ARTICLE pubs.acs.org/JPCC
Magnetic Manipulation and Half-Metal Prediction of One-Dimensional Bimetallic Organic Sandwich Molecular Wires [CpTM1CpTM2]¥ (TM1 = Ti, Cr, Fe; TM2 = Sc-Co) Xiuyun Zhang,†,‡ Zhi Tian,† Shuo-Wang Yang,§ and Jinlan Wang*,†,^ †
Department of Physics, Southeast University, Nanjing, 211189, China Department of Physics, Yangzhou University, Yanzhou, 225009, China § Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore ^ School of Chemistry & Chemical Engineering, Southeast University, Nanjing, 211189, China ‡
bS Supporting Information ABSTRACT: We systematically investigate the stability and electronic and magnetic properties of one-dimensional (1D) bimetallic organic sandwich molecular wires (BOSMWs), [CpTiCpTM]¥ (TM = Sc-Co, Cp = C5H5), [CpCrCpTM]¥ (TM = V, Mn, Co), and [CpFeCpTM]¥ (TM = Cr, Co), using ab initio methods. All the BOSMWs are highly stable due to mixed ionic-covalent bonding. With the exceptions of [CpTiCpV]¥, [CpTiCpMn]¥, and [CpCrCpV]¥ exhibiting antiferromagnetic behavior, all the other BOSMWs are ferromagnetic with tunable magnetic moments. In particular, magnetic moments of [CpTiCpCo]¥ and [CpCrCpMn]¥ can be as high as 5 μB per unit cell. Our calculations further show that [CpTiCpTM]¥ (TM = Cr, Fe), [CpCrCpTM]¥ (TM = Fe, Co), and [CpFeCpCo]¥ are robust half-metals (HMs) with large HM gaps. Most importantly, we identify an empirical valence electron filling rule for these BOSMWs, and a BOSMW is found to be a half-metallic ferromagnet whenever N - 5(10) = 5(7) (N is the sum of the valence electrons of two metal atoms). This electron filling rule, together with the HM equations formulized in this study, can be extended to predict new HM BOSMWs.
I. INTRODUCTION Multidecker linear organometallic sandwich clusters and their infinite 1D molecular wires have attracted great interest recently due to their intriguing electronic and magnetic properties. A typical example is vanadium-benzene sandwich molecular wires (SMWs),1-15 where clusters of finite sizes showed a linear correlation with its magnetic moments6,7,9,10,14,15 and its infinite SMW was predicted to be a (quasi) half-metal (HM) and a good spin filter through ab initio calculations.9,11-15 Its ferrocene analogues (TMCp)¥ (TM = V, Cr, Fe) were also theoretically predicted to be HMs.16,17 Moreover, the mixed metal-ligand sandwich clusters VnBzmCpk showed tunable magnetic behavior and enhanced magnetic stability,18 and its infinite SMW (CpVBzV)¥ was also an HM within the framework of ab initio calculation.19 Additionally, ultrahigh magnetic moments20,21 and high spin filtering22 were revealed in europium (Eu)-cyclootatetraene (COT = C8H8) multidecker clusters (EunCOTnþ1). The novel magnetism originates from the open-shell d (f) electrons of metal atoms through double exchange interactions.16,17,20,21 On the other hand, bimetallic organic sandwich complexes are also attracting growing attention as their physical and chemical properties can be tailored by tuning the chemical components. r 2011 American Chemical Society
The first multidecker bimetallic organic sandwich clusters TMn(FeCp2)nþ1 (TM = V, Ti) were successfully synthesized by a laser vaporization method in 2000.23 From the theoretical perspective, our recent DFT calculations showed that TMn(FeCp2)nþ1 (TM = Sc, Ti, V, Mn)24 clusters are stable compounds, of which Cp rings gain electrons from TM atoms. We also observed that TMn(FeCp2)nþ1 (TM = Ti, V, Mn) clusters are ferromagnetic with their magnetic moments showing a linear correlation with the chain length and their infinite SMWs (CpFeCpTM)¥ (TM = Sc, Ti, V, Mn) are ferromagnetic semiconductors.19,24,25 Besides, the (CpFeCpV)n clusters were found to be a good spin filter when they are sandwiched between magnetic Ni electrodes and their spin transport property can be manipulated by changing the contact condition or adjusting the molecular length.26 Despite these great advances, further studies are required for a more detailed insight on the mechanism of the intriguing electronic and magnetic behaviors in BOSMWs. In this article, we carry out a systematic theoretical investigation on a number of Received: September 28, 2010 Revised: January 5, 2011 Published: February 2, 2011 2948
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The Journal of Physical Chemistry C 1D BOSMWs, namely, [CpTiCpTM]¥ (TM = Sc-Co), [CpCrCpTM]¥ (TM = V, Mn, Co), and [CpFeCpTM]¥ (TM = Cr, Co), by means of a spin-polarized DFT approach. Our calculations show that the BOSMWs are highly stabilized through mixed ionic-covalent interactions. The BOSMWs show robust ferromagnetic properties with the exceptions of [CpTiCpV]¥, [CpCrCpV]¥, and [CpTiCpMn]¥. Their magnetic moments are as high as 5 μB for [CpTiCpCo]¥ and [CpCrCpMn]¥, which are significantly enhanced as compared with those of their constituted monometallic sandwich wires. Furthermore, [CpTiCpTM]¥ (TM = Cr, Fe), [CpCrCpTM]¥ (TM = Fe, Co), and [CpFeCpCo]¥ are found to be robust half-metals with large HM gaps. Most importantly, a valence electron filling rule is observed in these BOSMWs, which can be applied to understand the rich electronic and magnetic properties. Moreover, we note that the BOSMW is an HM whenever N - 5(7) = 5(10) (N is the total valence electrons of two metal atoms in the wire). This electron filling rule and HM formula can be extended to other BOSMWs and be helpful to predict new HM materials.
II. COMPUTATIONAL METHOD All calculations are performed within the framework of spinpolarized density functional theory as implemented in the Vienna Ab initio Simulation Package (VASP).27,28 The exchangecorrelation potentials are treated by generalized gradient approximation (GGA) parametrized by Perdew, Burke, and Ernzerholf (PBE).29 The interaction between valence electrons and ion cores is described by the projected augmented wave (PAW)30,31 method. The combination of PBE/PAW was commonly exploited to describe the interaction of metal atoms and organic molecules in our early work and other literature.16,17,19,25 Furthermore, we take CpTiCpCr as an example to explore the electronic and magnetic properties by different approaches, including LDA, LDA þ U, PW91, PW91 þ U, PBE, and PBE þ U. The comparison is presented in Table S1 in the Supporting Information. Clearly, different exchange-correlation functionals have negligible influence on the structural, electronic, and magnentic natures that we are mostly concerned with. Two typical configurations are considered for the BOSMWs: an eclipsed structure with C5v symmetry (E) (Figure 1a,b) and a staggered one (S) with the same symmetry, where one Cp ring is rotated by 36 with respect to the neighboring one (Figure 1c,d). The periodic complexes are optimized within one repeating unit [CpTM1CpTM2]¥, which consists of two metal atoms and two Cp radicals (Figure 1a,c, red dotted line). To explore both the ferromagnetic and the antiferromagnetic states, a supercell with two repeating units (Figure 1a,c, blue dotted line) containing four metal atoms and four Cp radicals labeled as [CpTM1CpTM2CpTM1CpTM2]¥ are used. The 1D periodic boundary condition is applied along the metal-ligand principal axis (z), and the vacuum space along the other two directions (x, y) is set as 15 Å to ensure that the interaction between the neighboring chains is negligible (Figure 1). The periodic unit is optimized by the conjugate gradient algorithm with an energy cutoff of 400 eV until the force acting on each atom is less than 0.01 eV/Å. The ions in the periodic unit are allowed to fully relax without any symmetry constraints. After the optimization, we use a loose criterion to get the closest high symmetry structure and reoptimize it under symmetry constraints. If the higher symmetry structure has lower energy than the lower symmetry one, we consider the higher symmetry to be the right symmetry of the
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Figure 1. Side and top views of two [CpTM1CpTM2]¥ configurations in unit cell (red dotted line) and supercell (double-unit cell, blue dotted line) representations: (a, b) eclipsed (E) configuration and (c, d) staggered (S) configuration.
structure. Reciprocal space is sampled by 1 1 15 or 1 1 7 grid meshes using the Monkhorst-Pack scheme for one and two repeating unit calculations, respectively. A much denser k-point grid (1 1 45) is used for the calculation of the band structures.
III. RESULTS AND DISCUSSION Calculated results for all the BOSMWs, including their structural, energetic, electronic, and magnetic properties, are summarized in Table 1. The related structural information of the lowest-energy structures and their higher-energy states are summarized in Figure S1 and Table S2 in the Supporting Information. Similar to [VBz]¥,9,11-15 all the BOSMWs favor the eclipsed (E) configurations, which are energetically preferred than their staggered (S) counterparts by 0.01-0.08 eV. Among which, [CpTiCpFe]¥, [CpCrCpFe]¥, and [CpCrCpCo]¥ are optimized to a lower symmetry structure (Cs) with two C atoms of Cp radicals bending slightly toward the TM atom. The energy differences between the high-symmetry structures (C5v) and the optimized low structures (Cs) are less than 0.07 eV. To evaluate the stability of the BOSMWs, we compute the binding energy per unit cell defined as follows Eb ¼ fEðTM1 Þ þ EðTM2 Þ þ 2EðCpÞ - Eð½CpTM1 CpTM2 ¥ Þg
ð1Þ
where E[•] is the total energy of the BOSMW, Cp molecule, and TM atoms, respectively. As listed in Table 1, the binding energies of these BOSMWs are rather large and are comparable to their monometallic analogues, (TMCp)¥,16,17 indicating that these BOSMWs are of high stability, and thus, syntheses of these compounds should be feasible. Interesting magnetic properties are observed in these BOSMWs. With the exception of [CpTiCpV]¥, [CpTiCpMn]¥, and [CpCrCpV]¥ being antiferromagnetic (AFM), all the other BOSMWs energetically favor ferromagnetic (FM) states. The energy differences between FM and AFM states are around 0.1-0.5 eV, indicating that these wires are robust ferromagnets at room temperature. Furthermore, high magnetic moments are found in some BOSMWs, which are pronouncedly enhanced in comparison with their constituted monometallic counterparts [CpTM]¥. For example, the magnetic moment is as high as 4 μB per unit cell for [CpFeCpCr]¥ and [CpTiCpFe]¥ 2949
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Table 1. Point Group Symmetry (PGS), Lattice Constant (c), Binding Energy (Eb) per Unit Cell, Energy Difference between the E and S Configurations (ΔE1) per Unit Cell, Energy Difference between the FM and AFM States (ΔE2a), Total Magnetic Moment (Mt), Electronic Ground State (GS), and Charge Distribution (CD) of the BOSMWs TM1 Ti
Cr
Fe a
TM2
PGS
Sc
C5v
c/Å
Eb/eV
7.93
ΔE1/eV
12.72
ΔE2a/eV
0.04
0.12
Mt/μB
GS
1
V
C5v
7.46
12.80
0.05
-0.08
0
Cr
C5v
7.36
13.67
0.07
0.25
2
a
a
CD 1-
1þ
FM SC
[Cp Ti Cp1-Sc1þ]¥
AFM metal
[Cp1-Ti1þCp1-V1þ]¥
FM HM
[Cp1-Ti2þCp1-Cr0þ]¥
AFM SC
[Cp1-Ti1þCp1-Mn1þ]¥
Mn
C5v
7.34
10.92
0.06
-0.09
0
Fe Co
Cs C5v
7.52 7.58
11.59 11.88
-0.03 0.01
0.19 0.33
4 5
FM HM FM SC
[Cp1-Ti1þCp1-Fe1þ]¥ [Cp1-Ti1þCp1-Co1þ]¥
V
C5v
7.16
12.92
0.08
-0.22
0a
AFM SC
[Cp1-Cr3þCp1-V1-]¥
Mn
C5v
7.53
11.20
0.07
0.05
5
FM SC
[Cp1-Cr1þCp1-Mn1þ]¥
Co
Cs
7.08
12.38
0.06
0.18
3
FM HM
[Cp1-Cr1þCp1-Co1þ]¥
Cr
Cs
7.16
12.02
0.06
0.53
4
FM HM
[Cp1-Fe0þCp1-Cr2þ]¥
Co
C5v
6.96
11.16
0.04
0.17
1
FM HM
[Cp1-Fe2þCp1-Co0þ]¥
Results of the supercell containing two repeating units. SC represents semiconductors.
Table 2. Tunable Magnetic Moment of [CpTM1CpTM2]¥b [CpSc]¥ (0) [CpTi]¥(1)
a
[CpV]¥ (2)
[CpCr]¥ (1)
[CpMn]¥ (0)
[CpFe]¥ (1)
[CpCo]¥ (0)
1a
2
3a
4
5
2
3a
5
4
3
4
5
1
[CpCr]¥(1) [CpFe]¥(1)
[CpTi]¥ (1)
1
4
3
1
Results of a single unit cell with one TM1 and TM2 atom in the molecular wires, and the ground state is AFM in a double unit cell. b The number in parentheses refers to the magnetic moment of the monometallic organic sandwich wires per unit cell.
Figure 2. (a) Band structures of [CpTiCpCo]¥ together with their monometallic counterparts. (b) Valence electron configurations of [CpTi]¥, [CpCo]¥, and [CpTiCpCo]¥. The labels a1, e1, and e2 represent the singly degenerate dz2 and doubly degenerate (dxz, dyz) and (dx2-y2, dxy) bands, respectively. The red and green arrows denote the spin-flipping electrons of the Ti and Co atoms, respectively.
and 5 μB per unit cell for [CpTiCpCo]¥ and [CpCrCpMn]¥, whereas it is only 1, 1, 1, 0, and 0 μB for [CpTi]¥, [CpFe]¥, [CpCr]¥, [CpCo]¥, and [CpMn]¥, respectively (see Table 2). In contrast, the magnetic moment for [CpTiCpV]¥ is only 1 μB per unit cell, smaller than the sum of [CpTi]¥ (1 μB) and [CpV]¥ (2 μB), whereas that of [CpTiCpSc]¥ (1 μB) and [CpFeCpSc]¥ (1 μB) is equal to the sum of [CpTi]¥ (1 μB) and [CpSc]¥ (0 μB), and [CpFe]¥ (1 μB) and [CpSc]¥ (0 μB). Therefore, the magnetic property can be controlled by employing different combinations of TM atoms. This tunable magnetic
behavior may offer more room in applications for future magnetic storage materials and spintronics. The intriguing magnetic properties can be well understood from the band structures displayed in Figures 2 and 3 and Figure S2 in the Supporting Information. We have to point out that the energy differences between the high-symmetry structure (C5v) and the optimized low structure (Cs) are less than 0.07 eV for even [CpTiCpFe]¥, [CpCrCpFe]¥, and [CpCrCpCo]¥. To simplify the picture of the electronic structure, we exploit the band structure under C5v symmetry rather than under Cs 2950
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Figure 3. Band structures of four representative HM wires.
symmetry for these three systems. Under a ligand field of C5v symmetry, the five degenerate d orbitals of a TM atom are split into a singly degenerate a1 (dz2) orbital and two sets of doubly degenerate e1 (dyz, dxz) and e2 (dxy, dx2-y2) orbitals. Taking [CpTiCpCo]¥ (Figure 2) as an example, we identify eight orbitals that are mainly composed of Co 3d electrons (in such a situation, two 4s electrons are transferred to 3d orbitals16,17,24,25) from the component analysis of band structures at the Γ point. Five of them fill a singly degenerate a1, two sets of the doubly degenerate e1 and e2 orbitals on the majority manifold, and three others occupy the minority a1 and e1 orbitals, resulting in two electrons being unpaired. On the other hand, three electrons from the Ti atom are found to occupy the majority d orbitals (a1, e1) unpairedly, leading to the local magnetic moment on the Ti atom being 3 μB. Thus, the total magnetic moment of [CpTiCpCo]¥ is as high as 5 μB per unit cell. Comparing with the electron configuration of Ti (3d24s2) and Co (3d74s2) atoms, our results show that they both donate one electron to their neighboring Cp ligands. Therefore, the charge distribution of this molecular wire can be represented as [Cp-TiþCp-Coþ]¥. Similar analyses can also be made on other BOSMWs, and their charge distributions are given in Table 1. From the calculations, it is clear that the TM atoms serve as electron donors and the Cp ligands act like electron acceptors in the BOSMWs, which results in ionic interactions between the TM atoms and Cp rings. This bonding characteristic can also be clearly seen from their charge density differences (CDDs) (see Figure S3 in the Supporting Information). To shed light on the tunability of the magnetism of BOSMWs, we examine the band structures of [CpTiCpCo]¥ as well as their constituted monometallic counterparts in Figure 2. As clearly shown in the figure, when the [CpTi]¥ and [CpCo]¥ wires are brought together, on one side, one electron locating on the e2 orbitals in the minority channel of [CpTi]¥ flips to the majority; on the other side, another minority electron locating on the e1 orbital in [CpCo]¥ flips to the majority e1 ones in the BOSMW. Thus, the magnetic moment of [CpTiCpCo]¥ is increased by
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4 μB in comparison with the sum of that of [CpTi]¥ and [CpCo]¥. The spin-flipping is actually a result of balancing the Pauli repulsive rule and the ligand field splitting and can be further understood from the electron filling rule that will be discussed below. A similar analysis can be made for other BOSMWs, in which the tunable magnetic moments in the BOSMWs can be further understood from an empirical valence electron filling rule below. Besides intriguing magnetic properties, the BOSMWs are also found to possess rich electronic properties. Five BOSMWs, [CpTiCpTM]¥ (TM = Sc, Mn, Co) and [CpCrCpTM]¥ (TM = V, Mn), are semiconducting in nature with the band gap varying in the range of 0.28-1.13 eV, whereas the [CpTiCpV]¥ wire is metallic. In particular, we find that five BOSMWs, [CpTiCpTM]¥ (TM = Cr, Fe), [CpCrCpCo]¥ (TM = Fe, Co), and [CpFeCpCo]¥, are half-metallic or quasi-half-metallic, which show semiconducting behavior in one spin channel while being metallic in the opposite one, as clearly displayed in Figure 3 and Figure S2d in the Supporting Information. Moreover, the HM gaps of these five HM wires, defined as the difference between the Fermi level and the topmost occupied band in the semiconductor channel, are wider than 0.3 eV, showing that they are large enough for operation under room-temperature conditions. Interestingly, we find that the valence electrons of TM atoms in the BOSMWs follow an empirical filling rule; the electron occupancy at the Γ point in the whole BZ (see Figure 4a) can account for the tunable magnetic properties of the BOSMWs. The electron filling rule includes four main points: (1) Two valence electrons are first transferred from TM atoms to Cp ligands according to the Huckel rule (4m þ 2, m is an integer). (2) The left valence electrons of TM atoms first occupy three spin-up orbitals (a1, e1), which is followed by the occupancy of the three spin-down orbitals (a1, e2), for example, [CpTiCpSc]¥ and [CpTiCpV]¥. (3) When more valence electrons are present (N > 8, N is the total valence electrons of two TM atoms), they turn back to fill the spin-up channel until another five orbitals are fully occupied, for example, [CpTiCpCo]¥ and [CpCrCpMn]¥. (4) If N > 13, the excess electrons begin to fill the spin-down orbitals, for example, [CpCrCpCo]¥ and [CpFeCpCo]¥. The electron filling rule is displayed in Figure 4a,b and can be further understood from Figure 4c, where the frontier occupied orbitals of [CpFeCpCo]¥ at the Γ point are displayed. According to ligand field theory, the pairing energy (the energy required to have two electrons, one spin-up and one spin-down, in an orbital) and the orbital splitting energy are competitive in these organometallic systems.32 Our results suggest that, in these BOSMWs, the pairing energy is greater than the energy gap between dz2 and (dxy, dx2-y2), whereas it is smaller than the energy gap between (dxy, dx2-y2) and (dxz, dyz). Thus, six electrons occupy the dz2 and (dxy, dx2-y2) orbitals in the spinup channel first and then turn to occupy three dz2 and (dxy, dx2-y2) orbitals in the spin-down channel [condition (2)]. As clearly seen from Figure 4c, the interior six orbitals (HOMO-9 to HOMO-14) are bonding orbitals, in which three d orbitals (dz2, dxy, dx2-y2) from the Fe or Co atom interact with three symmetry-matched Cp p orbitals and stabilize the sandwich complexes, which is similar to the cases in metallocenes.33 This also suggests that TM atoms interact with the Cp ligand through covalent bonding as well and contributes toward the stability of the BOSMW together with the aforementioned ionic interactions. On the other hand, as the metal-metal interaction is basically minimal in these sandwich complexes, the order of the 2951
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Figure 4. (a, b) Electron occupation of frontier orbitals of all the wires at the Γ point of BZ. (c) Isodensity surface of frontier occupied orbitals of [CpFeCpCo]¥ at the Γ point of BZ.
bands is mainly governed by the ligand field, which is similar to the d orbital levels of a metal center in a sandwich ligand environment. The left d electrons follow the Hund’s rule and tend to fill up the five spin-up orbitals before populating the spindown ones (condition (3)). These can be inferred from Figure 4c, in which eight d orbitals (HOMO to HOMO-8) are either nonbonding or antibonding orbitals and are similar to those observed in an isolated metal atom. Therefore, this electron filling rule is a result of balancing the pairing electrons (Hund’s rule) and the ligand field splitting (metal-ligand interaction). However, we need to point out that this rule is just a principle way for electron filling. The complicated interaction between metal atoms and ligand molecules (the ligand field splitting and the paired electron interaction) can repopulate the energy-closed orbitals and results in the orbitals' order being changed. As shown in Figure 4b, [CpTiCpCo]¥ and [CpCrCpCo]¥ follow a different filling order of (a1,e2,e1,a1,e2) in one or both spin channels, as a1(dz2) and e2(dxy, dx2-y2) have close orbital energies. More interestingly, we find that the BOSMW is half-metallic when its valence electrons at the Γ point satisfy any of the four equations below N - 2 - 3 ¼ N - 5 ¼ 5ð7Þ
ð2aÞ
N - 2 - 8 ¼ N - 10 ¼ 5ð7Þ
ð2bÞ
where N represents the sum of valence electrons of two metal atoms in the BOSMWs and the number “2” refers to the transfer of two valence electrons to the Cp rings (condition (1)). The number “3” corresponds to the number of spin-down valence electrons required by condition (2), and “8” is the number of the spin-up electrons required by conditions (2) and (3). Clearly, eqs 2a and 2b stand for the HMs with a metallic property in the
majority and minority channels, respectively. The four equations are actually the derivation of the above electron filling rule and correspond to the degenerate (e1, e2) orbitals that are partially filled by the valence electrons. Therefore, the bands cross the Fermi level in one spin channel, resulting in the appearance of half-metallicity. According to eqs 2a and 2b, [CpTiCpCr]¥ (N 5 = 5), [CpTiCpFe]¥ (N - 10 = 7), [CpCrCpCo]¥ (N - 10 = 5), and [CpFeCpCo]¥ (N - 10 = 7) are HMs (see Figure 3), which are in excellent agreement with our computations. From these HM equations, we can also predict that, for other BOSMWs, such as [CpScCpMn]¥ and [CpVCpMn]¥, they should also be HMs. These HM equations can assist in the search for new HM materials from a broad class of linear bimetallic organic sandwich complexes. However, we have to point out that these rules are only sufficient conditions but not necessary conditions. For example, although the valence electron number of [CpFeCpCr]¥ (N - 10 = 4) does not satisfy eq 2a or 2b, the [CpFeCpCr]¥ wire displays properties that are characteristic of a half-metal.
IV. CONCLUSION In summary, we have extensively investigated the electronic and magnetic properties of one-dimensional bimetallic organic sandwich infinite molecular wires, [CpTiCpTM]¥ (TM = ScCo, Cp = C5H5), [CpCrCpTM]¥ (TM = V, Mn, Co), and [CpFeCpTM]¥ (TM = Cr, Co), by using a spin-polarized density functional theory approach. All BOSMWs are remarkably stable due to the presence of ionic-covalent bonding inside the wires. The BOSMWs show robust ferromagnetic properties with the exceptions of [CpTiCpV]¥, [CpCrCpV]¥, and [CpTiCpMn]¥. Their magnetic moments are as high as 5 μB per unit cell for [CpTiCpCo]¥ and [CpCrCpMn]¥, which are significantly 2952
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The Journal of Physical Chemistry C enhanced as compared with those of their constituted monometallic sandwich wires. Furthermore, [CpTiCpTM]¥ (TM = Cr, Fe), [CpCrCpTM]¥ (TM = Fe, Co), and [CpFeCpCo]¥ are found to be robust half-metals with large HM gaps. [CpTiCpV]¥ is determined to be metallic, and the remaining five wires are semiconductors. Most importantly, the electronic and magnetic properties can be accounted by an empirical electron filling rule, in which the BOSMW is a half-metal ferromagnet when N 5(10) = 5 or 7 (N is the sum of the valence electrons of two TM atoms). This electron filling rule and four HM equations are the result of balancing the Pauli repulsive rule and the ligand field splitting and can be applied to a broad class of linear sandwich systems and hence be utilized in formulating novel HM materials.
’ ASSOCIATED CONTENT
bS
Supporting Information. The comparison of different approaches, including LDA, LDA þ U, PW91, PW91 þ U, PBE, and PBE þ U on [CpTiCpCr]¥ (Table S1); the energy differences of different spin states of [CpTM1CpTM2]¥ (Table S2); the optimized structures and geometric information (Figure S1); the band structures of bimetallic sandwich wires (Figure S2); and charge density differences (CDDs) of (a) [CpTiCpCo]¥ and (b) [CpTiCpCr]¥ wires (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ ACKNOWLEDGMENT This work is supported by the NSF (11074035 and 20873019), NBRP (2010CB923401, 2011CB302004, and 2009CB623200), SRFDP (20090092110025), the Outstanding Young Faculty Grant, and the Peiyu Foundation of SEU in China. The authors thank the computational resource at the Department of Physics, SEU. ’ REFERENCES (1) Hoshino, K.; Kurikawa, T.; Takeda, H.; Nakajima, A.; Kaya, K. J. Phys. Chem. 1995, 99, 3053. (2) Kurikawa, T.; Takeda, H.; Hirano, M.; Judai, K.; Arita, T.; Nagao, S.; Nakajima, A.; Kaya, K. Organometallics 1999, 18, 1430. (3) Nakajima, A.; Kaya, K. J. Phys. Chem. A 2000, 104, 176. (4) Pandey, R.; Rao, B. K.; Jena, P.; Blanco, M. A. J. Am. Chem. Soc. 2001, 123, 3799. (5) Kandalam, A. K.; Rao, B. K.; Jena, P.; Pandey, R. J. Chem. Phys. 2004, 120, 10414. (6) Miyajima, K.; Nakajima, A.; Yabushita, S.; Knickelbein, M. B.; Kaya, K. J. Am. Chem. Soc. 2004, 126, 13202. (7) Wang, J.; Acioli, P. H.; Jellinek, J. J. Am. Chem. Soc. 2005, 127, 2812. (8) Wang, J.; Jellinek, J. J. Phys. Chem. A 2005, 109, 10180. (9) Mokrousov, Y.; Atodiresei, N.; Bihlmayer, G.; Gel, S. Int. J. Quantum Chem. 2006, 106, 3208. (10) Miyajima, K.; Yabushita, S.; Knickelbein, M. B.; Nakajima, A. J. Am. Chem. Soc. 2007, 129, 8473. (11) Rahman, M. M.; Kasai, H.; Dy, E. S. Jpn. J. Appl. Phys. 2005, 44, 7954. (12) Xiang, H. J.; Yang, J. L.; Hou, J. G.; Zhu, Q. S. J. Am. Chem. Soc. 2006, 128, 2310. 2953
dx.doi.org/10.1021/jp109253a |J. Phys. Chem. C 2011, 115, 2948–2953
