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Electronic Structure-Transport Property Relationships of Polyferrocenylene, Polyferrocenylacetylene, and Polyferrocenylsilane Guiling Zhang,*,† Yue Qin,† Hui Zhang,† Yan Shang,† Miao Sun,† Bo Liu,† and Zesheng Li‡ College of Chemical and EnVironmental Engineering, Harbin UniVersity of Science and Technology, Harbin 150080, People’s Republic of China, and State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin UniVersity, Changchun 130023, People’s Republic of China ReceiVed: December 21, 2009; ReVised Manuscript ReceiVed: April 12, 2010
Combining nonequilibrium Green’s function technique with density functional theory, the electronic structure-transport property relationships of polyferrocenylene, polyferrocenylacetylene, and polyferrocenylsilane were comparatively studied. We have found that the bridge group between two adjacent ferrocene units plays an important role in tuning their conductivity. The conductivity follows the sequence polyferrocenylene, polyferrocenylacetylene, and polyferrocenylsilane, in agreement with the experimental observation. The sequence cannot be interpreted by different band gaps; electronic structure factors such as Fe-Fe, Fe-cyclopentadienyl, and cyclopentadienyl-bridge group interactions, which influence the conductivity, are identified. 1. Introduction Since the 1960s, ferrocene-containing polymers have attracted growing attention due to their potentially interesting optical, electronic, and magnetic behavior.1 Examples are polyferrocenylene (a), polyferrocenylacetylene (b), and polyferrocenylsilane (c), as given in Figure 1. Encouragingly, abundant derivatives of these polymers have also been successfully synthesized, which have already been used in modified electrodes, electrochemical sensors, nonlinear optical devices, and so forth.2 The a-c polymers as well as their derivatives compose a considerable well-defined class in the conducting field, which have been and still will be a hot topic.3 The bridge groups connecting ferrocene moieties possess an ability to tune their transport properties. Theoretical investigations on the electronic structure-transport property relationships of a-c are very attractive for the engineering of materials with improved characteristics, which is the main task of this work. In experiments, ferrocene-containing polymers have been produced mainly via the condensation route and thermal ringopening polymerization.1i Polyferrocenylene is a particularly attractive synthetic target owing to its potentially useful and unusual properties induced by the short ferrocene-ferrocene distance. Preparation of polyferrocenylene was first described by Korshak et al. in the early 1960s.4 Neuse et al. reported a conductance, σ, of approximately 10-12 S · cm-1 for neutral polyferrocenylene in 1981,5 while Sanechika et al. presented a higher value, 0.4-8 × 10-10 S · cm-1.6 Until 2002, convenient, reproducible routes to soluble polyferrocenylenes with substituents attached to the cyclopentadienyl were available.7 When partially or fully doped, polyferrocenylene exhibited high conductivity (σ ) 10-2 S · cm-1),8 strong intervalence chargetransfer band,9 and an extensive degree of Fe-Fe interaction by cyclic voltammetry.10 It has been demonstrated that the introduction of rigid-rod alkynyl into organometallics may introduce a range of properties that differ from those of * To whom correspondence should be addressed. † Harbin University of Science and Technology. ‡ Jilin University.
Figure 1. The studied systems in this paper.
conventional organic polymers.1i,11 Though alkynylferrocenes and their metal complexes have been well-studied,12 the incorporation of alkynyl into ferrocene backbone polymers had been a challenge for a long time due to a lack of useful starting materials.13 Excitingly, a series of oligoferrocenylacetylenes were prepared by Plenio et al.14 recently using coupling procedures. UV-visible measurements on oligoferrocenylacetylenes showed that the ferrocene d-d transition was electronically coupled to the conjugated chain. However, the extinction coefficient of the Feto-Fe charge-transfer bands was very low, suggesting that the electronic coupling of the Fe centers was significantly weak.14 Polyferrocenylsilane with high molecular weights was first reported in 1992 and showed about a 10-14 S · cm-1 conductance in the neutral state.15 Polyferrocenylsilanes are now a well-established class of ferrocene-containing polymers which are available in the form of well-defined and controlled architectures using living polymerization techniques.1e,2a,3c,16 These polyferrocenylsilane materials are relevant for many applications such as catalysis,17
10.1021/jp912030d 2010 American Chemical Society Published on Web 04/30/2010
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lithography,18 uses as redoxactive gels,19 molecular and ion recognition,20 and the formation of liquid crystalline21 and selfassembled supramolecular materials.22 A zigzag trans configuration was found for ferrocenylsilane units by substitution effect and X-ray diffraction.23 Cyclic voltammetric studies have revealed the presence of Fe-Fe interactions along the polyferrocenylsilane backbone, and when oxidatively doped, the hole conductance was up to ∼10-4-10-5 S · cm-1 weaker than that of the doped polyferrocenylene (10-2 S · cm-1).24 In most cases, ferrocene-containing materials, a-c, can become conductors exclusively under oxidative doping conditions. It is noteworthy that the transport ability in the doped state of a-c correlates well with their undoped state. For instance, the undoped a has a higher conductivity than the undoped c, and this is also true for their doped states. Therefore, investigating the transport properties of their undoped states could offer a clue to understand the conducting mechanism for their doped styles. To the best of our knowledge, only a few theoretical works are related to oligomers of a-c. Warratz et al. used a fourlevel, two-mode vibronic coupling model to treat ferroceneferrocenium dimers.25 This model provided satisfactory fits of the measured intervalence charge-transfer spectra and gave electronic and vibronic coupling parameters as well as CI mixing coefficients. Barlow et al. performed a molecular mechanics study of oligomeric models for polyferrocenylsilanes using the extensible systematic force field.26 They found that the conformations of neutral species were principally determined by Fe-cyclopentadienyl electrostatic interactions. The possibility of intermolecular Fe-cyclopentadienyl attractions in the solid state led to different conformations being found in crystal structures than those predicted for isolated molecules. Bo¨hm reported a semiempirical crystal orbital calculation of polyferrocenylene using the INDO method in 1984.27 It was predicted that the valence band (VB) and the conduction band (CB) were a ligand π-band with a narrow bandwidth, and the band gap was estimated to be 7.55 eV. Other theoretical works, especially on the electronic structure-transport property relationships of a-c, are seldom considered, which would be very desirable for the generation of ferrocene-containing materials with novel chemical and physical characteristics. The aim of this work is to systematically study the relationships between the electronic structures and the transport properties of a-c by combining nonequilibrium Green’s function technique with density functional theory (DFT). The analysis will be considered from the electron transmission property, the geometry, the band structure, and the bonding character. In order to facilitate discussions, the following symbols are used (c.f. Figure 1): -(Fc)n- for polyferrocenylene, -(CtC-Fc)n- for polyferrocenylacetylene, -(Si-Fc)n- for polyferrocenylsilane, and Cp for cyclopentadienyl. 2. Theoretical Methods Experiments have observed that the ferrocene units take a cis arrangement in a1c,7 and b,28 as shown in Figure 1. With regard to c, three orientations (trans, cis, and perpendicular conformers) were predicted (c.f. Scheme 1), but it prefers the trans configuration, confirmed by both experimental and theoretical investigations.23b,29 We also carried out VASP optimizations on these three structures by using the following method and still found that its most stable conformer was the trans conformation. Therefore, the orientations of a-c displayed in Figure 1 were selected for the present study.
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Figure 2. Schematic representations of the unit cell, L Å × 15 Å × 15 Å, of polyferrocenylsilane for VASP calculations. The red, purple, gray, and white balls denote Fe, Si, C, and H atoms, respectively.
SCHEME 1: Three Orientations for c as Well as Their Total Energies Obtained from VASP Optimizations
2.1. VASP Calculations. Periodic boundary conditions (PBC) were adopted to model infinite chains via repeated unit cells to relax the ions and predict band structures and densities of states (DOS) using DFT with the general gradient approximation (GGA).30 Each repeated cell included two ferrocene units, that is, a dimer model. Unit cells were set as L Å × 15.0 Å × 15.0 Å (x, y, z directions, respectively), as exemplified by polyferrocenylsilane in Figure 2. The lengths of L based on the experimental results7,23b,29 were 10.24, 14.79, and 13.74 Å for a, b, and c, respectively. The cutoff energy of plane waves was set as 250.0 eV. The functional proposed by Perdew and Wang,31 named PW91, was applied. The electron-ion interaction was represented by ultrasoft Vanderbilt-type pseudopotentials (USPP).32 The tetrahedron method with Blo¨chl corrections33 was used to determine partial occupancies for setting each wave function. Spin-polarized calculations were carried out for the studied a-c. The Monkhost-Pack mesh34 sampling with a 21 × 1 × 1 k-point in the string Brillouin zone (x, y, z directions, respectively) was employed. Computations were performed on an SGI 3800 workstation with the VASP program package,35 which was developed at the Institut fu¨r Theoretische Physik of Technische Universita¨t Wien.
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Figure 4. Current-voltage (I-V) characteristic of a-c units selfassembled on the Au(111) surface. Figure 3. The two-probe systems of a-c units self-assembled on the Au(111) surface. The chains together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while the remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region. The positive applied bias corresponds to that the current flows from the left to the right electrodes, and the negative applied bias corresponds to that the current flows from the right to the left electrodes.
GGA (0.153 µA for 0.2 V; 0.245 µA for 0.4 V; and 0.316 µA for 0.6 V) and LDA (0.144 µA for 0.2 V; 0.241 µA for 0.4 V; and 0.311 µA for 0.6 V). Since in the present work we were interested in the relative difference in transport properties between a, b, and c, the LDA exchange-correlation potential was used for the sake of easier convergence in computations. 3. Results and Discussions
2.2. Natural Bond Orbital Analysis. The natural bond orbital (NBO) analysis36 implemented in the Gaussion 03 package was performed for dimers a-c on the basis of the VASP optimized geometries to quantitatively evaluate the Fe-Fe, Fe-(Cp)2, and Cp-bridge group interactions. The B3LYP functional was employed. The Fe atom was treated with the Lanl2DZ basis set (the valence orbital of Fe was selected to be 3d4s4p), and other elements were treated with the 6-31+G* basis set. 2.3. ATK Calculations. The electronic transport properties of dimers a-c were calculated with the ATK 2.0 program,37 which combines the nonequilibrium Green’s function formalism and DFT. The method included full self-consistent treatment of the molecular device. Figure 3 shows our models of the twoprobe Aun-S-dimer-S-Aun systems. The semi-infinite electrodes were modeled by two Au(111)-(3 × 3) surfaces, and five layers were used for the left and right side. The whole system was divided into three parts, the left electrode, the scattering region (including two layers of Au atoms and the -S-dimer-Sregion), and the right electrode. The geometry of the dimer was the same as the VASP relaxed one. As the sulfur atom has good affinity with the gold surface, dithiolate derivatives have been used for the construction of metal-molecule-metal junctions in general.38 Therefore, in the present study, we also used the sulfur atom as the junction to link the Au electrode and the dimer. The sulfur atom was set to the hollow site of the electrode as most of the studies had elucidated that the hollow site was more favorable in energy than the top and bridge adsorption sites.38 In this model, the S-Au distance was set as 2.341 Å according to literature reports.39 Calculations were carried out by changing the applied bias by a step of 0.2 V in the range of -1.6-1.6 V. The positive bias corresponded to the current flowing from the left to the right electrodes, and the negative bias suggested an opposite direction. A single k-point was used for the one-dimensional chain perpendicular to the transport direction. A double-ζ basis functional with polarization (DZP) was used for all atoms. We compared the calculated current under 0.2, 0.4, and 0.6 V applied bias between GGA and LDA (local density approximation) exchange-correlation potentials for dimer a and found that there was a negligible difference of less than 0.009 µA between
In this section, we focus on the electron transport property from ATK calculated results and further analyze the influences of the geometry, the band structure, and the bonding characteristic on the transport mechanism by combining NBO and VASP calculated results. 3.1. Electron Transport Property. The current I(V) through the molecule was calculated from the well-known LandauerBu¨tiker formula40
I(V) ) G0
∫-∞+∞ n(E)T(E, V) dE
(1)
where G0 ) 2e2/h is the quantum unit of conductance, h is the Plank’s constant, and T(E,V) is the transmission function for electrons with energy E at certain bias V. It is described as
T(E, V) ) Tr[ΓL(E, V)G(E, V)ΓR(E, V)G†(E, V)]
(2)
where G is the Green’s function of the scattering region, ΓL/R is the coupling matrix, and V is the applied bias. n(E) is written as a function below
n(E) ) f(E - µL(V)) - f(E - µR(V))
(3)
where µL(V) and µR(V) are the electrochemical potentials of the left and right electrodes, respectively, µL/R(0) is the Fermi level (EF), and f is the Fermi function. Figure 4 plots the current-voltage (I-V) curves of dimers a-c. The magnitude of the electric current is in the order of a > b > c under the same applied bias voltage. Investigating the electron transport property of dimers a-c could provide valuable information to understand the conducting mechanism of their corresponding polymers. In experiments, neutral polyferrocenylene (σ ) 10-12-10-10 S · cm-1)5,6 also gave a higher conductivity than neutral polyferrocenylsilanes (σ ) 10-14 S · cm-1).15 Moreover, upon oxidative doping, polyferrocenylene (σ ) 10-2 S · cm-1) still exhibited higher hole conductance than polyferrocenylsilane (σ ) 10-4-10-5 S · cm-1). Therefore, the bridge group plays an important role in governing the conductivity of such ferrocene-containing materials. To further investigate the transport properties of these systems, the energy dependence of the transmission spectra was calculated. As shown in eq 1, the current I(V) is closely related
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Figure 5. Transmission spectra of the two-probe a-c units self-assembled on the Au(111) surface at bias voltages of 0.0, (0.8, and (1.6 V. Blue dashed lines indicate the bias window. The integral areas of the resonant peaks within the bias window, S, are also given.
to the transmission function T(E,V). Only electrons with the energy near the Fermi level [µL(V),µR(V)] contribute to the total current. Here, [µL(V),µR(V)] is usually called the bias window. In the ATK program, the Fermi level has been set to 0.0 eV. Therefore, the bias window mainly refers to [-V/2,V/2].37b The current could be indirectly determined by T(E,V) in the bias windows. The larger the integral area of the resonant peaks within the bias window (denoted as S), the higher the current, and vice versa. The transmission spectra at 0.0, (0.8, and (1.6 V applied bias voltage as well as the integral areas of the resonant peaks within the bias window, S, are shown in Figure 5. Clearly, the value of S in a increases with the increase of the applied bias voltage. A similar trend was found for b, but its S is smaller than that of a in the presence of the same applied bias voltage. As for c, the total integral areas of the resonant peaks in the bias window are almost zero under various applied bias voltages, indicating that electrons cannot permeate easily from one Au electrode to another. Apparently, as far as the transmission spectra are concerned, the conductivity is in the order a > b > c, in line with the I-V character in Figure 4. Conductivity, as a complex phenomenon, is dependent on multiple factors, which include, for example, the geometry, the band structure, the bonding character, and so forth. In the following sections, we analyze these factors, correlating to the conductivities of the a-c systems. 3.2. Geometry. The bond lengths of the relaxed polymers, a-c, obtained from VASP calculations as well as the experimental observations are listed in Table 1. The atoms are labeled in Figure 1. The relaxed values are in good agreement with the experimental results.23,29 No apparent changes occur upon the C1-C2, C2-C3, and C1-C5 bond lengths after incorporating the CtC and SiH2 groups in the backbone. The C3-C4 and C4-C5 bond lengths are enlongated by 0.007 Å in b and by 0.003-0.004 Å in c compared with a. It is clear from Table 1 that some Fe-C bond lengths increase and some decrease if a is changed to b or c. In polyferrocenylacetylene, the distances between Fe and C1,2 are shortened (Fe-C1,2: 2.047 Å), while those between Fe and C3,4,5 are lengthened (Fe-C3,5: 2.052 Å; Fe-C4: 2.079 Å) in comparison with polyferrocenylene (Fe-C1,2: 2.050 Å;
TABLE 1: Selected Bond Lengths from VASP Relaxationsa bond
a (Å)
Fe-Fe 5.119 (5.38) Fe6-Si7
b (Å) b
c(exp.) (Å) c
7.394 6.872 (6.9) (6.056-6.913)d 3.463 (3.50-3.54)d
C-C Bond Lengths of Cp 1.435 1.435 C1-C2 1.434 C2-C3 1.433 1.432 1.431 C3-C4 1.443 1.450 1.447 C4-C5 1.443 1.450 1.446 C1-C5 1.433 1.432 1.432 Fe-C Bond Lengths between Fe and Cp Fe6-C1 2.050 2.047 2.054 (2.051-2.056)d Fe6-C2 2.050 2.047 2.054 (2.051-2.056)d Fe6-C3 2.048 2.052 2.037 (2.037-2.038)d Fe6-C4 2.065 2.079 2.039 (2.036-2.044)d Fe6-C5 2.048 2.052 2.037 (2.037-2.038)d Bond Lengths Relating to Bridge Atoms 1.413 C4-C7 1.453 C4-Si7 1.846 (1.830-1.867)d (1.835-1.883)c C7tC8 1.220 a
The values in brackets are those from experiments. The atoms are labeled in Figure 1. b Reference 7. c Reference 29. d Reference 23b.
Fe-C3,5: 2.048 Å; Fe-C4: 2.065 Å). However, polyferrocenylsilane exhibits converse bond length changes of Fe-C1,2 (2.054 Å) and Fe-C3,4,5 (Fe-C3,5: 2.037 Å; Fe-C4: 2.039 Å). It is surmisable that the CtC group and the SiH2 group could induce different Fe-(Cp)2 interactions, which will be documented in the following sections. As expected, polyferrocenylene possesses the shortest Fe-Fe separation (5.119 Å) followed by polyferrocenylsilane (6.872 Å), and polyferrocenylacetylene has the longest Fe-Fe distance (7.394 Å). 3.3. Band Gap. The band gap, Eg, is usually a major parameter to judge whether a material is promising for electric applications. Figure 6 shows the calculated band structures of a-c. These polymers display a direct band gap in the k (wave vector) space. The valence band is fully occupied by electrons, and hence, the Fermi level is located at the top of the valence
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∆Eg σ(b/c) ≈ 1 + γ (a) (a) σ Eg γ)
β/E(a) g 1 + β/E(a) g
(10)
(11)
The value of β is positive; therefore, the data of γ is in the range of 0 e γ e 1. Hence, the maximum ratio of σ(b/c)and σ(a)can be obtained as
( ) σ(b/c) σ(a)
Figure 6. Band structures of a-c obtained from VASP calculations. The Fermi level is set as 0.0 eV.
band. From the following discussions, we found that the conductivity of a-c cannot be completely decided by the band gap. The relationship between the effective mass of the charge carrier, m*, and the band gap, Eg, is as below41
m 2 |〈υ|Px |c〉| 2 )1+ m* mEg
(4)
where Px is the momentum matrix unit between the valence band and the conduction band, m is the mass of the charge carrier, and 〈υ| and |c〉 are the light hole states of the valence band and the lowest states of the conduction band, respectively. For a semiconductor, the conductance, σ, can be expressed by the hole effective mass, m*, p and the electron effective mass, m*n
σ)
pq2τp nq2τn + m*p m*n
(5)
where τp and τn are the mean free time for the hole and the electron, respectively, p and n are the hole concentration and electron concentration, respectively, and q is the quantity of electricity. Therefore, the conductance and the band gap have a following relationship
(
)
(6)
(A stands for p or n)
(7)
σ)R1+
β Eg
where
R)
Aq2τ m β)
2 |〈υ|Px |c〉| 2 m
(8)
Supposing a ∆Eg change in the band gap of b or c related to a, the conductance of b or c can be approximated as
(
σ(b/c) ) R 1 +
Then
E(a) g
) [
(
∆Eg β β ≈ R 1 + (a) 1 + (a) - ∆Eg Eg Eg
)]
(9)
)1+ max
∆Eg E(a) g
(12)
Table 2 lists the calculated values of Eg. Adding CtC groups between ferrocene units leads to a 0.22 eV decrease of the band gap and, consequently, should result in a 10.3% increase of the conductance, but in fact, b has lower conductivity than a. Inserting SiH2 groups induces a 0.32 eV increase of Eg and only a 15.2% decrease of the conductance. Therefore, different conductivities between a, b, and c cannot be completely attributed to their different band gaps. Other factors such as the bandwidth and the bonding characteristic should be significant to affect the conductivity. 3.4. Bandwidth and Effective Mass. The bandwidth is crucial to rationalize the transport property. Larger bandwidth implies stronger nonlocal property of the electrons, which is favorable to the tunneling. Table 2 lists the bandwidths of the valence band (VB) and the conduction band (CB). Clearly, a (VB: 0.11 eV; CB: 0.31 eV) has wider bandwidths compared to b (VB: 0.08 eV; CB: 0.30 eV), and b is wider than c (VB: 0.02 eV; CB: 0.20 eV), indicating that the nonlocal property of electrons orders as a > b > c. This is in agreement with the I-V characteristic. In fact, the VB and the CB are all very flat in these polymers, showing that the eigenstates corresponding to these bands mainly consist of localized atomic orbitals, that is, the electrons in these bands have strong localization characteristic. This case is reflected from the partial density of states (PDOS). Figure 7a shows the calculated PDOS for Fe3d, (Cp)2-2p, Si-3p, and Si-3d. It is evident that the valence band and the conduction band mainly originate from the Fe-3d state. This is inconsistent with the INDO calculated result that the VB and the CB are a ligand π-band.27 Maybe, the semiempirical theory which does not consider the electron correlation effect in the INDO method is responsible for this disagreement. The sharp peak of the Fe-3d state again illustrates the localization character of the electrons. Usually, larger bandwidth corresponds to smaller effective mass of the charge carrier, and this accordance can be found in Table 2. Smaller effective mass implies stronger mobility of the charge carrier, which is in accordance with the I-V behavior. 3.5. Fe-Fe Interaction. Electrochemical studies of a-c by cyclic voltammetry revealed the presence of two reversible waves with a separation of ∼0.5,7 0.145,14 and 0.33 V42 for a, b, and c, respectively, which is suggestive of the strongest and weakest Fe-Fe interaction in a and b, respectively. In most cases, ferrocene-containing polymers of a-c can become conductors only under oxidative doping conditions, for example, iodine doping. Experiments have demonstrated that the oxidized polyferrocenylene43 and polyferrocenylsilane44 can, in principle, exist as mixed valence polycations with alternating ferrocenylene and ferrocenium units (alternating Fe2+ and Fe3+ centers) along the backbone. The electronic coupling between the two mixed valence metal units plays an important role in the conducting behavior. Therefore, the strong Fe-to-Fe communication is beneficial to the electron tunneling in the polymer backbone.7,23b,45
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Figure 7. (a) Partial densities of states of Fe-3d and Cp-2p in a-c. (b) Partial density of states (PDOS) of the bridges CtC 2p and Si-3p/3d. The Fermi level is set as 0.0 eV.
TABLE 2: Some Parameters of the Band Structures and the Density of States Obtained from VASP Calculations bandwidth (eV)
m* (×10-31 kg)
integration intensity of Fe-3d PDOS
polymer
Eg(eV)
VB
CB
VB
CB
1e1′′
2a1′
1e2′
a b c
2.12 1.90 2.45
0.11 0.08 0.02
0.31 0.30 0.20
-157.4 -209.9 -524.7
41.4 44.3 64.2
0.30 1.02 0.33
1.58 0.79 1.64
2.69 3.61 2.21
The Fe-Fe distances intuitively show a sign that the Fe-Fe interaction is in the order of a > c > b. The shortest Fe-Fe distance, 5.119 Å, in polyferrocenylene gives the strongest Fe-Fe interaction. Polyferrocenylsilane has a weaker Fe-Fe interaction than polyferrocenylene owing to its longer Fe-Fe distance (6.872 Å). In polyferrocenylacetylene, the two Fe units are separated far away (7.394 Å) by the rigid-rod CtC bridge, resulting in the weakest Fe-Fe coupling. To get a further insight of the Fe-Fe interaction, we carried out NBO analysis of the dimers of a-c. In NBO analysis, the extent of the bond interaction could be evaluated from the stabilization energy, E(2), between an electron-donating and a neighboring electron-accepting orbital. This stabilization energy is expressed as36
E(2) ) -2
(〈ψD |F|ψA*〉)2 εA*-εD
(13)
where F is the Fock operator and εD and εA* are the NBO energies of the donor and acceptor orbitals, respectively. If the stabilization energy is large, strong interaction occurs between the two bonds. The calculated Fe-Fe stabilization energies are 6.8, 0.0, and 0.9 kcal · mol-1 for a, b, and c, respectively (cf. Table 3). This again confirms the difference in Fe-Fe interaction between a, b, and c. The strong Fe-Fe interaction is the crucial reason why a possesses a very high conductivity. 3.6. Fe-(Cp)2 Interaction. The Fe-(Cp)2 interaction is also a significant factor to affect the ability of the electron transfer along the chain. Strong Fe-(Cp)2 interaction confines the electrons intensively within the ferrocene unit and hinders the electrons’ escape from one ferrocene unit to another. First, we consider the results from the NBO analysis on the a-c dimers. It is known that the Fe-(Cp)2 interaction is
dominated by a π f d coordination interaction (occupied (Cp)22p orbitals contribute electrons to empty Fe-3d orbitals) and a feedback d f π coordination interaction (occupied Fe-3d orbitals contribute electrons to empty (Cp)2-2p orbitals). The calculated stabilization energies of the π f d interaction and the d f π interaction are summarized in Table 3, which reflects the different effect of the bridge group on the Fe-(Cp)2 interaction. In dimer b (π f d: 331.5 kcal · mol-1; d f π: 413.1 kcal · mol-1), the values of E(2) of both d f π and π f d interactions are largely increased by comparing with those of dimer a (π f d:193.4 kcal · mol-1; d f π: 281.7 kcal · mol-1), indicating that the Fe-(Cp)2 interaction is significantly strengthened by inserting a CtC segment between two ferrocene units. In dimer c (π f d: 178.6 kcal · mol-1; d f π: 303.8 kcal · mol-1), both π f d and d f π interactions have no remarkable change, in contrast to dimer a. This clarifies that the bounded extent of electrons within the ferrocene unit in dimer c is similar to that of dimer a. The Fe-(Cp)2 interactions in dimers a-c correlate well with their corresponding polymers, as addressed in the following section. Then, we take into account the density of states of a-c polymers. According to the schematic MO diagram of the interactions between Fe-3d and (Cp)2-2p given by Lein et al.46 (cf. Scheme 2), the peaks of the PDOS of the Fe-3d and (Cp)22p can be assigned by corresponding bands of 1e1′′, 1e1′, 2a1′, 1e2′, 2e1′′, 1e2′′, and 2e2′ as shown in Figure 7a (where some degenerate states of e1,2 are coupled into one peak). The corresponding numbers of states can be obtained by integrating the density of states of each band, which are listed in Table 2. In ferrocene, the unoccupied dxz and dyz atomic orbitals of iron directly overlap with the occupied pz orbitals of the (Cp)2 along the z direction. This overlap makes up the 1e1′′ and 2e1′′ bands,
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TABLE 3: Stabilization Interaction Energies between Electron-Donating and Electron-Accepting Orbitals, E(2) (kcal · mol-1), Obtained by Natural Bond Orbital Analysis
SCHEME 2: Orbital Interaction Diagram for Ferrocene
and a π f d coordination bond forms between (Cp)2-2p and Fe-3d. A larger PDOS of 1e1′′ of Fe-3d corresponds to a stronger π f d coordination bond. The dx2-y2 and dxyorbitals of Fe-3d point away from the (Cp)2-2p orbital and slightly couple with e2′ of the (Cp)2, forming occupied 1e2′ and unoccupied 2e2′ bands. The 1e2′ band mainly comes from Fe-3d states, and the 2e2′ band mainly originates from the (Cp)2-2p states; thus, a feedback d f π coordination bond forms. The remaining dz2 orbital of Fe-3d points directly to the center of the Cp ring and forms a nonbonding 2a1′ band. As the energy levels of 2a1′ and 1e2′ are very close,46 the distribution of Fe-3d electrons of the occupied 1e2′ and 2a1′ bands indicates the electron number participating in the d f π bonding. As shown in the changes in the PDOS (cf. Table 2), compared with those in -(Fc)n-, apparent increase occurs in the Fe-3d PDOS of 1e1′′ in -(CtC-Fc)n-, suggesting a stronger π f d coordination bond. On the other hand, the Fe-3d PDOS of 1e2′ in -(CtC-Fc)n- increases, and that of 2a1′ decreases. This case demonstrates that more d electrons participate in the d f π bonding, that is, the d f π interaction in -(CtC-Fc)n- is stronger than that in -(Fc)n-. In a word, both π f d and d f π interactions are enhanced as polymer a changes into polymer
b. A similar analysis was taken for -(Si-Fc)n-. It is found that polyferrocenylsilane has a similar Fe-(Cp)2 interaction to polyferrocenylene. Clearly, the Fe-(Cp)2 interactions in polymers a-c are in line with those in their dimers. It is noteworthy that the heavily enhanced Fe-(Cp)2 interaction in b locks up more electrons within the ferrocene unit, which is responsible for the reduction of its conductivity compared with a, though b has the lowest band gap. 3.7. Cp-Cp and Cp-Bridge Group Interactions. The Cp-Cp interaction of adjacent ferrocene units in -(Fc)n-, the Cp-CtC interaction in -(CtC-Fc)n-, and the Cp-Si interaction in -(Si-Fc)n- are especially important for electron tunnelling along the chain. If the interaction is strong, the electrons can easily transfer from one ferrocene unit to another, which is essential for the conducting. Table 3 lists the stabilization interaction energies for the Cp-Cp interaction in dimer a and Cp-bridge group interactions in dimers b and c. It is clear that the π-bond of the acetylene unit maintains a well-conjugated π-system between two ferrocene units (E(2) ) 10.9-15.9 kcal · mol-1 for the Cp-CtC interaction), a comparable strength to the Cp-Cp interaction in dimer a (E(2) ) 13.1 kcal · mol-1 for the Cp-Cp interaction), and in dimer c, the π-systems of two adjacent ferrocene units are separated by a linker providing only σ-bonds. The PDOS for their corresponding polymers also gives the same conclusion. Figure 7b is the PDOS of the bridge groups, CtC and Si. Obviously, the CtC 2p has contribution to the bands of 1e1′′, 1e1′, 2a1′, 1e2′, 2e1′′, 1e2′′, and 2e2′, while Si-3p/3d contribute little to these bands except 2e2′. This case illustrates that the CtC group can serve as a more effective electron transfer path than a Si linkage. This is a key reason why -(CtC-Fc)n- shows better conductivity than -(Si-Fc)n-. 4. Conclusions The electronic structure-transport property relationships of polyferrocenylene, polyferrocenylacetylene, and polyferrocenylsilane were comparatively studied by combining the nonequilibrium Green’s function technique and density functional theory. We have found that the bridge group between two adjacent ferrocene units plays an important role in tuning their conductivity. The conductivity is in the order of a > b > c, in agreement with the experimental observation. The sequence cannot be explained by different band gaps; electronic structure factors such as Fe-Fe, Fe-cyclopentadienyl, and cyclopentadienyl-bridge group interactions which influence the conductivity are identified. In a, a direct overlap between adjacent ferrocene units and a good C-Cp interaction are responsible for its high conductivity. In b, there is no direct Fe-Fe overlap, but the π-bond of the acetylene unit maintains a conjugate π-system between two ferrocene units. However, the heavily enhanced Fe-(Cp)2 interaction in b locks up more electrons within the ferrocene unit, which is responsible for the decrease of the conductivity compared with a. In c, the π-systems of
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two adjacent ferrocene units are separated by a linker providing only σ-bonds, leading to the weakest conductivity. Here, we must point out that although we used the VASP relaxed conformations to carry out ATK computations, the real structures under the two-probe system may not be completely the same as the relaxed ones because we neglected the conformational change under the applied biases, which may have influence on the transmission properties. The present investigation however is expected to be a basis for the analysis of such effects in the future. Acknowledgment. The authors thank two reviewers for their constructive and pertinent comments. The authors also thank the NSF of China (50743013, 20272011), the SF for leaders in academeofHarbinCityofChina(2010RFJGG016,2007RFXXG027), the SF for Postdoctoral of Heilongjiang province of China (LBHQ07058), and the SF for elitists of Harbin University of Science and Technology for financial support. References and Notes (1) (a) Roncali, J. Chem. ReV. 1997, 97, 173. (b) Novak, P.; Mu¨ller, K.; Santhanam, K. S. V.; Haas, O. Chem. ReV. 1997, 97, 207. (c) Barlow, S.; O’Hare, D. Chem. ReV. 1997, 97, 637. (d) Rehahn, M. Acta Polym. 1998, 49, 201. (e) Manners, I. Chem. Commun. 1999, 857. (f) Kulbaba, K.; Manners, I. Macromol. Rapid Commun. 2001, 22, 711. (g) Manners, I. J. Opt. A: Pure Appl. Opt. 2002, S221. (h) Manners, I. Macromol. Symp. 2003, 196, 57. (i) Schwab, P. F. H.; Smith, J. R.; Michl, J. Chem. ReV. 2005, 105, 1197. (2) (a) Manners, I. Science 2001, 294, 1664. (b) Kulbaba, K.; Manners, I. Polym. News 2002, 27, 43. (c) Manners, I. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 179. (3) (a) Jones, N. D.; Wolf, M. O. Organometallics 1997, 16, 1352. (b) Sun, Q.; Lam, J. W. Y.; Xu, K.; Xu, H.; Cha, J. A. K.; Wong, P. C. L.; Wen, G.; Zhang, X.; Jing, X.; Wang, F.; Tang, B. Z. Chem. Mater. 2000, 12, 2617. (c) Sun, Q.; Xu, K.; Peng, H.; Zheng, R.; ussler, M. H.; Tang, B. Z. Macromolecules 2003, 36, 2309. (d) Kim, K. T.; Han, J.; Ryu, C. Y.; Sun, F. C.; Sheiko, S. S.; Winnik, M. A.; Manners, I. Macromolecules 2006, 39, 7922. (e) Hatanaka, Y.; Okada, S.; Minami, T.; Goto, M.; Shimada, K. Organometallics 2005, 24, 1053. (f) Liu, K.; Clendenning, S. B.; Friebe, L.; Chan, W. Y.; Zhu, X. B.; Freeman, M. R.; Yang, G. C.; Yip, C. M.; Grozea, D.; Lu, Z.-H.; Manners, I. Chem. Mater. 2006, 18, 2591. (g) Friebe, L.; Liu, K.; Obermeier, B.; Petrov, S.; Dube, P.; Manners, I. Chem. Mater. 2007, 19, 2630. (h) Kumar, M.; Metta-Magana, A. J.; Pannell, K. H. Organometallics 2008, 27, 6457. (i) Huo, J.; Wang, L.; Yu, H.; Deng, L.; Ding, J.; Tan, Q.; Liu, Q.; Xiao, A.; Ren, G. J. Phys. Chem. B 2008, 112, 11490. (j) Michinobu, T.; Kumazawa, H.; Noguchi, K.; Shigehara, K. Macromolecules 2009, 42, 5903. (k) Miles, D.; Ward, J.; Foucher, D. A. Macromolecules 2009, 42, 9199. (4) (a) Korshak, V. V.; Sosin, S. L.; Alekseera, V. P. Dokl. Akad. Nauk SSSR 1960, 132, 360. (b) Korshak, V. V.; Sosin, S. L.; Alekseera, V. P. Vysokomol. Soed. 1961, 2, 1322. (c) Nesmeyanov, A. N.; Korshak, V. V.; Voevodskii, V. V.; Skochetkova, N.; Sosin, S. L.; Materikova, R. B.; Chibrikin, V. M.; Bazhin, N. M. Dokl. Akad. Nauk SSSR 1961, 137, 370. (5) (a) Neuse, E. W.; Bednarik, L. Macromolecules 1979, 12, 187. (b) Neuse, E. W.; Macromol, J. Sci. Chem. 1981, A16, 3. (6) Sanechika, K.; Yamamoto, T.; Yamamoto, A. Polym. J. 1981, 13, 255. (7) Park, P.; Lough, A. J.; Foucher, D. A. Macromolecules 2002, 35, 3810. (8) Yamamoto, T.; Sanechika, K.; Yamamoto, A.; Katada, M.; Motoyama, I.; Sano, H. Inorg. Chim. Acta 1983, 73, 75. (9) LeVanda, C.; Cowan, D. O.; Leitch, C.; Bechgaard, K. J. Am. Chem. Soc. 1974, 96, 6788. (10) Hirao, T.; Mamoru, K.; Aramaki, K.; Nishihara, H. J. Chem. Soc., Dalton Trans. 1996, 14, 2929. (11) Grosshenny, V.; Harriman, A.; Ziessel, R. Angew. Chem. 1995, 107, 1211. (12) (a) Ingham, S. L.; Khan, M. S.; Lewis, J.; Long, N. J.; Raithby, P. R. J. Organomet. Chem. 1994, 470, 153. (b) Russo, M. V.; Furlani, A.; Licoccia, S.; Paolesse, R.; Chiesi-Villa, A.; Guastini, C. J. Organomet. Chem. 1994, 469, 245. (c) Koridze, A. A.; Zdanovich, V. I.; Kizas, O. A.; Yanovsky, A. I.; Struchkov, Y. T. J. Organomet. Chem. 1994, 464, 197. (d) Sato, M.; Mogi, E.; Kamakura, S. Organometallics 1995, 14, 3157. (e) Sato, M.; Mogi, E.; Katada, M. Organometallics 1995, 14, 4837. (f) Lavastre, O.; Even, M.; Dixneuf, P. H.; Pacreau, A.; Vairon, J. P. Organometallics 1996, 15, 1530. (g) Colbert, M. C. B.; Lewis, J.; Long, N. J.; Raithby, P. R.; White, A. J. P.; Williams, D. J. J. Chem. Soc., Dalton
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