Electronic transport properties of (fluorinated) metal phthalocyanine

The magnetic and transport properties of the metal phthalocyanine (MPc) and F$_{16}$MPc (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Ag) families of molecules in contact with S-Au wires are investigated by density functional theory within the local density approximation, including local electronic correlations on the central metal atom. The magnetic moments are found to be considerably modified under fluorination. In addition, they do not depend exclusively on the configuration of the outer electronic shell of the central metal atom (as in isolated MPc and F$_{16}$MPc) but also on the interaction with the leads. Good agreement between the calculated conductance and experimental results is obtained. For M = Ag, a high spin filter efficiency and conductance is observed, giving rise to a potentially high sensitivity for chemical sensor applications.


I. INTRODUCTION
Metal phthalocyanines (MPcs) constitute a family of medium sized molecular semiconductors, which are of considerable interest for numerous applications such as chemical sensors [1], fuel cells [2], solar cells [3], and optoelectronic devices [4]. A large number of MPcs can be synthesized [5] and geometrically arranged in large areas at low cost [6], which is important from the technological point of view. In particular, the photoconductivity of MPcs has been studied intensively with the purpose of increasing the electrical conductivity of devices based on these molecules by doping [7]. The improvement of the organic semiconductor devices relies on the quality of the metal-organic interfaces [8], in particular, on the efficiency of charge injection and on the mobility of the charge carriers [9,10]. For example, there is a charge transfer shift of the electronic levels at the CuPc/Au interface in the early stages of CuPc deposition on Au [11], and new occupied molecular states are created [12,13].
The replacement of the M atom as well as the substitution of H by F (fluorinated MPc) alters the electronic band gap [14], the latter resulting in n-type conduction, in contrast to the p-type behavior of the standard MPcs [15,16]. The charge transport through the molecule can be measured directly [17,18] or indirectly by photo-induced electron transfer [19], time resolved microwave conductivity [20], and scanning tunneling microscopy [21]. Au-CuPc-Au structures have been built by Nazin et al. [22], who observed a shift and splitting of the molecular orbitals as well as modifications of the electrode orbitals by scanning tunneling microscopy. Field-effect transistors and metal-insulator-semiconductor diodes have been used to study the transport through CuPc for different leads such as Ca, Au, and F 4 TCNQ/Au, demonstrating both electron or hole transport with a strong dependence on the geometry of the molecule-metal contact [23]. CuPc sandwiched between two semi-infinite Au electrodes has been investigated theoretically in Refs. [24,25]. The transmission coefficient, T (E), shows two peaks near the Fermi energy (E F ) which have been dissected in terms of molecular orbitals. The electronic states of CuPc hardly change when leads are attached.
On the other hand, the Landauer approach and Green's function formalism have been used to address the quantum transport in MPc structures. MPcs with M = Mn, Fe, Co, Ni, Cu and Zn sandwiched between semi-infinite armchair single-walled carbon nanotubes (SWNT) have been considered in Ref. [26] using the SMEAGOL package [27,28]. Within the generalized gradient approximation (GGA) it has been concluded that FePc and MnPc can be used as spin filters, and that the spin filter efficiency increases when N-doped graphene nanoribbons are used as leads for FePc [29]. To overcome the weak interaction between Au contacts and MPcs, S atoms have been added, leading to a distinct molecular bonding. The transport properties of such AuS-MPc-SAu (M = Cu, Mn) systems have been studied by the WanT code, with the result that electronic correlations are likely to be irrelevant [30].
Additionally, the authors have concluded that CuPc is a molecular conductor, and MnPc a spin filter.
In this article we extend previous works on AuS-MPc-SAu and AuS-F 16 MPc-SAu junctions by including spin polarization, and by considering a variety of different metals (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Ag). The effect of local electronic interactions on the central metal atom are also studied systematically. In Sec. II we discuss the computational method and present the magnetic properties. Then (Sec. III) the transport properties and finally (Sec. IV) the spin filter efficiency and electronic conductance are discussed. A summary is given in the concluding Sec. V.

II. COMPUTATIONAL METHOD AND MAGNETIC MOMENTS
The transport properties are investigated using non-equilibrium Green's function and density functional theory as implemented in the SMEAGOL [27,28] and SIESTA packages [31]. The wave functions are expanded in atomic orbitals with an energy cutoff of 300 Ry [32]. The nuclei and core electrons are represented by Troullier-Martins pseudopotentials [33]. We employ the local density approximation with Coulomb interaction (LDA+U). The on-site Coulomb interaction, U, is applied to the d orbitals on the central metal ions. Forces below 0.04 eV/Å are achieved in the structural optimization of MPc, using the conjugate gradient method. Since for metallic chains a Peierls gap is expected around the Fermi energy, we do not relax the structure after attaching the leads to the molecule [34]. We use the first two of the five-Au-atom leads, respectively, to calculate the surface Green's function, while the other three, closer to the molecule, are assumed to be part of what is usually called "scattering region". The Au-Au distance is chosen to be 2.89Å [22,23,30], and the interface distance between MPc and Au is set to 1.37Å [23].
The electronic and magnetic properties of isolated MPc and F 16 MPc molecules have been studied before [35], where it was found that the magnetic moment (MM) is carried mainly by the metal atom. Below we will compare, in particular, isolated molecules with molecules connected to leads, with emphasis on the differences. In addition, since the central atom is a transition metal, we will encounter all possible d orbital occupations, which usually give rise to considerable correlation effects. Thus it will be important to also investigate, not only for a few selected cases but systematically, the effect of a local Coulomb interaction on the electronic structure as well as on transport properties. Since the interaction parameter (U) is not known a priori for the junctions to be considered, we study values from U = 0 to U = 8 eV, in order to describe the range from weak to very strong correlation.
The structure of the devices is shown in Fig. 1. As a general remark, we note that the Mulliken analysis shows a considerable charge redistribution due to the leads (Au atoms), mainly involving the M atom, and the N and C atoms close to the central atom and at the contact between leads and molecule.
The calculated magnetic moments are summarized in Table I. We first discuss the total MMs for the AuS-MPc-SAu system. For M = Sc the MM differs slightly from that of the isolated molecule (1 µ B ), and there is no effect of the U parameter, whereas the MM of the M = Ti system is higher than for the isolated molecule (2 µ B ), inceasing with U. Apparently the d-d electron interaction of Ti enhances the charge transfer from the gold chain to the molecule when correlation increase. For V and Cr the MM for U = 0 is smaller than that of the isolated molecule (3 µ B for VPc, 2 µ B for CrPc). As U increases from 4 to 8 eV, the MMs get closer to the isolated molecule value. For Mn junctions the MM is mainly located on Mn (4.8 µ B for plain MnPc) and hardly depends on U.
For the Fe case, the magnetic moment of isolated FePc happens to be close to 2 µ B , but is found to be strongly increased in the junction due to the overlap between Au orbitals and molecular orbitals. For the last five columns in the table, Co . . . Ag, we note, first of all, that the total MM of the respective isolated molecules are close to 1, 0, 1, 0, 1 µ B , respectively. Thus it is apparent that the coupling to the leads has a significant effect in all cases for MPc, while the disturbance due to the leads is rather small for the fluorinated counterparts (considering first U = 0). For both, MPc and fluorinated MPc, we find a considerable correlation dependence for Co and Ni. However, due to the strong coupling to the leads for MPc, this dependence cannot straightforwardly explained by the electronic configurations of the respective isolated metal atoms. On the other hand, there is hardly any U-dependence for Cu, Zn and Ag (filled d shells).
Table I also shows that the magnetic moment on the central metal atom in most cases differs considerably from the total magnetic moment. The U-dependence of the metal magnetic moment generally is small, except for Co and Ni.   and molecular states). We find zero transmission at the Fermi energy, also in contrast to the results for FePc connected to SWNT [26,29].
For the case of Co in the center of the Pc molecule, the T (E) peaks are sharp lines, and their positions vary with U. There are two peaks below and one peak above E F for every U value, see right hand side of Fig. 4. For U = 0, the peak in T (E) at −0.5 eV is related to molecular as well as Au and b 1g states. There are two additional peaks at 0.5 eV (molecular orbitals with b 1g ) and at 1.4 eV (molecular orbitals with e g b 1g a 1g ).
For the AuS-CuPc-SAu junction, several transmission peaks are found below the Fermi The energy difference between the first peak below and the first one above E F for U = 4 is smaller than the corresponding one for U = 0 and 8 eV.
Last but not least we discuss AuS-AgPc-SAu and AuS-F 16 AgPc-SAu (Fig. 6). The T (E) peaks demonstrate a good coupling between lead and molecule as shown in the left hand side of Fig. 6 (AuS-AgPc-SAu). We find peaks for spin up states at E F , independent of U, which indicates that this configuration has a very good potential as a spintronic device.
The change of the interaction parameter does not affect the positions of the peaks below the Fermi energy. However, we observe a strong dependence of the peak position and intensity on U above the Fermi energy: as U increases, the peak moves further away from E F , and the intensity increases almost by a factor of two. This indicates that as electron localization increases, the transmission also increases for that particular state. For the AuS-F 16 AgPc-SAu junction, right hand side of Fig. 6, the transmission peak near −0.1 eV is finite for both spin polarizations, and independent of U. The transmission near the Fermi energy is dominated by molecular states with a 1g b 1g orbitals.

IV. SPIN FILTER EFFICIENCY AND CONDUCTANCE
The spin filter efficiency (SF E) for an electronic device, defined as is the ability of a device to pass a particular spin component. Here, T ↑ (E F ) and T ↓ (E F ) denote the transmission coefficients of spin up and spin down electrons at the Fermi energy, respectively. Our findings are summarized in Table II, the positive values corresponding to the case where "up" is the majority spin, while a negative sign means that the majority spin is "down". We note that the magnitude and the sign of the spin filter efficiency can vary with the interaction parameter. In some cases the majority spin in F 16    However, a significant electronic conductance is also essential for the performance of a device, hence we determine in addition the conductance, For the uncorrelated case, U = 0, the junction which includes AgPc shows the highest conductance, close to 0.22 G 0 . The next higher one is CuPc with 1.8 × 10 −4 G 0 . This value is smaller than the experimental result found in aromatic molecules by two orders of magnitude [38,39], but our result roughly agrees with another theoretical calculation [25].
Differences in theoretical results generally depends on the construction of the junctions, as well as the employed calculational method and the details of the (weak) interaction between molecule and leads. From a practical point of view, the results will also depend on the interaction between the junction and the substrate, which is not taken into account here and in most other studies.
The conductance of ZnPc is found to be 3 × 10 −5 G 0 , which is the same order as previous experimental and theoretical results for an oligo-porphyrin molecular wire by using Zn in the molecule center [44]. We mention in passing that for TiPc and VPc, which are also chemically unstable [37,[40][41][42][43], a vanishing conductance is obtained.
In F 16 MPc, the conductances in most cases are less than for the corresponding MPc. The highest conductance is found for F 16 AgPc, namely 0.002 G 0 , the next highest value being

V. SUMMARY
In this paper we studied systematically the magnetic, electronic and transport properties of metal phtahlocyanines and fluorinated metal phthalocyanines connected to Au leads, including some MPc molecules which are chemically unstable. We employed the LDA+U approach, with values of the Coulomb interaction parameter ranging from U = 0 to U = 8 eV. The magnetic moments are largely determined by the hybridization between d metal and Au states near the Fermi energy. The magnetic moments (Table I) to some extent vary with the electron-electron interaction on the central metal atom, U, which also for some systems considerably modifies the spin filter efficiency (Table II). Considering Eq. (1), it is apparent that the spin filter efficiency is a very sensitive quantity whenever the transmission coefficients for both channels are very small.
In particular, the magnetic moments are found to increase with increasing correlation, or are roughly independent of U. For the transport properties, the situation is less clear: it appears that for some systems the spin filter efficiency hardly depends on U, while others are quite sensitive to correlation effects. There can be a remarkable difference between MPc and its fluorinated counterpart. In detail, the results can be explained by the respective electronic structure near the Fermi surface, which, however, is not only determined by the orbitals of the central metal atom but also by the coupling to the leads. In order to finally clarify the role of electronic correlation in the series of junctions considered, additional experimental efforts will be needed. Overall we find very good agreement between our theoretical results and other theoretical and experimental results for the electronic conductance where these are available.
The structures with Ag in the center of the junction are a notable exception: they show both a good spin filter efficiency and a reasonable electronic conductance since the contribution of Ag states at the Fermi energy is large. Hence AgPc and F 16 AgPc junctions can potentially be used in spintronic devices.