Structures, electronic and magnetic properties of transition metal inserted W6O18 clusters

Structures, electronic, and magnetic properties of transition metal (TM) inserted W6O18 clusters have been investigated by using density functional theory. The Ti@W6O18, Ni@W6O18, Zr@W6O18, Rh@W6O18, W@W6O18, and Ir@W6O18 clusters are more structurally stable while the V@W6O18, Fe@W6O18, Zn@W6O18, Y@W6O18, Nb@W6O18, Pd@W6O18, La@W6O18, Re@W6O18, Hg@W6O18 clusters are more chemically stable. The amount of charge transfer between the TM atoms and W6O18 clusters decreases with the increase of the subgroup number except for subgroup number is equal to 11 and 12. The d orbital of the 3d TM@W6O18 clusters start to make the main contributions to Fermi level except for the Cu@W6O18 and Zn@W6O18 clusters.


Introduction
Tungsten oxides (WO 3 ) are an important material with many industrial applications, such as electrochromic devices, chemical sensors, and catalysts [1][2][3][4][5][6][7][8]. However, the relative wide band gap (2.6-3.2 eV) of WO 3 severely limits the applications [9]. Transition metal (TM) doping is an effective method to reduce the band gap of the host [9]. Experimentally, Karuppasamy [10] have fabricated the Ti-doped WO 3 thin films by co-sputtering. Karuppasamy et al. [11] have prepared the vanadium-doped tungsten oxide thin films by the electron beam evaporation technique. Cheng et al. [12] have prepared the Zn-doped WO 3 photocatalysts by the sol-gel method. Song et al. [13] have fabricated the Modoped WO 3 nanowires by the hydrothermal method. Mal et al. [14] have investigated the influence of dopants (Co, Cu, Fe, and Ni) on the electronic and magnetic properties of multiferroic MnWO 4 by using magnetization measurements. Hameed et al. [15] have studied the effect of different TM (TM = Fe, Co, Ni, Cu, and Zn), at different concentrations, on the photocatalytic activity of WO 3 for splitting of water under UV laser irradiation. In fact, the WO 3 clusters are randomly dispersed on the surface of the WO 3 thin films by SEM [16,17]. The clusters consisting of less than 50-60 atoms exhibit dissimilar electronic structures compared to the respective bulk counterparts [18]. Theoretically, Li et al. [19] have investigated the structures of a series of (WO 3 ) n clusters (n = 1-6) by using the B3LYP gradient-corrected exchange-correlation functional. Rothgeb et al. [20] have investigated the structures of the Mo-doped small WO 3 clusters and their associated anions by density functional theory (DFT). Wang et al. [21] have investigated (Mo, Cr, Ti, Zr, or Hf) doped WO 3 by DFT. In order to save computational cost and highlight the influence of TM doping on tungsten oxide clusters, it is desirable to reduce the size of tungsten oxide clusters. Jin et al. [5] have revealed that the W 6 O 18 clusters with the spherical buckyball structure can be regarded as the smallest WO 3 self-assemble unit. Xu et al. [22] have designed a much enhanced chemical sensor made of plasmonic Ag x @(2D-WO 3 ).
In this study, the structures, electronic, and magnetic properties of the TM-inserted W 6 O 18 clusters are investigated by using DFT. It will provide guidance for the design the novel TM-doped WO 3 materials.

Computational details
The structure of the W 6 O 18 clusters was adopted from the Ref. [5]. A TM atom was inserted to the W 6 O 18 clusters to construct hypothetical TM@W 6 O 18 clusters. The geometry optimization on the TM@W 6 O 18 clusters was performed by using DFT implemented in the DMol 3 package of Materials studio software [23,24]. The generalized gradient approximation (GGA) with the parameterization by Perdew-Burke-Ernzerhof (PBE) was selected to treat the exchange-correction interaction [1,25]. Spin unrestricted was chosen to calculate the different orbits for different spins. Formal spin as initial was introduced for each atom and the initial value was optimized during the calculation [26]. In order to determine the ground state spin state by performing spin unrestricted calculations, auto was set to multiplicity. All structures of the TM@W 6 O 18 clusters were optimized without any symmetry constraint [18]. All-electron relativistic DFT results were employed [27]. A basis set of double numerical plus polarization (DNP) was used for the electronic calculations [23]. Mülliken population analysis was adopted to acquire the net charge and magnetic properties of each atom of the TM@W 6 O 18 clusters [28]. Harmonic vibrational analysis of frequency was performed on the TM@W 6 O 18 clusters to determine true minimum values on the potential energy surfaces [29,30]. The vibrational spectra of pristine W 6 O 18 and TM@W 6 O 18 clusters have real frequencies and are true minima. SCF calculations were performed with a convergence criterion of 10 −5 hartree on the total energy [31]. A convergence criterion of 0.002 hartree/Å for forces and 0.005 Å for displacement were adopted [31]. The width of smearing was chosen as 0.005 eV [31].
The binding energies per atom were calculated to determine the thermodynamic stability of pristine W 6 [18]). The appropriate of the PBE functional adopted to the TM atoms was confirmed by our previous study [32]. In words, it indicates that the PBE functional is appropriate to calculate the TM@WO 3 clusters.

Structures
The typical structures of the calculated pristine W 6 O 18 and TM@W 6 O 18 clusters have been shown in Fig. 1. The light blue, red, and light gray balls represent the W, O, and TM atoms, respectively. It can be found that the external structure of pristine W 6 O 18 clusters is maintained to some extent and the TM atoms locate at the center of pristine W 6 O 18 clusters. Matxain et al. [33] have pointed out that the inserted atoms prefer to locate at the center of most spherical clusters. The structure of pristine W 6 O 18 clusters has been distorted severely by the Cr, Co, Ru, Ta, W, Re, Os, and Ir atoms. There is d electrons of the TM atoms to provide the driving force for the Jahn-Teller distortion [14,29,34]. The additional distortion related to the crystal field comes from the interaction of the 3d TM ion and neighboring O atoms [14].
The average distances of the W atoms on the diagonal of the cavity of the W 6 O 18 clusters have been plotted in Fig. 2 Fig. 4. Although the specific values of the HOMO-LUMO gaps depend on the basis set [37], the relative values of the HOMO-LUMO gaps can be used to investigate the electronic stability of clusters. That is, the clusters with larger HOMO-LUMO  [18]. It indicates that both σ and π symmetry along the W-O directions [29,38]. As for the TM@ W 6 O 18 clusters, the interaction between unpaired d orbital electrons of the TM atoms and p orbital electrons of neighboring O atoms make the main contributions to the HOMO and LUMO states of the TM@W 6 O 18 clusters [36]. Among them, as for the LUMO states of the TM@W 6 O 18 (TM = Sc, Ti, V, Cr, and Zn) clusters, the hybridization between the O atoms on the cage and the TM atoms is less. As for the LUMO states of the Co@W 6 O 18 clusters, the hybridization between the O atoms on the cage and W atoms is less. As for the HOMO states of the Ni@W 6 O 18 clusters, the hybridization between the O atoms on the cage at the outer and W atoms is less. As for the HOMO states of the Cu@W 6 O 18 clusters, the hybridization between O atoms on the cage and W, TM atoms is less.

Electronic properties
The net charges of the TM atoms of the TM@W 6 O 18 clusters have been shown in Fig. 7. Generally, the amount of charge transfer between TM atoms and pristine W 6 O 18 clusters decreases with the increase of the subgroup number except for subgroup number is equal to 11 and 12. It results from the difference of electron affinity of the TM atoms. The amount of charge transfer between 4d TM atoms and pristine W 6 O 18 clusters is larger than that between 3d TM atoms and pristine W 6 O 18 clusters. It means that the hybridization between the 4d TM atoms and pristine W 6 O 18 clusters is larger than that between 3d TM atoms and pristine W 6 O 18 clusters. While for the 5d TM@W 6 O 18 clusters, the La, Hf, and Ta atoms lose more electrons than corresponding 3d TM@W 6 O 18 clusters while other 5d TM atoms lose less electrons than corresponding 3d TM@W 6 O 18 clusters.
Partial density of states (PDOS) of pristine W 6 O 18 and TM@W 6 O 18 clusters have been plotted in Fig. 8. The Fermi level is set to be zero [40]. As for pristine W 6 O 18 clusters, the O(p) states contribute to the highest valence band and the W(d) states contribute to the bottom of conduction band [14,25,40,41]. The O(p) states make the main contribution to Fermi level [40]. As for the TM@W 6 [14]. It results from the valence bands of Cu@W 6 O 18 and Zn@W 6 O 18 is consisted by the occupied O 2p orbitals, whereas the bottom of the conduction bands is composed by the empty W 5d orbitals [35,42].

Magnetic properties
The spin densities of the TM atoms of the TM@W 6 O 18 clusters have been plotted in Fig. 9. The calculated spins of the TM atoms of the TM@W 6 [43] and that between s and d orbitals of the TM atoms leads to the level splitting of the TM-d orbitals [44]. Compared the spin densities of the TM (TM = Mn, Fe, Co, and Ni) atoms of the TM@W 6 O 18 clusters with those (Mn: 5|e|, Fe: 4|e|, Co: 3|e|, Ni: 2|e|) of isolated TM atoms, the spin densities of the TM atoms of TM@W 6 O 18 clusters decrease. It is in agreement with the result of Mal et al. [14]. That is, spin density is more around Mn and least around Ni as Mn has the highest magnetic moment and Ni has the least magnetic moment [14]. It can be explained by the electronic  density of states change of TM atoms [14]. As for certain magnetic TM atoms, take the Mn atoms as an example, the electronic states of isolated Mn atoms are mainly 3d states and empty up 3d states in the vicinity of Fermi level. A Mn atom is encapsulated into W 6 O 18 clusters, the charge transfer between Mn atom and W 6 O 18 clusters is only 1.232 |e|. It leads to the unpaired 3d states are maintained to some extent.
Similarly, the spin densities of TM (TM = Mn, Fe, Co, Mo, Tc, Ru, Rh, and Ir) atoms of the TM@W 6 O 18 clusters are maintained to some extent. Local magnetic moment of the TM@W 6 O 18 clusters mainly depends on the TM atoms and secondary relies on the local environment [45]. The 3d TM@ W 6 O 18 clusters exhibit larger spins than corresponding 4d TM@W 6 O 18 and 5d TM@W 6 O 18 clusters, it mainly results from the 3d wave function is more localized [46] and then leads to weaker hybridization between 3d TM atoms and the W 6 O 18 clusters [43].

Conclusions
The structures, electronic, and magnetic properties of the TM@W 6