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Ab Initio Study of Bond Characteristics and Magnetic Properties of Mixed-Sandwich VnBzmCpk Clusters Xiuyun Zhang† and Jinlan Wang*,†,‡ Department of Physics and School of Chemistry & Chemical Engineering, Southeast UniVersity, Nanjing 211189, People’s Republic of China ReceiVed: August 13, 2009; ReVised Manuscript ReceiVed: December 4, 2009
Ab initio spin-polarized density functional calculations have been performed on mixed-sandwich clusters VnBzmCpk (n ) 1-3, m + k ) n + 1, Bz ) benzene, Cp ) cyclopentadienyl) to study their size-dependent and composition-dependent structural, electronic, and magnetic properties. All of the mixed-sandwich clusters are thermodynamically stable with larger binding energies than those of VnBzn+1. Furthermore, the binding energies of VnBzmCpk show clear dependence on the number of Cp rings as well as on the relative positions of Cp (or Bz) rings inside of the molecules. More interestingly, the replacement of a Bz with a Cp ring in VnBzn+1 brings one net spin into the cluster, which is attributed to the transfer of one minority dδ electron from the V atom to its adjacent Cp ligand. In addition, the ferromagnetism stability of VnBzn+1 is significantly enhanced upon Cp replacement. 1. Introduction Molecular magnets are of ever-growing interest due to their potential application in spintronics devices, among which, vanadiumn-benzenem (VnBzm) clusters and their one-dimensional (1D) infinite molecular chains have been extensively investigated because of their novel structural, electronic, and magnetic properties.1-18 Structurally, VnBzn+1 clusters tend to adopt multidecker sandwich forms rather than riceball structures and appear to be helical for large sizes of n ) 4-6.6,7 Magnetically, monotonically increasing magnetic moments were observed in VnBzn+1.5-7,10,12 Their infinite [V(Bz)]∞ wire was theoretically predicted to be a robust ferromagnetic half metal.12,14-17 The finite VnBzm molecules suspended between Co or Ni electrodes were perfect spin filters.16 Similarly, suspending them between two single-wall carbon nanotube (or graphene) electrodes was also predicted to be an efficient spin filter with a high transmission spin polarization of 73-99%.18 Actually, V atom can interact with various organic molecules to form stable sandwich clusters besides VnBzm.19-29 One example is the vanadium-cyclopentadienyl sandwich cluster (VCp2) synthesized in 1975.19 Its electron configuration was predicted to be 4A1′.29 However, no multidecker VnCpm has been synthesized yet.23 Similar to [VBz]∞, a 1D infinite [VCp]∞ molecular wire was also predicted to be a half metallic ferromagnet, and their finite clusters suspended on Li electrodes displayed high spin filter and negative differential resistance (NDR) effects.30 On the other hand, mixed-sandwich clusters20,31-34 have also attracted much attention. The first triple-decker benzene bridging sandwich cluster (CpV)2Bz was synthesized in 1983.20 Later, a smaller cluster, CpVBz, was also synthesized by reacting (CpV)2Bz with LiCp.21 Photoelectron spectroscopy (PES) and extended Huckel calculations determined that the ground state of CpVBzVCp has four unpaired electrons.32,33 Magnetic susceptibility measurements indicated that CpVBzVCp and * To whom correspondence should be addressed. † Department of Physics. ‡ School of Chemistry & Chemical Engineering.
CpVBz obey the Curie-Weiss law in the range of 4-300K, and their effective magnetic moments are 4.81 and 2.83 µB, respectively.33 Recently, CpVBzVCp was found to have a more stable FM state than V2Bz3.13 Furthermore, three mixed sandwich clusters of V2BzCp2, V4Bz2Cp3, and V6Bz3Cp4 were found to have high magnetic moments of 4, 7, and 10 µB.34 However, there is still a lack of systematic theoretical exploration on these mixed-sandwich VnBzmCpk clusters. Will the mixing process bring new features different from the pure V-Bz or V-Cp clusters? Will the ratios of Cp to Bz and their relative locations affect the magnetic properties of the mixed-sandwich VnBzmCpk clusters? In this paper, we have exploited spin-polarized density functional theory to investigate the structural, electronic, and magnetic properties of the mixed VnBzmCpk (n ) 1-3, m + k ) n + 1) multidecker sandwich clusters, considering different ratios and locations of Cp to Bz. Our investigation shows that replacing Bz with Cp in VnBzn+1 can largely enhance the structural stability and effectively tune the magnetic moments. For example, the magnetic moment increases by 1 µB when introducing a Cp ring into the VnBzn+1 clusters, independent of the relative locations of Cp (or Bz) rings inside of the clusters. 2. Computational Method All of the calculations were implemented within the framework of spin-polarized density functional theory (DFT) in the Vienna Ab Initio Simulation Package (VASP).35,36 The electron-core interaction was described by the projected augmented wave (PAW)37,38 pseudopotential within the Perdew-Wang (PW91)39 general gradient approximation (GGA). We used a simple cubic supercell of 20 × 20 × C (C ) 20-23) to ensure that interaction between the supercells was negligible. The cutoff energy was set to 400 eV, and the Brillouin zone was meshed only by the gamma point. The structures were relaxed without any symmetry constraints using a conjugate-gradient algorithm until the Hellmann-Feynman force acting on each atom was less than 0.02 eV/Å. Furthermore, to avoid the cluster being trapped in a local-minimum spin state, various spin projection
10.1021/jp907834v 2010 American Chemical Society Published on Web 01/25/2010
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TABLE 1: Comparison of Our Calculations with the Measured and Calculated Results for Selected Clustersa system VBz
VBz2
CpVBz VCp2
V2Bz3
BzVCpVBz BzVBzVCp CpVCpVBz CpVBzVCp V2Cp3 V3Bz4
properties RC-C (Å) RC-H (Å) RV-Bz (Å) Eb (eV) M (µB) RC-C (Å) RC-H (Å) RV-Bz (Å) Eb (eV) M (µB) RV-Bz (Å) M (µB) RC-C (Å) RC-H (Å) RV-Cp (Å) M (µB) RC-C (Å) RC-H (Å) RV-Bz (Å) Eb (eV) M (µB) M (µB) M (µB) M (µB) M (µB) M (µB) M (µB)
GGA 1.44 1.09 1.51 1.54 1 1.43 1.09 1.68 3.48 1 1.691 2 1.426 1.086 1.927 3 1.428(e)/1.445(m) 1.089/1.087 1.652/1.732 2.55 0 3 3 4 4 5 1
GGA+U 1.442 1.091 1.509 0.57 1 1.43 1.09 1.71 3.30 1 1.691 2 1.425 1.086 1.960 3 1.428(e)/1.446(m) 1.089/1.087 1.649/1.734 2.47 2 3 3 4 4 5 3
others 1.42,4 1.456 1.094,6 1.97,4 1.486 1, 144 16,9,11 1.436 1.096 1.68,4 1.696 3.574 14-7,9-12 1.7233 2.8333 1.434 ( 0.0037 1.133 ( 0.0147 1.928 ( 0.0067 329 1.429/1.4482 1.118/1.11812 1.648/1.7222 2.207 0,4 25-7,9-12
4.8133 1,9,11 35-7,10,12
a RC-C, RC-H, and RV-Bz (RV-Cp) are the equilibrium interatomic distances, and Eb is the binding energy; for VBz, Eb ) E(V) + E(Bz) E(VBz); for VnBzn+1 (n ) 1,2), Eb ) E(VBz) + E(Vn-1Bzn) - E(VnBzn+1). M is the total magnetic moments. RC-C(e) (RC-C(m)) and RC-H(e) (RC-H(m)) in V2Bz3 are the bond lengths on the edge (middle) of Bz rings.
values were assigned to the cluster. The accuracy of this combination of PW91/PAW was evaluated on selected clusters. As shown in Table 1, our calculations are in good agreement with earlier computed and measured results.2,4-7,9-12,29,33 The GGA+U calculation was also performed to consider the Coulomb interaction effect for the V atom. The GGA calculation gave an AFM ground state for V2Bz3 and V3Bz4, while GGA+U (U g 2.0 eV for V2Bz3 and U g 3.0 eV for V3Bz4) identified the FM ground state. In fact, this near degeneracy of FM and AFM states was also found in previous works, and different computational approaches and implemented codes predicted a different ground state.2,5-7,9-12 As the experimental results5 suggested FM ground states for both V2Bz3 and V3Bz4, we selected the GGA+U (U ) 3.0 eV) results for both of them. On the other hand, GGA+U (U ) 3.0 eV) was also carried out on the mixed sandwich clusters with close FM and AFM states and identified same FM ground states as those of the GGA calculation. Moreover, we also noted that GGA+U and GGA gave very close structural and energetic information for these tested systems. Therefore, we still stuck to the GGA description for the VnBzmCpk clusters, while GGA+U (U ) 3.0 eV) was exploited to describe the correct electronic and magnetic properties of V2Bz3 and V3Bz4. 3. Results and Discussion The lowest-energy structures of the mixed VnBzmCpk, n ) 1-3, sandwich clusters are shown in Figure 1 and Figures S1 and S2 in the Supporting Information. With the exception of VCp2 (D5h), CpVBzVCp (C2V), and CpVBzVBzVCp (C2V), most clusters are found to have no point group symmetry. Two diagonal C atoms of the Bz ligand in CpVBz (Figure 1a) deviates from the plane of the other four C atoms by about 1.84°, while for CpVBzVCpVBz (Figure 1c), small rotated angles
Figure 1. Optimized structures of the mixed-sandwich clusters [CpVBz], [CpVBzVCp], [CpVBzVCpVBz], and [CpVBzVBzVCp]. The Arabic numbers 5 and 6 represent the Cp and Bz rings, respectively.
along the molecular axis ( Eb(6,5,6) and Eb(5,6,6,6) > Eb(6,5,6,6), and (2) the Cp rings energetically favor sitting far apart from each other, namely, Eb(5,6,5) > Eb(5,5,6), Eb(5,6,6,5) > Eb(5,6,5,6) > Eb(5,5,6,6) > Eb(6,5,5,6), and Eb(5,5,6,5) > Eb(5,5,5,6). This interesting position-dependent BE behavior can be well understood from their different bonding characteristics, as shown in Figure 3, in which the isodensity surface of the frontier occupied orbitals of (5,6,5) and (5,5,6) are plotted. In the case of (5,6,5), very few densities are detected on the two Cp rings, except the slight densities on the HOMO and HOMO-1 orbitals, while in (5,5,6), the medium Cp ring has significant densities, although the edge Cp ring possesses negligible densities, indicating that the former has more ionic bonding between the V atom and Cp rings than the latter, which is the origin of the larger binding energy in (5,6,5). Total magnetic moments of the ground-state structures of the VnBzmCpk clusters are displayed in Figure 4. First, for the pure VnBzn+1 and VnCpn+1 clusters, the magnetic moments increase with size; adding a VBz or VCp unit increases the magnetic moment by 1 and 2 µB, respectively. Second, for the clusters with a given n (the number of V atoms), their magnetic moments increase linearly with the number of Cp rings. For example, the magnetic moments are 1, 2, and 3 µB for (6,6), (5,6), and (5,5); 2, 3, 4, and 5 µB for (6,6,6), (5,6,6), (5,6,5), and (5,5,5);
Figure 5. PDOS of an individual V and all of the C atoms (left) and spin densities (right) of VBz2, CpVBz and VCp2 clusters. The red and blue colors refer to the spin-up and spin-down densities, respectively.
and 3, 4, 5, 6, and 7 for (6,6,6,6), (5,6,6,6), (5,6,6,5), (5,5,5,6), and (5,5,5,5), respectively. Moreover, this linearly increasing magnetic behavior is independent of the relative location of the Cp or Bz inside of the clusters. Third, for the clusters having the same number of Cp’s, increasing a VBz unit enhances the magnetic moment by 1 µB, while for those having same number of Bz rings, their magnetic moments increase by 2 µB as the VCp unit increases. For example, the magnetic moment of (5,6), (5,6,6), and (5,6,6,6) is 2, 3, and 4 µB, while that of (5,6), (5,5,6), and (5,5,5,6) is 2, 4, and 6 µB, respectively. Therefore, we can argue that the magnetic moments of these sandwich clusters can be tuned by adjusting the ratio of Cp to Bz besides adding or subtracting a metal atom, which might be helpful in the magnetic control in practical application. To shed light on the electronic and magnetic properties of VnBzmCpk clusters, we plot the partial density of states (PDOS) on individual V and on all of the carbon atoms in the clusters with the sizes of n ) 1 and 2 in Figure 5 and Figure S3 in the Supporting Information. Under the D6h or D5h crystal field, the five degenerate d orbitals (dxy, dx2-y2, dxz, dyz, dz2) of V atom are split into two degenerate dπ (dxz, dyz) and dδ (dxy, dx2-y2) orbitals and one nondegerate dσ(dz2) orbital, and they are fully split under a crystal field of low symmetry. We can clearly see that the
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DOS near the Fermi level (Ef) is mainly from the d orbitals of the V atom, while those from the Bz and Cp rings are located deep and far from Ef; then, the magnetic properties of the clusters are mainly decided by the d oprbitals of V atoms. In VBz2, three d electrons of the V atom occupy the nondegenerate dσ (d5) orbital and doubly degenerate dδ (d1, d2) orbital in the majority channel, and the other two d electrons reside in the degenerate dδ (d3, d4) orbital on the minority manifold, leaving the dσ (d5) electron unpaired, and the total magnetic moment of this cluster is 1 µB. In CpVBz, under the asymmetric crystal field, those degenerate dπ and dδ orbitals in VBz2 are split, accompanied by the appearance of overlapping of dσ-dδ orbitals. Obviously, one dδ (d3) electron (mainly from V) on the minority channel of VBz2 is transferred to the Cp ring in CpVBz. Because the LUMO of the minority manifold of the Cp radical is much lower in energy than that of the HOMO (minority) component of the VBz unit (see Figure S4 in the Supporting Information), one minority electron on the HOMO of VBz inevitably transfers to the Cp ligand in forming CpVBz. This transfer empties this orbital and shifts it above the Fermi level. Accordingly, the dδ (d4) electron in VBz2 locates in the lower dπ (d4′) orbital in the case of CpVBz. Differently, no majority d electron is transferred to the Cp ligand, but the dδ (d2) electron in VBz2 moves to the lower dπ orbital d2′ in CpVBz. As a result, the diminishing of one minority d electron enhances the total magnetic moment to 2 µB. Similarly, in the VCp2 cluster, two minority d electrons of V located in the degenerate dδ (d3, d4) orbitals in VBz2 are completely transferred to its two neighboring Cp rings; the total magnetic moment of VCp2 is thus 3 µB. We also note that the overlap between V 3d orbitals and C 2p orbitals in CpVBz and VCp2 is much smaller than that in VBz2, indicating that the ionic bonding in V-Cp is much stronger than that in V-Bz. The above distinct magnetic behavior can also be clearly seen from the spin density, as displayed in the right panel of Figure 5. Large spin density is localized on the V atom, little is on the Bz rings, and much less is on Cp radicals, showing the different bonding features between V-Bz (covalent) and V-Cp (ionic). On the other hand, the negative (blue) spins on the ligands decrease, and the positive (red) spins on the V atom increase with increasing the number of Cp molecules, witnessing the magnetic enhanced behavior of the clusters visually. Similar analysis can also be extended to those larger clusters. In V2Bz3 (V3Bz4), 10 (15) valence electrons of the 2 (3) V atoms occupy 2 (3) nondegenerate dσ orbitals (unpaired) and 4 (6) doubly degenerate dδ orbitals (paired), respectively, leading to the total magnetic moment of 2 (3) µB. The same as VBz2, the replacement of a certain number of Bz’s with Cp rings will result in the same amount of dδ electrons in the minority channel transferred to its neighboring Cp rings (Figure S3 in Supporting Information), which eventually enhances the magnetic moments of the clusters. The energy differences between the ground state (GS) and the second lowest energy AFM excited states (ES) of all of the clusters are also considered and summarized in Figure 6. Very small energy differences have been found between the FM and AFM states in VnBzn+1. For example, the FM state is only 0.004 eV lower than its AFM state for both V2Bz3 and V3Bz4, while the energy differences are enlarged to 0.049-0.488 eV in the Cp-doped clusters, showing that the FM stability is greatly enhanced upon the replacement of Bz with Cp. A similar conclusion was also obtained by Weng et al.;13 they pointed out that replacing the edge Bz rings by Cp rings in V2Bz3 could lead to a large spin split of the V atoms and small magnetic
Zhang and Wang
Figure 6. Energy difference between FM ground states and the second lowest energy excited states of VnBzmCpk clusters. *GGA+U (U ) 3.0 eV) results.
polarization on the edge ligands and stabilize the FM ground state. As clearly displayed in Figure 5b-d, greater spin densities are observed on Bz rings than on Cp rings as one Cp ring captures one valence electron from the V atom; this ionic bonding significantly reduces the magnetic polarization of Cp as compared to that of Bz and enlarges the degree of spin polarization of d orbitals, which eventually enhances the FM stabilities. 4. Conclusion Mixed organometallic sandwich VnBzmCpk (n ) 1-3, m + k ) n + 1) clusters have been systematically studied using spinpolarized density functional theory. All of the mixed clusters have quite large binding energies (>5 eV); therefore, they are of high stability and are feasible to synthesize experimentally. On one hand, the binding energies of those clusters with the same number of V atoms increase monotonically with the number of Cp rings, and on the other hand, for the clusters with same number of V atoms and Cp rings, a little bit larger binding energies are found for those with Cp rings located as far away as possible. The magnetic moments of the mixed-sandwich clusters in a given n increase linearly with the number of Cp rings, independent of the relative location of Cp or Bz in the clusters. Careful analysis of the electronic structures show that one dδ electron of V in the minority channel is transferred to the π orbital of its nearby Cp rings and leaves one more electron unpaired, which is responsible for the increasing magnetism. Therefore, we can tune the magnetism of the clusters by altering the number of Cp rings instead of the metal atom, which might be helpful in future applications. Moreover, the replacement of Bz rings by Cp rings reduces the magnetic polarization of the organic ligands and largely enhances the ferromagnetic stability of the clusters. Acknowledgment. This work is supported by the SRFDP (Contract No. 20090092110025), NSFC (Grants 10604013 and 20873019), NBRP (Contracts 2010CB923401 and 2009CB623200), NCET (Contract NCET-06-0470), and Peiyu Foundations of SEU in China. The authors thank the computational resources at the Department of Physics, SEU. Supporting Information Available: The geometric parameters of the lowest energy structures of VnBzmCpk are presented in Table S1. The lowest-energy structures of VnBzmCpk are plotted in Figures S1 and S2. The frontier orbital energy level diagrams of VBz2, VBz, and CpVBz clusters are plotted in Figure S3. This material is available free of charge via the Internet at http://pubs.acs.org.
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