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Theoretical Study on Sandwich-Like Transition-Metal− Cyclooctatetraene Clusters and One-Dimensional Infinite Molecular Wires Weicheng Gao,† Xiaojing Yao,‡ Yi Sun,† Weikang Sun,† Hongfei Liu,† Jianshuang Liu,† Yongjun Liu,† and Xiuyun Zhang*,† †
College of Physics Science and Technology, Yangzhou University, No.180 Siwangting Road, Yangzhou 225002, China College of Physics Science and Information Engineering, Hebei Normal University, No. 20 Road East. 2nd Ring South, Yuhua District, Shijiazhuang 050024, China
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‡
S Supporting Information *
ABSTRACT: Using density functional theory calculations, we investigated the structure and electronic properties of cyclooctatetraene (C8H8, COT)-ligand mono- or bi-transition-metal (M) sandwich clusters, Mn(COT)n+1 (M = Sc, Ti, Cr, Mn, n = 1, 2) or (COT)M1(COT)M2(COT), as well as their one-dimensional infinite molecular wires. All the sandwich M−COT clusters and molecular wires are rather stable with their binding energies ranging from 3.20 to 7.48 eV per transition-metal atom. Superior to MnBzn+1 complexes, most sandwich M−COT complexes are in their high spin states with ultrahigh magnetic moments. Moreover, one-dimensional infinite molecular wires, [Cr(COT)]∞, [(COT)V(COT)Ti]∞ and [(COT)Sc(COT)Cr]∞, are predicted to be ferromagnetic half-metals. Our findings suggest that such M−COT sandwich complexes may be potential candidates for applications in spintronics.
1. INTRODUCTION Since the synthesis of ferrocene, Fe(C5H5)2, in 1950s,1 organometallic sandwich compounds, composed of transition-metal (M) atoms and organic hydrocarbon ligands, have attracted great attention because of their extraordinary electronic, magnetic, and optical properties, which have potential applications in catalysis, spintronic devices, biosensor, and so on.2−22 To date, various organometallic sandwich compounds have been identified, the metal elements cover alkali (alkaline-earth) metals, 3d-transition-metals, 4(5)flanthanide (actinide)-metals, and so forth, and the organic ligands include Bz (benzene, C6H6), Cp (cyclopentadienide, C5H5), COT (cyclooctatetraene, C8H8), Np (naphthalene, C8H10), and so forth. It should be noted that the Bz- and Cpligand organometallic sandwich compounds are the most studied. For example, size-dependent magnetic moments (MMs) have been found for VnBzm,5 particularly, replacing the Bz by Cp can bring one more net spin into the clusters.8 One dimensional (1D) infinite molecular wires, for example, [VBz]∞, [MnBz]∞, [NbBz]∞, and [TcBz]∞, as well as the Cpligand analogues like [FeCp]∞, [VCp]∞, and [CrCp]∞, were © 2019 American Chemical Society
proved to be robust ferromagnetic (FM) half-metals (HMs).6,7,9,23 Interestingly, the HM feature of 1D [VBz]∞ can be kept even under the elongation up to 12%.7 Additionally, the lanthanide (Ln) atoms-COT ligand sandwich compounds, LnnCOTm (Ln = Ce, Nd, Eu, Tb, Ho, Tm, and Yb, et al.), have also attracted great interest because of their ultrahigh MMs and large thermodynamic stability.10,16 Zhang et al. found that the MMs of EunCOTn+1 increase linearly with the size of the cluster, under the law of (7n + 2)μB.11 Unfortunately, the FM and antiFM (AFM) states of these clusters are energetically competitive,11,24 which largely blocks their applications in spintronic devices. Compared with the extensively studied Bz- and Cp-ligand sandwich complexes, people’s attention on M−COT sandwich compounds are relatively scarce.14,27 Experimentally, the transition-metal (e.g., Ti, V, Fe, Ni, and Ag)−COT compounds have been produced by the laser vaporization method;25,26 therefore, it is curious to Received: March 7, 2019 Accepted: May 9, 2019 Published: June 4, 2019 9739
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ascribed to the nonequilibrium charge distribution in the COTs as discussed below. The stabilities of these sandwich compounds can be evaluated by calculating the binding energy (Eb), which is defined by the following equation
know the structure, electronic and magnetic properties, and bonding characteristics of these M−COT compounds. On the other hand, sandwiching bi- or multiple-metal atoms between hydrocarbon cyclic ligands has been proven to be an effective way to modulate the electronic and magnetic properties28−34 and determine what the effects to the clusters as well as the molecular wires by sandwiching different transition-metal atoms between COT ligands are. In this work, we systematically investigate the structures, electronic, and magnetic behaviors of M−COT sandwich clusters, Mn(COT)n+1 (M = Sc, Ti, and Cr, Mn, n = 1, 2), as well as their 1D infinite molecular wires. Besides, the structure analogues having bimetal atoms, (COT)M1(COT)M2(COT) and [(COT)M1(COT)M2]∞, are also explored. Our results show that all the studied M−COT clusters and molecular wires are very stable and most of them are FM with ultrahigh MMs. Besides, three one-dimensional infinite molecular wires, [Cr(COT)]∞, [(COT)V(COT)Ti]∞, and [(COT)Sc(COT)Cr]∞ are found to be FM HMs.
E b = [nEM + (n + 1)ECOT − E M n(COT)n+1] /n
where EM, ECOT, and EMn(COT)n+1 are the energies of transitionmetal atom, COT ring, and Mn(COT)n+1 clusters, respectively. Our results show that all the studied systems are rather stable with their binding energies varying from 3.30 to 7.04 eV per TM atom (see Table 1), greater than those of Eun(COT)m clusters (∼3.82−5.70 eV).11 Except Ti(COT)2 which has the small highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap of 0.03 eV, all the other systems have the gaps ranging from 0.18 to 0.37 eV (see Table 1), showing that they are kinetically stable and can act as building blocks for larger M−COT clusters. Moreover, the charge density difference (CDD) calculations show that significant electrons are accumulated on the M−C bonds, indicating the coordinate covalent bonds between transitionmetal and COT rings (see Figure S1). Different from Sc(COT)2, Ti(COT)2, and Mn(COT)2, in which a nearly equivalent amount of electrons are transferred to the two COT ligands, the electrons transferred to the two COTs for Cr(COT)2 are 0.67 and 0.52 e, respectively, which is the cause for their nonequilibrium Cr−COT distances. For M2(COT)3, the charges transferred from transition-metal atoms to the terminal COTs are much larger than those of the internal ones. Taking Sc2(COT)3 as an example, the electrons donated from Sc atoms to two terminal COT ligands are 0.86 and 0.87 e, respectively, while those transferred to the internal ones are only 0.57 and 0.55 e, respectively, such distinct charge distribution is responsible for the aforementioned different M−COT bonding characters. Comparable to the mono-metal Mn(COT)n+1 clusters, five types of bimetal compounds, (COT)M1(COT)M2(COT) with (M1, M2) = (V, Ti), (Sc, Cr), (Cr, Fe), (Mn, Fe), and (Cr, Mn), are also explored (see Figure S2 in Supporting Information). Similar with Mn(COT)n+1s, all the studied bimetal isomers are rather stable with high binding energies of ∼3.20−6.54 eV per transition-metal atom. Moreover, all the bimetal complexes have nonequilibrium M−COT distances (see Figure S2 and Table S2 in Supporting Information) due to the nonequilibrium charge transfer among them. As shown in Table S3 in Supporting Information, the charges transferred from the transition-metal atom to the neighboring COT ligands for M = Sc, Ti, Mn, and Fe atom are very close. Differently, the charges gained on the two neighboring COT rings from one transition-metal atom is largely enlarged in the case of M = V and Cr, which is in accordance with the fact that for the (COT)M1(COT)M2(COT)s with V and Cr, the distance difference between them and two neighboring COTs are the largest. Interestingly, rich magnetic properties are identified for these Mn(COT)n+1 and (COT)M1(COT)M2(COT) clusters. Except Ti(COT)2 which is nonmagnetic and Ti2(COT)3 which is AFM, the other three Mn(COT)n+1 (M = Sc, Cr, and Mn) systems are FM (see Figure S3 in Supporting Information), in which the MMs of TM2(COT)3 are almost doublet of that in their M(COT)2 counterparts (see Table 1). Besides, all the bimetal (COT)M1(COT)M2(COT) clusters
2. RESULTS AND DISCUSSIONS 2.1. Mn(COT)n+1 (n = 1, 2, M = Sc, Ti, Cr, and Mn) Sandwich Clusters. Most of the Mn(COT)n+1 (n = 1, 2) clusters with normal sandwich configurations have D4h symmetry (Table 1), except Cr(COT)2 and Mn2(COT)3 Table 1. Geometric Symmetry, Binding Energies (Eb), MMs, HOMO−LUMO Gaps (Δ), the Bader Charges from Transition-Metal Atoms (M_e) to the Terminal (COT_e(T)), and Internal COT (COT_e(I) for M2(COT)3), Respectively sys
M
symmetry
Eb (eV)
MM (μB)
Δ (eV)
M_e (e)
COT_e (e)
(1,2)
Sc Ti Cr
D4h D4h C8v
5.60 7.04 3.58
1 0 4
0.27 0.03 0.37
1.56 1.50 1.19
Mn Sc
D4h D4h
3.38 4.08
5 2
0.35 0.18
1.25 1.43
Ti
C2h
7.48
0
1.24
1.37
Cr
D4h
3.49
8
0.20
1.18
Mn
D8h
3.30
12
0.51
1.22
0.78(T) 0.75(T) 0.67(T), 0.52(T) 0.62(T) 0.56(I) 0.86(T) 0.55(I) 0.82(T) 0.56(I) 0.63(T) 0.44(I) 0.78(T)
(2,3)
(1)
which have C8v and D8h symmetry, respectively. The geometric structures of Mn(COT)n+1 are shown in Figure 1, in which Ti2(COT)3 cannot form a stable sandwich structure with three COT ligands tilted in some degree (see Figure 1f). The structure parameters of all the sandwich complexes are summarized in Table S1 in the Supporting Information. The C−H bonds of COT rings are 1.09 Å and the C−C bonds are in the range of 1.38−1.45 Å, close to those of Fen(COT)n+1 (1.39−1.42 Å).27 For Sc(COT)2, Ti(COT)2 and Mn(COT)2, the spacing between transition-metal atom and two terminal COT rings (RM−COT) are uniform. A different case is found for Cr(COT)2, wherein nonequivalent distances of 1.41 and 2.13 Å are identified. While in the case of M2(COT)3, the distance of the transition-metal atom to the internal COTs are around 1.78−2.28 Å, a bit larger than that to the terminal ones, ∼1.37−1.65 Å. Such distinct geometric characters can be 9740
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Figure 1. Top and side view of the optimized structures for M(COT)2 (a−d) and M2(COT)3 (e−h), M = Sc, Ti, Cr, and Mn, respectively. The distances between transition-metal atoms to the COT ligands are shown in the figures.
types (positive and negative) of spin directions to make sure their better interaction with two-side Ti atoms. As a result, such electron configuration in Ti2(COT)3 makes the middle COT ring inclined to interact with Ti atoms, and the same is true for the end rings. In the case of Cr2(COT)3, Mn2(COT)3, and bimetal (COT)M1(COT)M2(COT), the transition-metal atoms in the clusters are ferromagnetically coupled, and the MMs are chiefly provided by d electron states of transitionmetal atoms, a fraction of them comes from the p orbitals of C atoms (see Figures S3−S5 in Supporting Information). 2.2. One-Dimensional Infinite Organometallic Sandwich Molecular Wires, [M(COT)]∞ & [(COT)M1(COT)M2]∞. The optimized structures of all the 1D mono-metal [M(COT)]∞ (M = Sc, Ti, Cr, and Mn) and bimetal [(COT)M1(COT)M2]∞ infinite organometallic sandwich molecular wires (IOSMWs) are shown in Figure S6a−d in Supporting Information. To confirm the magnetic ground states of the molecular wires, 1 × 1 × 2 supercells containing two transition-metal atoms are considered (see Figure S6 in Supporting Information). The lattice constants (L) of these 1D mono-metallic [M(COT)]∞ wires follow the orders of L(Mn) > L(Cr) > L(Sc) > L(Ti), namely, it is 7.50, 7.46, 6.96, and 6.90 Å for [Mn(COT)]∞, [Cr(COT)]∞, [Sc(COT)]∞, and [Ti(COT)]∞, respectively. In addition, for the 1D bimetal [(COT)Ti(COT)V]∞ and [(COT)Sc(COT)Cr]∞ IOSMWs, their lattice parameters are 7.30 and 7.58 Å, respectively. In contrast, heavy structural distortion happened for 1D [(COT)Cr(COT)Mn] ∞ , [(COT)Cr(COT)Fe] ∞ , and [(COT)Mn(COT)Fe]∞, which is recovered to normal sandwich structures on injecting one electron (see Figure S6g−i in Supporting Information). The lattice constants for sandwich [(COT)Cr(COT)Mn]∞−, [(COT)Cr(COT)Fe]∞−, and [(COT)Mn(COT)Fe]∞− are 7.76, 7.58, and 7.84 Å, respectively. The binding energies of the 1D IOSMWs are defined by eqs 2&3
studied here are found to be FM (see Figure S4 in Supporting Information). The total MMs of these bimetal systems are nearly half of the sum of MMs of (M1)2(COT)3 and (M 2 ) 2 (COT) 3 . As shown in Table 2, the MMs of Table 2. Binding Energies (Eb), MMMs, HOMO−LUMO Gaps (Δ), Electron Transferred from M Atoms (TE) to the COT Rings for (COT)M1(COT)M2(COT) Clusters, and 1D [(COT)M1(COT)M2]∞ Molecular Wires. For 1D [(COT)M1(COT)M2]∞, the Band Gaps (Δ) of SCs and HMs Are Also Listed sys cluster
molecular wires
(M1, M2)
Eb (eV)
MM (μB)
Δ (eV)
TE (e) (M1, M2)
(V, Ti) (Sc, Cr) (Cr, Fe) (Mn, Fe) (Cr, Mn) (V, Ti)
6.54 5.81 3.42 3.54 3.20 4.79
5.00 5.00 10.00 11.00 11.00 5.00
0.21 0.24 0.20 0.21 0.05 1.72
1.1, 1.4 1.5, 1.1 1.1, 1.0 1.2, 1.1 1.1, 1.2 1.12, 1.36
(Sc, Cr) (Cr, Fe)− (Mn, Fe)− (Cr, Mn)−
4.53
5.00 8.28 9.00 9.12
1.44 0.86 0.89 0.92
1.52, 1.05, 1.20, 1.05,
1.02 1.07 1.01 1.23
Sc2(COT)3, Cr2(COT)3, Fe2(COT)3,27 and Mn2(COT)3 are 2, 8, 10, and 12 μB, respectively, while those of the mixed (COT)Sc(COT)Cr(COT), (COT)Cr(COT)Fe(COT), and (COT)Mn(COT)Fe(COT) are 5, 10, and 11 μB, respectively (see Table 2). The origin of such magnetic behaviors can be well understood from the orbitals plots (see Figures 2 and S5 in Supporting Information). The MM of Sc(COT)2 is contributed from the C-pz state from COT rings, while that of Sc2(COT)3 come mainly from two dz2 states from Sc atoms. For Ti(COT)2, the electrons occupy equally on two spin channels, while for Ti2(COT)3, the dz2 electrons from two Ti atoms couple antiferromagnetically (see Figure S3 in Supporting Information), as a result, the total MMs of these two clusters are zero. Moreover, we noted that the COT rings on two ends of Ti2(COT)3 couples antiferromagnetically. Particularly, the spins of the middle COT ligand displays two
E b = [2EM + 2ECOT − E[M(COT)]∞] /2
(2)
E b = [2ECOT + EM1 + EM2 − E[(COT)M1(COT)M2]∞] /2 (3) 9741
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Figure 2. Energy orbitals for M(COT)2 (a−d) and M2(COT)3 (e−h) clusters (M = Sc, Ti, Cr, and Mn). The Fermi level is indicated by the green dotted line.
Figure 3. (a−d) Band structures and PDOS for 1D [M(COT)]∞ at M = Sc, Ti, Cr, and Mn, respectively. Insets are their spin density plots.
charge analysis shows that every COT ring capture about 1.25 e from transition-metal atoms, and the lessened electrons for Sc, Ti, V, and Cr are 1.52, 1.37, 1.12, and 1.02 e, respectively. Furthermore, for the electron-injected [(COT)Cr(COT)Mn]∞−, [(COT)Cr(COT)Fe]∞−, and [(COT)Mn(COT)Fe]∞− systems, the electrons donated from every transitionmetal atom are around 1 e. The band structures and partial density of states (PDOS) for these 1D molecular wires are displayed in Figures 3 and 4. In the crystal field of COT, the five degenerated d orbitals are split into one single-occupied dz2 and two degenerated (dxy, dx2−y2)/(dxz, dyz) orbitals. It is found that 1D [M(COT)]∞ is NM metal, FM metal, FM HM, and AFM semiconductor for M = Sc, Ti, Cr, and Mn, respectively (see Figure 3). For 1D [Ti(COT)]∞, it is the dz2 and dx2−y2 electrons from Ti atom contributes to the MM (Figure 3a). The AFM state of
where EM, ECOT, E[M(COT)]∞, and E[(COT)M1(COT)M2]∞ are the energies of transition-metal atom, COT ring, [M(COT)]∞, and bimetal [(COT)M1(COT)M2]∞ molecular wires, respectively. The binding energies of these molecular wires are in the range of 2.36−6.58 eV (see Tables 2 and S4 in Supporting Information). Based on the Bader charge analysis, the electrons transferred from TM atoms to COT ligands in 1D [M(COT)]∞ IOSMWs are 1.37, 1.27, 1.14, and 1.27 e for Sc, Ti, Cr, and Mn, respectively. Such significant charge transfer is responsible for the stable planar structure of COT ligands. Besides, five 1D bimetal molecular wires, [(COT)M1(COT)M2]∞, with (M1, M2) = (V, Ti), (Sc, Cr), (Cr, Fe), (Mn, Fe), and (Cr, Mn) are also extended. It is found that 1D [(COT)M1(COT)M2]∞ with (M1, M2) = (V, Ti) and (Sc, Cr) combinations have stable linear sandwich configurations at high spin states, for example 5.0 and 5.0 μB per unit cell. Bader 9742
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Figure 4. Band structures of [(COT)M1(COT)M2]∞ molecular wires for (M1, M2) = (V, Ti) and (Sc, Cr) (a,b) and [(COT)M1(COT)M2]∞− molecular wires for (M1, M2)=(Cr, Fe)−, (Mn, Fe),− and (Cr, Mn)− (c−e), respectively. Spin density plots for all the systems are also shown. (f) Summary of the MMs and half-metallic band gaps of [M(COT)]∞ (SMWs) and [(COT)M1(COT)M2]∞ (MMWs).
MMs of sandwich Mn(COT)n+1 are insensitive to different U values. Thus, our results are without considering the on-site correlation effects. The electronic wave functions were expanded on a plane-wave basis with a cutoff energy of 400 eV. Periodic boundary conditions were applied along the molecular wire with the unit cell containing two metal atoms and two ligands. The vacuum region between wires was larger than 10 Å, all the atoms were fully relaxed until the Hellmann− Feynman force on each atom was less than 0.01 eV/Å. The reciprocal space was sampled by 1 × 1 × 11 grid meshes using the Monkhorst−Pack scheme39 for geometry optimization. A denser k-point grid (1 × 1 × 45) was used for electronic structure calculations. It should be noted that, most systems are largely deformed after full optimization because of the insufficient charge transferred to the COT ligands. However, the structures can be well recovered to normal sandwich configurations in high spin states. Here, we chose the normal sandwich structures to explore the bonding characters, electronic and magnetic properties of these compounds.
[Mn(COT)]∞ is favorable than the FM state by 0.15 eV lower in energy, in which the local MMs on Mn atoms are +4.28 and −4.28 μB, respectively. 1D [Mn(COT)]∞ is direct gap semiconductor with the band gap of 1.08 eV. While 1D [Cr(COT)]∞ is robust FM HM with a direct gap of 2.02 eV in the spin down channel. Moreover, four d electrons (dz2, dx2−y2, dxy, and dxz) in spin up channel results in the total MM of 4 μB. Interestingly, the 1D [(COT)Cr(COT)Mn]∞−, [(COT)Cr(COT)Fe]∞−, and [(COT)Mn(COT)Fe]∞− IOSMWs are all quasi-HMs with the quasi-half-metallic band gaps ∼1.0 eV (Figure 4f).
3. CONCLUSIONS By first-principles calculations, the structure, bonding characters, electronic and magnetic behaviors of M−COT sandwich clusters, Mn(COT)n+1 (n = 1, 2), and infinite molecular wires, [M(COT)]∞, are investigated. Except Ti2(COT)3, all the structures have high geometric symmetries with high spin states. Besides, all the sandwich clusters and molecular wires are energetically stable with high binding energies. For the bimetal (COT)M1(COT)M2(COT) sandwich clusters, combination of two different metal atoms can effectively modulate the electronic properties, and the metal atoms in all the clusters are ferromagnetically coupled with high MMs. Furthermore, the 1D infinite [M(COT)]∞ and [(COT)M1(COT)M2]∞ molecular wires, (M1, M2) = (V, Ti) and (Sc, Cr) are stable HMs. Besides, injecting one electron in [(COT)M1(COT)M2]∞ molecular wires at (M1, M2) = (Cr, Fe), (Mn, Fe), and (Cr, Mn) can help stabilize the sandwich structures and all the systems exhibit quasi-half metallic properties.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b00637. Optimized structures, structure parameters, CDDs and spin densities of sandwich clusters, and molecular wires (PDF)
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AUTHOR INFORMATION
Corresponding Author
4. COMPUTATIONAL METHODOLOGY AND MODELS All the calculations were performed within the framework of spin-polarized density functional theory implemented in the Vienna ab initio simulation package.35,36 We adopted the Perdew−Burke−Ernzerholf37 generalized gradient approximation as the exchange−correlation potential and the electron-ion interaction was described by the projector-augmented wave potential.38 To evaluate the correlation effects of d orbitals of transition-metal atoms, we tested the influence of different onsite Hubbard parameters, U (U = 0−3 eV), for sandwich Mn(COT)n+1 (n = 1−2) clusters. Our results show that the
*E-mail:
[email protected]. ORCID
Xiuyun Zhang: 0000-0001-9977-4273 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the NSFC (11574262), the Qinglan Project of Jiangsu Province, the Personnel Training Plan of Yangzhou University, the Natural Science Foundation of the 9743
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Jiangsu Higher Education Institutions of China (15KJB510031) and the Scientific Research Foundation of Hebei Normal University (L2018B03).
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DOI: 10.1021/acsomega.9b00637 ACS Omega 2019, 4, 9739−9744
