Vibronic couplings in C60 derivatives for organic photovoltaics

Chemical Physics Letters 590 (2013) 169–174

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Vibronic couplings in C60 derivatives for organic photovoltaics Naoya Iwahara a,1, Tohru Sato a,b,⇑, Kazuyoshi Tanaka a, Hironori Kaji c a

Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan Unit of Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan c Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan b

a r t i c l e

i n f o

Article history: Received 9 July 2013 In final form 28 October 2013 Available online 6 November 2013

a b s t r a c t Vibronic coupling constants (VCCs) and reorganisation energies of C60 derivative anions including [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) are evaluated. The results are analysed in terms of the vibronic coupling density. As long as the electronic state is conserved, the VCCs are similar to those in C 60 . The VCCs are large when (1) the distribution of LUMO is large around the substituent or (2) the structure of the orbital is significantly changed by the symmetry lowering, which would be unsuitable for an organic photovoltaic material from the viewpoint of vibronic couplings. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Fullerene derivatives have been employed as acceptors or electron-transporting materials in organic photovoltaics (OPV) [1,2], model systems for artificial photosynthesis [3], and so on. In these applications, vibronic coupling (VC) or vibrational reorganisation energy [4–6] plays an important role. In the carrier-transporting process, VC gives rise to inelastic scattering of carriers, and power loss [7], i.e., the stronger the VCs are, the larger the power loss becomes [8,9]. Thus, small VCs and reorganisations are desired for transporting materials. Further, a small vibrational reorganisation energy is required to design artificial photosynthetic models [10,11,3]. Reorganisation energies have been evaluated in some systems such as porphyrin-fullerene dyads and donor:PCBM blends, where PCBM is [6,6]-phenyl-C61-butyric acid methyl ester [10–18]. The estimated energies of fullerene derivatives depend on their substituents and range from ca. 70 to ca. 150 meV in the theoretical works and from ca. 100 to ca. 250 meV in the experimental works. Experimentally, the reorganisation energies have been estimated from the Stokes shift of the emission spectra from the charge-transferred state [10,11,15]. One should note that experimental estimates include the effect of surroundings. On the other hand, theoretically, the vibrational reorganisation energies were obtained from the difference between the total energies of the neutral and charge-transferred states [13,14,16,17]. However, the origin of the VCs in C60 derivatives have not been understood

clearly, and hence insight into the VCs from the view of electronic and vibrational structures is useful for molecular design. The vibronic coupling constants (VCCs) can be analysed in terms of the vibronic coupling density (VCD) [21,6]. The VCD provides a local picture of the VC from the electronic and vibrational structures and demonstrates the strengths of the VCs of the C60 monoanion [22]. Moreover, using the VCD analysis, we have succeeded in designing hole- and electron-transporting molecules with small VCCs [8,9]. In this study, we calculate the VCCs or reorganisation energies in C60 derivative anions (see Figure 1) and compare the VCs with those in the C60 anion. As C60 derivatives, we consider PCBM (Figure 1, 1), fullerene pyrrolidines (Figure 1, 2 and 3), methylfullerene C61H2 (Figure 1, 4), fluorofullerene C61F2 (Figure 1, 5), and C60H2 (Figure 1, 6). PCBM is employed as an acceptor in organic thin film solar cells [1] and fullerene pyrrolidines are used as acceptors in donor–acceptor dyads [3,11]. Systems 5 and 6 were reported to have large reorganization energies (1a in Ref. [14] and II in Ref. [13], respectively), and the system 4 [16] is for comparison with the system 5. The calculated results are analysed in terms of VCD analysis. 2. Theory The VCC [4–6] for a vibrational mode a is defined by

Va ¼ ⇑ Corresponding author at: Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan. Fax: +81 75 383 2556. E-mail address: [email protected] (T. Sato). 1 Present address: Division of Quantum and Physical Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium. 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.10.083

 !  +    @ HðQ ; rÞ WðR0 ; rÞ ; WðR0 ; rÞ  @Q a   R0

*

ð1Þ

where W denotes the electronic wavefunction for the anionic state at the equilibrium structure of the neutral state R0 , r ¼ ðr1 ;    ; ri ;    ; rN Þ denotes a set of electron coordinates, H is a molecular Hamiltonian, and Q ¼ ðQ 1 ;    ; Q a ;   Þ is a set of the

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normal coordinate Q a . The direction of mode a is defined so that V a is negative. The vibronic Hamiltonian can be written as

Hvibro ¼ E0 þ

3M6 X

 1 jV a jQ a þ x2a Q 2a ; 2

a

ð2Þ

where E0 is the ground-state electronic energy of the anion at R0 . The vibronic Hamiltonian can be rewritten as

Hvibro ¼ E0 þ

3M6 X

a

" #  2 1 2 V 2a jV a j x Qa  2  2 : 2 a xa 2xa

ð3Þ

From Eq. (3), the reorganisation energy for mode a is obtained as

V 2a : 2x2a

ER;a ¼

ð4Þ

The total reorganisation energy is calculated from

ER ¼

X ER;a :

ð5Þ

a Figure 1. Calculated C60 derivatives. 1 is [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), 2 is fullerene pyrrolidine, 3 is a fullerene pyrrolidine derivative, 4 is a methyl fullerene, 5 is a fluoromethylene fullerene, and 6 is a C60H2.

The VCD for a vibrational mode a is defined by [21,6]

ga ðri Þ ¼ Dqðri Þ  v a ðri Þ;

ð6Þ

where Dqðri Þ ¼ qðri Þ  q0 ðri Þ is the electron density difference between the anionic density q and the neutral density q0 . The potential derivative v a ðri Þ is defined using the nuclear attraction potential acting on a single electron:

uðri Þ ¼

M X



A¼1

Z A e2 ; 4p0 jri  RA j

ð7Þ

where M is the number of nuclei, 0 is the electric constant, and RA and Z A denote the position and charge of nucleus A, respectively. The potential derivative is defined by

v a ðri Þ ¼



@uðri Þ @Q a

 ð8Þ

; R0

The space integral of the VCD ga yields the VCC:

Va ¼

Z

ga ðri Þ d3 ri ¼

Z

3

Dqðri Þ  v a ðri Þ d ri :

ð9Þ

The VCC can be analysed in terms of the electronic structure Dq and the vibrational structure v a through the VCD ga based on Eq. (9). Note that the VCD is sometimes canceled in a certain region since the VCD distributes with positive and negative values [7]. The effective mode with the VCC

rffiffiffiffiffiffiffiffiffiffiffiffi X 2ffi Va

V eff ¼

ð10Þ

a

3. Method of calculation We employed the B3LYP functional with the 6-311G (d,p) basis set, The reference structures were obtained by geometry optimisations of the neutral states. Vibrational analyses were applied to the optimized structures to check if the structure is a stationary minimum. Analytical force calculations were performed on the optimized structures of the neutral states. We employed GAUSSIAN 09 packages for the optimisations, vibrational analysis, and force calculations [23]. The VCCs were evaluated using the results of the force calculations. This method has been used for the calculation of the VCCs of C 60 which were found to agree well with the constants derived in Ref. [20] from the high-resolution photoelectron spectrum [19]. Therefore, the present theoretical methodology can be applied for the accurate estimations of VCCs in C60 derivatives. The VCD analyses were performed using the electronic wavefunctions of the neutral and anionic states at their reference geometry as well as the vibrational modes. The VCC and VCD calculations were performed using our codes. In order to analyse the electronic structures, we performed fragment molecular orbital (FMO) analysis using the YAeHMOP program [24,25].

4. Results and discussion 4.1. Vibronic coupling constants and reorganisation energies

is defined by 3M6 X

ueff ¼

a¼1

 jV a j ua ; V eff

ð11Þ

where ua is a vibrational vector of mode a. For the effective mode, the frequency and reorganisation energy are

x2eff ¼

X V 2 x2 a

a

Eeff ¼

V 2eff

V 2eff ; 2x2eff

respectively.

a

;

ð12Þ

ð13Þ

Figure 2 shows the calculated VCCs V a (1) of C 60 [20] and the anions of C60 derivatives 1, 5, and 6 (Figure 1). The VCCs of 2, 3, and 4 anions are shown in Figure S1 of the Supplemental material. Since the symmetry of C60 is Ih and the LUMOs belong to the t 1u irreducible representation, the electronic state of C 60 is T 1u . The T 1u electronic state couples with the ag and hg modes according to the selection rule, ½T 21u  ¼ ag  hg . C60 has two ag modes and eight sets of hg modes, and thus, it has 42 active modes. For C 60 , the VCCs of the ag ð2Þ (1492 cm1), hg ð7Þ (1442 cm1), and hg ð8Þ (1608 cm1) modes are strong (Figure 2 (a)) [20]. The VCCs of derivatives 1–4 are similar to those of C 60 except for the number of active modes. The symmetries of these derivatives are lower than that of C60, and hence, the derivatives have a larger number of active modes than C60 does. For example, since PCBM

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(b) |Vα| (10 a.u.)

3

1

0

0

1000

2000

2

Frequency (cm-1)

3

|Vα| (10 a.u.)

(d)

0

1000

2000

0

1000

2000

Frequency (cm-1)

3000

3

2

-4

2

1

0

3000

-4

|Vα| (10 a.u.)

(c)

3

-4

2

-4

|Vα| (10 a.u.)

(a)

1

0

0

1000

2000

-1

1

0

3000

Frequency (cm )

-1

3000

Frequency (cm )

(a)

20

(b)

20

ER,α (meV)

10

ER,α (meV)

4    Figure 2. Vibronic coupling constants of (a) C a.u. 60 , (b) 1 , (c) 5 (C 2v ), and (d) 6 (C 1 ) in 10

10

(c)

150

100

1000

Frequency (cm-1)

0

1500

20

(d)

20

ER,α (meV)

500

0

ER,α (meV)

0

10

0

500

1000

1500

0

500

1000

1500

Frequency (cm-1)

15 10 5 50

0

0

0

500

500

1000 1000

Frequency (cm-1)

1500 1500

0

-1 Frequency (cm )

   Figure 3. Reorganisation energies ER;a of (a) C 60 , (b) 1 , (c) 5 , and (d) 6 in meV.

(Figure 1, 1) is C 1 , all of the 258 vibrational modes are active. Among the active modes of the derivatives, the modes originating from the ag ð2Þ mode of C60 is the most intense, and the mode from the hg ð8Þ mode of C60 is the second strongest (Figure 2b–d). On the other hand, the VCCs for the modes which do not originate from the active modes of C 60 , the ag and hg modes, are weak. Although the structures of 4 and 5 are similar to each other, the distributions of their VCCs are different from each other (Figure S1c and Figure 2c, respectively). The large peaks seen in 4 around 1500 cm1 split into several in 5 and the VCCs for the low frequency modes

become larger than those of 4. In the case of 6 anion (Figure 2d), the VCs for the modes which are not originating from the ag ð2Þ and the hg ð8Þ are stronger than those of 1. The reorganisation energies ER;a (4) are shown in Figure 3 and Figure S2 in the Supplemental material and the total reorganisation energies ER (5) are tabulated in Table 1. The reorganisation energies of derivatives 1–4 are close to that of C 60 , while those of 5 and 6 are larger. The distribution of PCBM is in line to the result in Ref. [17]. The present reorganisation energies of ca. 70 meV (2 and 3) are smaller than the experimental value of ca. 100 meV [10] because

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Table 1 Total reorganisation energies ER (meV). Frequencies xeff (cm1), vibronic couplings V eff (104 a.u.), and stabilisation energies Eeff (meV) of the effective modes. Sums of Mulliken charges on the substituent groups.

C 60 1  2 3 4 5 6

ER

xeff

V eff

Eeff

Charge

67.2 74.0 69.2 69.1 68.0 262.9 121.8

1450 1452 1466 1460 1449 1308 1222

4.01 4.03 4.00 4.00 3.97 4.15 4.00

50.1 50.4 48.8 49.1 49.3 66.2 70.2

0.098 0.095 0.109 0.258 0.272 0.286

modes are large compared with the former molecules, which is consistent with the distributions of their VCCs. One should note that the reorganization energy and the Mulliken charges on the substituent group is almost irrelevant to each other, which implies that the VCs have to be discussed based on the distribution of the electronic wavefunction. 4.2. Vibronic coupling density

the experimental value includes ER of the donor as well as acceptor parts. The energies of 4 and 6 agree well with the previous estimate of 68 meV [16] and ca. 150 meV [13], respectively. However, the reorganization energy of 5 of 262.9 meV is larger than 146.5 meV reported in Ref. [14]. Among the active modes, the reorganization energy for the mode originating from the hg ð1Þ of C60 (185.0 cm1) is as large as 144.4 meV (Figure 3c). The contribution from this mode should be overestimated because the higher order vibronic couplings which reduce the stabilization by the mode are not taken into account in the present calculation. The frequencies (12), VCCs (10), and total reorganisation energies (13) for the effective modes of derivatives 1-4 are almost the same as those of C60, as tabulated in Table 1. Since each of C60 and 1–4 has a few prominent peaks around 1500 cm1, the discrepancy between ER and Eeff is relatively small. It is expected that their effective modes give useful picture of the VCs. On the other hand, the discrepancies of 5 and 6 are rather large, which come from the couplings between the effective mode and the other active modes. The effective frequencies of 5 and 6 are lower than the others. This result indicates that the VCs for the low frequency

Figure 4 shows the LUMO and the electron density difference Dq of PCBM. The white and blue areas indicate positive and negative values, respectively. The LUMO (Figure 4a) is almost completely localized on the C60 fragment. The distribution of the electron density difference Dq (Figure 4b) is similar to the LUMO density. However, Dq appears not only on C60 but also on the substituent (Figure 4b). The charge transfer from the C60 cage to the substituent (see Mulliken charge in Table 1), though small, causes a change in the electron density distribution of the electron density, and consequently, Dq appears on the substituent. In addition, a negative polarization of Dq is found on the C60 cage because of the Coulomb interactions between electrons in doubly occupied orbitals and an additional electron in the anion [22]. In other words, the many-body effect strongly affects Dq, and therefore, the VCCs [26]. Since the electron density difference Dq is mainly localized on the C60 cage, Dq of the derivative anions strongly couples to the vibrational modes corresponding to the ag ð2Þ and hg ð8Þ modes of C60. Therefore the potential derivative v a (8) for the effective mode (Figure S3 in the Supplemental material) is localized on the C60 fragment (Figure 5a), and the distributions of the VCD (6) in the PCBM anion (Figure 5b) are similar to that of C 60 [22]. Furthermore, the effective mode of the PCBM anion is the stretching mode of the

Figure 4. (a) LUMO (isosurface value = 0.025 a.u.) and (b) Dq (isosurface value = 0.001 a.u.) of 1 (PCBM).

Figure 5. (a) v eff (isosurface value = 0.005 a.u.) and (b) geff value = 5106 a.u.) for the effective mode in PCBM.

(isosurface

N. Iwahara et al. / Chemical Physics Letters 590 (2013) 169–174

Figure 6. Dq’s of (a) 5 and (b) 6 (isosurface value = 0.001 a.u.).

6:6 C@C double bond, which is the same as that in C 60 [27]. A similar discussion holds for 2-4 anions. The electron density differences of 5 and 6 anions are shown in Figure (6). Though Dq of 5 is similar to that of PCBM (and 2-4), Dq distributes around the substituent group. The electronic state strongly couples to the C = C stretching modes. However, because of the CF2 group, the pattern of the modes originating from the ag and the hg modes of C60 are mixed with each other. One difference is the bending motion at the CF2 group which is seen in the effective mode though the displacement could be exaggerated (Figure S4a). The contribution to V eff from the carbon atoms of the CF2 group and the bridged atoms are large and the VCCs from them are 0.426 and 0.292 in 104 a.u., respectively. The electron density difference of 6 is localized around the substituents due to the symmetry lowering. Consequently, the symmetry of the effective mode is also low and the displacements are localized around the atoms where Dq are localized (Figure S4b). 4.3. Fragment molecular orbital analysis The VCCs or reorganisation energies of C 60 and the derivatives are close to each other because the distribution of the LUMOs of the derivatives are similar to that of C60. This conservation of the

LUMO can be explained based on the FMO analysis. In FMO analysis, we split a molecule into two fragments and describe the orbitals of the system using the orbitals of fragments as their basis. For the analysis, each C60 derivative is divided into C60 (Fragment A) and the substituted group (Fragment B). The FMO of PCBM is shown in Figure 7. The HOMO of PCBM consists of the hu and t 1u frontier orbitals of the C60 fragment (Frag. A) and the LUMO of the substituent (Frag. B). One of the t1u LUMOs contributes to the HOMO of PCBM, while the others do not. The latter orbitals are almost unchanged after the addition of the substituent. Therefore, the LUMO of PCBM is almost the same as one of the LUMOs of C60. In the case of 5, the orbital level corresponding to the LUMO+2 of PCBM lowers due to the large distortion of C@C bond and becomes the LUMO (Figure S5 in the Supplemental material). Compared with the distance between the carbon atoms bridged by the methyl group in 4 (1.634 Å), the distance of the corresponding atoms in 5 is enlongated (2.077 Å) by 0.44 Å. The LUMO of 6 is localized around the substituents due to the orbital mixing (Figure S6).

5. Summary The VCCs and reorganisation energy of C60 derivative anions including PCBM were evaluated. The results were analysed in terms of the VCD. Molecules 1–4 exhibit almost the same VCCs in C 60 , while 5 and 6 do not. Since the LUMO of the former derivatives originate from the t 1u LUMO, Dq is localized on the C60 fragment and its structure is close to to Dq of C 60 . Though the reorganisation energy of the former systems are larger than that of C60 due to their low-symmetry, the increase is slight because of the conservation of the electronic structure of C60. On the other hand, the reorganization energies of 5 and 6 are significantly enhanced. The former case is due to the change in the active modes by the substituent group and the latter is due to the localization of Dq and the increase of the number of active modes by the symmetry lowering. In order to avoid any increase in the reorganisation energy, (1) the structure of the LUMO of C60 should be conserved and (2) the molecular symmetry should be high. The

−9.5

−10

−10.5

−11

−11.5

−12

Frag. A

173

System

Frag. B

Figure 7. FMO analysis for 1 (PCBM). Threshold of the MO is 0.03 a.u. for the system and fragment A and 0.05 a.u. for the fragment B.

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molecule which violates these points would exhibit large VCCs and hence is unsuitable for an OPV material or a model system of photosynthesis from the viewpoint of vibronic couplings. Acknowledgement Numerical calculations were performed partly in the Supercomputer Laboratory of Kyoto University and Research Center for Computational Science, Okazaki, Japan. This ‘‘Letter’’ was also supported in part by the Global COE Program ‘International Center for Integrated Research and Advanced Education in Materials Science’ (No. B–09) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, administrated by the Japan Society for the Promotion of Science. Note added in proof Recently Larson et al. [28] have measured photoelectron spectra of PCBM anion. The structure of the spectra is close to that of C 60 . This result indicates that the VCCs of PCBM anion, which agrees with the present work. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2013. 10.083. References [1] G. Yu, J. Gao, J.C. Hummelen, F. Wudl, A.J. Heeger, Science 270 (1995) 1789. [2] B.C. Thompson, J.M.J. Fréchet, Angew. Chem. Int. Ed. 47 (2008) 58.

[3] H. Imahori, Bull. Chem. Soc. Jpn. 80 (2007) 621. [4] I.B. Bersuker, V.Z. Polinger, Vibronic Interactions in Molecules and Crystals, Springer–Verlag, Berlin and Heidelberg, 1989. [5] I.B. Bersuker, The Jahn–Teller Effect, Cambridge University Press, Cambridge, 2005. [6] T. Sato, K. Tokunaga, N. Iwahara, K. Shizu, K. Tanaka, in: H. Köppel, D.R. Yarkony, H. Barentzen (Eds.), The Jahn–Teller Effect: Fundamentals and Implications for Physics and Chemistry, Springer–Verlag, Berlin, 2009, p. 99. [7] T. Sato, K. Shizu, T. Kuga, K. Tanaka, H. Kaji, Chem. Phys. Lett. 458 (2008) 152. [8] K. Shizu, T. Sato, K. Tanaka, H. Kaji, Appl. Phys. Lett. 97 (2010) 142111. [9] K. Shizu, T. Sato, A. Ito, K. Tanaka, H. Kaji, J. Mater. Chem. 21 (2011) 6375. [10] H. Imahori, N.V. Tkachenko, V. Vehmanen, K. Tamaki, H. Lemmetyinen, Y. Sakata, S. Fukuzumi, J. Phys. Chem. A 105 (2001) 1750. [11] H. Imahori et al., Angew. Chem. Int. Ed. 41 (2002) 2344. [12] H. Kawauchi et al., J. Phys. Chem. A 112 (2008) 5878. [13] K. Tokunaga, Chem. Phys. Lett. 476 (2009) 253. [14] K. Tokunaga, S. Ohmori, H. Kawabata, Thin Solid Films 518 (2009) 477. [15] K. Vandewal, K. Tvingstedt, A. Gadisa, O. Inganäs, J.M. Manca, Phys. Rev. B 81 (2010) 125204. [16] R.C.I. MacKenzie, J.M. Frost, J. Nelson, J. Chem. Phys. 132 (2010) 064904. [17] T. Liu, A. Troisi, J. Phys. Chem. C 115 (2011) 2406. [18] The reorganization energy in this article (5) is the half of that used in the Marcus theory. Throughout this article, the reorganization energy always means Eq. (5). [19] X.B. Wang, H.K. Woo, L.S. Wang, J. Chem. Phys. 123 (2005) 051106. [20] N. Iwahara, T. Sato, K. Tanaka, L.F. Chibotaru, Phys. Rev. B 82 (2010) 245409. [21] T. Sato, K. Tokunaga, K. Tanaka, J. Phys. Chem. A 112 (2008) 758. [22] N. Iwahara, T. Sato, K. Tanaka, J. Chem. Phys. 136 (2012) 174315. [23] M.J. Frisch et al., GAUSSIAN 09 Revision B.1, gaussian Inc. Wallingford CT. [24] G.A.Landrum and W.V.Glassey, bind (ver 3.0). bind is distributed as part of the YAeHMOP extended Hückel molecular orbital package and is freely available on the WWW at: http://sourceforge.net/projects/yaehmop/. [25] G.A.Landrum, viewkel (ver 3.0). viewkel is distributed as part of the YAeHMOP extended Hückel molecular orbital package and is freely available on the WWW at: http://sourceforge.net/projects/yaehmop/. [26] T. Sato, K. Shizu, K. Uegaito, N. Iwahara, K. Tanaka, H. Kaji, Chem. Phys. Lett. 507 (2011) 151. [27] T. Sato, N. Iwahara, N. Haruta, K. Tanaka, Chem. Phys. Lett. 531 (2012) 257. [28] B.W. Larson, J.B. Whitaker, X.-B. Wang, A.A. Popov, G. Rumbles, N. Kopidakis, S.H. Strauss, O.V. Boltalina, J. Phys. Chem. C 117 (2013) 14958.