Magnetic and Quantum Transport Properties of Small-Sized Transition

Article pubs.acs.org/JPCC

Magnetic and Quantum Transport Properties of Small-Sized Transition-Metal-Pentalene Sandwich Cluster Zhi Yang,*,†,‡ Donghong Wang,‡ Xuguang Liu,*,§,∥ Li-Chun Xu,‡ Shijie Xiong,⊥ and Bingshe Xu§ †

Key Lab of Advanced Transducers and Intelligent Control System, Ministry of Education and Shanxi Province, ‡College of Physics and Optoelectronics, §Key Lab of Interface Science and Engineering in Advanced Materials, Ministry of Education, and ∥College of Chemistry and Chemical Engineering, Taiyuan University of Technology, Taiyuan 030024, China ⊥ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China S Supporting Information *

ABSTRACT: The chemical bonds and magnetic and quantum transport properties of small-sized transition-metal-pentalene sandwich clusters TM2nPnn+1 (TM = V, Cr, Mn, Co, and Ni; n = 1, 2) were investigated by using density functional theory and nonequilibrium Green’s function method. Theoretical results show that TM2nPnn+1 sandwiches have high stabilities. The TM−TM bond order gradually decreases with the increase of 3d electron number of TM atoms and TM2nPnn+1 could exhibit different spin states. With Au as two electrodes, significant spin-filter capability was observed in TM2nPnn+1, and such a filter can be switched on/off by changing the spin state. In addition, giant magnetoresistance was also found in the systems. These interesting quantum transport properties indicate that TM2nPnn+1 sandwiches are promising materials for designing molecular junction with different functions.

1. INTRODUCTION

It would be interesting to note that polycyclic-hydrocarbon ligands may also make sandwich clusters, and the ligands can hold more TM atoms in the sandwich regions. Several efforts have been dedicated to the field.3,38−50 For example, vanadiumnaphthalene VmNpn (Np = C10H8) and vanadium-anthracene VmAntn (Ant = C14H10) sandwiches have been synthesized by reacting V vapor with C10H8 and C14H10 in the gas phase.3 Theoretical studies revealed that V2nAntn+1 exhibits magnetic transition as the cluster size n increases,47 while V2nNpn+1 sandwiches are all FM.48 Furthermore, (TM2Np)∞ was predicted to be antiferromagnetic (AFM) for TM = Ti, V, and Nb, and FM only for TM = Mn, but nonmagnetic (NM) for TM = Sc.44 A pentalene (Pn = C8H6) molecule can be viewed as two fused Cp rings. Katz and co-workers were the first to synthesize transition-metal-pentalene sandwich clusters TM2Pn2 (TM = Co, Ni).38,39 Recently, various TM2Pn*2 (TM = V, Cr, Mn, Co, Ni; Pn* = C8Me6) were systemically investigated in both experiment and theory.40 The results show that, depending on specific TM atom, TM2Pn*2 has η3 or η5 coordination mode and a different TM−TM bond order. In addition, TM2(pent†)2 [TM = Rh, Pd; pent† = 1,4-bis(triisopropylsilyl)pentalene] was also synthesized and structurally characterized.41 Because of existence of complicated TM−TM bonds, transition-metalpentalene sandwiches show electronic and magnetic properties

The discovery of sandwich clusters in the 1950s, notably, the ferrocene FeCp2 (Cp = C5H5), heralded the beginning of modern organometallic chemistry.1,2 Similar to the well-known FeCp2, a number of multidecker sandwich clusters can be stable, e.g., TMnBzn+1 (TM = transition metal, Bz = C6H6)3−21 and TMnCpn+1 complexes,22−28 as well as lanthanide rare earth metal-C8H8 complexes.29−32 Monocyclic-hydrocarbon ligand sandwiches have intriguing physical or chemical properties and potential applications in different areas, such as materials science and molecular electronics.33 Combining molecular electronics with spintronics represents one of the most exciting avenues in building future electronic nanodevices.34−37 Novel charge and spin transport properties were suggested in these monocyclic-hydrocarbon ligand sandwiches. For example, according to the results of density functional theory (DFT), one-dimensional infinite sandwich molecular wires (TMBz)∞ (TM = V, Mn, Tc) and (TMCp)∞ (TM = Ti, Cr, Fe) are ferromagnetic (FM) half-metals; i.e., in the system one spin channel is metallic while the opposite spin channel is insulating.11,24 For [TM(FeCp2)]∞ (TM = Sc, Ti, V, Mn), however, the ground states are all FM semiconductors.25 Finite sandwiches such as V3Bz4 and Fe3Cp4 may possess spinfilter capability, if the sandwich is placed between two proper electrodes.12,27 Outstanding giant magnetoresistance (GMR) was observed in different types of FemCpn,28 while the spinvalve GMR effect was found in Sc3Bz4 in our recent study.21 © XXXX American Chemical Society

Received: November 15, 2014

A

dx.doi.org/10.1021/jp511443j | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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markedly different from those found for their ferrocene analogues. In present study, different TM2nPnn+1 (TM = V, Cr, Mn, Co, Ni, n = 1, 2) sandwiches are theoretically explored. Because Fe2Pn2 and Fe2Pn*2 have not been synthesized in experiments, only FePn2 was obtained,38,40 Fe2Pn2 is not considered here. The study of TM 2n Pn n+1 is based on the following considerations. First, although Wu et al. calculated the band structures of (TM2Pn)∞ (TM = V, Cr, Mn, Co, Ni),43 the physical and chemical properties of the molecular wires are different from those of small-sized sandwiches owing to the quantum size effect. Using the DFT method, Bendjaballah et al. investigated the electron counting formalism of the smallest TM2Pn2 complexes.50 However, the magnetic properties and chemical natures of TM−TM bond in TM2Pn2 and larger systems are still unclear. Our results show that, for a given TM2nPnn+1, low spin (LS) and high spin (HS) states are both stable, and the LS state is the ground state except for Mn2nPnn+1. The TM−TM bond order gradually decreases with the increase of 3d electron number of TM atom. Second, as mentioned above, monocyclic-hydrocarbon ligand sandwiches have interesting transport properties such as spin-filter capability. With Au as two electrodes, we also found spin-filter capability in the TM2nPnn+1 sandwich. More importantly, such a filter can be switched on/off by changing the spin state. Furthermore, the GMR effect can be realized in TM2nPnn+1, but the mechanism is different from that of monocyclic-hydrocarbon ligand sandwiches.28

Figure 1. (a) Different magnetic states of TM4Pn3. Black arrow represents the local magnetic moment of TM atom. (b) The twoterminal molecular junction: Au-TM4Pn3-Au.

SFE =

T↑(E F) − T↓(E F) T↑(E F) + T↓(E F)

× 100% (Vb = 0.0 V)

(1)

or

2. COMPUTATIONAL METHODS Quantum-chemical calculations of the sandwiches were performed by using spin-polarized DFT as implemented in DMOL3 package.51 The geometries were optimized without any symmetry constraints. The Perdew−Burke−Ernzerhof (PBE) functional and double numerical basis set with polarization functions (DNP) were employed.52 For a given sandwich, all possible LS and HS states were examined. Here, LS and HS states include many different magnetic states; the LS state could be NM or AFM, while the HS state is FM, as shown in Figure 1a. The Jahn−Teller distortion was considered for the sandwich with high symmetry, and the vibrational frequencies were analyzed to ensure that the optimized structures are stable. To confirm the ground-state properties, different-sized sandwiches were further investigated by using B3LYP functional and DNP basis set.53,54 In the Table S1 of the Supporting Information, the results of B3LYP/DNP are listed. We obtained very similar geometries and electronic properties using two different functionals, and thus the results presented here are reasonable and reliable. The quantum transport properties of the sandwiches were studied by the real-space nonequilibrium Green’s function (NEGF) method as implemented in Atomistix ToolKit (ATK) package.55 PBE functional and double-ζ plus polarization basis set (DZP) were adopted. The (001) surface of face-centered cubic Au was chosen as electrode, and the two-terminal molecular junction, Au-TM4Pn3-Au, is given in Figure 1b. The structure of the molecular junction was optimized at the PBE/ DZP level. The spin-filter capability and GMR of the sandwich at different bias voltage Vb were calculated. The spin-filter capability can be measured through spin-filter efficiency (SFE) at zero or finite bias voltage

SFE =

I↑ − I↓ I↑ + I↓

× 100% (Vb > 0.0 V)

(2)

where T↑(EF) and T↓(EF) are the transmission coefficients at Fermi energy EF of spin-up (↑) and spin-down (↓) channels, respectively; I↑ and I↓ are the spin-polarized currents. I↑ and I↓ can be calculated by using the Landauer−Büttker formula56 I↑ (↓) =

e h

∫ T↑(↓)(E)[fL (E) − fR (E)] dE

(3)

where e is the electron charge, h is the Planck’s constant, T↑(↓)(E) is the spin-up (spin-down) transmission spectrum, and f L(R)(E) is the Fermi−Dirac distribution function for the left (right) electrode. The GMR effect was investigated by changing the spin state of the sandwich. The GMR value can be obtained from the following equation: GMR =

G HS − G LS × 100% G LS

(4)

where GHS and GLS are the conductances when the sandwich is in the HS and LS states. The transition of spin state can be easily controlled by means of an external stimulus, e.g., light, pressure, or magnetic field.57

3. RESULTS AND DISCUSSION 3.1. The Magnetic States and Stabilities of TM2nPnn+1 Sandwich Clusters. The stabilities and magnetic properties of the sandwiches are important for designing new molecular junctions. In this section, we will discuss these basic properties first. The calculated data of the ground-state TM2nPnn+1 (n = 1, 2) are listed in Table 1, whereas the corresponding structures are presented in the Supporting Information (Figure S1). B



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Table 1. Point Group PG, Spin Multiplicity M, Magnetic State and TM−TM MBO of the Ground-State TM2nPnn+1 (n = 1, 2) cluster

PG

M

magnetic state

V2Pn2 Cr2Pn2 Mn2Pn2 Co2Pn2 Ni2Pn2 V4Pn3 Cr4Pn3 Mn4Pn3 Co4Pn3 Ni4Pn3

D2h C1 D2h C1 D2h D2h C1 D2h C1 C1

1 1 3 1 1 1 1 5 1 1

AFM NM FM AFM NM AFM NM FM NM NM

TM−TM MBO 1.862 1.749 0.890 0.401 0.314 1.470, 1.005, 0.806, 0.313, 0.181,

1.470; 1.004; 0.806; 0.312; 0.181;

0.133, 0.148, 0.120, 0.103, 0.084,

0.133 0.146 0.120 0.102 0.084

V2Pn2 and V4Pn3. The ground state of V2Pn2 has D2h symmetry, and the magnetic state is AFM; i.e., the local magnetic moments of two V atoms are antiparallel with each other (−1.112 and 1.112 μB). To analyze the V−V chemical bond, the Mayer bond order (MBO) was calculated. From Table 1, one can see that the MBO of V2Pn2 is 1.862, indicating the V−V bond is a double covalent bond. The FM and NM states of V2Pn2 are stable, but the total energies are higher than the ground state by about 0.218 and 0.304 eV, respectively. Therefore, V2Pn2 can exhibit rich magnetic states under proper external stimulus. The bond order of V−V in V2Pn2 is different from V2Pn*2, for the latter the value is 2.83, corresponding to a typical triple covalent bond.40 We performed a calculation on V2Pn*2 at the present theoretical level and found the MBO is 2.679, in good agreement with previous results. The optimized structures and geometric parameters of V2Pn2 and V2Pn*2 are given in Figure S2 in the Supporting Information for comparison. Clearly, the average distance of the two ligands of V2Pn2, 3.721 Å, will be enlarged to 3.882 Å in V2Pn*2 owing to the repulsions of neighboring Me functional groups. The V−C bond lengths of V2Pn*2 are much longer, and the V−C bond orders are much smaller. As a result, the V−V bond length gets shorter and the bond order becomes larger. When cluster size increases to n = 2, the ground-state V4Pn3 is still AFM. The spin charge densities of V4Pn3 are given in Figure 2. This AFM state can be viewed as the building unit of (V2Pn)∞ molecular wire.43 Just like n = 1 case, the NM and FM states of V4Pn3 are also stable, but have higher energies. In addition, the MBO of intralayered V atoms is significant, 1.470, while the value of interlayered V atoms is very small, only 0.133, indicating the indirect interactions of V atoms through Pn ligand may be important. Cr2Pn2 and Cr4Pn3. The ground-state Cr2Pn2 is LS and is NM. There is no AFM solution for the system. The MBO of Cr−Cr bond is 1.749, which is very close to that of V−V bond in V2Pn2. The Cr−Cr bond length of 2.179 Å is also close to the corresponding V−V value of 2.173 Å. Therefore, like V−V bond, the Cr−Cr bond is a double covalent bond. It is very interesting to note that the bond order of Cr−Cr in Cr2Pn*2 is 1.98,40 and the Cr−Cr bonds in Cr2Pn2 and Cr2Pn*2 are similar in nature. Further theoretical results show that the average distances of Pn−Pn and Pn*−Pn* in two sandwiches are nearly the same, implying the Cr−C bonds are robust and will not be affected by different ligands. Bendjaballah et al. predicted ground-state Cr2Pn2 is a triplet state with D2h symmetry.50 However, in the present study the

Figure 2. Spin densities of TM4Pn3. The NM states are also given for comparison. ΔE represents energy difference between the magnetic state and ground state. The isovalue of isosurface is 0.05 e·Å−3.

D2h triplet state is only a transition state with a negative frequency of −81.3 cm−1. After further relaxation, a C1 triplet state was achieved. This C1 structure is corresponding to a local minimum on the potential energy surface, but the energy is higher than the ground state by about 0.113 eV. In fact, the ground-state Cr2Pn2 is also predicted to be singlet state at B3LYP/DNP level. The closed-shell electronic configuration of Cr2Pn2 is similar to that of Cr2Pn*2.40 In a word, Cr2Pn2 should be singlet state. For Cr4Pn3, the ground state is NM. It is very interesting that the MBO of the intralayered Cr−Cr bond is 1.004, indicating the Cr−Cr bond sharply varies from double bond to single bond as n changes from 1 to 2. We can manipulate the bond order and related chemical properties through cluster size. The ground state of (Cr2Pn)∞ molecular wire is AFM.43 As an independent test, large sandwiches Cr6Pn4 and Cr8Pn5 were explored. However, the ground states of the two sandwiches are still NM, and one can reasonably infer that an NM-to-AFM transition must exist when n further increases. Mn2Pn2 and Mn4Pn3. All possible spin states were considered for Mn2Pn2 and Mn4Pn3. Unlike V2Pn2 and Cr2Pn2, the magnetic state of Mn2Pn2 is FM, and the local magnetic moments of two Mn atoms are both 1.007 μB. The Mn−Mn bond of Mn2Pn2 is a typical single covalent bond with MBO = 0.890, which is different from previous V−V and Cr− Cr bonds. The magnetic state of Mn2Pn2 is the same as that of Mn2Pn*2.40 Bendjaballah et al. also pointed out that the spin multiplicity of Mn2Pn2 is 3.50 The AFM state was identified for Mn2Pn2 but the energy difference between the FM and AFM is 0.509 eV. The large energy difference suggests that two Mn atoms exhibit strong tendency to couple ferromagnetically with each other. For Mn4Pn3, the ground state is also FM. Mn4Pn3 has the largest magnetic moment, 4 μB, in the investigated range. Two stable AFM states were found, as shown in Figure 2. In the first AFM state, the local magnetic moments of intralayered Mn atoms are parallel, while for the interlayered Mn atoms they are C



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antiparallel. The exchange interaction between interlayered Mn atoms should be weak since the energy difference of the FM state and the first AFM state is small, only about 0.137 eV. For the second AFM state, however, the energy difference becomes much larger because of the strong exchange interaction of intralayered Mn atoms. Co2Pn2 and Co4Pn3. The ground-state Co2Pn2 is AFM and our theoretical prediction is in good agreement with experimental observations.38 The local magnetic moments of two Co atom are −0.904 and 0.910 μB, respectively. Similar to V2Pn2, the FM and NM states of Co2Pn2 were found to be stable but have higher energies. The MBO of Co−Co bond in Co2Pn2 is 0.401, indicating that the covalent bond of two Co atoms is weak. The weak Co−Co bond can be further confirmed from the long bond length, 2.522 Å. As to Co4Pn3, it is NM and has closed-shell electronic configuration. For the limit case, the infinite molecular wire (Co2Pn)∞ is NM metal.43 It is very interesting that Co2Pn2 and Co4Pn3 have different magnetic states, exhibiting size-dependent magnetic properties. In addition, an FM state was found for Co4Pn3 (see Figure 2), and there is no AFM solution to the sandwich. Ni2Pn2 and Ni4Pn3. The calculated point group of Ni2Pn2 is D2h, which was confirmed by the NMR spectrum.39 The MBO and length of Ni−Ni bond of Ni2Pn2 are 0.314 and 2.702 Å, respectively, corresponding to a very weak Ni−Ni interaction. In addition, we found that the NM and AFM states are nearly degenerate; the energy difference is only about 0.022 eV. The nearly degenerate NM and AFM states were further identified at the B3LYP/DNP level. An FM state was observed but has much higher energy. The MBO of intralayered Ni−Ni bond in Ni4Pn3 is very small, only 0.181. Similar to Ni2Pn2, the ground state of Ni4Pn3 is NM. Both AFM and FM states are stable, but the energies are relatively high, as shown in Figure 2. The above discussion suggests that the TM−TM bond order of TM2nPnn+1 gradually decreases with the increase of 3d electron number of TM atom. Besides the TM−TM bond order, the other important aspect of TM2nPnn+1 is the coordination mode of TM atom. For TM2Pn2, by analyzing the bond length and bond order, we found the TM atom could adopt η5 (TM = V, Cr, Mn) and η3 (TM = Co, Ni) coordination modes. More importantly, the results show that large sandwich TM4Pn3 keeps the same coordination mode as TM2Pn2. Therefore, the growth of the sandwich will not cause significant structure deformation. The binding energy Eb and the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are presented in Figure 3. Here, Eb is calculated from E b = 2nE(TM) + (n + 1)E(Pn) − E(cluster)

Figure 3. (a) Binding energy Eb and (b) HOMO−LUMO gap of TM2nPnn+1.

Figure 4. (a) The deformation charge densities of Cr2nPnn+1 and Co2nPnn+1. (b) The charges on Pn ligands in Cr2Pn2 and Co2Pn2. e is the unit charge.

two Cr atoms, showing strong covalent bond. While almost zero charge density is found for Co−Co bond in Co2Pn2. The strong Cr−Cr covalent bond may enhance the stability of Cr2Pn2. On the other hand, like Cp, the Pn tends to capture two electrons to form a stable aromatic configuration with 4m +2 (where m is an integer) valence electrons (the Hückel rule). It is obvious that the main interaction between Cr or Co and Pn is ionic, and the charges on Pn ligands in both Cr2Pn2 and Co2Pn2 are nearly the same. The contributions of ionic bonds to Eb in the two sandwiches are basically equal. As a result, the stability of TM2Pn2 is only dependent on the TM−TM bond order. As to TM4Pn3, because of the more complicated structure and subsequent direct or indirect interactions, the bond order is not the unique factor to determine the stability of the system. Co4Pn3 is even more stable than Cr4Pn3. In addition, the HOMO−LUMO gaps of the sandwiches are given in Figure 3. The gap could well reflect the kinetic stability of a cluster.58 We found the smaller sandwich has a larger gap, exhibiting higher kinetic stability. Co2Pn2 has the largest gap, 0.841 eV, while the gap of Ni4Pn3 is 0.280 eV and is the smallest. For a given temperature T, the energy fluctuation due to thermal excitation is kBT, where kB is Boltzmann’s constant. At room temperature

(5)

where E(·) is the total energy of TM atom, free Pn ligand or cluster, respectively. An outstanding feature of Eb is that TM4Pn3 always has higher binding energy compared with TM2Pn2, and thus the growth of sandwich is exothermic. The binding energy ranges from 12.291 to 26.933 eV, indicating both TM2Pn2 and TM4Pn3 have high thermal stabilities. Furthermore, we found that the Eb of TM2Pn2 is dependent on the bond order; i.e., the system with larger TM−TM bond order is more stable. To understand this, as two examples, the deformation charge densities of Cr2Pn2 and Co2Pn2 are given in Figure 4. For Cr2Pn2, significant charge density exists between D



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T = 300 K, the energy fluctuation is only about 0.026 eV. Therefore, all the TM2nPnn+1 sandwiches have relatively high kinetic stabilities even at room temperature. To further understand the chemical bonds of the sandwich, the molecular orbitals of several typical systems are plotted in Figure 5. It is clear that the V−V double bond in V2Pn2 is

different complexes was discussed. The results show that the Cr−Cr bond length and bond order significantly depend on the ligand and oxidation state of the system. According to the above discussion, TM2nPnn+1 sandwiches have different magnetic states and excellent thermal and kinetic properties, which ensure that such complexes could be employed to design new molecular junctions. In the next section, the quantum transport properties of TM2nPnn+1 will be discussed. 3.2. Quantum Transport Properties of TM2nPnn+1 Sandwich Clusters. Because TM 2nPnn+1 has different magnetic states, only two cases were investigated for each sandwich. For example, Ni4Pn3 could be NM, AFM, or FM (see Figure 2). As two representatives, the quantum transport properties of NM and FM states of Ni4Pn3 were calculated; the AFM state was not considered for simplicity. In other words, for Ni4Pn3, we chose NM and FM states to represent the LS and HS states, respectively. In the Table S2 of the Supporting Information, the selected LS and HS states for each sandwich are listed. Recently, Chattopadhyaya et al. investigated a complicated molecule Ti@C32-C2-Ti@C32 and found that the molecule can exhibit different quantum transport properties at FM and AFM states.59 The calculated SFE and GMR values at zero bias voltage are summarized in Table 2. It is obvious that some sandwiches have Table 2. SFE (%) and GMR (%) of Au-TM2nPnn+1-Au Molecular Junction at Zero Bias Voltagea

Figure 5. Occupied molecular orbitals of (a) V2Pn2, Cr2Pn2 and Ni2Pn2 and (b) Cr4Pn3. The isovalue of isosurface is 0.05 e·Å−3. a

mainly comprised of HOMO-1 and HOMO-2. The main component of HOMO-1 is the 3dxy orbitals of V atoms; HOMO-1 is a π bond. For HOMO-2, however, it is a σ bond and is the linear combination of 3dxy, 3dz2, and 3dx2−y2 of V atoms. Although the HOMO of V2Pn2 is a weak bonding state, it has little contribution to the bond order. From the view of formal charge, the 4s electrons of V atoms will transfer to Pn rings and form Pn2− anions. The six 3d electrons of two V atoms will form a double covalent bond, or interact with 2pz states of C atoms. The orbital picture of Cr2Pn2 is slightly different from that of V2Pn2. We found the HOMO of Cr2Pn2 is a weak antibonding state, which will weaken the stability of the system. As mentioned before, the Cr−C bonds are robust, and the distances of two ligands in Cr2Pn2 and Cr2Pn*2 are basically the same. Nevertheless, owing to the existence of the HOMO antibonding state, the binding energy of Cr2Pn2 is smaller than that of V2Pn2. In addition, the double bond of Cr2Pn2 is also comprised of a σ bond and a π bond, corresponding to the HOMO-2 and HOMO-3 orbitals. For Ni2Pn2, more antibonding or nonbonding states are occupied. It is not surprising Ni2Pn2 has the lowest binding energy. As to Cr4Pn3, it is found that the Cr−Cr σ bond disappears but the Cr−Cr π bond is kept (HOMO-3); thus the bond order will change with cluster size n for Cr2nPnn+1. The TM−TM bond order depends on many different factors, such as ligand and coordination mode. For example, in recent studies,60,61 the Cr2 bond was calculated, and the bond order in

cluster

SFE(LS/HS)

GMR

cluster

SFE(LS/HS)

GMR

V2Pn2 Cr2Pn2 Mn2Pn2 Co2Pn2 Ni2Pn2

0/92 0/−83 0/96 0/59 0/15

623 1132 3480 −561 1077

V4Pn3 Cr4Pn3 Mn4Pn3 Co4Pn3 Ni4Pn3

0/90 0/74 0/97 0/53 0/-44

−1588 1261 2944 188 32

The SFE values of LS and HS states are both given.

high spin-filter capabilities at HS state. The SFE of Mn4Pn3 is as high as 97%, which can be viewed as a perfect spin filter. More importantly, the SFEs of LS states are all zero, indicating that the filter can be switched on/off by tuning the spin state. The SFEs of Cr2Pn2 and Ni4Pn3 are negative. According to eq 1, negative SFE suggests that T↓(EF) is larger than T↑(EF); i.e., at EF the conductance is dominated by spin-down channels. Furthermore, significant GMR effect was observed. The GMR phenomenon was first predicted in an Fe/Cr magnetic superlattice.62,63 The GMRs of the sandwiches are in a wide range, from −1588% to 3480%, and Mn2Pn2 has the largest value of 3480%. Although the GMR effect was also found in FeCp2, the corresponding value at zero bias is only 992%.28 In addition, the transport properties of the molecular junctions at zero bias voltage were also investigated at a higher theoretical level. We optimized the molecular junctions using the DFT-D method64 and then calculated the GMR and SFE values using Meta-GGA (TB09LDA) functional. 65 The obtained results are summarized in the Table S3 of the Supporting Information. We found the results at different theoretical levels are consistent, and the PBE functional used here is suitable for calculating the transport properties. It is noted that the GMR effect obtained here is through the spin-state transition of the sandwich. Because the coupling of the sandwich and the Au electrode surface is dependent on the spin state, LS and HS states will produce spin-dependent E



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transport channels, leading to the difference of GLS and GHS and the appearance of GMR. In a previous study, however, the GMR was realized by changing the magnetization directions of two magnetic electrodes, but the spin state of the sandwich remained unchanged in the whole transport process.28 Since TM2nPnn+1 has different spin states, our study shows that the GMR effect can be acquired by different mechanisms. The SFE and GMR at finite bias voltage Vb were further investigated. As two examples, the SFE and GMR curves of Mn4Pn3 and Ni4Pn3 are shown in Figure 6. The results of other

In the HS state, however, a nearly linear current−voltage relationship was observed when Vb is low (from 0.0 to 0.2 V), exhibiting “metallic” behavior. The current reaches a maximum at 0.6 V and then gradually decreases, which represents a typical negative differential resistance (NDR) effect. The NDR effect can be modulated by tuning the spin state. Under larger Vb, the current significantly decreases in the HS state but keeps nearly unchanged in the LS state; the difference of currents or conductances of two spin states gets smaller and smaller, consistent with the decrease of GMR (see Figure 6). From the inset of Figure 7, one can see that, in the HS state, the spin-polarized currents I↑ and I↓ of Mn4Pn3 have different trends. At a given Vb, I↑ has a large value but I↓ is small. The spin-up channels provide the main contribution to the current. In addition, we slightly compressed and elongated the molecular junction to model the stress and strain and found the current−voltage relationship is not sensitive to the structure deformation of the molecular junction. To give an explanation for the microscopic mechanism of SFE and GMR, the transmission spectra of Au-Mn4Pn3-Au molecular junction under different bias voltages were analyzed. As can be seen from Figure 8, the spin-up and spin-down

Figure 6. SFE and GMR curves of (a) Au−Mn4Pn3-Au and (b) Au− Ni4Pn3-Au molecular junctions.

sandwiches are given in the Supporting Information (Figure S3). At finite Vb, the SFEs of Mn4Pn3 and Ni4Pn3 are still zero for LS state but are opposite for HS state, which provides us the ability to get two types of spin currents. Furthermore, the GMR curves of Mn4Pn3 and Ni4Pn3 exhibit different behaviors. For Mn4Pn3, the GMRs still keep relatively large values at finite bias voltage. An outstanding peak was observed when Vb = 0.6 V. In contrast, the GMRs of Ni4Pn3 are small and the maximum is only about 95%. The I−Vb curve of Mn4Pn3 is shown in Figure 7. It is obvious that the molecular junction has different current−voltage

Figure 8. Transmission spectra of Au-Mn4Pn3-Au: (a) HS state, Vb = 0.0 V; (b) LS state, Vb = 0.0 V; (c) HS state, Vb = 0.6 V; (d) LS state, Vb = 0.6 V. The dotted line indicates the Fermi level. The pink solid lines in (c) and (d) represent the bias window.

transmission spectra are different if Mn4 Pn3 is in the HS state. When Vb = 0.0 V, there is a significant peak, P1, that appears at the Fermi level (Figure 8a). The P1 peak comes from the HOMO of Mn4Pn3 and will produce a large T↑(EF) and conductance GHS. In contrast, the T↓(EF) approaches zero. According to eq 1, the SFE at zero bias is a large positive value. The P1 peak implies that the HOMO of Mn4Pn3 could couple well with the surfaces of two Au electrodes. The main eigenstate of P1 peak at zero bias is depicted in Figure 9. Obviously, it is delocalized and the spin-up electrons can easily pass through the system. If the spin state changes from HS to LS, the transmission spectra vary dramatically, as shown in Figure 8b. Because the LS state of Mn4Pn3 considered here is NM (see Table S2 in the Supporting Information), the spectra are degenerate for two spins. Therefore, it is not surprising that the SFE value at LS state is zero. For the LS state, there is no peak at the Fermi level when Vb = 0.0 V; thus the conductance GLS is very small. Although the P5 peak comes from the HOMO of the sandwich, it is far away from EF and has no contribution to the

Figure 7. I−Vb curve of Au-Mn4Pn3-Au molecular junction in the LS and HS states. The inset contains I↑ and I↓ currents of the HS state.

characteristics for LS and HS states. In the LS state, the current approaches zero if Vb is in the range of 0.0−0.3 V, exhibiting ”insulator” behavior and then slowly grows with Vb. The low current indicates the molecular orbitals of the sandwich cannot couple well with the surface state of the Au electrodes. F



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(n = 1, 2) sandwich clusters by using DFT and NEGF methods. The results are summarized as follows. (1) Theoretical results show that all the ground-state TM2nPnn+1 sandwiches have high thermal and kinetic stabilities. Except for Mn2nPnn+1, the ground-state TM2nPnn+1 prefers to adopt the LS state, while Mn2nPnn+1 is the HS state. The TM− TM bond order decreases with the increase of the 3d electron number. It is found that TM2Pn2 and TM4Pn3 have the same coordination modes, which ensures the growth of the sandwich will not cause significant structure deformation. (2) Outstanding spin-filter capability was observed in AuTM2nPnn+1-Au molecular junctions, and such a filter can be switched on/off by changing the spin state of the sandwich. In addition, a significant GMR effect could be obtained if the spin state of the sandwich changes. An NDR phenomenon was observed in Au-Mn4Pn3-Au. These interesting transport properties indicate that TM2nPnn+1 sandwiches are promising materials for designing molecular junctions with different functions. We hope the present study provides a more complete picture about transition-metal-pentalene sandwich cluster and related nanodevices.

Figure 9. Main transmission eigenstates of P1, P2, and P3 peaks: (a) P1, Vb = 0.0 V; (b) P1, Vb = 0.6 V; (c) P2, Vb = 0.6 V; (d) P3, Vb = 0.6 V.

conductance. The HOMOs of LS and HS states have very different couplings to two Au electrodes, giving rise to different transport channels. Finally, a large GMR value will appear at zero bias if the spin state varies. When Vb increases to a finite bias voltage such as 0.6 V, for the HS state, the peak P1 is still in the range of bias window (see Figure 8c). At the same time, peaks P2 and P3 also enter the bias window. These three peaks will produce a large current and GHS. Although the P3 will enhance I↓, P1 and P2 will give a larger I↑. The SFE is still positive. In fact, the main transmission state of P1 at Vb = 0.6 V is delocalized, while the transmission states of P2 and P3 are more localized, as shown in Figure 9. If the spin state changes to LS, as can be seen from Figure 8d, both P4 and P5 peaks are out of the bias window and hardly have contributions to the transport process, leading to a small GLS, and then a large GMR value appears. If Vb > 0.6 V, P2 and P3 peaks will be compressed but P1 keeps nearly unchanged (the transmission spectra are not shown here). The total current becomes small and the NDR appears at HS state. At the same time, for the LS state, the P5 peak gradually enters the bias window and produces a large current and GLS, and finally leads to the decrease of GMR. Therefore, the transmission state that comes from HOMO of Mn4Pn3 plays an important role in the whole transport process for both LS and HS states. Because the electronic structure of TM2nPnn+1 is dependent on the specific TM atom and cluster size n, the transport properties of the Au-TM2nPnn+1-Au molecular junction are different (see Figure 6 and Figure S3 in the Supporting Information). In other words, the transport properties of the molecular junction can be tuned by different sandwiches. In addition, all the calculations performed here are within the scope of coherent transport under zero temperature, and several factors such as electron−phonon scattering and Coulomb blockade are not considered. These higher order factors may cause noncoherent transport or more complicated many-body interactions and probably weaken the SFE and GMR effects. Although the predicted SFE and GMR are the theoretical upper limit, our results show that TM2nPnn+1 sandwiches are indeed promising materials for designing molecular junctions with different functions and deserve further experimental research.

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ASSOCIATED CONTENT

S Supporting Information *

The ground-state structures of TM2nPnn+1 are depicted in Figure S1. The geometric parameters and deformation densities of V2Pn2 and V2Pn*2 are given in Figure S2. The SFE and GMR curves of several sandwiches are depicted in Figure S3. The point group and magnetic state of TM2nPnn+1 obtained at B3LYP/DNP level are summarized in Table S1. The selected LS and HS states for each sandwich are listed in Table S2. The calculated zero-bias SFE and GMR values at higher theoretical level are given in Table S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*(Z.Y.) E-mail: [email protected]. Phone: +86(0) 3516014138. Fax: +86(0)3516018030. *(X.L.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (11104199), Program for Changjiang Scholar and Innovative Research Team in University (IRT0972), Shanxi Provincial Key Innovative Research Team in Science and Technology (2012041011), and Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.

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REFERENCES

(1) Coulson, C. A.; Higgs, P. W.; March, N. H. Theoretical Determination of Electron Density in Organic Molecules. Nature 1951, 168, 1039. (2) Wilkinson, G.; Rosenblum, M.; Whiting, M. C.; Woodward, R. B. The Structure of Iron Bis-Cyclopentadienyl. J. Am. Chem. Soc. 1952, 74, 2125−2126. (3) Kurikawa, T.; Takeda, H.; Hirano, M.; Judai, K.; Arita, T.; Nagao, S.; Nakajima, A.; Kaya, K. Electronic Properties of Organometallic

4. CONCLUSIONS In summary, we have theoretically investigated the bond orders and magnetic and quantum transport properties of TM2nPnn+1 G



Article

Metal-Benzene Complexes [Mn(benzene)m (M = Sc-Cu)]. Organometallics 1999, 18, 1430−1438. (4) Miyajima, K.; Yabushita, S.; Knichelbein, M. B.; Nakajima, A. Stern-Gerlach Experiments of One-Dimensional Metal-Benzene Sandwich Clusters: Mn(C6H6)m (M = Al, Sc, Ti, and V). J. Am. Chem. Soc. 2007, 129, 8473−8480. (5) Miyajima, K.; Nakajima, A.; Yabushita, S.; Knichelbein, M. B.; Kaya, K. Ferromagnetism in One-Dimensional Vanadium-Benzene Sandwich Clusters. J. Am. Chem. Soc. 2004, 126, 13202−13203. (6) Jaeger, T. D.; Heijnsbergen, D. van; Klippenstein, S. J.; Helden, G. von; Meijer, G.; Duncan, M. A. Vibrational Spectroscopy and Density Functional Theory of Transition-Metal Ion-Benzene and Dibenzene Complexes in the Gas Phase. J. Am. Chem. Soc. 2004, 126, 10981−10991. (7) Heijnsbergen, D. van; Helden, G. von; Meijer, G.; Maitre, P.; Duncan, M. A. Infrared Spectra of Gas-Phase V+-(benzene) and V+(benzene)2 Complexes. J. Am. Chem. Soc. 2002, 124, 1562−1563. (8) Lyon, J. T.; Andrews, L. V. Nb and Ta Complexes with Benzene in Solid Argon: An Infrared Spectroscopic and Density Functional Study. J. Phys. Chem. A 2005, 109, 431−440. (9) Jaeger, T. D.; Pillai, E. D.; Duncan, M. A. Structure, Coordination, and Solvation of V+(benzene)n Complexes via Gas Phase Infrared Spectroscopy. J. Phys. Chem. A 2004, 108, 6605−6610. (10) Martínez, J. I.; García-Lastra, J. M.; López, M. J.; Alonso, J. A. Optical to Ultraviolet Spectra of Sandwiches of Benzene and Transition Metal Atoms: Time Dependent Density Functional Theory and Many-Body Calculations. J. Chem. Phys. 2010, 132, 044314. (11) Xiang, H. J.; Yang, J. L.; Hou, J. G.; Zhu, Q. S. One-Dimensional Transition Metal-Benzene Sandwich Polymers: Possible Ideal Conductors for Spin Transport. J. Am. Chem. Soc. 2006, 128, 2310− 2314. (12) Maslyuk, V. V.; Bagrets, A.; Meded, V.; Arnold, A.; Evers, F.; Brandbyge, M.; Bredow, T.; Mertig, I. Organometallic BenzeneVanadium Wire: A One-Dimensional Half-Metallic Ferromagnet. Phys. Rev. Lett. 2006, 97, 097201. (13) Koleini, M.; Paulsson, M.; Brandbyge, M. Efficient Organometallic Spin Filter between Single-Wall Carbon Nanotube or Graphene Electrodes. Phys. Rev. Lett. 2007, 98, 197202. (14) Wu, M. H.; Zeng, X. C. Transition-Metal-Molecular Sandwich Nanowires as Magnetic On/Off Switch. Appl. Phys. Lett. 2011, 99, 053121. (15) Rabilloud, F. Geometry and Spin-Multiplicity of Half-Sandwich Type Transition-Metal-Benzene Complexes. J. Chem. Phys. 2005, 122, 134303. (16) Sohnlein, R. B.; Li, S.; Yang, D. S. Electron Spin Multiplicities and Molecular Structures of Neutral and Ionic Scandium Benzene Complexes. J. Chem. Phys. 2005, 123, 214306. (17) Maynez, R. M.; Castro, M. Theoretical Study of Neutral and Charged Scn≤2-(benzene)m≤3 Clusters. J. Nanopart. Res. 2013, 15, 1367. (18) Sohnlein, B. R.; Lei, Y. X.; Yang, D. S. Electronic States of Neutral and Cationic Bis(benzene)Titanium and Vanadium Sandwich Complexes Studied by Pulsed Field Ionization Electron Spectroscopy. J. Chem. Phys. 2007, 127, 114302. (19) Liu, H. B.; Li, Q. S.; Xie, Y. M.; King, R. B.; Schaefer, H. F. Triple-Decker-Sandwich Versus Rice-Ball Structures for Tris(benzene)dimetal Derivatives of the First-Row Transition Metals. J. Phys. Chem. A 2011, 115, 9022−9033. (20) Kua, J.; Tomlin, M. Computational Study of Multiple-Decker Sandwich and Rice-Ball Structures of Neutral Titanium-Benzene Clusters. J. Phys. Chem. A 2006, 110, 11988−11994. (21) Yang, Z.; Zhang, B. L.; Liu, X. G.; Yang, Y. Z.; Li, X. Y.; Xiong, S. J.; Xu, B. S. Spin-Valve Giant Magnetoresistance in ScandiumBenzene Sandwich Cluster. EPL 2013, 104, 50006. (22) Wu, M. H.; Burton, J. D.; Tsymbal, E. Y.; Zeng, X. C.; Jena, P. Multiferroic Materials Based on Organic Transition-Metal Molecular Nanowires. J. Am. Chem. Soc. 2012, 134, 14423−14429. (23) Nagao, S.; Kato, A.; Nakajima, A. Multiple-Decker Sandwich Poly-Ferrocene Clusters. J. Am. Chem. Soc. 2000, 122, 4221−4222.

(24) Shen, L.; Yang, S. W.; Ng, M. F.; Ligatchev, V.; Zhou, L. P.; Feng, Y. P. Charge-Transfer-Based Mechanism for Half-Metallicity and Ferromagnetism in One-Dimensional Organometallic Sandwich Molecular Wires. J. Am. Chem. Soc. 2008, 130, 13956−13960. (25) Zhang, X. Y.; Wang, J. L.; Gao, Y.; Zeng, X. C. Ab Initio Study of Structural and Magnetic Properties of TMn(ferrocene)n+1 (TM = Sc, Ti, V, Mn) Sandwich Clusters and Nanowires (n = ∞). ACS Nano 2009, 3, 537−545. (26) Wu, J. C.; Wang, X. F.; Zhou, L. P.; Da, H. X.; Lim, K. H.; Yang, S. W.; Li, Z. Y. Manipulating Spin Transport via Vanadium-Iron Cyclopentadienyl Multidecker Sandwich Molecules. J. Phys. Chem. C 2009, 113, 7913−7916. (27) Zhou, L. P.; Yang, S. W.; Ng, M. F.; Sullivan, M. B.; Vincent, B. C.; Shen, L. One-Dimensional Iron-Cyclopentadienyl Sandwich Molecular Wire with Half Metallic, Negative Differential Resistance and High-Spin Filter Efficiency Properties. J. Am. Chem. Soc. 2008, 130, 4023−4027. (28) Yang, J. F.; Zhou, L. P.; Han, Q.; Wang, X. F. Bias Controlled Giant Magnetoresistance through Cyclopentadienyl-Iron Multidecker Molecules. J. Phys. Chem. C 2012, 116, 19996−20001. (29) Atodiresei, N.; Dederichs, P. H.; Mokrousov, Y.; Bergqvist, L.; Bihlmayer, G.; Blügel, S. Controlling the Magnetization Direction in Molecules via Their Oxidation State. Phys. Rev. Lett. 2008, 100, 117207. (30) Hosoya, N.; Takegami, R.; Suzumura, J.; Yada, K.; Koyasu, K.; Miyajima, K.; Mitsui, M.; Knickelbein, M. B.; Yabushita, S.; Nakajima, A. Lanthanide Organometallic Sandwich Nanowires: Formation Mechanism. J. Phys. Chem. A 2005, 109, 9−12. (31) Miyajima, K.; Kurikawa, T.; Hashimoto, M.; Nakajima, A.; Kaya, K. Charge Distributions in Multiple-Decker Sandwich Clusters of Lanthanide-Cyclooctatetraene: Application of Na-Atom Doping. Chem. Phys. Lett. 1999, 306, 256−262. (32) Takegami, R.; Hosoya, N.; Suzumura, J.; Nakajima, A.; Yabushita, S. Geometric and Electronic Structures of Multiple-Decker One-End Open Sandwich Clusters: Eun(C8H8)n− (n = 1−4). J. Phys. Chem. A 2005, 109, 2476−2486. (33) Long, N. M. Metallocenes; Blackwell Science: Oxford, 1998, and references therein. (34) Rocha, A. R.; Garcia-Suarez, V. M.; Bailey, S. W.; Lambert, C. J.; Ferrer, J.; Sanvito, S. Towards Molecular Spintronics. Nat. Mater. 2005, 4, 335−339. (35) Ratner, M. A. Brief History of Molecular Electronics. Nat. Nanotechnol. 2013, 8, 378−381. (36) Sanvito, S. Organic Spintronics: Filtering Spins with Molecules. Nat. Mater. 2011, 10, 484−485. (37) Callsen, M.; Caciuc, V.; Kiselev, N.; Atodiresei, N.; Blügel, S. Magnetic Hardening Induced by Nonmagnetic Organic Molecules. Phys. Rev. Lett. 2013, 111, 106805. (38) Katz, T. J.; Acton, N. Bis(pentalenylnickel). J. Am. Chem. Soc. 1972, 94, 3281−3283. (39) Katz, T. J.; Acton, N.; McGinnis, J. Sandwiches of Iron and Cobalt with Pentalene. J. Am. Chem. Soc. 1972, 94, 6205−6206. (40) Ashley, A. E.; Cooper, R. T.; Wildgoose, G. G.; Green, J. C.; O’Hare, D. J. Homoleptic Permethylpentalene Complexes: Double Metallocenes of the First-Row Transition Metals. J. Am. Chem. Soc. 2008, 130, 15662−15677. (41) Summerscales, O. T.; Rivers, C. J.; Taylor, M. J.; Hitchcock, P. B.; Green, J. C.; Cloke, F. G. N. Double-Sandwich Pentalene Complexes M2(pent†)2 (M = Rh, Pd;pent†= 1,4-Bis(triisopropylsilyl)pentalene): Synthesis, Structure, and Bonding. Organometallics 2012, 31, 8613−8617. (42) Pramanik, A.; Kang, H. S. Electronic and Magnetic Properties of Metal-(4,4-bipyridine) Sandwich Complexes and Their Nanowires. J. Phys. Chem. A 2011, 115, 219−224. (43) Wu, X. J.; Zeng, X. C. Double Metallocene Nanowires. J. Am. Chem. Soc. 2009, 131, 14246−14248. (44) Zhang, Z. H.; Wu, X. J.; Guo, W. L.; Zeng, X. C. CarrierTunable Magnetic Ordering in Vanadium-Naphthalene Sandwich Nanowires. J. Am. Chem. Soc. 2010, 132, 10215−10217. H



Article

(45) Li, Y. F.; Zhou, Z.; Chen, Z. F. From Vanadium Naphthalene (Vn−1Npn) Sandwich Clusters to VNp Sandwich Nanowire: Structural, Energetic, Electronic, and Magnetic Properties. J. Phys. Chem. A 2012, 116, 1648−1654. (46) Zhang, X. Y.; Han, J.; Liu, Y. J.; Wang, J. L. Structural, Electronic, and Magnetic Properties of One-Dimensional Organic Bimetal-Naphthalene Sandwich Nanowires. J. Phys. Chem. C 2012, 116, 5414−5419. (47) Wang, L.; Cai, Z. X.; Wang, J. Y.; Lu, J.; Luo, G. F.; Lai, L.; Zhou, J.; Qin, R.; Gao, Z. X.; Yu, D.; Li, G.; Mei, W. N.; Sanvito, S. Novel One-Dimensional Organometallic Half Metals: VanadiumCyclopentadienyl, Vanadium-Cyclopentadienyl-Benzene, and Vanadium-Anthracene Wires. Nano Lett. 2008, 8, 3640−3644. (48) Yang, Z.; Zhang, B. L.; Liu, X. G.; Yang, Y. Z.; Li, X. Y.; Xiong, S. J.; Xu, B. S. The Spin-Filter Capability and Giant Magnetoresistance Effect in Vanadium-Naphthalene Sandwich Cluster. Org. Electron. 2013, 14, 2916−2924. (49) Zhang, T. T.; Zhu, L. Y.; Wu, Q. S.; Yang, S. W.; Wang, J. L. Structures and Magnetism of Multinuclear Vanadium-Pentacene Sandwich Clusters and Their 1D Molecular Wires. J. Chem. Phys. 2012, 137, 164309. (50) Bendjaballah, S.; Kahlal, S.; Costuas, K.; Bévillon, E.; Saillard, J. Y. The Versatility of Pentalene Coordination to Transition Metals: A Density Functional Theory Investigation. Chem.Eur. J. 2006, 12, 2048−2065. (51) Delley, B. An All-Electron Numerical Method for Solving the Local Density Functional for Polyatomic Molecules. J. Chem. Phys. 1990, 92, 508. (52) Perdew, J. P.; Burke, J. P.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (53) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (54) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into A Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (55) Brandbyge, M.; Mozos, J. L.; Ordejon, P.; Taylor, J.; Stokbro, K. Density-Functional Method for Nonequilibrium Electron Transport. Phys. Rev. B 2002, 65, 165401. (56) Rungger, I.; Sanvito, S. Algorithm for the Construction of SelfEnergies for Electronic Transport Calculations Based on Singularity Elimination and Singular Value Decomposition. Phys. Rev. B 2008, 78, 035407. (57) Gütlich, P.; Garcia, Y.; Goodwin, H. A. Spin Crossover Phenomena in Fe(II) Complexes. Chem. Soc. Rev. 2000, 29, 419−427. (58) Wang, J. L.; Zhang, X. Y.; Schleyer, P. V. R.; Chen, Z. F. Density Functional Theory Studies of Inorganic Metallocene Multidecker Vn(P6)n+1 (n=1C4) Sandwich Clusters. J. Chem. Phys. 2008, 128, 104706. (59) Chattopadhyaya, M.; Alam, M. M.; Sen, S.; Chakrabarti, S. Electrostatic Spin Crossover and Concomitant Electrically Operated Spin Switch Action in a Ti-Based Endohedral Metallofullerene Polymer. Phys. Rev. Lett. 2012, 109, 257204. (60) Brynda, M.; Gagliardi, L.; Roos, B. O. Analysing the ChromiumChromium Multiple Bonds Using Multiconfigurational Quantum Chemistry. Chem. Phys. Lett. 2009, 471, 1−10. (61) Panas, I. A Coulomb Hole Approach to the Binding in Cr2. Mol. Phys. 1996, 89, 239−246. (62) Baibich, M. N.; Broto, J. M.; Fert, A.; Nguyen Van Dau, F.; Petroff, F.; Etienne, P.; Creuzet, G.; Friederich, A.; Chazelas, J. Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices. Phys. Rev. Lett. 1988, 61, 2472. (63) Binasch, G.; Grünberg, P.; Saurenbach, F.; Zinn, W. Enhanced Magnetoresistance in Layered Magnetic Structures with Antiferromagnetic Interlayer Exchange. Phys. Rev. B 1989, 39, 4828. (64) The DFT-D calculations were performed by using DMOL3 package. Here, TS method was applied to DFT-D correction. Tkatchenko, A.; Scheffler, M. Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102, 073005.

(65) Tran, F.; Blaha, P. Accurate Band Gaps of Semiconductors and Insulators with a Semilocal Exchange-Correlation Potential. Phys. Rev. Lett. 2009, 102, 226401.

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Magnetic and Quantum Transport Properties of Small-Sized Transition

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