It is worth noting that cluster
2a is similar to the known [(Ni@Ge
9)Ni(Ni@Ge
9)]
4− [
33] reported by Sevov from the view of the coordination way. Specifically, the central Cd and Ni ions of these two clusters coordinate respectively with two triangle faces of Ni@E
9 units (E = Sn and Ge) to form an approximately octahedral environment. To understand the relationship between the geometries and electronic structures of these above-mentioned clusters, we performed density functional theory at the PBE0/def2tzvp level of theory [
34,
35]. The PCM polarizable conductor calculation model was performed with the solvent data for ethylenediamine (
ξ = 12.9) to simulate the confining effects of the cationic environment in the solid-state in all cases [
36,
37]. Default convergence criteria were used for the optimization tasks with Gaussian 09 program. The initial structures for optimizations of cluster
2a and [(Ni@Ge
9)Ni(Ni@Ge
9)]
4− were taken from the experimentally observed structures (single-crystal X-ray diffraction analysis) with a restriction of D
3d symmetry by adjusting the coordinates, but their optimized results show C
2h and C
i symmetries, respectively. Full details of the Cartesian coordinates and the optimized bond lengths are given in Supporting information. The deviation between optimized bond lengths and those corresponding experimental values are within a reasonable 2% range, which is a common observation in calculations on zintl chemistry that may be due to the absence of an explicit crystal environment in the computational model. Frequency calculations confirmed that these optimized structures correspond to their respective minima in the potential energy surfaces. A comparison of the optimized geometries exhibits the superficial similarities between these related clusters, but also some subtle differences (
Fig. 2). The most obvious difference is that the Cd-Ni contacts of 4.31 Å effectively confirm non-bonding interactions while the Ni-Ni distances of 2.43 Å compare well with bonding distances in the corresponding clusters containing Ni-Ni bonds [
38,
39]. The more subtle differences appear in the shape of triangles that coordinated with the Cd/Ni atoms and the E-E distances between the two Ni@E
9 units. In cluster
2a, the two Sn-Sn distances are 3.26 Å and 5.42 Å respectively, and the ratio between the two is 0.60. In contrast, the ratio of the two corresponding Ge-Ge distances is 1.04. In the D
2h-symmetric [Cu
4@Sn
18]
4− optimized at the same level of theory, representing the two E
9 cages are complete fusion, the corresponding ratio is 1.55 (Fig. S16 in Supporting information) [
40]. Hence, cluster
2a, representing the completely separated state, can be viewed as a starting stage of fusion, which is further to form partly fusion cluster, such as [(Ni@Ge
9)Ni(Ni@Ge
9)]
4−, and finally to achieve the total coalescence defined by [Cu
4@Sn
18]
4−.