Quantum Chemistry Study on the Structures and Electronic Properties of Bimetallic Ca2-Doped Magnesium Ca2Mgn (n = 1–15) Clusters

Here, by utilizing crystal structure analysis through the particle swarm optimization (CALYPSO) structural searching method with density functional theory (DFT), we investigate the systemic structures and electronic properties of Ca2Mgn (n = 1–15) clusters. Structural searches found that two Ca atoms prefer to occupy the external position of magnesium-doped systems at n = 2–14. Afterward, one Ca atom begins to move from the surface into the internal of the caged skeleton at n = 15. Calculations of the average binding energy, second-order difference of energies, and HOMO–LUMO gaps indicated that the pagoda construction Ca2Mg8 (as the magic cluster) has higher stability. In addition, the simulated IR and Raman spectra can provide theoretical guidance for future experimental and theoretical investigation. Last, further electronic properties were determined, including the charge transfer, density of states (DOS) and bonding characteristics. We hope that our work will provide theoretical and experimental guidance for developing magnesium-based nanomaterials in the future.


Introduction
Nanomaterials with small particle sizes, specific surface areas and high surface energies possess wide applications in chemistry, physics, biology, medicine, materials and nanodevices. Magnesium atoms contain s 2 closed-shell electron configuration similarly to helium, which plays an essential role in aerospace, mobile electronics, automobile and biomedical applications [1][2][3][4]. Currently, metal-doped magnesium clusters with unique geometries and fascinating electronic properties have received considerable attention in magnesium-based multi-function materials.
In the past decades, many experimental techniques and theoretical studies have been reported for the related structures and properties of pure magnesium clusters [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For instance, on the experimental side, the transition points of Mg n clusters were determined at n = 20 by Diederich's group [5]. By measuring the photoelectron spectra and observing the sp band gaps of Mg n (n = 3-35) clusters, Thomas et al. found that the anion magnesium clusters exhibited a metallic character from n = 18 [6]. On the theoretical side, the ground state van der Waals potential of a magnesium dimer was described by five essential parameters of the Tang-Toennies potential model [7].
Janecek et al. studied the structures of neutral and cationic Mg n (n to 30) clusters using the local spin density functional [8]. Based on the MP4 (SDTQ) and CCSD(T) levels, the electron affinities were calculated for magnesium dimers and trimers [9]. By using the spin-unrestricted density functional theory with a local density approximation, Gong and co-workers studied the electronic structures of Mg n (n < 57) clusters [10]. Their results found that more 3p electrons will be involved in the sp hybridization with the cluster size increasing. More recently, Akola and co-workers focused on the structural and electronic properties of Mg n (n < 13) clusters [11]. Their investigations showed that the onset of metallization of Mg n clusters is difficult to assign due to the energy gap and sp hybridization.
Subsequently, electron binding energies, structural and electronic properties and the nonmetal-to-metal transition were studied systemically by Jellinek and Acioli [12,13]. In addition, by using ab initio theoretical methods (B3PW91, B3LYP and MP4), Lyalin et al. investigated the structure and electronic properties of neutral and singly charged Mg n (n = 2-21) clusters [14]. The above study by Lyalin et al. suggested that the hexagonal ring structure determines the cluster growth from Mg 15 . Moreover, the electronic shell effects and the Jellium-like behavior manifest themselves in the formation of geometrical properties; however, the shell effects do not determine the geometry of the Mg clusters completely.
Moreover, the stability mainly originating from the σ-type covalent bond, is formed by the interaction between Be-s and Mg-p orbitals. Zhao's group performed the structural and electronic properties of BeMg n (n = 10-20) clusters and their anions [34]. The research concluded that the position of Be atom changes from completely encapsulated sites to surface sites after reverting to the caged magnesium motif. Subsequently, the structures and electronic properties have been investigated for two Be-, Sr-and Ba-atom-doped smallsized magnesium clusters by our group [35][36][37]. For Be 2 Mg n (n = 1-20) clusters, from n = 10, the structures transfer from 3D to filled cage-like frameworks [35].
Furthermore, in the small size, one Be atom prefers the surface sites, and the other Be atom tends to embed inside magnesium motif. However, for the large size clusters (n > 18), two Be atoms were completely encapsulated into magnesium cages. In addition, the Be 2 Mg 8 cluster possesses robust stability, and Be-2p and Mg-3p orbitals revealed increasing metallic behavior. More interestingly, based on the same calculated method, studies on the structural evolution and electronic properties were performed for SrMg n 0/− (n = 1-12) clusters [36]. As a result, the tower-like framework of the Sr 2 Mg 8 cluster possesses higher stability out of the studied systems.
Moreover, the stronger sp hybridization leads to stronger Sr-Mg bonds, which is supported by the analysis of the multi-center bonds. Subsequently, our groups systemically reported the structures and electronic properties of two-barium-atom-doped magnesium in both neutral and anionic species [37]. A pagoda-like Ba 2 Mg 8 was determined by analyzing the relative stability.
Analysis of the molecular orbitals indicated that the high stability comes mainly from the interaction between Ba-6s and Mg-3p orbitals. In conclusion, the stronger sp hybridization leads to stronger M-Mg bonds and metallic behavior. Last, the geometric structures and electronic properties have been investigated systemically for lithium-doped magnesium clusters [38]. The results indicated that lithium atoms prefer to occupy the convex sites of LiMg n structures. The LiMg 9 cluster possesses relatively higher stability. In addition, the charges transfer from the Li to Mg atoms, and there exists strong hybridization among sp orbitals.
Thus, metal-atom-doped magnesium clusters provide an effective approach to creating novel structures and electronic properties. As the same group of alkaline earth metals, Ca and Be, Mg, Sr and Ba have the identical valence electronic configuration of ns 2 . Nevertheless, due to the different electronegativity and atomic radius of Ca atoms compared with Be, Mg, Sr and Ba atoms, are there similar frameworks for two-calcium-atom-doped magnesium clusters? If yes, do these clusters possess novel electronic and bonding properties? How does hybridization change?
To date, minor investigations on the structures and electronic properties of twocalcium-atom-doped magnesium clusters have been reported in theoretical calculations and experimental works. Thus, in the present work, motivated by Be-, Mg-, Sr-and Badoped magnesium, we performed a systematic investigation for two-calcium-atom-doped magnesium Ca 2 Mg n (n = 1-15) clusters.
First, we conducted wide structural searching and precise structural optimization to explore the structural evolution rule. Second, determining the stable configuration of Ca 2 Mg n (n = 1-15) clusters was conducted by analyzing the stability properties. Finally, some electronic properties, such as the charge transfer, IR and Raman spectra, DOS and bonding characteristics, are discussed for Mg-doped alkaline-earth clusters. We hope that our investigations will provide a theoretical and experimental basis for studying the microscopic mechanism of magnesium doped with alkaline-earth nanomaterials.
In particular, the B3PW91 functional has been widely tested for magnesium and magnesium-based clusters [35,36]. In addition, the spin multiplicity (1, 3, 5 and 7) is included, no imaginary frequencies are validated. All calculations were performed using the Gaussian09 program package [53]. In the following works, the relative stabilities of the ground state Ca 2 Mg n (n = 1-15) and Mg n+2 (n = 1-15) clusters were studied by computing the average binding energy (E b ) and second-order difference energy (∆ 2 E). Subsequently, the IR and Raman spectra, DOS, molecular orbitals and AdNDP were systemically investigated using the Multiwfn software for the studied clusters [54]. To ensure the reliability of our computational method, the bond length (r e ), vibration frequencies (ω e ) and dissociation energies (D e ) were calculated for Mg 2 , Ca 2 and CaMg dimers, respectively.
For the Mg 2 dimer, our calculated values were r e = 3.651 Å, D e = 0.0790 eV, which are in good agreement with the experimental results (3.891 Å, 0.0866 eV) [55]. For the Ca 2 and CaMg dimers, there are no experimental values available. Our calculated results for the bond lengths, vibration frequencies and dissociation energies are 4.2667 Å, 72.32 cm −1 and 0.1478 V for the Ca 2 dimer and 3.909 Å, 82.63 cm −1 and 0.1114 V for the CaMg dimer, respectively. Moreover, the bond length and frequency of Ca 2 dimer are also in excellent agree with Soltani's theoretical values (4.285 Å and 65.2 cm −1 ), respectively [56]. This indicated the reliability of the proposed method in this work.

Geometric Structures
In Figure 1, the lowest and lower-lying energy structures are present for Ca 2 Mg n (n = 1-15) and Mg n+2 (n = 1-15) clusters. These isomers with energies from low to high are designated by na, nb, nc and nd. Moreover, the electronic states and point symmetry are also collected in Table 1. Simultaneously, the Cartesian coordinates of the lowest energy structures of Ca 2 Mg n (n = 1-15) clusters are given in Table S1 in the Supplementary Materials. First, the lowest energy structures of the Mg n clusters agree with previous research by Zhang and Li et al. [35,37], which indicates that the present functional and basis sets are reliable. Moreover, the Ca 2 Mg n (n = 1-8) clusters possess similar geometric structures compared with the Mg n+2 clusters. Second, Ca 2 Mg possesses a triangular plane structure, and the lowest energy structures of Ca 2 Mg n (n = 2-15) clusters maintain a three-dimensional (3D) configuration. Specifically, Ca 2 Mg n (n = 2-6) clusters can be obtained by adding one Mg atom to the Ca 2 Mg n−1 clusters, and Ca 2 Mg n (n = 7-9) clusters can be generated from the substitution of Mg n+2 clusters by two Ca atoms, respectively. Interestingly, the lowest energy structure of the Ca 2 Mg 8 cluster possesses the same geometrical form as those of X 2 Mg 8 (X = Be, Sr and Ba) clusters. Finally, from 2 to 14, the doped two Ca atoms prefer to locate outside the host Mg n+2 cluster. At n = 15, one Ca atom starts to move from the surface into the internal of the caged skeleton.

Relative Stability
To determine the relative stabilities of Ca 2 Mg n and Mg n+2 (n = 1-15) clusters, the average binding energy (E b ) and second-order difference of energy ∆ 2 E are calculated as follows: E denotes the total energy of the corresponding clusters or atoms. The calculated results are plotted in Table 1 and Figure 2A  The HOMO-LUMO energy gap (E g ) is the other powerful tool to study the relative stabilities. Generally speaking, large values indicate stronger stability. In the present section, the HOMO-LUMO energy gaps are presented in Table 2 and Figure 2C. First, values of E g (Mg n+2 ) are larger than those of E g (Ca 2 Mg n ) clusters, indicating that Ca 2 Mg n clusters are more stable, which is in reasonable agreement with previous research on averaged binding energies. Second, Ca 2 Mg 2, 6,8,9,15 clusters with local maxima of E gap suggests that those clusters are more stable than their neighbors. In summary, combining the conclusions of E b , ∆ 2 E and E g values, the Ca 2 Mg 8 cluster corresponds to the magic numbers and exhibits robust stability.

Charge Transfer
In this section, the charge-transfer information is analyzed by natural population analysis (NPA) in Table 1 and Figure 2D. Clearly, the doped Ca atoms possess positive charges in doped systems, meaning the charges transfer from calcium to magnesium atoms.
Thus, the role of magnesium atoms is as charge acceptors, and Ca atoms are the charge donors. This is expected as Ca (1.00) has a smaller electronegativity compared with that of Mg (1.31) [57]. Second, the transferred charges increase with increasing cluster size. However, the value falls sharply at n = 15, and this situation may be the result of the position of Ca atom in the caged skeleton. In addition, the transfer charges in the range of n = 5-14 are all greater than 1.0 eV except for Ca 2 Mg 6 .

Infrared (IR) and Raman Spectra
In order to facilitate the characterization of spectra, we computationally simulated the infrared (IR) and Raman spectra of the lowest energy structures of Ca 2 Mg 8 cluster. The simulated spectra with atomic labels are shown in Figure 3. The results found the highest intense IR frequency was located at 197.74 cm −1 with 4Mg-7Mg-10Mg bond tensile vibration; however, two Ca atoms were almost silent. The second and third strongest peaks can be found at 129.62 and 218.78 cm −1 . For Raman spectra, the strongest peak at 181.51 cm −1 corresponds to the breathing vibration of all atoms. The second-and third-strongest Raman frequencies at 138.28 and 129.62 cm −1 correspond to the swing vibration of all atoms. In addition, IR and Raman spectra revealed that the strongest spectral frequencies are displayed in the range of 100-200 cm −1 .

The Density of States
To understand the nature of the chemical bonding, the total density of states (TDOS) and partial density of states (PDOS) of the lowest energy structures of Ca 2 Mg n (n = 1-15) are displayed in Figure 4. The TDOS is represented by the khaki shade; PDOS of Ca-s, Ca-p, Mg-s and Mg-p AOs (atomic orbitals) are represented by the red and blue solid lines as well as magenta and green dotted lines, respectively. We found that the contribution to TDOS mainly comes from the PDOS of Ca-s, Mg-s and Mg-p AOs in the region of occupied orbitals. This indicates that sp hybridization has occurred in Ca-Mg atoms and Mg-Mg atoms. In fact, the sp hybridization of Mg-Mg promotes the formation of Mg n frames in Ca 2 Mg n clusters. The sp hybridization of Ca-Mg can promote the interaction between the two doped calcium atoms and magnesium frames of Ca 2 Mg n clusters, which is also the main reason why the stability of Ca 2 Mg n is higher than that of their corresponding pure magnesium clusters.

Bonding Characters
Based on the above analyses, a pagoda-like Ca 2 Mg 8 structure possesses superior stability. To illustrate the source of higher stability, the bonding nature, such as the MOs (molecular orbitals) and multi-center bonds, are discussed for the lowest energy structure of Ca 2 Mg 8 cluster. The molecular energy levels and corresponding orbitals are presented in Figure 5. First, calcium and magnesium atoms are composed of the same valence configuration of s 2 , and Ca 2 Mg 8 with 20 valence electrons meets the requirement of the Jellium model in terms of the valence electron number. Moreover, the shell structures consist of one 1S orbital, three 1P orbital, five 1D orbitals and one 2S orbital, all of which are occupied by the paired electrons. The energy of 1S, 1P, 1D and 2S states are arranged in order from low to high without energy levels overlapping, and the energy levels are also relatively concentrated. In addition, all the splitting energy levels of 1D orbital are lower in energy than the 2S orbital. As a result, Ca 2 Mg 8 cluster is a closed shell 1S 2 1P 6 1D 10 2S 2 filled with 20 valence electrons.
In addition, the contributions of molecular orbital for Ca 2 Mg 8 cluster were probed utilizing Multiwfn 3.8 program. The HOMO corresponding to 2S state involves Ca-s (30.98%), Mg-s (19.53%) and Mg-p (44.86%). The HOMO-m (m = 1-5) exhibit 1D state, in which HOMO-1 and HOMO-4 are mainly composed of Ca-s (10.62%, 26.60%), Mg-s (41.87%, 16.99% for) and Mg-p (43.70%, 53.33%), respectively, and the remaining 1D state orbital is mainly contributed to by Mg atoms. The compositions of HOMO-6, 7, 8 corresponding to three 1P orbitals comes mainly from the Mg-s and p AOs as well as to a small extent from the Ca-s and p AOs. In the case of HOMO-9 (1S), Mg atoms provide more than 90% of the orbital contribution. Hence, the sp hybridization between the Ca and Mg atoms could promote the interaction between the doped-Ca and host-Mg atoms and form stronger Ca-Mg bonds.

Conclusions
In summary, a detailed investigation of the structures and electronic properties of Ca 2 Mg n (n = 1-15) was performed using the CALYPSO searching method and DFT calculations. Structural searching found that two Ca atoms prefer to occupy the external position of magnesium-doped systems at n = 2-14 and that one Ca atom tends to move from the surface into the internal of the caged skeleton at n = 15. The size-dependent binding energies, second-order difference of energies, and HOMO-LUMO gaps found a pagoda-like Ca 2 Mg 8 as a magic cluster that possessed higher stability.
Upon charge transfer analysis, charges transferred from calcium to magnesium atoms. The simulated IR and Raman spectra of the magic cluster revealed that the strongest spectral frequencies were displayed in the range of 100~200 cm −1 . In addition, the high stability of Ca 2 Mg 8 with a 20 valence electron cluster possessed a closed-shell electron configuration of 1S 2 1P 6 1D 10 2S 2 in terms of the Jellium model. Last, the sp hybridization of Ca-Mg and Mg-Mg bonds was confirmed by the molecular orbitals and AdNDP, which contribute to the high stability of the Ca 2 Mg 8 cluster.