Insights into the structural, electronic and magnetic properties of V-doped copper clusters: comparison with pure copper clusters

The structural, electronic and magnetic properties of Cun+1 and CunV (n = 1–12) clusters have been investigated by using density functional theory. The growth behaviors reveal that V atom in low-energy CunV isomer favors the most highly coordinated position and changes the geometry of the three-dimensional host clusters. The vibrational spectra are predicted and can be used to identify the ground state. The relative stability and chemical activity of the ground states are analyzed through the binding energy per atom, energy second-order difference and energy gap. It is found that that the stability of CunV (n ≥ 8) is higher than that of Cun+1. The substitution of a V atom for a Cu atom in copper clusters alters the odd-even oscillations of stability and activity of the host clusters. The vertical ionization potential, electron affinity and photoelectron spectrum are calculated and simulated for all of the most stable clusters. Compare with the experimental data, we determine the ground states of pure copper clusters. The magnetism analyses show that the magnetic moments of CunV clusters are mainly localized on the V atom and decease with the increase of cluster size. The magnetic change is closely related to the charge transfer between V and Cu atoms.

gold cluster doped with V can bind a high number of oxygen molecules over pure gold cluster and is an improved novel catalyst for CO oxidation 51 . As it is known, Cu and Au have a similar electronic configurations nd 10 (n + 1)s 1 . Presumably, the copper clusters doped with V should also be a potential catalyst for the oxidation of CO. On the other hand, some experiments which are used to shed light on the structures of clusters must rely on theoretical calculations of geometries of possible low lying isomers. Therefore, in this paper, the geometric, electronic, and magnetic moments of the small Cu n+1 and Cu n V (n = 1-12) clusters will be studied systematically on the basis of density functional theory (DFT). It is wished that this work would be helpful to understand the influence of material structure on its properties and could provide practical guidelines for coming experimental research.

Computational Methods
Geometry optimizations and vibrational frequency analyses of Cu n+1 and Cu n V clusters have carried out in the framework of a DFT-based method using the GAUSSIAN09 package 52 . The exchange-correlation functional B3LYP and an effective core potential basis set LanL2DZ were used for all of the computations [53][54][55][56] . The convergence thresholds are set to 4.5 × 10 −4 a.u. for maximum force, 3.0 × 10 −4 a.u. for root mean square (RMS) force, 1.8 × 10 −3 a.u. for maximum displacement and 1.2 × 10 −3 a.u. for RMS displacement. The accuracy of the theoretical level has been checked by calculations on copper dimer and vanadium dimmer. The results have summarized in Table 1. To search the lowest energy structures of Cu n+1 and Cu n V clusters, lots of initial isomers, which include one-, two-and three-dimensional (3D) configurations, had been taken into account in our geometry optimizations. Owing to the spin polarization, every initial configuration was optimized at possible spin multiplicities. If an imaginary vibraional mode is found, a relaxation of the structure is performed until the true local minimum is actually obtained.

Results and Discussion
Geometrical structures and vibrational spectra. The optimized results for Cu 2 and CuV dimmers show the former in singlet spin state is 1.86 eV lower than in triplet spin state and the latter in single, triplet and septet spin states is less stable than in quintet spin state by 2.94, 0.47 and 1.38 eV, respectively. Accordingly, the singlet Cu 2 and quintet CuV are the ground states. Their bond lengths are 2.26 Å for Cu 2 and 2.49 Å for CuV. The bond length of the Cu 2 is shorter than that of the CuV. This may be attributed to the fact that the radius of Cu atom (1.28 Å) is smaller than that of V atom (1.34 Å). For each Cu n+1 and Cu n V (n = 2-12) clusters, Figs 1 and 2 display the ground state structure and low-lying isomers. According to the energy order from low to high, these isomers are denoted by nA, nB, nC, nD, nI, nII, nIII, and nIV, where n represents the number of Cu atoms in pure copper and Cu n V clusters. Meantime, their symmetry, spin multiplicity, and energy difference compared to each of the ground state structures are also indicated in the two figures. The geometric features and mean static polarizabilities ( ) of the ground state Cu n+1 and Cu n V (n = 1-12) clusters are listed in Table 2. The most stable structures of Cu n+1 and Cu n V (n = 2-5) clusters evidently prefer planar configurations. All isomers of copper clusters, which do not include 5C, are found to be in the lowest spin state. The ground state structures of Cu 3 , Cu 4 , Cu 5 and Cu 6 clusters are angular, rhombic, trapezoidal and triangular structures, respectively, and no low-lying 3D isomer is obtained for Cu 4 cluster. When a Cu atom in copper clusters is replaced by one V atom, the number of optimized Cu n V structures apparently increases. But only four isomers of each Cu n V cluster are depicted in Fig. 2. The lowest energy structures of Cu 2 V, Cu 3 V, Cu 4 V and Cu 5 V clusters is similar to those of Cu 3 , Cu 4 , Cu 5 and Cu 6 clusters. The energies of similar structures decrease as the coordination number of V atom increase. The 3IV isomer is the first 3D structure of Cu n V clusters. The tetragonal bipyramid and pentagonal pyramid is not unstable for Cu 5 V cluster. Other isomers, which not displayed in Figs 1 and 2, are higher in energy than the nD or nIV isomer.
Starting from n = 6, many stochastic configurations were optimized for Cu n+1 and Cu n V clusters. The optimized structures show that almost all lower energy isomers possess 3D configurations and V atom in lower energy Cu n V cluster tend to occupy the position with the more ligands. As a result, a series of 3D structures for the Cu n+1 and Cu n V clusters (n = 6-12) were considered and optimized again. Moreover, various 3D Cu n V isomers with V atom occupying the most highly coordinated site were optimized further to ensure that the lowest energy structures obtained are the true minimum. To avoid missing the ground state structures, we had also used the strategies of substituting a Cu by one V atom from the pure copper cluster or adding Cu atom(s) to former Cu n or Cu n V clusters in geometry optimizations. The ground state structure of Cu 7 cluster is a pentagonal bipyramid (7A), lying just below the 7B. The 8A isomer with T d symmetry, which can be treated as a face-capped 7B, is found to be the lowest energy structure of Cu 8 cluster. The 9A and 9B are nearly degenerate and ref. 57 suggests 9B as the most stable structure. Nevertheless, in view of vertical ionization potential (VIP) which will be discussed later, we deduce that the 9A is the ground state structure of Cu 9 cluster. Simultaneously, the most stable structures of small Cu n (n = 2-9) clusters had studied by means of optical absorption spectra 58 . Our results are consistent with the previous conclusion. From Cu 10 to Cu 13 clusters, the flat cage-like configurations are more stable than other structures, e.g. close-packing and globe-shaped structures. The 10A, 11A, 12A and 13A are the lowest energy structures of Cu 10 , Cu 11 , Cu 12 and Cu 13 clusters, respectively. Several isomers reported in ref. 56 have also been optimized at B3LYP/LanL2DZ level and are higher in energy than our lowest energy structures. This is in agreement with Ramirez et al. 's studies 57 .
With regard to Cu n V (n = 6-12) clusters, the ground state structures (6I, 7I, 8I, 9I, 10I, 11I and 12I) are entirely different from the most stable structure of the corresponding Cu n+1 clusters. The 6I, 7I and 8I structures are similar to the low-lying isomers (7D, 8D and 9C) of pure copper clusters. The 9I, 10I, 11I and 12I configurations are unstable or do not exist for Cu clusters in the lowest spin state. The 11I is obtained by distorting the geometry starting from C 5v to C s symmetry. The 12I has a small deviation from I h symmetry. The Cu n V isomers, which resemble the lowest energy structures and low-lying isomers of Cu n+1 clusters, lay above each of the ground state structures (nI). The most stable structures of Cu n V (n = 7-12) clusters all contain a pentagonal bipyramid. In addition, due to the Jahn-Teller effect, the 6IV and 7II isomers with C s symmetry have a slight deviation from C 3v symmetry. The 10I and 12I strucutres are more stable in doublet spin state than in quartet spin state. The V atom in Cu n V clusters tends to occupy the site with the maximum coordination number. This may be ascribed to the principle of maximum overlap in molecular orbital theory. Because the orbital overlap between Cu and V atoms increases, the energy of Cu n V cluster will decrease.
The combination of theoretical and experimental vibrational spectra is a good method for the structural determination of small isolated clusters and the method has been successfully applied in practice 59 . Consequently, the vibrational spectra of the lowest energy Cu n+1 and Cu n V (n = 1-12) clusters are shown in Fig. 3. The Cu 2 dimer merely has a stretching vibration without change of dipole moment, so there is no absorption peak. The absorbed peaks of planar or highly symmetrical clusters are less than those of other configuration clusters. The intense   Table 2. The maximum and minimum bond lengths (R max , R min ) and chemical bond per atom (C) for the most stable Cu n+1 and Cu n V clusters. The averaged bond length between V and Cu atoms (R v ) and coordination number (N) of V atom in the ground state Cu n V clusters. The mean static polarizabilities (a). Relative stabilities and electronic properties. In this part, the relative stabilities and electronic properties of the ground state Cu n+1 and Cu n V (n = 1-12) clusters are discussed by means of the atomic averaged binding energies, second-order energy differences, energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), the VIP, the vertical electron affinity (VEA) and photoelectron spectroscopy (PES). The atomic averaged binding energies (E B ) of the Cu n+1 and Cu n V clusters can be calculated as follows where E(Cu n+1 ), E(Cu), E(Cu n V) and E(V) are the energy of Cu n+1 cluster, Cu atom, Cu n V cluster and V atom, respectively. The calculated binding energies per atom for the lowest energy Cu n+1 and Cu n V clusters are shown in Fig. 4. As seen from this figure, the size dependence of E B for Cu n+1 clusters have an apparent peak at n = 7. That is to say, the Cu 8 cluster possesses relatively higher thermic stability. The E B of Cu n V clusters, which is larger than that of Cu n+1 clusters for n≥ 8, is a monotonically increasing function of the number of atoms in clusters. This implies that the doped clusters can continue to gain energy during growth process. The substitution of a V atom for a Cu atom in Cu n+1 (n≥ 8) clusters can evidently enhance the stability of the host clusters. The phenomenon may be caused by structural changes. The configuration of Cu n V (n≥ 8) clusters is entirely different from that of Cu n+1 clusters. In cluster physics, the second-order energy differences (Δ 2 E), which can be compared with the relative abundances determined in mass spectroscopy experiment, is a particularly sensitive quantity that reflects the relative stability of clusters. For the ground state Cu n+1 and Cu n V clusters, it can be calculated as where E is the energy of the ground-state clusters. The calculated second-order energy differences as a function of the cluster size are illustrated in Fig. 5. It is obvious from Fig. 5 that the even-numbered copper clusters are more stable than the odd-numbered ones. However, the introduction of a V atom in copper cluster alters the stable pattern of the host clusters significantly. For the Cu n V clusters, three maxima are observed at n = 4, 7 and 9. Accordingly, it can be inferred that the Cu 4 V, Cu 7 V and Cu 9 V clusters are magic clusters and have an enhanced abundance in mass spectra. The HOMO-LUMO energy gap (E g ), which relies on the eigenvalues of the HOMO and LUMO energy levels, is viewed as an important parameter that characterizes chemical stability of small clusters. A big energy gap usually relates to a high chemical inertness. For the ground state Cu n+1 and Cu n V clusters, the energy gaps are plotted in Fig. 6. The pure copper clusters show an odd-even alternation in their energy gaps. This phenomenon can be interpreted by the electron pairing effect that the electron in a doubly occupied HOMO has stronger effective core potentials because the electron screening is weaker for electrons in the same orbital than for inner shell electrons. When a Cu atom ([Ar]3d 10 4s 1 ) in Cu n+1 cluster is replaced by a V ([Ar]3d 3 4s 2 ) atom, the closed electronic shell will become an opened electronic shell. So, the E g of Cu n V cluster for n = odd is smaller than that of Cu n+1 cluster. For n = 2, 4, 6 and 8, the unpaired electrons of Cu n V cluster is more than those of the corresponding Cu n+1 cluster. The energy of the LUMO of Cu n V cluster will rise because of the electrostatic interaction of unpaired electrons. The E g of Cu n V are larger than that of the Cu n+1 cluster. For n = 10 and 12, the Cu n V cluster is equal to Cu n+1 cluster in unpaired electrons. However, the formers have a highly symmetrical geometry. Hereby, the E g of Cu 10 V and Cu 12 V clusters is also larger than that of the Cu 11 and Cu 13 clusters, respectively.
The VIP and VEA are two basic quantities to get an insight into the electronic property and can be estimated as follows (cluster anion) ( 6) where E(cluster cation) and E(cluster anion) are the single-point energies of the cationic and anionic clusters in the neutral geometry. For the lowest energy Cu n+1 and Cu n V clusters, Table 3 give the calculated VIP and VEA along with the available experimental data. The calculated VIPs of pure copper clusters are in good agreement with previous measurements obtained at discrete 2.5 nm intervals. The agreement confirmed reliability of the  60 . Thus, we deduced that the 9A structure is the most stable structure of Cu 9 cluster. To offer reference material for PES experiment in future, the theoretical PES spectra of the global minimum structures of Cu n+1 and Cu n V (n = 1-12) clusters were simulated by adding the occupied orbital energy relative to the HOMO to the VIP and fitting them with a broadening factor of 0.1 eV, as plotted in Fig. 7. The distribution of energy level for all clusters is in the range of 6 to 11 eV. The doped V atom made a change for the PES spectra  Magnetic properties. The magnetic properties of the clusters are not only widely used in the preparation of nano electronic devices and high density magnetic storage materials, but also have a very important theoretical significance in the basic research of physics. The total magnetic moments of cluster mainly include the orbital and spin magnetic moments of electrons. The orbital magnetic moment of an electron is far less than the spin magnetic moment and, consequently, the magnetic moment of cluster is dominated by the spin magnetic moment. For the ground-state Cu n+1 and Cu n V (n = 1-12) clusters, the total magnetic moments are calculated and displayed in Fig. 8. The lowest energy copper clusters show an odd-even alternations with the increase of Cu atom in the total magnetic moment. The magnetic moment of Cu n+1 clusters with odd n is completely quenched.  For the doped clusters, the magnetic moment of Cu n V (n = 1-8) cluster is far larger than that of Cu n+1 clusters. The substitution of a V atom for a Cu atom can enhance the magnetism of the small host cluster. The Cu 2 V, Cu 4 V, Cu 6 V and Cu 8 V clusters have a magnetic moment of 3 μ B , which is also the magnetic moment of a V atom. The magnetic moment (4 μ B ) of each Cu n V (n = 1, 3, 5 and 7) clusters is just equal to the sum of the magnetic moments of the Cu n cluster (1 μ B ) and an isolated V atom (3 μ B ). These imply that the interaction of Cu and V atoms may have similarities among Cu n V (n = 1-8) clusters. In case of big Cu n V (n = 9-12) cluster, the Cu 10 V and Cu 12 V clusters have the same magnetic moments as Cu 11 and Cu 13 clusters. The magnetic moment (2 μ B ) of Cu 9 V and Cu 11 V clusters be greater than that (1 μ B ) of Cu 9 and Cu 11 clusters and less than that (3 μ B ) of V atom. The foregoing relation indicates that the big Cu n V (n = 9-12) clusters have a different interaction between Cu and V atoms relative to Cu n V (n = 1-8) clusters. As an effort to explain the magnetism, Fig. 9 gives the spin density of states (SDOS) for the global minimum structures of Cu n+1 and Cu n V clusters. All the ground states have an intense band between − 5 and − 2 eV, which consists principally of the valence s and d orbitals of the constituent atoms. It is clear from the density difference that the magnetic moment of Cu n V clusters mostly comes from the electrons near the HOMO (E− E H = − 2~0 eV). The Cu n V clusters have some very small magnetic domains, which vary with the size of cluster.
To gain insight into the magnetic properties further, we have performed the natural bond orbital analysis 61 Fig. 8. Overall, with the increase of cluster size, the magnetic moments of V atoms gradually decrease. The magnetic moments of V atom in Cu n V clusters is larger for n = 1-8 and smaller for n = 9-12 than that of free V atom. Compared to the free V atom, the change of magnetic moments of V atoms in Cu n V clusters (see Fig. 10) should reflect the strength of the interaction between V and Cu atoms. The magnetic moment provided by Cu atoms is very small. Furthermore, Cu atoms in Cu n V (n = 1, 9, 11 and even) clusters exhibit an antiferromagetic alignment with respect to the V atom's magnetic moment. That is to say, the magnetic moments of these Cu n V clusters primarily are from a paramagnetic V atom. The charge and magnetic moment on 4s, 3d, 4p and 5p orbitals of V atom in Cu n V clusters are listed in Table 4. It can be seen from the table that the partially filled 3d orbital play a substantial role in determining the magnetism of V atom. The magnetic moment of 3d orbital is 1.81~3.98 μ B . The 4s and 4p orbitals, which are non-magnetic for a free V atom, contribute a few of magnetic moment, apart from 4p orbital of V in CuV dimer. This may be ascribed to the internal charge transfer from 4s to 3d, 4p and 5p orbitals. Simultaneously, there are    an interatomic charge transfers in Cu n V clusters. Namely, 0.13-0.36 electrons transfer from V atom to Cu atoms for n = 1, 3-5 and 0.28-3.46 electrons from Cu atoms to V atom for n = 2, 6-12. As we know, the d orbital can contain up to 10 electrons. If N represents the sum of valence electron on V atom in Cu n V clusters, we found that 10-N and the magnetic moment of V atom have the same change trend, as shown in Fig. 11. The charge transfer hints that the V atom in Cu n V clusters has a hybridization among s, p and d orbitals. The energy of d orbital of V atom is gradually decreased with the increase of clusters size and more and more electrons are transferred to the d orbital. Hence, the larger the cluster, the smaller the magnetic moment of V atom. The orbital hybridization and charge transfer should be responsible for the magnetic moment alteration of the dopant atom.

Conclusions
Density functional calculations have been performed for the structural, electronic, and magnetic properties of Cu n+1 and Cu n V (n = 1-12) clusters. The results show that V atom in low energy Cu n V clusters tend to occupy the position with the maximum coordination number and changes the geometry of the 3D host clusters. The vibrational and photoelectron spectroscopy spectra are given to identify the most stable structures in times to come. The substitution of a Cu atom in copper clusters by a V atom enhances the binding energy of big clusters and alters the odd-even oscillations of relative stability and chemical activity of the host clusters. The ground states of copper clusters are confirmed by comparing the theoretical vertical ionization potential with experimental findings. At the same time, we predict the vertical ionization potential and electron affinity of Cu n V clusters and electron affinity of Cu n+1 cluster. The magnetism calculation indicates that V atom in Cu n V clusters carries most of the total magnetic moment. The local magnetic moment of the doped atom decreases with the increase of cluster size because of the orbital hybridization and charge transfer.