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Electronic structures of metallocene-containing polymers
Chemical Physics Letters 447 (2007) 101–104 www.elsevier.com/locate/cplett
Electronic structures of metallocene-containing polymers Yukihito Matsuura *, Kimihiro Matsukawa Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya, Joto-ku, Osaka 536-8553, Japan Received 3 July 2007; in final form 31 August 2007 Available online 7 September 2007
Abstract The band structures of polymers containing first row transition metal metallocenes were calculated using the one-dimensional tightbinding crystal orbital method along with the extended Hu¨ckel approximation. The metallocene polymers, except for ferrocene and chromocene polymers, possessed a partially occupied band. The ferrocene and chromocene polymers exhibit semiconductor character. Cobaltocene, nickelocene, and vanadocene polymers have a metallic character. The manganocene polymer has a partially occupied band that is localised. A change in the band structures of the metallocene polymers was compatible with an alternation of the energy levels of the 3dz2 band of the transition metals. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Ferrocene has been well studied by many researchers because the reversible oxidation–reduction process is considered to be applicable to organic electronic devices [1,2]. The doping of linked ferrocene polymers provides a low-dimensional conductor such as the oxidation products of polyferrocenylene [3]. Some linked ferrocene systems possess significant antiferromagnetic interactions between metal centers [4]. These interactions are reported to be dependent on intermetallic interactions in the main chain of the ferrocene polymers [3]. Strong interaction among neighbouring ferrocene is found in the ferrocene systems with unsaturated hydrocarbons or heteroatom bridges. We have examined the band structures of ferrocene polymers and confirmed that the unsaturated hydrocarbons and heteroatom bridges of the ferrocene polymers are shown to be different from each other in the crystal orbital (CO) phases near the Fermi level [5,6]. A great deal of research effort has been expended on studies on bis(g5-cyclopentadienyl)–metal complexes (metallocene) [7]. Although Manners synthesised poly(ferr*
Corresponding author. Fax: +81 6 6963 8015. E-mail address: [email protected] (Y. Matsuura).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.08.093
ocenylsilane)–poly(chromarenosilane) copolymers that were air or moisture sensitive [8], polymers containing metallocene in the main chain have not yet been synthesised. Bimetallocenes formed by vanadium, nickel, and cobalt have been synthesised and their magnetic properties have been investigated using electron spin resonance (ESR) and magnetic susceptibility measurements [9]. Bivanadocene shows weak antiferromagnetic coupling and binickelocene displays strong antiferromagnetic coupling. In contrast, bicobaltocene exhibits ferromagnetic interaction. We have studied the band structures of polyferrocenylene (PFC) and other ferrocene polymers using the tightbinding crystal orbital calculation method and have examined the relation between the band structures and the metal–metal interaction among the nearest unit cells [5,6]. Linked metallocene polymers, except for ferrocene polymers, are also considered to be valuable for providing characteristic electronic or magnetic properties due to the absence of the stable 18-electron structure of ferrocene. The band structures are the dominant factor determining the electronic or magnetic properties of the polymers, and hence we have designed metallocene polymers that contain transition metals in the main chain and have calculated band structures.
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Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
2. Calculation method
Table 2 Distances from the transition metal atom to the center of Cp ring
The one-dimensional tight-binding crystal orbital calculations were performed using the YAeHMOP program [10]. The Hu¨ckel parameters were determined as described in Table 1. If the metallocene polymers possess linked species comprising hydrocarbons or heteroatoms, the band structures are probably simple and flat, similar to the metallocene monomers. Therefore, the metallocene polymers chosen were directly linked metallocene polymers as shown in Fig. 1. We have calculated the band structures of polyvanadocenylene (PVaC), polychromocenylene (PCrC), polymanganocenylene (PMnC), polyferrocenylene (PFC), polycobaltocenylene (PCoC), and polynickelocenylene (PNiC). In this study, the chemical structures of the metallocene polymers were determined using typical chemical structures of the organic compounds described in Refs. [5,6,11]. When we constructed a structural model of the unit cell of the metallocene polymers, the symmetry of the unit cell of metallocene was determined to be C2h and
Metal atom ˚) M–Cp (A
V
Cr
Mn
Fe
Co
Ni
1.96
1.89
2.08
1.68
1.77
1.86
the angle of the CAH bond outside the Cp ring was 0°. Furthermore, when we determined the distance between the transition metal atom and the Cp ring, we referred to the results calculated at the B3LYP DZP level, as described in Table 2 [5]. 3. Results and discussion Fig. 2a shows the band structure of PFC, which possesses semiconductor character. The highest occupied crystal orbital (HOCO) was calculated to be the p orbitals of
a -6
Table 1 Parameters for H, C, and the first row transition metals f1
H C
1s 2s 2p 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d
13.60 21.40 11.40 8.81 5.52 11.00 8.66 5.24 11.22 9.75 5.89 11.67 9.10 5.32 12.60 9.21 5.29 13.18 10.95 6.27 14.20
1.3000 1.6250 1.6250 1.3000 1.3000 4.7500 1.7000 1.7000 4.9500 0.9700 0.9700 5.1500 1.9000 1.9000 5.3500 2.0000 2.0000 5.5500 2.1000 2.1000 5.7500
V
Cr
Mn
Fe
Co
Ni
a
f2
C1a
C2a
-8
1.7000
0.4755
0.7052
1.8000
0.5058
0.6747
1.7000
0.5139
0.6929
2.0000
0.5505
0.6260
2.1000
0.5679
0.6059
2.3000
0.5493
0.6082
Coefficients used in the double-f expansion of the 3d orbitals.
dxz + π (Cp) NLU
-10
dyz + π (Cp) LU
NLUCO (k=π/a) LUCO (k=π/a)
EF π (Cp) HO
2 -12 NHO dz
-14
HOCO (k=π/a) 0
k
NHOCO (k=π/a)
π/a
b
c -6
-6
-8
-8
-10
Energy (eV)
Hii (eV)
Energy (eV)
Orbital
Energy (eV)
Atom
EF
-10 EF
-12
-12
-14
-14
M n 0
k
M=V, Cr, Mn, Fe, Co, Ni Fig. 1. Geometrical structures of the metallocene polymers.
π/a
0
k
π/a
Fig. 2. (a) A band structure and CO phases of PFC. Band structures of (b) PCoC and (c) PNiC.
Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
a -6 dyz + π (Cp)
LU
-8 Energy (eV)
LUCO (k=π/a)
-10 PO
POCO (k=π/a) dz2
EF
dx2-y2 + π (Cp) HO NHO dxy
-12
HOCO (k=π/a) -14
0
k
NHOCO (k=π/a)
π/a
b
c -6
-6
dyz + π (Cp) NLU
-10
-8
dz2 LU EF
HO
dx2-y2 + π (Cp)
-12
NHO dxy
Energy (eV)
-8 Energy (eV)
the Cp ring, and the lowest unoccupied crystal orbital (LUCO) exhibited an anti-bonding character between Fe 3dyz and the p orbitals of the Cp ring. The p electrons in bicyclopentadienyl were delocalised in the HOCO or LUCO; however, p delocalisation was not observed for the iron atoms in ferrocene. The next HOCO (NHOCO) and next LUCO (NLUCO) were formed by Fe 3dz2 and 3dxz with the p orbitals of the Cp ring, respectively. The atomic orbitals of a-carbon in the Cp rings did not contribute to NHOCO or NLUCO, and hence these bands possessed very small bandwidths. Fig. 2b shows the band structure of PCoC, whose band provides a deeper energy level as compared to that of PFC. The ground state of a unit cell of PCoC has one electron more than that of PFC, and hence PCoC consists of a partially occupied band. The CO phase of the partially occupied band exhibits an anti-bonding character between the iron atoms and the Cp ring. If we consider electron–electron repulsions in the band calculation, the partially occupied band probably splits due to the Jahn–Teller effect [12]. Therefore, the band structure of PCoC would possess a small band gap. As a result, PCoC possesses considerable reactivity due to the additional electron occupying the anti-bonding orbital and a smaller energy gap as compared to PFC. Fig. 2c shows the band structure of PNiC. The ground state of nickelocene has two electrons more than ferrocene, and hence the anti-bonding character between the Cp ring and the nickel atoms is greater than that in PCoC. The molecular structure of the unit cell in PNiC is also modified by the Jahn–Teller effect [12]. The band structures of PCoC and PNiC are similar to the band structure of PFC. In contrast, PMnC, PCrC, and PVaC possess a band structure different from that of PFC. Fig. 3a shows the band structure of PMnC. The unit cell of PMnC is only one electron short of that of PFC, and hence PMnC has a partially occupied band. The partially occupied crystal orbital (POCO) of PMnC consists of 3dz2 orbitals, which are located at a higher level as compared to that of PFC. The small bandwidth suggests that the electron occupying the band is considerably localised. PMnC probably possesses characteristic magnetic properties along with ferromagnetic or antiferromagnetic interaction. The CO phases of the HO and LU bands are formed by the hybridization of the Mn 3d orbital and the p orbitals of the Cp ring. The CO phase of the next HO (NHO) band is formed by the isolated Mn 3dxy orbital. The band structure of PCrC is similar to that of PMnC. The unit cell of PCrC is one electron short of that of PMnC, and hence PCrC possesses a band gap. The band gap of PCrC is smaller than that of PFC, and the HO and LU bands, whose CO phases are formed by dx2 y 2 and dz2 , respectively, possess small bandwidths that result in the low charge mobility. If the polymer is a stable compound, n-type doping possibly provides a localised electron in the LU band that consists of the Cr 3dz2 orbital; the supply of the electron plays an important role in the magnetic properties of the polymers.
103
-10 EF
-12
-14
-14
0
k
π/a
0
k
π/a
Fig. 3. (a) A band structure and CO phases of PMnC. Band structures of (b) PCrC and (c) PVaC.
PVaC exhibits a metallic character, similar to PCoC and PNiC. The partially occupied dx2 y 2 band crosses the Fermi level at 11.03 eV. The NHO band formed by isolated Fe 3dxy is also located near the Fermi level and the bandwidth is very small. PVaC can undergo structural changes due to the Jahn–Teller effect, and this would result in its exhibiting semiconductor character. In particular, we must consider the fact that the extended Hu¨ckel approximation is a qualitative empirical method. It is suitable for comparing the electronic structures of different chemical compounds; however, the open-shell electron systems of the metallocene polymers may allow other electronic states such as multiplet spin states or electron localisation derived from the pairing distortion such as a charge density wave (CDW) [13]. It is widely accepted that ordinary polymers cannot exhibit a multiplet spin state due to their chemical stability [14]. On the other hand, the pairing distortion may occur in polymer systems that have unpaired electrons.
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Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
Table 3 Differences in the total energies of a unit cell of the metallocene polymers Polymer Etot
2E0tot ðeVÞa
PVaC
PCrC
PMnC
PFC
PCoC
PNiC
0.085
0.026
0.056
0.023
0.086
0.056
a
Etot is the total energy of a unit cell of the metallocene polymers with pairing distorsion. E0tot is the total energy of a unit cell of the metallocene polymers with no pairing distorsion.
We calculated the band structures of the metallocene polymers with a pairing distortion of the nearest unit cells. The pairing distortion was achieved solely by altering the bond lengths between the nearest unit cells. The bond lengths between the nearest a-carbons of the Cp rings were ˚ , and other structures in the unit cell are the 1.44 and 1.54 A same as those of the polymers with no pairing distortion. Therefore, a unit cell of the polymers with the pairing distortion includes the two metallocenes. The band structures of the metallocene polymers were found to be similar to the folding relationship when doubling the unit cell size of the metallocene polymers with no pairing distortion [15]. Table 3 shows the difference between the total energies of a unit cell of the metallocene polymers. Among the metallocene polymers, PVaC, PMnC, PCoC, and PNiC, which have unpaired electrons in the unit cell, possess relatively larger energy differences as compared to PCrC or PFC. Especially, PVaC and PCoC have a large energy difference. This suggests that the pairing distortion for stabilizing the chemical structures may occur easily in these metallocene polymers. 4. Conclusion As mentioned above, it is found that a change of transition metal permits a drastic change in the band structures of the metallocene polymers. The 3dz2 bands of PFC, PCoC, and PNiC are stabilised when two electrons occupy them. The band structures of the metallocene polymers can be classified as follows: (1) semiconductor (PFC, PCrC), (2) metallic character with the possibility of an insulator transition (PCoC, PNiC, PVaC), and (3) localised partially occupied band (PMnC). PCoC, PNiC, and PVaC can possess considerable chemical reactivity that is comparable to metallocene monomers. If PMnC is a chemically stable compound, it is expected to exhibit characteristic magnetic properties. PCrC probably exhibits a semiconductor char-
acter with a higher electrical conductivity that is greater than that of PFC. We have also examined the possibility of occurrence of a pairing distortion in the metallocene polymers. Although the occurrence of multiplet spin states in polymers is unusual, we cannot eliminate the possibility of the spin states. Furthermore, it is difficult to evaluate the spin states in the polymer systems using the tight-binding crystal orbital method. Therefore, in a future study, the chemical structure of the model oligomers of the metallocene polymers will be optimized and the electronic structures of the various spin states will be examined by employing a better approximation method such as the DFT B3LYP method. Acknowledgements The authors would like to 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 in the University of Bristol. References [1] A. Togni, T. Hayashi (Eds.), Ferrocenes, VCH Publishers, NY, 1995. [2] C. Engtrakul, L.R. Sita, NanoLetters 1 (2001) 541. [3] D.O. Cowan, J. Park, C.U. Pittman Jr., Y. Sasaki, T.K. Mukherjee, N.D. Diamond, J. Am. Chem. Soc. 94 (1972) 5110. [4] S. Barlow, D. O’Hare, Chem. Rev. 97 (1997) 637. [5] Y. Matsuura, K. Matsukawa, Chem. Phys. Lett. 428 (2006) 321. [6] Y. Matsuura, K. Matsukawa, Chem. Phys. Lett. 436 (2007) 224. [7] Z.-F. Xu, Y. Xie, W.-L. Feng, H.F. Schaefer III, J. Phys. Chem. A 107 (2003) 2716. [8] K.C. Hultzsch, J.M. Nelson, A.J. Lough, I. Manners, Organometallics 14 (1995) 5496. [9] H. Hilbig, P. Hudeczek, F.H. Ko¨hler, X. Xie, P. Bergerat, O. Kahn, Inorg. Chem. 37 (1998) 4246. [10] G.A. Landrum, Yet Another extended Hu¨ckel Molecular Orbital Package (YAeHMOP), Cornell University, 1997. [11] Cottrell, The Strengths of Chemical Bonds, second edn., Butterworths, London, 1958; S.W. Benson, J. Chem. Edu. 42 (1965) 502. [12] M.C. Bo¨hm, J. Chem. Phys. 80 (1984) 2704. [13] M.-H. Whangbo, Acc. Chem. Res. 16 (1983) 95. [14] J.S. Miller, A.J. Epstein, Angew. Chem., Int. Ed. Engl. 33 (1994) 385. [15] R. Hoffmann, C. Janiak, C. Kollmar, Macromolecules 24 (1991) 3725.
Electronic structures of metallocene-containing polymers Yukihito Matsuura *, Kimihiro Matsukawa Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya, Joto-ku, Osaka 536-8553, Japan Received 3 July 2007; in final form 31 August 2007 Available online 7 September 2007
Abstract The band structures of polymers containing first row transition metal metallocenes were calculated using the one-dimensional tightbinding crystal orbital method along with the extended Hu¨ckel approximation. The metallocene polymers, except for ferrocene and chromocene polymers, possessed a partially occupied band. The ferrocene and chromocene polymers exhibit semiconductor character. Cobaltocene, nickelocene, and vanadocene polymers have a metallic character. The manganocene polymer has a partially occupied band that is localised. A change in the band structures of the metallocene polymers was compatible with an alternation of the energy levels of the 3dz2 band of the transition metals. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Ferrocene has been well studied by many researchers because the reversible oxidation–reduction process is considered to be applicable to organic electronic devices [1,2]. The doping of linked ferrocene polymers provides a low-dimensional conductor such as the oxidation products of polyferrocenylene [3]. Some linked ferrocene systems possess significant antiferromagnetic interactions between metal centers [4]. These interactions are reported to be dependent on intermetallic interactions in the main chain of the ferrocene polymers [3]. Strong interaction among neighbouring ferrocene is found in the ferrocene systems with unsaturated hydrocarbons or heteroatom bridges. We have examined the band structures of ferrocene polymers and confirmed that the unsaturated hydrocarbons and heteroatom bridges of the ferrocene polymers are shown to be different from each other in the crystal orbital (CO) phases near the Fermi level [5,6]. A great deal of research effort has been expended on studies on bis(g5-cyclopentadienyl)–metal complexes (metallocene) [7]. Although Manners synthesised poly(ferr*
Corresponding author. Fax: +81 6 6963 8015. E-mail address: [email protected] (Y. Matsuura).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.08.093
ocenylsilane)–poly(chromarenosilane) copolymers that were air or moisture sensitive [8], polymers containing metallocene in the main chain have not yet been synthesised. Bimetallocenes formed by vanadium, nickel, and cobalt have been synthesised and their magnetic properties have been investigated using electron spin resonance (ESR) and magnetic susceptibility measurements [9]. Bivanadocene shows weak antiferromagnetic coupling and binickelocene displays strong antiferromagnetic coupling. In contrast, bicobaltocene exhibits ferromagnetic interaction. We have studied the band structures of polyferrocenylene (PFC) and other ferrocene polymers using the tightbinding crystal orbital calculation method and have examined the relation between the band structures and the metal–metal interaction among the nearest unit cells [5,6]. Linked metallocene polymers, except for ferrocene polymers, are also considered to be valuable for providing characteristic electronic or magnetic properties due to the absence of the stable 18-electron structure of ferrocene. The band structures are the dominant factor determining the electronic or magnetic properties of the polymers, and hence we have designed metallocene polymers that contain transition metals in the main chain and have calculated band structures.
102
Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
2. Calculation method
Table 2 Distances from the transition metal atom to the center of Cp ring
The one-dimensional tight-binding crystal orbital calculations were performed using the YAeHMOP program [10]. The Hu¨ckel parameters were determined as described in Table 1. If the metallocene polymers possess linked species comprising hydrocarbons or heteroatoms, the band structures are probably simple and flat, similar to the metallocene monomers. Therefore, the metallocene polymers chosen were directly linked metallocene polymers as shown in Fig. 1. We have calculated the band structures of polyvanadocenylene (PVaC), polychromocenylene (PCrC), polymanganocenylene (PMnC), polyferrocenylene (PFC), polycobaltocenylene (PCoC), and polynickelocenylene (PNiC). In this study, the chemical structures of the metallocene polymers were determined using typical chemical structures of the organic compounds described in Refs. [5,6,11]. When we constructed a structural model of the unit cell of the metallocene polymers, the symmetry of the unit cell of metallocene was determined to be C2h and
Metal atom ˚) M–Cp (A
V
Cr
Mn
Fe
Co
Ni
1.96
1.89
2.08
1.68
1.77
1.86
the angle of the CAH bond outside the Cp ring was 0°. Furthermore, when we determined the distance between the transition metal atom and the Cp ring, we referred to the results calculated at the B3LYP DZP level, as described in Table 2 [5]. 3. Results and discussion Fig. 2a shows the band structure of PFC, which possesses semiconductor character. The highest occupied crystal orbital (HOCO) was calculated to be the p orbitals of
a -6
Table 1 Parameters for H, C, and the first row transition metals f1
H C
1s 2s 2p 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d 4s 4p 3d
13.60 21.40 11.40 8.81 5.52 11.00 8.66 5.24 11.22 9.75 5.89 11.67 9.10 5.32 12.60 9.21 5.29 13.18 10.95 6.27 14.20
1.3000 1.6250 1.6250 1.3000 1.3000 4.7500 1.7000 1.7000 4.9500 0.9700 0.9700 5.1500 1.9000 1.9000 5.3500 2.0000 2.0000 5.5500 2.1000 2.1000 5.7500
V
Cr
Mn
Fe
Co
Ni
a
f2
C1a
C2a
-8
1.7000
0.4755
0.7052
1.8000
0.5058
0.6747
1.7000
0.5139
0.6929
2.0000
0.5505
0.6260
2.1000
0.5679
0.6059
2.3000
0.5493
0.6082
Coefficients used in the double-f expansion of the 3d orbitals.
dxz + π (Cp) NLU
-10
dyz + π (Cp) LU
NLUCO (k=π/a) LUCO (k=π/a)
EF π (Cp) HO
2 -12 NHO dz
-14
HOCO (k=π/a) 0
k
NHOCO (k=π/a)
π/a
b
c -6
-6
-8
-8
-10
Energy (eV)
Hii (eV)
Energy (eV)
Orbital
Energy (eV)
Atom
EF
-10 EF
-12
-12
-14
-14
M n 0
k
M=V, Cr, Mn, Fe, Co, Ni Fig. 1. Geometrical structures of the metallocene polymers.
π/a
0
k
π/a
Fig. 2. (a) A band structure and CO phases of PFC. Band structures of (b) PCoC and (c) PNiC.
Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
a -6 dyz + π (Cp)
LU
-8 Energy (eV)
LUCO (k=π/a)
-10 PO
POCO (k=π/a) dz2
EF
dx2-y2 + π (Cp) HO NHO dxy
-12
HOCO (k=π/a) -14
0
k
NHOCO (k=π/a)
π/a
b
c -6
-6
dyz + π (Cp) NLU
-10
-8
dz2 LU EF
HO
dx2-y2 + π (Cp)
-12
NHO dxy
Energy (eV)
-8 Energy (eV)
the Cp ring, and the lowest unoccupied crystal orbital (LUCO) exhibited an anti-bonding character between Fe 3dyz and the p orbitals of the Cp ring. The p electrons in bicyclopentadienyl were delocalised in the HOCO or LUCO; however, p delocalisation was not observed for the iron atoms in ferrocene. The next HOCO (NHOCO) and next LUCO (NLUCO) were formed by Fe 3dz2 and 3dxz with the p orbitals of the Cp ring, respectively. The atomic orbitals of a-carbon in the Cp rings did not contribute to NHOCO or NLUCO, and hence these bands possessed very small bandwidths. Fig. 2b shows the band structure of PCoC, whose band provides a deeper energy level as compared to that of PFC. The ground state of a unit cell of PCoC has one electron more than that of PFC, and hence PCoC consists of a partially occupied band. The CO phase of the partially occupied band exhibits an anti-bonding character between the iron atoms and the Cp ring. If we consider electron–electron repulsions in the band calculation, the partially occupied band probably splits due to the Jahn–Teller effect [12]. Therefore, the band structure of PCoC would possess a small band gap. As a result, PCoC possesses considerable reactivity due to the additional electron occupying the anti-bonding orbital and a smaller energy gap as compared to PFC. Fig. 2c shows the band structure of PNiC. The ground state of nickelocene has two electrons more than ferrocene, and hence the anti-bonding character between the Cp ring and the nickel atoms is greater than that in PCoC. The molecular structure of the unit cell in PNiC is also modified by the Jahn–Teller effect [12]. The band structures of PCoC and PNiC are similar to the band structure of PFC. In contrast, PMnC, PCrC, and PVaC possess a band structure different from that of PFC. Fig. 3a shows the band structure of PMnC. The unit cell of PMnC is only one electron short of that of PFC, and hence PMnC has a partially occupied band. The partially occupied crystal orbital (POCO) of PMnC consists of 3dz2 orbitals, which are located at a higher level as compared to that of PFC. The small bandwidth suggests that the electron occupying the band is considerably localised. PMnC probably possesses characteristic magnetic properties along with ferromagnetic or antiferromagnetic interaction. The CO phases of the HO and LU bands are formed by the hybridization of the Mn 3d orbital and the p orbitals of the Cp ring. The CO phase of the next HO (NHO) band is formed by the isolated Mn 3dxy orbital. The band structure of PCrC is similar to that of PMnC. The unit cell of PCrC is one electron short of that of PMnC, and hence PCrC possesses a band gap. The band gap of PCrC is smaller than that of PFC, and the HO and LU bands, whose CO phases are formed by dx2 y 2 and dz2 , respectively, possess small bandwidths that result in the low charge mobility. If the polymer is a stable compound, n-type doping possibly provides a localised electron in the LU band that consists of the Cr 3dz2 orbital; the supply of the electron plays an important role in the magnetic properties of the polymers.
103
-10 EF
-12
-14
-14
0
k
π/a
0
k
π/a
Fig. 3. (a) A band structure and CO phases of PMnC. Band structures of (b) PCrC and (c) PVaC.
PVaC exhibits a metallic character, similar to PCoC and PNiC. The partially occupied dx2 y 2 band crosses the Fermi level at 11.03 eV. The NHO band formed by isolated Fe 3dxy is also located near the Fermi level and the bandwidth is very small. PVaC can undergo structural changes due to the Jahn–Teller effect, and this would result in its exhibiting semiconductor character. In particular, we must consider the fact that the extended Hu¨ckel approximation is a qualitative empirical method. It is suitable for comparing the electronic structures of different chemical compounds; however, the open-shell electron systems of the metallocene polymers may allow other electronic states such as multiplet spin states or electron localisation derived from the pairing distortion such as a charge density wave (CDW) [13]. It is widely accepted that ordinary polymers cannot exhibit a multiplet spin state due to their chemical stability [14]. On the other hand, the pairing distortion may occur in polymer systems that have unpaired electrons.
104
Y. Matsuura, K. Matsukawa / Chemical Physics Letters 447 (2007) 101–104
Table 3 Differences in the total energies of a unit cell of the metallocene polymers Polymer Etot
2E0tot ðeVÞa
PVaC
PCrC
PMnC
PFC
PCoC
PNiC
0.085
0.026
0.056
0.023
0.086
0.056
a
Etot is the total energy of a unit cell of the metallocene polymers with pairing distorsion. E0tot is the total energy of a unit cell of the metallocene polymers with no pairing distorsion.
We calculated the band structures of the metallocene polymers with a pairing distortion of the nearest unit cells. The pairing distortion was achieved solely by altering the bond lengths between the nearest unit cells. The bond lengths between the nearest a-carbons of the Cp rings were ˚ , and other structures in the unit cell are the 1.44 and 1.54 A same as those of the polymers with no pairing distortion. Therefore, a unit cell of the polymers with the pairing distortion includes the two metallocenes. The band structures of the metallocene polymers were found to be similar to the folding relationship when doubling the unit cell size of the metallocene polymers with no pairing distortion [15]. Table 3 shows the difference between the total energies of a unit cell of the metallocene polymers. Among the metallocene polymers, PVaC, PMnC, PCoC, and PNiC, which have unpaired electrons in the unit cell, possess relatively larger energy differences as compared to PCrC or PFC. Especially, PVaC and PCoC have a large energy difference. This suggests that the pairing distortion for stabilizing the chemical structures may occur easily in these metallocene polymers. 4. Conclusion As mentioned above, it is found that a change of transition metal permits a drastic change in the band structures of the metallocene polymers. The 3dz2 bands of PFC, PCoC, and PNiC are stabilised when two electrons occupy them. The band structures of the metallocene polymers can be classified as follows: (1) semiconductor (PFC, PCrC), (2) metallic character with the possibility of an insulator transition (PCoC, PNiC, PVaC), and (3) localised partially occupied band (PMnC). PCoC, PNiC, and PVaC can possess considerable chemical reactivity that is comparable to metallocene monomers. If PMnC is a chemically stable compound, it is expected to exhibit characteristic magnetic properties. PCrC probably exhibits a semiconductor char-
acter with a higher electrical conductivity that is greater than that of PFC. We have also examined the possibility of occurrence of a pairing distortion in the metallocene polymers. Although the occurrence of multiplet spin states in polymers is unusual, we cannot eliminate the possibility of the spin states. Furthermore, it is difficult to evaluate the spin states in the polymer systems using the tight-binding crystal orbital method. Therefore, in a future study, the chemical structure of the model oligomers of the metallocene polymers will be optimized and the electronic structures of the various spin states will be examined by employing a better approximation method such as the DFT B3LYP method. Acknowledgements The authors would like to 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 in the University of Bristol. References [1] A. Togni, T. Hayashi (Eds.), Ferrocenes, VCH Publishers, NY, 1995. [2] C. Engtrakul, L.R. Sita, NanoLetters 1 (2001) 541. [3] D.O. Cowan, J. Park, C.U. Pittman Jr., Y. Sasaki, T.K. Mukherjee, N.D. Diamond, J. Am. Chem. Soc. 94 (1972) 5110. [4] S. Barlow, D. O’Hare, Chem. Rev. 97 (1997) 637. [5] Y. Matsuura, K. Matsukawa, Chem. Phys. Lett. 428 (2006) 321. [6] Y. Matsuura, K. Matsukawa, Chem. Phys. Lett. 436 (2007) 224. [7] Z.-F. Xu, Y. Xie, W.-L. Feng, H.F. Schaefer III, J. Phys. Chem. A 107 (2003) 2716. [8] K.C. Hultzsch, J.M. Nelson, A.J. Lough, I. Manners, Organometallics 14 (1995) 5496. [9] H. Hilbig, P. Hudeczek, F.H. Ko¨hler, X. Xie, P. Bergerat, O. Kahn, Inorg. Chem. 37 (1998) 4246. [10] G.A. Landrum, Yet Another extended Hu¨ckel Molecular Orbital Package (YAeHMOP), Cornell University, 1997. [11] Cottrell, The Strengths of Chemical Bonds, second edn., Butterworths, London, 1958; S.W. Benson, J. Chem. Edu. 42 (1965) 502. [12] M.C. Bo¨hm, J. Chem. Phys. 80 (1984) 2704. [13] M.-H. Whangbo, Acc. Chem. Res. 16 (1983) 95. [14] J.S. Miller, A.J. Epstein, Angew. Chem., Int. Ed. Engl. 33 (1994) 385. [15] R. Hoffmann, C. Janiak, C. Kollmar, Macromolecules 24 (1991) 3725.