilities in the vertical absorption process. 2005 Elsevier B.V. All rights reserved.
1. Introduction Charge separation originating from photoinduced electron-transfer is a key function for the construction of optoelectronic devices or artificial photosynthetic systems [1]. Many synthetic and theoretical researches have been devoted to finding molecular systems which allow long-range electron or energy transfer [2]. Efficient photoinduced electron transfer from a conjugated polymer to a fullerene [3] has been found application in low-cost plastic solar cells [4], because the fullerene has small reorganization energies in electron-transfer reactions, therefore leading to slow charge recombination [5,6]. Thiophene oligomers are studied experimentally [7] and theoretically [8,9], because of their remarkable electronic and optical properties (such as their ready accessibility, structural modifications, high p-conjugation, *
Corresponding author. E-mail address: [email protected] (M. Sun). 1 Present address: State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China. 0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.07.070
low oxidation potentials, and environmental stability) [10,11], and their potential commercial applications in field-effect transistor (TFTs) [12,13] and solar cells [14]. The oligothiophene–fullerene dyad system [15–17] has been studied experimentally, which shows marked photoinduced electron transfer from the oligomer to the terminal fullerene; moreover, they are successfully put to practical use in the fabrication of photovoltaic cells [18]. The rational design of novel plastic materials requires insight into the connection between the chemical structures with the properties of excited states, such as the charge and energy transfer [19,20], electron–hole coherence and delocalization size [21–23], and photoexcitation dynamics [24–26]. Two-dimensional real space analysis method of transition density matrix [21–26] has been employed to study electron–hole coherence and delocalization of the conjugated molecules. Beenken and Pullerits [8,9] developed 3D real-space analysis method of transition density (TD) and charge difference density (CDD), which has been used to analyze the charge and energy transfer in several conjugated polymers [20,26–28].
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Fig. 1. The chemical structure of fullerene-linked quarter-thiophenes dyad.
In this Letter, the ground and the excited state properties of the fullerene-linked quarter-thiophenes dyad (see Fig. 1) was studied theoretically with the quantum chemistry method. Charge and energy transfer, and the electron–hole coherence of them on the vertical absorption process are studied with 3D and 2D methods, respectively. Upon excitation both dipole moment and polarizability of a molecule can change. These changes exhibit non-linear optical (NLO) behaviour. The results of the ICT excited states were interpreted with the offresonant and resonant non-linear polarizabilities.
of the transition density matrix reflects the dynamics of this exciton projected on a pair of atomic orbitals given by its indices [24], which gives the probability of finding one charged particle on site x and the second one on site y [23]. In the 3D cube representation, the transition density from the ground state to the excited state is given by [8,9], X C lai ua ðrÞui ðrÞ ð2Þ ql0 ðrÞ ¼ a2unocc i2occ
where Clai represents the ith eigenvector of the Configuration-Interaction (CI) Hamiltonian based on the single-excitations from the occupied Hartree–Fock molecular orbital ui ð~ rÞ to the unoccupied one ua ð~ rÞ. The transition density determines the dipole transition moment (or transition dipole) [8,9], Z l ¼ rql0 ðrÞ d3 r ð3Þ giving the strength and the orientation for the interaction with the electromagnetic field. The CDD is given by [8,9], X Dqll ðrÞ ¼ C laj C lai uj ðrÞui ðrÞ a2unocc i;j2occ
2. Method The geometry of the fullerene-linked quarter-thiophenes dyad (FQT) at the ground states was optimized using the DFT method with B3LYP function and 321G basis sets. The excited state properties of FQT were calculated with TD-DFT [29] method, B3LYP functional and STO-3G basis set. The dipole moment (l) and polarizability (a) of FQT at the ground state were calculated with the optimized ground state geometry. The transition energy dependence on the static electric field F can be expressed as [30] Eexc ðF Þ ¼ Eexc ð0Þ DlF 12DaF 2 ;
111
ð1Þ
where Eexc(0) is the excitation energy at zero field, Dl is the change in dipole moment, and Da is the change in polarizability. Higher order terms have been neglected here. From this equation, it is easy to see that since the energy is linearly dependent on the change in dipole during excitation, the effect will not be the same for positive and negative fields, leading to an asymmetric dependence. The change in dipole moment and polarizability were obtained by fitting the TDDFT calculations to Eq. (1). Then, the excited state dipole and polarizability were calculated with l(S1) = l(S0) + Dl and a(S1) = a(S0) + Da. All the calculations were preformed with GAUSSIAN 03 package [31]. Two-dimensional and 3D real space analysis methods have been described in [8,9,21–26]. Briefly, in the 2D site representation, photoexcitation creates an electron–hole pair or an exciton by moving an electron from an occupied orbital to an unoccupied orbital [21]. Each element
X
C lbi C lai ub ðrÞua ðrÞ.
ð4Þ
a;b2unocc i2occ
The first and the second terms in Eq. (4) stand for hole and electron in the CDD.
3. Results and discussion The calculated dipole moment (l), polarizability (a) of FQT at the ground and excited states, the transition energies and their corresponding oscillator strengths (40 excited states) were calculated (listed in Tables 1–3, respectively), which are consistent with the experimental
Table 1 The calculated dipole moment l (Debye)
lxx
lyy
lzz
l
lgg lee lgg lee
0.7681 54.0 53.23
0.5586
0.3723
1.0201
Table 2 The calculated dipole polarizability a(a.u.)
axx
axy
ayy
axz
ayz
azz
agg aee agg
825.990 0.5
5.555
475.697
1.470
20.460
343.853
aee
826.490
112
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 3 The calculated transition energies and the corresponding oscillator strengths of the fullerene-linked quarter-thiophenes (F-4T) dyad for the first 40 excited states States
Transition energy (nm)
Oscillator strength
S1 S2 S3 S4 S5 S6 S7 S8 S9
693.47 (707) 652.03 573.88 502.81 482.60 476.60 475.34 471.46 464.15
0.0002 0.0020 0.0000 0.0030 0.0059 0.0000 0.0001 0.0003 0.0000
CI expansion coefficients 0.7054(H ! L) 0.7049(H ! L + 1) 0.7057(H ! L + 2) 0.6716(H 3 ! L) 0.6759(H 1 ! L) 0.6716(H 3 ! L + 1) 0.6745(H 4 ! L + 1) 0.6117(H 1 ! L + 1) 0.6006(H 5 ! L)
Excited state properties ICT ICT ICT LE(F) LE(F) LE(F) LE(F) LE(F) LE(F)
S10
446.37
0.0002
0.5391(H 6 ! L + 1) 0.4331(H 4 ! L + 1)
LE(F)
S11
440.85
0.0016
0.5391(H 5 ! L + 1) 0.3375(H 3 ! L + 2)
LE(F)
S12
440.50
0.0000
0.5179(H 6 ! L) 0.3388(H 2 ! L)
LE(F)
S13
439.22
0.0004
0.5761(H 2 L)
LE(F)
S14
432.01
0.0011
0.4029(H 6 ! L + 1) 0.4614(H 4 ! L + 1)
LE(F)
S15 S16
425.96 423.02
0.0037 0.0007
0.6085(H ! L + 3) 0.5681(H 1 ! L + 2)
ICT LE(F)
S17
422.02
0.0035
0.4720(H 2 ! L + 1) 0.3072(H 1 ! L + 2)
ICT
S18
419.77
0.0031
0.3400(H 5 ! L + 1) 0.5463(H 2 ! L + 2)
LE(F)
S19
410.12
0.0001
0.6449(H 5 ! L + 2)
LE(F)
S20
409.42
0.0020
0.4691(H 6 ! L + 2) 0.4882(H 4 ! L + 2)
LE(F)
S21
408.60
0.0068
0.6883(H ! L + 4)
ICT
S22
398.13
0.0004
0.45843(H 6 ! L + 2) 0.4403(H 4 ! L + 2)
LE(F)
S23 S24 S25 S26
388.32 380.44 377.80 377.27 (378)
0.0001 0.0235 0.0793 1.7975
0.6681(H 2 ! L + 2) 0.6179(H 11 ! L) 0.6013(H 11 ! L + 1) 0.6036(H ! L + 5)
ICT LE(F) LE(F) LE(4T)
S27
375.37
0.0003
S28 S29
370.71 363.53
0.0201 0.0005
0.6815(H ! L + 6) 0.5215(H 8 ! L + 1)
ICT ICT
S30
359.25
0.0058
0.4350(H 7 ! L) 0.4425(H ! L + 7)
ICT
S31
358.89
0.0083
0.3510(H 7 ! L) 0.5211(H ! L + 7)
ICT
S32
356.68
0.0001
0.4514(H 10 ! L + 1) 0.3292(H 9 ! L + 1) 0.3805(H 8 ! L + 1)
ICT
S33
349.53
0.0000
0.5019(H 10 ! L) 0.4464(H 9 ! L)
ICT
S34
348.71
0.0017
0.5682(H 11 ! L + 2)
LE(F)
S35
347.57
0.0000
0.3528(H 9 ! L + 1) 0.5592(H 7 ! L + 1)
ICT
0.5000(H 8 ! L) 0.3558(H 7 ! L)
ICT
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
113
Table 3 (continued) States
Transition energy (nm)
Oscillator strength
CI expansion coefficients
Excited state properties
S36
345.80
0.0070
0.5111(H 12 ! L) 0.2558(H 11 ! L + 2) 0.3405(H 5 ! L + 3)
LE(F)
S37
345.32
0.0000
0.4535(H 10 ! L + 1) 0.3275(H 9 ! L + 1) 0.3838(H 8 ! L + 1)
ICT
S38
341.87
0.0000
0.4980(H 12 ! L + 1) 0.4254(H 3 ! L + 4)
LE(F)
S39
338.91
0.0000
0.6453(H 1 ! L + 3)
LE(F)
S40
338.60
0.0000
0.5026(H 10 ! L + 1) 0.4437(H 9 ! L + 1)
ICT
Table 4 The HOMOs and LUMOs, and their energy levels (eV)
Green and red correspond to the different phases of the molecular wave functions for the HOMOs and LUMOs, and the isovalue is 0.02 a.u. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 5 The charge difference densities of fullerene-linked quarter-thiophenes dyad
Green colour represents the hole, red electron, respectively. The isovalue is 4 · 104 in a.u. (For interpretation of the references to colour in this figure legend, the
-2.0 -2.5 -3.0
LUMO HO MO
-3.5 -4.0 eV
results. The first excited state is mainly the orbital transition from HOMO to LUMO, and the CI coefficient is 0.71. From the shape and energies of HOMO and LUMO (see Table 4), the first excited state is the ICT state, since the densities of HOMO and LUMO are totally localized on the thiophene and the fullerene units, respectively, suggesting that the thiophene and fullerene moieties act as an electron–donor and an electron– acceptor, respectively. As a result of the charge transfer from the thiophene unit to the fullerene unit (see the CDD in Table 5), the holes and the charges are localized in the thiophene unit and the fullerene unit, respectively; and the quantitative charge transfer is 0.00669 e, according to the distribution the mulliken charges. The localization of the densities of HOMO and LUMO in the thiophene unit and the fullerene unit respectively result from the large energy separation [26,32] of the HOMO and LUMO between the thiophene and the fullerene units, DE(HOMO) = 0.898 eV and DE(LUMO) = 1.030 eV, respectively (see Fig. 2). The large energy separation leads to the weak interaction potentials between the two units, and the localization of the densities of HOMO and LUMO [26,32]. The electron– hole coherence and the delocalization in the contour plot of the transition density matrix (see in Fig. 3) also support the results of the charge difference density, i.e. the first excited state is the ICT state. The energy gap of HOMO–LUMO is 1.796 eV, which is slightly larger
1.030 eV
-4.5 -5.0
4T
-5.5 0.898 eV -6.0
F4T F
Fig. 2. The energies of the HOMO and LUMO for fullerene, quarterthiophenes dyad and fullerene-linked quarter-thiophenes dyad.
than the transition energy (1.789 eV) of S1. The relationship of the energy separation of the HOMO–LUMO and the transition energy was discussed by Tretiak [33]. Prototypical organic chromophores for second-order non-linear optics contain a polarizable p-electron system and donor and acceptor groups to create an asymmetric polarizability in the molecule. It has been hypothesized that there is an optimal combination of donor/acceptor strengths that will maximize b [34,35]. The large b results in strong non-linear optical (NLO) effects, then results in the charge transfer excited state. This analysis has been based upon a two-state model for b derived from static perturbation theory [34] in which the domi-
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
115
Eexc(1*10-3 Hartree)
80
75
70
65
60 0.0
0.1
0.2
0. 3
Field strength (1*10-3a.u.) Fig. 4. Excitation energy plotted vs electric field strength for lowest singlet excitation in the fullerene-linked quarter-thiophenes dyad.
Fig. 3. The contour plots of transition density matrix of the fullerenelinked quarter-thiophenes dyad. The colour bar is shown (absolute values of matrix elements, scaled to a maximum value of 1.0), and the electron–hole coherence increases with the increase of absolute values of matrix elements. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
nant contribution to b arises from the ground state and a charge-transfer excited state. In this two-state model ! l2ge b / ðlee lgg Þ 2 ; ð5Þ Ege where g labels the ground state, e labels the CT excited state, l is the dipole matrix element between the subscripted states, and E is the transition energy between the two states. The terms in this equation are proportional to (i) the dipole moment change between the two states, (ii) the square of the transition dipole moment between the two states, and (iii) the inverse square of the transition energy between the ground and CT states. The field dependent excitation energy is demonstrated by the TDDFT calculations as shown in the Fig. 4, and the excitation energy varies very slightly quadratically with the field strength, because of smaller Da = 0.5 a.u. Excess dipole moment and the polarizability reported was obtained by calculating the excitation energy at zero field and at three different field strengths 5 · 107 V/m (1 · 104 a.u.), 1 · 108 V/m (2 · 104 a.u.)
and 1.5 · 108 V/m (3 · 104 a.u.) along the x axis. The change in the dipole moment Dl = lee lgg = 21.245 a.u. (54 Debye) and Da = aee agg = 0.5 a.u. was fitted by Eq. (1), which are listed in the Tables 1 and 2, respectively. So, the dipole moment of the first excited state is lee = Dl + lgg = 53.23 Debye. Using Eq. (2), the transition density was obtained, which determines the orientation and strength of the dipole transition moment. The orientation of the dipole moment at the first excited state is opposite to that at the ground state, which can be supported by the transition density (listed in Table 6), since the orientation at the first excited state is from thiophene to the fullerene (the orientation of the dipole moment is from the electron to the hole); while the orientation at the ground state is from fullerene to thiophene (see the setting of the axis in Fig. 1). So, according to Eq. (5), the large Dl results in the large b (the large NLO effect), then results in the CT excited state (S1). There are the similar results for the excited states S1– S3, S15, S17, S21, S23, S27–S33, S35, S37 and S40, which are the ICT excited states, resulting from the large NLO effect (large b). The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S1 and S28 show such chrematistics. With the above method, one can also discuss ICT by fitting the b at higher excited states. For the excited states S4–S14, S16, S18–S20, S22, S24, S25, S34, S36, S38 and S39, there are the similar results, which are the locally excited states. The charge transfer and electron–hole pairs are localized in the fullerene unit. The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S5, S24 and S25 show such chrematistics. It should be noted that for the excited state S26, it is also a locally excited state, but it is different from the
116
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 6 The transition densities of fullerene-linked quarter-thiophenes dyad
Green colour represents the hole, red electron, respectively. The isovalue is 1 · 106 in a.u., respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
other locally excited state, the charge transfer and electron–hole pairs are localized in 4 thiophenes, not in the fullerene unit. The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S26 show such chrematistics. Experimentally, the authors [15] found there is no charge and energy transfer between the fullerene unit and thiophene units on the vertical absorption process from the absorption spectra, due to the weak interaction between them; furthermore, the absorption spectra of the fullerene-linked quarter-thiophenes dyad is the result of the superposition between the spectra of the fullerene and that of the quarter-thiophenes. The calculated results not only support the experiment data, but also found some new phenomenon. There are some ICT excited states, which result in the charge and energy transfer from the thiophene unit to the fullerene unit (the holes are localized in the thiophene unit and the electron localized in the fullerene unit), though the mainly excited states with large oscillator strengths are the localized excited states.
4. Conclusion The ground and the excited properties of the fullerene-linked quarter-thiophenes dyad were studied theoretically with the quantum chemistry method as well as 2D and 3D real space analysis methods. The theoretical results revealed there are also some ICT excited states in the vertical absorption process, which results from the ONL effect (large b).
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 10374040) and the Wenner-Gren Foundation of Sweden.
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Intramolecular charge transfer and locally excited states of the fullerene-linked quarter-thiophenes dyad Mengtao Sun
a,b,*
, Yuehui Chen a, Peng Song
a,1
, Fengcai Ma
a
a
b
Department of Physics, Liaoning University, Shenyang 110036, China Department of Chemical Physics, Lund University, Box 124, Lund SE221 00, Sweden Received 8 May 2005; in final form 17 July 2005 Available online 8 August 2005
Abstract The ground and the excited state properties of the fullerene-linked quarter-thiophenes dyad were studied theoretically with the quantum chemistry method. To reveal the excited state properties of them in the vertical absorption process, the energies and densities of the HOMO and LUMO, the intramolecular charge transfer (ICT), locally excited (LE) are studied with transition density matrix, charge difference density and the off-resonant and resonant non-linear polarizabilities. The conclusion is drawn that there are also some intramolecular charge transfer (ICT) excited states, which result from large data of off-resonant and the resonant nonlinear polarizabilities in the vertical absorption process. 2005 Elsevier B.V. All rights reserved.
1. Introduction Charge separation originating from photoinduced electron-transfer is a key function for the construction of optoelectronic devices or artificial photosynthetic systems [1]. Many synthetic and theoretical researches have been devoted to finding molecular systems which allow long-range electron or energy transfer [2]. Efficient photoinduced electron transfer from a conjugated polymer to a fullerene [3] has been found application in low-cost plastic solar cells [4], because the fullerene has small reorganization energies in electron-transfer reactions, therefore leading to slow charge recombination [5,6]. Thiophene oligomers are studied experimentally [7] and theoretically [8,9], because of their remarkable electronic and optical properties (such as their ready accessibility, structural modifications, high p-conjugation, *
Corresponding author. E-mail address: [email protected] (M. Sun). 1 Present address: State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China. 0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.07.070
low oxidation potentials, and environmental stability) [10,11], and their potential commercial applications in field-effect transistor (TFTs) [12,13] and solar cells [14]. The oligothiophene–fullerene dyad system [15–17] has been studied experimentally, which shows marked photoinduced electron transfer from the oligomer to the terminal fullerene; moreover, they are successfully put to practical use in the fabrication of photovoltaic cells [18]. The rational design of novel plastic materials requires insight into the connection between the chemical structures with the properties of excited states, such as the charge and energy transfer [19,20], electron–hole coherence and delocalization size [21–23], and photoexcitation dynamics [24–26]. Two-dimensional real space analysis method of transition density matrix [21–26] has been employed to study electron–hole coherence and delocalization of the conjugated molecules. Beenken and Pullerits [8,9] developed 3D real-space analysis method of transition density (TD) and charge difference density (CDD), which has been used to analyze the charge and energy transfer in several conjugated polymers [20,26–28].
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Fig. 1. The chemical structure of fullerene-linked quarter-thiophenes dyad.
In this Letter, the ground and the excited state properties of the fullerene-linked quarter-thiophenes dyad (see Fig. 1) was studied theoretically with the quantum chemistry method. Charge and energy transfer, and the electron–hole coherence of them on the vertical absorption process are studied with 3D and 2D methods, respectively. Upon excitation both dipole moment and polarizability of a molecule can change. These changes exhibit non-linear optical (NLO) behaviour. The results of the ICT excited states were interpreted with the offresonant and resonant non-linear polarizabilities.
of the transition density matrix reflects the dynamics of this exciton projected on a pair of atomic orbitals given by its indices [24], which gives the probability of finding one charged particle on site x and the second one on site y [23]. In the 3D cube representation, the transition density from the ground state to the excited state is given by [8,9], X C lai ua ðrÞui ðrÞ ð2Þ ql0 ðrÞ ¼ a2unocc i2occ
where Clai represents the ith eigenvector of the Configuration-Interaction (CI) Hamiltonian based on the single-excitations from the occupied Hartree–Fock molecular orbital ui ð~ rÞ to the unoccupied one ua ð~ rÞ. The transition density determines the dipole transition moment (or transition dipole) [8,9], Z l ¼ rql0 ðrÞ d3 r ð3Þ giving the strength and the orientation for the interaction with the electromagnetic field. The CDD is given by [8,9], X Dqll ðrÞ ¼ C laj C lai uj ðrÞui ðrÞ a2unocc i;j2occ
2. Method The geometry of the fullerene-linked quarter-thiophenes dyad (FQT) at the ground states was optimized using the DFT method with B3LYP function and 321G basis sets. The excited state properties of FQT were calculated with TD-DFT [29] method, B3LYP functional and STO-3G basis set. The dipole moment (l) and polarizability (a) of FQT at the ground state were calculated with the optimized ground state geometry. The transition energy dependence on the static electric field F can be expressed as [30] Eexc ðF Þ ¼ Eexc ð0Þ DlF 12DaF 2 ;
111
ð1Þ
where Eexc(0) is the excitation energy at zero field, Dl is the change in dipole moment, and Da is the change in polarizability. Higher order terms have been neglected here. From this equation, it is easy to see that since the energy is linearly dependent on the change in dipole during excitation, the effect will not be the same for positive and negative fields, leading to an asymmetric dependence. The change in dipole moment and polarizability were obtained by fitting the TDDFT calculations to Eq. (1). Then, the excited state dipole and polarizability were calculated with l(S1) = l(S0) + Dl and a(S1) = a(S0) + Da. All the calculations were preformed with GAUSSIAN 03 package [31]. Two-dimensional and 3D real space analysis methods have been described in [8,9,21–26]. Briefly, in the 2D site representation, photoexcitation creates an electron–hole pair or an exciton by moving an electron from an occupied orbital to an unoccupied orbital [21]. Each element
X
C lbi C lai ub ðrÞua ðrÞ.
ð4Þ
a;b2unocc i2occ
The first and the second terms in Eq. (4) stand for hole and electron in the CDD.
3. Results and discussion The calculated dipole moment (l), polarizability (a) of FQT at the ground and excited states, the transition energies and their corresponding oscillator strengths (40 excited states) were calculated (listed in Tables 1–3, respectively), which are consistent with the experimental
Table 1 The calculated dipole moment l (Debye)
lxx
lyy
lzz
l
lgg lee lgg lee
0.7681 54.0 53.23
0.5586
0.3723
1.0201
Table 2 The calculated dipole polarizability a(a.u.)
axx
axy
ayy
axz
ayz
azz
agg aee agg
825.990 0.5
5.555
475.697
1.470
20.460
343.853
aee
826.490
112
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 3 The calculated transition energies and the corresponding oscillator strengths of the fullerene-linked quarter-thiophenes (F-4T) dyad for the first 40 excited states States
Transition energy (nm)
Oscillator strength
S1 S2 S3 S4 S5 S6 S7 S8 S9
693.47 (707) 652.03 573.88 502.81 482.60 476.60 475.34 471.46 464.15
0.0002 0.0020 0.0000 0.0030 0.0059 0.0000 0.0001 0.0003 0.0000
CI expansion coefficients 0.7054(H ! L) 0.7049(H ! L + 1) 0.7057(H ! L + 2) 0.6716(H 3 ! L) 0.6759(H 1 ! L) 0.6716(H 3 ! L + 1) 0.6745(H 4 ! L + 1) 0.6117(H 1 ! L + 1) 0.6006(H 5 ! L)
Excited state properties ICT ICT ICT LE(F) LE(F) LE(F) LE(F) LE(F) LE(F)
S10
446.37
0.0002
0.5391(H 6 ! L + 1) 0.4331(H 4 ! L + 1)
LE(F)
S11
440.85
0.0016
0.5391(H 5 ! L + 1) 0.3375(H 3 ! L + 2)
LE(F)
S12
440.50
0.0000
0.5179(H 6 ! L) 0.3388(H 2 ! L)
LE(F)
S13
439.22
0.0004
0.5761(H 2 L)
LE(F)
S14
432.01
0.0011
0.4029(H 6 ! L + 1) 0.4614(H 4 ! L + 1)
LE(F)
S15 S16
425.96 423.02
0.0037 0.0007
0.6085(H ! L + 3) 0.5681(H 1 ! L + 2)
ICT LE(F)
S17
422.02
0.0035
0.4720(H 2 ! L + 1) 0.3072(H 1 ! L + 2)
ICT
S18
419.77
0.0031
0.3400(H 5 ! L + 1) 0.5463(H 2 ! L + 2)
LE(F)
S19
410.12
0.0001
0.6449(H 5 ! L + 2)
LE(F)
S20
409.42
0.0020
0.4691(H 6 ! L + 2) 0.4882(H 4 ! L + 2)
LE(F)
S21
408.60
0.0068
0.6883(H ! L + 4)
ICT
S22
398.13
0.0004
0.45843(H 6 ! L + 2) 0.4403(H 4 ! L + 2)
LE(F)
S23 S24 S25 S26
388.32 380.44 377.80 377.27 (378)
0.0001 0.0235 0.0793 1.7975
0.6681(H 2 ! L + 2) 0.6179(H 11 ! L) 0.6013(H 11 ! L + 1) 0.6036(H ! L + 5)
ICT LE(F) LE(F) LE(4T)
S27
375.37
0.0003
S28 S29
370.71 363.53
0.0201 0.0005
0.6815(H ! L + 6) 0.5215(H 8 ! L + 1)
ICT ICT
S30
359.25
0.0058
0.4350(H 7 ! L) 0.4425(H ! L + 7)
ICT
S31
358.89
0.0083
0.3510(H 7 ! L) 0.5211(H ! L + 7)
ICT
S32
356.68
0.0001
0.4514(H 10 ! L + 1) 0.3292(H 9 ! L + 1) 0.3805(H 8 ! L + 1)
ICT
S33
349.53
0.0000
0.5019(H 10 ! L) 0.4464(H 9 ! L)
ICT
S34
348.71
0.0017
0.5682(H 11 ! L + 2)
LE(F)
S35
347.57
0.0000
0.3528(H 9 ! L + 1) 0.5592(H 7 ! L + 1)
ICT
0.5000(H 8 ! L) 0.3558(H 7 ! L)
ICT
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
113
Table 3 (continued) States
Transition energy (nm)
Oscillator strength
CI expansion coefficients
Excited state properties
S36
345.80
0.0070
0.5111(H 12 ! L) 0.2558(H 11 ! L + 2) 0.3405(H 5 ! L + 3)
LE(F)
S37
345.32
0.0000
0.4535(H 10 ! L + 1) 0.3275(H 9 ! L + 1) 0.3838(H 8 ! L + 1)
ICT
S38
341.87
0.0000
0.4980(H 12 ! L + 1) 0.4254(H 3 ! L + 4)
LE(F)
S39
338.91
0.0000
0.6453(H 1 ! L + 3)
LE(F)
S40
338.60
0.0000
0.5026(H 10 ! L + 1) 0.4437(H 9 ! L + 1)
ICT
Table 4 The HOMOs and LUMOs, and their energy levels (eV)
Green and red correspond to the different phases of the molecular wave functions for the HOMOs and LUMOs, and the isovalue is 0.02 a.u. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 5 The charge difference densities of fullerene-linked quarter-thiophenes dyad
Green colour represents the hole, red electron, respectively. The isovalue is 4 · 104 in a.u. (For interpretation of the references to colour in this figure legend, the
-2.0 -2.5 -3.0
LUMO HO MO
-3.5 -4.0 eV
results. The first excited state is mainly the orbital transition from HOMO to LUMO, and the CI coefficient is 0.71. From the shape and energies of HOMO and LUMO (see Table 4), the first excited state is the ICT state, since the densities of HOMO and LUMO are totally localized on the thiophene and the fullerene units, respectively, suggesting that the thiophene and fullerene moieties act as an electron–donor and an electron– acceptor, respectively. As a result of the charge transfer from the thiophene unit to the fullerene unit (see the CDD in Table 5), the holes and the charges are localized in the thiophene unit and the fullerene unit, respectively; and the quantitative charge transfer is 0.00669 e, according to the distribution the mulliken charges. The localization of the densities of HOMO and LUMO in the thiophene unit and the fullerene unit respectively result from the large energy separation [26,32] of the HOMO and LUMO between the thiophene and the fullerene units, DE(HOMO) = 0.898 eV and DE(LUMO) = 1.030 eV, respectively (see Fig. 2). The large energy separation leads to the weak interaction potentials between the two units, and the localization of the densities of HOMO and LUMO [26,32]. The electron– hole coherence and the delocalization in the contour plot of the transition density matrix (see in Fig. 3) also support the results of the charge difference density, i.e. the first excited state is the ICT state. The energy gap of HOMO–LUMO is 1.796 eV, which is slightly larger
1.030 eV
-4.5 -5.0
4T
-5.5 0.898 eV -6.0
F4T F
Fig. 2. The energies of the HOMO and LUMO for fullerene, quarterthiophenes dyad and fullerene-linked quarter-thiophenes dyad.
than the transition energy (1.789 eV) of S1. The relationship of the energy separation of the HOMO–LUMO and the transition energy was discussed by Tretiak [33]. Prototypical organic chromophores for second-order non-linear optics contain a polarizable p-electron system and donor and acceptor groups to create an asymmetric polarizability in the molecule. It has been hypothesized that there is an optimal combination of donor/acceptor strengths that will maximize b [34,35]. The large b results in strong non-linear optical (NLO) effects, then results in the charge transfer excited state. This analysis has been based upon a two-state model for b derived from static perturbation theory [34] in which the domi-
M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
115
Eexc(1*10-3 Hartree)
80
75
70
65
60 0.0
0.1
0.2
0. 3
Field strength (1*10-3a.u.) Fig. 4. Excitation energy plotted vs electric field strength for lowest singlet excitation in the fullerene-linked quarter-thiophenes dyad.
Fig. 3. The contour plots of transition density matrix of the fullerenelinked quarter-thiophenes dyad. The colour bar is shown (absolute values of matrix elements, scaled to a maximum value of 1.0), and the electron–hole coherence increases with the increase of absolute values of matrix elements. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
nant contribution to b arises from the ground state and a charge-transfer excited state. In this two-state model ! l2ge b / ðlee lgg Þ 2 ; ð5Þ Ege where g labels the ground state, e labels the CT excited state, l is the dipole matrix element between the subscripted states, and E is the transition energy between the two states. The terms in this equation are proportional to (i) the dipole moment change between the two states, (ii) the square of the transition dipole moment between the two states, and (iii) the inverse square of the transition energy between the ground and CT states. The field dependent excitation energy is demonstrated by the TDDFT calculations as shown in the Fig. 4, and the excitation energy varies very slightly quadratically with the field strength, because of smaller Da = 0.5 a.u. Excess dipole moment and the polarizability reported was obtained by calculating the excitation energy at zero field and at three different field strengths 5 · 107 V/m (1 · 104 a.u.), 1 · 108 V/m (2 · 104 a.u.)
and 1.5 · 108 V/m (3 · 104 a.u.) along the x axis. The change in the dipole moment Dl = lee lgg = 21.245 a.u. (54 Debye) and Da = aee agg = 0.5 a.u. was fitted by Eq. (1), which are listed in the Tables 1 and 2, respectively. So, the dipole moment of the first excited state is lee = Dl + lgg = 53.23 Debye. Using Eq. (2), the transition density was obtained, which determines the orientation and strength of the dipole transition moment. The orientation of the dipole moment at the first excited state is opposite to that at the ground state, which can be supported by the transition density (listed in Table 6), since the orientation at the first excited state is from thiophene to the fullerene (the orientation of the dipole moment is from the electron to the hole); while the orientation at the ground state is from fullerene to thiophene (see the setting of the axis in Fig. 1). So, according to Eq. (5), the large Dl results in the large b (the large NLO effect), then results in the CT excited state (S1). There are the similar results for the excited states S1– S3, S15, S17, S21, S23, S27–S33, S35, S37 and S40, which are the ICT excited states, resulting from the large NLO effect (large b). The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S1 and S28 show such chrematistics. With the above method, one can also discuss ICT by fitting the b at higher excited states. For the excited states S4–S14, S16, S18–S20, S22, S24, S25, S34, S36, S38 and S39, there are the similar results, which are the locally excited states. The charge transfer and electron–hole pairs are localized in the fullerene unit. The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S5, S24 and S25 show such chrematistics. It should be noted that for the excited state S26, it is also a locally excited state, but it is different from the
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M. Sun et al. / Chemical Physics Letters 413 (2005) 110–117
Table 6 The transition densities of fullerene-linked quarter-thiophenes dyad
Green colour represents the hole, red electron, respectively. The isovalue is 1 · 106 in a.u., respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
other locally excited state, the charge transfer and electron–hole pairs are localized in 4 thiophenes, not in the fullerene unit. The charge difference densities (see Table 5) and contour plots of the transition density matrixes (see Fig. 3) of S26 show such chrematistics. Experimentally, the authors [15] found there is no charge and energy transfer between the fullerene unit and thiophene units on the vertical absorption process from the absorption spectra, due to the weak interaction between them; furthermore, the absorption spectra of the fullerene-linked quarter-thiophenes dyad is the result of the superposition between the spectra of the fullerene and that of the quarter-thiophenes. The calculated results not only support the experiment data, but also found some new phenomenon. There are some ICT excited states, which result in the charge and energy transfer from the thiophene unit to the fullerene unit (the holes are localized in the thiophene unit and the electron localized in the fullerene unit), though the mainly excited states with large oscillator strengths are the localized excited states.
4. Conclusion The ground and the excited properties of the fullerene-linked quarter-thiophenes dyad were studied theoretically with the quantum chemistry method as well as 2D and 3D real space analysis methods. The theoretical results revealed there are also some ICT excited states in the vertical absorption process, which results from the ONL effect (large b).
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 10374040) and the Wenner-Gren Foundation of Sweden.
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