Chemical Physics Letters 436 (2007) 224–227 www.elsevier.com/locate/cplett
Electronic structures of ferrocene-containing polymers with heteroatom-bridges Yukihito Matsuura *, Kimihiro Matsukawa Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya, Joto-ku, Osaka 536-8553, Japan Received 27 October 2006; in final form 21 December 2006 Available online 24 January 2007
Abstract The electronic structures of ferrocene-containing polymers with heteroatom-bridges have been examined using the tight-binding crystal orbital method. The relationship between the band structures of the polymers and their bridging moieties was examined. The highest occupied (HO) band of the polymers with saturated carbon-bridges consisted of p-type p orbitals of cyclopentadienyl ring. On the other hand, the polymers with silicon-bridges possessed a localised HO band, which was formed by 3d2z orbitals of iron atom. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Many researchers have studied ferrocene and its related metallocene compounds [1]. They exhibit various functionalities such as stable redox properties, good solubility in organic solvents and a potential for chemical modification, and hence, it is thought that ferrocene is a promising material for fabricating some molecular conductors [2,3]. Manners and his coworkers have remarkably developed metallocene-containing polymers such as polyferrocenylsilane (PFS) using ring-opening polymerisation of siliconbridged [1] ferrocenophane [4]. PFS exhibited a drastic increase in electrical conductivity in the I2-doped state and possessed two redox peaks in the cyclic voltammetry [5], which indicated that there was some interaction between the ferrocenes along the polymers chains [6]. It was reported that the bridging moieties of both the unsaturated carbon-bridges and the elements from the second and lower rows of the periodic table resulted in some interaction between the ferrocenes [7]. Although the ferrocene polymers have not been applied to fabricate the electronic devices, it is worthwhile to examine the effect of the bridging moieties on the band structures of the polymers by *
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[email protected] (Y. Matsuura).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.01.055
using a theoretical calculation method. We have already calculated the band structures of the ferrocene-containing polymers with carbon-bridges and have clarified that the unsaturated carbon-bridges resulted in limited p conjugation between the nearest ferrocenes [8]. In this study, the band structures of the ferrocene-containing polymers with heteroatom-bridges were examined using a one-dimensional tight-binding calculation method. 2. Method As described in our previous Letter [8], this calculation method is suitable for comparing the electronic properties between the different chemical species. The one-dimensional tight-binding crystal orbital calculations were carried out under the extended Hu¨ckel approximation using a YAeHMOP program [9]. The Hu¨ckel parameters were provided in the YAeHMOP program, and are listed in Table 1. In this study, the chemical structures of PFS were determined using the X-ray results of the oligomers [6], as shown in Fig. 1; further, the chemical structures of other polymers were determined using the typical chemical structures of the organic compounds described in a reference [10]. Furthermore, it was assumed that the chemical structure of ferrocene in a unit cell showed C2h symmetry in which the angle of the C–H bond outside the cyclopentadienyl ring
Y. Matsuura, K. Matsukawa / Chemical Physics Letters 436 (2007) 224–227 Table 1 Parameters for H, C, Si, Ge, Sn, Fe, and Ru atoms Atom
Orbital
H C
1s 2s 2p 3s 3p 4s 4p 5s 5p 4s 4p 3d 5s 5p 4d
Si Ge Sn Fe
Ru
a
Hii (eV) 13.60 21.40 11.40 17.30 9.20 16.00 9.00 16.16 8.32 9.10 5.32 12.60 10.40 6.80 14.90
f1 1.3000 1.6250 1.6250 1.3830 1.3830 2.1600 1.8500 2.1200 1.8200 1.9000 1.9000 5.3500 2.0800 2.0400 5.3800
f2
225
a C1
a
o
C2a
2.04
Fe
H 113 H 1.10
C
Fe
1.54 C 110o
H
H
b o
H113 H
Fe
2.0000
0.5505
1.85 Si 110o
1.48
Si
Fe H
H
0.6260
c 2.3000
0.5342
o
H113 H
0.6368
Coefficients used in the double-f expansion of the d orbitals.
was 0°, which was identical to our previous results. In this study, we have calculated the band structures of the following ferrocene-containing polymers: polyferrocenylmethylene (PFM), PFS, polyferrocenylgermane (PFGe), polyferrocenylstannane (PFSn) and polyferrocenylethylene (PFE). Furthermore, in order to examine the differences in the metallocene units, we calculated the band structures of polyruthenocenylethylene (PRuE).
Fe
1.53
1.95 Ge 110o
H
H
d o
H113 H
Fe
2.16 Sn 110o
1.70
e
Sn
Fe H
H
3. Results and discussion
H
H C
120o
The band structure of PFM is shown in Fig. 2a. As mentioned in our previous Letter [8], the coupling of the p-type p orbitals between the nearest ferrocenes was broken at the methylene group, and hence, the entire band structure was flat. The band structure of PFS was calculated, as shown in the Fig. 2b. The bandwidth of the HO band was narrow, which was identical to that of PFM, and the level of the highest occupied crystal orbital (HOCO) of PFS ( 9.181 eV) was slightly higher than that of PFM ( 9.173 eV). Fig. 2c and d show the band structures of PFGe and PFSn, respectively. Their band structures were very similar to that of PFS, and their entire bandwidths were narrow. However, the crystal orbital of the HO band of PFM is different from those of the other polymers. In the band structure of PFM, as shown in Fig. 3a, the HOCO at k = 0 consisted of the p-type p orbitals of the cyclopentadienyl ring. On the other hand, in the band structure of PFS, as shown in Fig. 3b, the HOCO primarily consisted of the 3d2z orbitals of iron atom. In addition, we observed the small contribution of the 2p orbitals of the a-carbon of the cyclopentadienyl ring and the silicon atoms to the bridging moieties. The 3d2z orbitals of iron atom in the HOCO exhibited a non-bonding state with the a-carbon of the cyclopentadienyl ring. The HOCOs of PFGe and PFSn are similar to that of PFS. It was reported that the wavelengths of UV–vis absorption of these polymers were not almost affected by the bridging moieties, and the exper-
Ge
Fe
120o
C 1.54
Fe
H
f
H
H
H C
120o
120o
C 1.54
2.15 H
H
Ru
Fig. 1. Chemical structures of the unit cells of (a) PFM, (b) PFS, (c) ˚. PFGe, (d) PFSn, (e) PFE and (f) PRuE. The unit of bond length is A
imental results were well explained by the band structures of these polymers [4]. The difference in the crystal orbitals between PFM and PFS was also consistent with the results of the density of states (DOS) of the polymers. Projected density of states (PDOS) of the HO band of PFM does not consist of PDOS of the iron atoms, as shown in Fig. 3c. The energy bands formed by the iron atoms are positioned at a slightly deeper
226
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Fig. 2. Band structures of (a) PFM, (b) PFS, (c) PFGe and (d) PFSn.
a
level of approximately 12.2 eV. Therefore, it is possible to anticipate that the cyclopentadienyl rings are mainly charged in the first step of the positively doped PFM. DOS of the HO band of PFS consists of the PDOS of iron atom, as shown in Fig. 3d. In addition to some extent, the HOCO also consists of the atomic orbitals of silicon atom. In cases where PFS is positively charged due to doping, it is considered that the iron atoms are mainly oxidized. Furthermore, the width of the HO band of PFS is narrow, and hence, the depopulation of the HO band leads to only a localised charge at the iron atoms. From the results of the cyclic voltammetry, metal–metal interaction was observed in the heteroatom-bridge systems such as PFS, PFGe, and PFSn [7]. The metal–metal interaction is possibly due to the following calculated results. The width of the HO band of PFS is very small (0.01 eV), which suggests that the transfer integral t along the polymer chain has a small value. As reported in a reference [11], the on-site coulomb repulsion (U) at the iron atom of ferrocene is approximately 10 eV. Therefore, the value of U/t is so large that PFS exhibits relatively strong electron–electron interaction at the iron atom. It was reported that PFS shows two redox peaks, and it was clarified that PFS exhibits some contribution of the PDOS of the iron atoms. PFGe and PFSn had identical tendencies to PFS with regard to the experimental and the calculated results. On the other hand, only one redox peak of diferrocenylmethylene, which is considered to be a unit cell of PFM, showed a weaker interaction between the ferrocenes [7]. Our calculations clarify that PFM possesses a small amount of the PDOS of iron atom from the HO band. As mentioned in our previous Letter, the HOCO of PFE consisted of the atomic orbitals of the cyclopentadienyl ring, and PFE possessed only one redox peak [12]. It was also reported that PRuE had only one redox peak [13]. Therefore, we calculated the band structure of PRuE and compared it with that of PFE, as shown in Figs. 4b. PRuE had a larger bandwidth of the HO band as compared to PFE, however, the level of the HOCO decreased and that of the lowest unoccupied crystal orbital
b H
H
H C
C H
Si H
H
H
c 80
d Density of states
HOCO at k=0
Density of states
HOCO at k=0 80
40
Fe 0 -12.4
H Si
-12.3
-12.2
-12.1
Total
-12.0
Energy (eV)
-11.9
-11.8
Total
Fe
40
Si 0 -12.4
-12.3
-12.2
-12.1
-12.0
-11.9
Energy (eV)
Fig. 3. DOS and PDOS of (a) PFM and (b) PFS. The HOCO patterns of (c) PFM and (d) PFS.
-11.8
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HO band with a narrow bandwidth, hence, we cannot expect high electrical conductivity. A change in the bridging moieties is not effective to improve the band structures. However, the HOCOs of the polymers were different between the polymers with heteroatom-bridges and those with a CH2 bridge. The HO band of the polymers with heteroatom-bridges was localised at the 3d2z orbital of an iron atom. On the other hand, the polymers with a CH2 bridge possessed the HO band formed by the atomic orbitals of cyclopentadienyl rings. Although our calculation cannot clarify both the physical phenomena and the application of the polymers, it can be assumed that the PDOS of the iron atom contributes to the investigated metal–metal interactions. Acknowledgements The authors thank Prof. R. Hoffmann and his coworkers for their permission to use the YAeHMOP program. The author (Y.M.) also thanks to Prof. I. Manners for providing an opportunity to study the synthesis of the polyferrocenylsilane. References
Fig. 4. Band structures of (a) PFE and (b) PRuE. The HOCO patterns of (c) PFE and (d) PRuE.
increased with an increase in the band gap as compared to PFE. Furthermore, the HOCO of PRuE consisted of the p-type p orbitals of the cyclopentadienyl ring, and there was almost no contribution of the atomic orbitals of the iron atoms, as shown in Fig. 4d. 4. Conclusion In this study, we have presented the band structures of the ferrocene-containing polymers with heteroatombridges. The polymers possessed a large band gap and a
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