Synthesis, crystal and electronic structure of BaLi₂Cd₂Ge₂

2.1 Synthesis

The starting materials were purchased from Alfa Aesar, all with stated purity 99.9 wt% or better. The metals were stored in an argon gas filled glovebox and used as received; the surface of the Li rod was cleaned with a scalpel blade prior to cutting and using it.

Single crystals of BaLi₂Cd₂Ge₂ were grown from excess Cd, intended as a flux. An elemental mixture with the ratio Ba:Li:Cd:Ge = 1:10:20:2 was loaded into an alumina crucible, which was subsequently placed in a fused silica tube. The crucible was covered with a plug, made from quartz wool to be used as a filter during the removal of the molten Cd via centrifugation. Before placing the tube in the furnace, it was connected to a vacuum line and flame-sealed. Heat-treatment proceeded in the following manner: i) temperature was ramped up to 473 K at a rate 20 K h⁻¹, allowing the Li to melt, before further raising the temperature to 973 K with a ramp rate of 50 K h⁻¹. ii) After annealing at this temperature for 10 h, a cooling to 773 K was initiated with a rate of 5 K h⁻¹. iii) At this point of the synthesis, the sealed tube was taken out from the furnace, flipped, and the molten metallic flux was separated from the grown crystals by using a centrifuge.

The procedure mirrors that used for growing BaLi₂In₂Ge₂ crystals [1], where it was established that the success of the experiment is incumbent upon using a large excess of Li. We do not believe that molten Li acts as a flux at the given reaction conditions, rather, the 5× over stoichiometric amount used in the reaction is deemed necessary to compensate for the loss of Li due to evaporation and side reactions with the reactor walls. Upon completion of the heat-treatment, the tube was brought back into the glovebox and was break-opened. The visually inhomogeneous products consisted of the known phases BaCd₂Ge₂ and BaCd₁₁, which were easily identified by powder X-ray diffraction as the main products. Closer inspection under an optical microscope revealed the presence of some small black plates with metallic luster dispersed within the larger BaCd₂Ge₂ and BaCd₁₁ crystallites. Single-crystal X-ray diffraction confirmed that they were the new BaLi₂Cd₂Ge₂ phase.

Following the structure elucidation of BaLi₂Cd₂Ge₂, reactions aimed at the production of AELi₂Cd₂Ge₂ (AE = Ca, Sr, Eu) were set up with the same nominal compositions as the ones described in the preceding paragraph, but they were unsuccessful. An attempt to grow crystals from the close-to-the-stoichometry Pb flux reaction were unsuccessful. Similarly, reactions intended to produce AELi₂Zn₂Ge₂ (AE = Ca, Sr, Ba, Eu) also did not yield the desired materials. In all of the above cases, stable Zn- and Cd-bearing binaries, such as Ba₂Zn or BaZn₁₃ were the most recurring side products.

2.2 Powder X-ray diffraction (PXRD) and single-crystal X-ray diffraction (SCXRD)

Samples for PXRD were prepared by grinding the as-synthesized materials with an agate mortar and pestle. The X-ray powder diffraction patterns were then recorded using a Rigaku Miniflex powder diffractometer utilizing Ni-filtered CuKα radiation (λ = 1.5418 Å) and could be only used for main-phase identification.

Single crystals for SCXRD were selected under an optical microscope, and cut to suitable dimensions for subsequent data collection (to mitigate potential issues arising from X-ray absorption, the sizes of the selected crystals were smaller than 100 μm in any direction). The crystals were then mounted on low background MiTeGen plastic loops using Paratone-N oil. A Bruker APEX II CCD-based diffractometer, equipped with a monochromated MoKα radiation source (λ = 0.71073 Å) was used. Intensity data were collected and integrated using the Bruker-supplied software, and absorption correction was applied using Sadabs [7]. The structure was solved and refined to convergence by full-matrix least-square methods on F ² by using Shelxt and Shelxl, respectively [8, 9]. All sites, including Li, were refined with anisotropic displacement parameters. The final difference Fourier map was featureless.

One specific aspect of the refinements concerning the site occupation factors (SOF) requires a special mention. All SOFs were checked by freeing an individual SOF, while other variables were kept fixed. No statistically significant deviations were observed for the SOF of the heavy elements; the Li position indicated a freely-refined SOF of ca. 125%. This is indicative of potential disordering at the Li site, likely due to a Li/Ge admixture (in analogy with Li/Ge disorder in many RE-Li-Ge ternary phases (RE = rare earth metal) [10, 11]), or Li/Cd co-occupation (in analogy with the Li/Cd disorder in Ba₄Li₂Cd₂ Pn ₆ and Li/In disorder in the isotypic BaLi_2+x In_2−x Ge₂ (0 ≤ x ≤ 0.66) quaternary phases [1, 12]). Since the detected “over-occupation” of the Li atom barely had statistical significance (deviations were within ca. 4σ), and since no additional experimental work has been conducted so far to confirm/refute the possibilities of Li/Cd or Li/Ge mixing, the final refinements presented in this paper reflect a devoid of a disordered chemical composition BaLi₂Cd₂Ge₂ (Table 1). Further details of the structural work are discussed later on.

CCDC 2101506 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

2.3 Electronic structure calculations

First-principle calculations were performed within the density functional theory framework (DFT) with the aid of the TB-LMTO-ASA code [13]. For all calculations, the von Barth-Hedin version of the local density approximation functional (LDA) was employed [14]. The Brillouin zone was sampled by a 24 × 24 × 24 k-point grid after checking for convergence of the total energy. Chemical bonding was inspected utilizing crystal orbital Hamilton population analysis (COHP) and electron localization function (ELF) [15], [16], [17].

3.1 Crystal structure

BaLi₂Cd₂Ge₂ crystallizes in the space group R 3 ‾ m (No. 166), and there are four independent atomic positions in the asymmetric unit (Table 2). Formally, the crystal structure is an ordered quaternary derivative of the CaCu₄P₂ structure [18]. As mentioned earlier, there are other compounds adopting the same structure type, among which a parallel between AELi₂In₂Ge₂ (AE = Sr, Eu, Ba) [1] and BaLi₂Cd₂Ge₂ is most relevant. These phases are isotypic, although not isoelectronic. Exactly the same structure and valence electron count are only observed for BaLi_2+x In_2−x Ge₂ (x = 0.66) and BaLi₂Cd₂Ge₂. To the contrary, BaLi₂Cd₂Ge₂ and BaLi₂Mg₂ Tt ₂ (Tt = Si, Ge) [4] are isoelectronic, but not isostructural since the latter, although crystallizing in the same R 3 ‾ m space group with exactly the same Wyckoff sequence c ³ a, have slightly different elemental distribution. These subtle differences are discussed later.

BaLi₂Cd₂Ge₂ can be viewed as a Zintl phase, where the anionic substructure is made up of alternating [Cd₂Ge₂] double-layers. The large Ba²⁺ cations are located between the polyanionic 2D fragments, and the small Li⁺ cations are found within them (Figure 1). The single [CdGe] layers are puckered and consist of 3-coordinate Cd and Ge atoms. Two such layers come close together with the shortest distance being just under 3.3 Å (between neighboring Cd atoms). Tetrahedral voids in the packing of the Ge atoms created by this arrangement are filled by Li⁺ cations, and octahedral holes between two [Cd₂Ge₂] slabs are filled by Ba²⁺. Alternatively, the structure can be described as layers consisting of edge-sharing [LiGe₄] tetrahedra (Figure 1(a)), identical to those in the CaAl₂Si₂ structure type, with Ba and Cd atoms located between and within the 2D fragments, respectively.

Figure 1:

(a) Representation of the structure of rhombohedral BaLi₂Cd₂Ge₂. Local coordination environment of Ba (b), Li (c), and Cd (d).

A closer look at the [Cd₂Ge₂] double-layers is necessary for a better understanding of the nature of the bonding and the electronic structure (Section 3.3). These 2D fragments are extending parallel to the ab plane, and a single [CdGe] sheet can be considered as being a puckered variant of the ZrBeSi-type structure, also known as LiGaGe-type structure [19]. While each Cd atom is trigonally coordinated by three Ge atoms, it slightly protrudes by ca. 0.5 Å (or ca. 11.6% of the total interlayer distance) from the imaginary plane formed by the Ge atoms (Figure 2).

Figure 2:

Structural relationships between BaMg₂Li₂Ge₂, CaCu₄P₂, BaLi₂Cd₂Ge₂, and BaLi₂In₂Ge₂.

The protruding value was calculated as a ratio of the atom-to-plane distance to the interplane distance.

The shortest distance between layers is represented by the Cd–Cd contacts (3.28 Å). This separation is 15% longer than the sum of the covalent radius assigned to Cd (1.44 Å) [20], suggestive of an absence of homoatomic Cd–Cd bonding. Electronic structure calculations, vide infra, support this notion. Interestingly, the crystal structure of the β-CaZnGe phase also features puckered [ZnGe] layers without interlayer bonding [21].

An interesting comparison can be made with the [CuP] layers in the archetype CaCu₄P₂ structure (Figure 2) [18]. The Cu atoms “protrude” 0.33 Å out of the plane of the P atoms (ca. 8.9% of the plane-to-plane total distance) with no evidence of Cu–Cu interlayer bonding. Thus, CaCu₄P₂ can be rationalized as a charge-balanced Zintl phase, i.e., (Ca²⁺)(Cu⁺)₄(P³⁻ )₂. Similarly, partitioning of the valence electrons in BaLi₂Cd₂Ge₂ can be described by the formulation (Ba²⁺)(Li⁺)₂(Cd²⁺)₂(Ge⁴⁻)₂. The same charge-balance scheme applies to BaMg₂Li₂ Tt ₂ (Tt = Si, Ge), where the assignment of charges is as follows: (Ba²⁺)(Mg²⁺)₂(Li⁺)₂(Tt ⁴⁻)₂. One will notice that the order of Li and Cd and Li and Mg in the respective formulae is interchanged to reflect the different bonding patterns [4]. Divalent Mg and monovalent Li in BaMg₂Li₂ Tt ₂ occupy the Li and Cd sites in BaLi₂Cd₂Ge₂, respectively. In this view, the [LiGe] layers are almost flat (Li deviates from the plane of Ge atoms by only 0.15 Å, or ca. 3.9%) and all Mg atoms are located between two layers, retaining their tetrahedral coordination by the Tt atoms (Figure 2).

The discussed bonding patterns are slightly different for the AELi₂In₂Ge₂ (AE = Sr, Eu, Ba) family of compounds, where the presence of homoatomic In–In bonding (ca. 3.03 Å) was detected (Figure 2) [1]. The latter serves as an interconnection between two layers, uniting the slab, which eventually has to be considered as built up of staggered ethane-like [Ge₃In–InGe₃] fragments linked via Ge atoms. Indium atoms are 0.86 Å away from the plane of the Ge atoms (ca. 18.1%). This structural feature is observed in some pnictides, such as the structurally related hexagonal SrIn₂As₂ phase (puckering 22.7%) and the rhombohedral CaGa₂As₂ phase (22.5%) [22, 23]. All given examples boast homoatomic In–In or Ga–Ga bonding, which causes large deviations from planarity, and requires assigning the triel elements not in the 3+ state, but rather 2+ state. Consequently, the electron counts reflect this consideration: Both (Ba²⁺)(Li⁺)₂(In²⁺)₂(Ge⁴⁻)₂ and (Sr²⁺)(In²⁺)₂(As³⁻)₂ satisfy the charge balance criteria and can be rationalized based on the Zintl concept.

The structural relationships described above are associated with the strivings of the constituent elements to form certain coordination environments. A trigonal-planar coordination is known for Li, for the coinage metals (Cu, Ag, Au), Zn, and, in very rare cases, for Cd [24]. At the same time this type of coordination is less common for Mg, Ga, and In, which are usually tetrahedrally or octahedrally (in case of Mg [25]) coordinated. This may explain the observed difference in bonding and the specific site preferences for all phases mentioned above within the discussed structure type. Homoatomic Cd–Cd bonds in BaLi₂Cd₂Ge₂, Cu–Cu bonds in CaCu₄P₂, and Li–Li bonds in BaMg₂Li₂ Tt ₂ are unfavorable from the point of view of charge balance, despite that a tetrahedral coordination is preferred for these elements. With the trigonal planar coordination for the Cd atom being far from optimal, one might consider Zn → Cd substitution with the expectation that the Zn atoms may favor the trigonal planar coordination more so than Cd. With this idea in mind, we pursued the compounds ALi₂Zn₂Ge₂ (A = Ca, Sr, Ba); they were considered as possible isostructural analogs of BaLi₂Cd₂Ge₂, where the [ZnGe] layers will be very close to being “flat”. However, as was stated in the experimental section, such synthetic attempts have been, so far, unsuccessful.

The role of Li in the formation of compounds with this structure should also be discussed; after all the Li atoms can occupy multiple sites in this arrangement. A binary Li₅Ge₂ compound is known beyond the discussed cases of BaLi₂ M ₂Ge₂ (M = Cd, In) and BaMg₂Li₂ Tt ₂. In the Li₅Ge₂ structure, the Li atoms can be seen as forming [LiGe] layers and filling the space within and between them. While the crystal structure of this binary phase is not unequivocally established to date, computational work suggests its existence with the same rhombohedral structure discussed in this paper [26]. One should notice that in the structure of the binary phase, the Ge atoms are expected to be dimerized, forming strong Ge–Ge bonds. With the Ge atoms located at the atomic site that corresponds to that of the Cd/In atoms in BaLi₂ M ₂Ge₂, the remaining three sites occupied by Ba, Li, and Ge are taken by Li. Therefore, the electron count in Li₅Ge₂ leads to the imbalanced formulation (Li⁺)₅(Ge³⁻)₂(h ⁺), where h ⁺ denotes an electron hole. We have attempted to experimentally validate these speculations, but preliminary structural analysis has shown that the length of the Ge–Ge bonds can vary depending on the synthetic conditions, which is indicative of the existence of a homogeneity range in Li_5−x Ge_2+x . This also signals the unique role of Li in the formation of the novel phases within the discussed structure type.

A brief comparison of selected crystallographic metrics for BaLi₂Cd₂Ge₂ and BaLi₂In₂Ge₂ is presented next. Similar values of the covalent radii for In (1.42 Å) and Cd (1.44 Å) account for the almost identical unit cell parameters for both phases. While the overall unit cell volumes are indeed very similar (ca. 475 vs ca. 477 Å³ for In-bearing and Cd-bearing phases, respectively), the unit cell parameters a and c are noticeably different: a = 4.52, c = 26.8 Å for BaLi₂In₂Ge₂, and a = 4.59, c = 26.12 Å for BaLi₂Cd₂Ge₂. In → Cd substitution causes a shortening of the c axis and can be associated with the different coordination observed for In and Cd in both compounds. The larger Cd atom within the [CdGe] layer (parallel to the ab plane) apparently is the reason for the slight expansion in the latter directions. Cd–Ge distances in BaLi₂Cd₂Ge₂ (Table 3) are close to the sum of the covalent radii for Cd (1.44 Å) and Ge (1.22 Å) [20].

The local coordination environments for the Ba, Li and Cd atoms are visualized in Figure 1, panels b), c) and d). The distorted octahedral coordination of the Ba atoms in the BaLi₂Cd₂Ge₂ compound consists of six Ge neighbors with distances within the typical range for Ba germanides [1], [2], [3], [4]. The coordination sphere can be extended by including six Cd atoms, with Ba–Cd contacts approaching 3.8 Å (Table 3). Although too long to be considered as typical bonds, the Ba–Cd interactions play some role in the overall electronic stability, as supported by our calculations, vide infra. The Li atoms are surrounded by four Ge atoms in a distorted tetrahedral coordination environment. The shortest Li–Ge bond is oriented along the c axis (Table 3). The Li atoms also have some close Cd neighbors, but only three out of the six Li–Cd contacts are within bonding distances (Table 3), whereas the other three are much longer (ca. 3.46 Å) and similar in magnitude to the Li–In contacts in BaLi_2+x In_2−x Ge₂ (x ≈ 0.66) [1]. Not surprisingly, In–In interatomic distances in the latter compound are comparable to the Cd–Cd contacts observed in the title phase.

3.2 Electronic structure

The electronic density of states (DOS) for the BaLi₂Cd₂Ge₂ phase is shown in Figure 3(a). The deep lying states below the Fermi level (E _F ) are mainly composed of the occupied, localized Cd(4d) and Ge(4s) states. The latter signal the presence of lone pairs of electrons on the Ge atoms. Close to the Fermi level, significant mixing of electronic states is observed, similar to the case of the structurally related BaLi₂In₂Ge₂ and BaMg₂Li₂Ge₂ [1, 4].

Figure 3:

(a) Total and projected electronic densities of states (DOS) for BaLi₂Cd₂Ge₂. (b–e) Crystal orbital Hamilton population curves (COHP, solid curves) and their integrals (ICOHP, dashed curves) for selected interactions. (f) Section of the Electron Localization Function (ELF) though a Cd⋯Cd–Ge plane.

Quite unexpectedly, the Fermi level in BaLi₂Cd₂Ge₂ crosses a distinct peak in the DOS. As discussed above, the electron partitioning suggests that the studied compound can be classified as a Zintl phase, according to the scheme: (Ba²⁺)(Li⁺)₂(Cd²⁺)₂(Ge⁴⁻)₂ (N.B. One should be mindful that here we greatly overstate the ionicity of the chemical bonding, neglecting the possible covalency of Li–Ge and especially Cd–Ge interactions). Therefore, the presence of an electronic band gap or a dip in the electronic density of states at the Fermi level would indeed be anticipated. In fact, the two related phases mentioned above, BaLi₂In₂Ge₂ and BaMg₂Li₂Ge₂, display pronounced pseudogaps at E _F [1]. The apparent deviation of BaLi₂Cd₂Ge₂ from the expected behavior poses questions as to the applicability of the Zintl concept in this case and whether or not there may exist disorder, akin to that in BaLi_2+x In_2−x Ge₂.

To better understand the electronic properties of BaLi₂Cd₂Ge₂, we analyzed the chemical bonding in this compound. Crystal orbital Hamilton population curves (COHP) for selected interatomic contacts are given in Figure 3(b)–(e). A notable feature is the presence of partially filled bonding states observed for the Ba–Ge and Ba–Cd contacts at the Fermi level (Figure 3(b)). These states appear to be responsible for the emergence of the peak in the DOS. In comparison, the COHP curves for the Li–Ge, Li–Cd, and Cd–Ge contacts reveal pseudogaps at E _F (Figure 3(c)–(e)). The Li–Ge and Li–Cd interactions are bonding, but are somewhat underoptimized due to the presence of unoccupied bonding states above E _F or antibonding states just below (Figure 3(c) and (d)). The strongest interaction, Cd–Ge, is essentially optimized – only a small number of bonding states are still available above the Fermi level (Figure 3(e)). As expected from the electron counting arguments presented earlier, the absence of Cd–Cd bonds in the structure is confirmed by the calculations – this notion is reflected in the nonbonding character seen for the pair Cd–Cd (Figure 3(e)). An inspection of the Electron Localization Function (ELF), which does not show any maxima between the Cd atoms from adjacent layers (Figure 3(f)), reaffirms this reasoning.

The provided analysis suggests that the maximum in the electronic density of states at E _F observed for the BaLi₂Cd₂Ge₂ phase mainly stems from underoptimized Ba–Ge and Ba–Cd interactions. Although the corresponding Ba–Ge and Ba–In interactions in the structurally related BaLi₂In₂Ge₂ phase were found to be underoptimized as well [1], the respective unoccupied bonding states were found shifted away from the Fermi level, resulting in a pseudogap in the electronic spectrum. Since both BaLi₂Cd₂Ge₂ and BaLi₂In₂Ge₂ are formally electron-balanced according to the formula (Ba²⁺)(Li⁺)₂(M ²⁺)₂(Ge⁴⁻)₂ (M = Cd or In; recall that the charge 2+ is assigned to In due to the presence of In–In bonds), the difference in the electronic structures between the two compounds is rather unexpected.

The valence electron count in the other quaternary germanide with an analogous structure, BaMg₂Li₂Ge₂, also appears to be amenable to a full breakdown if one were to use the classic inorganic concepts. In this situation, the ionic picture (Ba²⁺)(Mg²⁺)₂(Li⁺)₂(Ge⁴⁻)₂ may be more appropriate compared to BaLi₂Cd₂Ge₂, considering the electronegativities of the constituting elements, especially Mg (χ _P  = 1.2) and Cd (χ _P  = 1.7). An important structural difference between the two compounds needs to be remembered though, the sites of Mg and Li are interchanged relative to those of Cd and Li. If the resultant [LiGe] sheets are regarded as polyanionic units with covalent bonding, with one valence electron provided by Li and four by Ge, the [LiGe]³⁻ layers in BaMg₂Li₂Ge₂ allow for all atoms to attain closed-shell configurations. Unlike BaLi₂Cd₂Ge₂ and BaLi₂In₂Ge₂, the structure of the Mg phase features almost planar [LiGe] sheets, vide supra, which allows describing the atoms in the layers as sp ²-hybridized, in contrast to the sp ³-hybridized species in the Cd and In representatives. The sp ² hybridization can be compatible with a higher bond order than a single bond for the Li–Ge contacts. In a rather naïve picture, one may consider two out of three Li–Ge bonds in the local coordination as single bonds and one as a double bond. Then, every atom would need four valence electrons to satisfy the octet rule (or 16 electrons per [Li₂Ge₂] unit), which is fulfilled for the [Li₂Ge₂]⁶⁻ layers in BaMg₂Li₂Ge₂. Owing to the electron conjugation provided by the sp² hybridization, all three bonding contacts around Li (or, equivalently, Ge) can be of the same length and an intermediate bond order in this representation. We notice that a similar scenario could be realized for the layers in BaLi₂Cd₂Ge₂ if they were flat.

To check this hypothesis, we ran first-principle calculations on a hypothetical BaLi₂Cd₂Ge₂ model where Cd and Ge were shifted (equally, in opposite directions from their actual positions) to lie in the same plane, while the coordinates of other atoms were unchanged. In line with the rationale provided above, the electronic density of states for this model exhibits a pseudogap at the Fermi level (Figure 4(a)). Analysis of the chemical bonds shows that all principal bonding interactions are almost optimized at E _F in this model (Figure 4(b)). A question to ask here is: If the bonding is optimized for the model with flat [CdGe] sheets, why does the experimentally observed structure show displacement of the Cd atoms away from the Ge plane? It is important to note that the optimized bonding does not guarantee a lower total energy. Location of the Cd atoms in the Ge plane would likely lead to high chemical pressure due to the shortened Cd–Ge contacts. The high spatial requirements of the Cd atoms (in comparison with, e.g., the smaller Li atoms in BaMg₂Li₂Ge₂) result in rippling of the [CdGe] layers. By corrugating the layers, the system appears to become electron-deficient, evidenced by the presence of underoccupied bonding states at E _F . If the geometric factor is indeed at play in this case, studying other representatives with smaller M atoms in the [MGe] layers, e.g., Zn or Mn, will be instructive. The Zn phase could not be made so far, as mentioned earlier, and more dedicated efforts need to be done; the Mn phase, if it exists, may also be interesting from a perspective of magnetism.

Figure 4:

(a, b) Total and projected electronic densities of states (DOS) for a BaLi₂Cd₂Ge₂ model with flat [CdGe] layers and the corresponding Crystal Orbital Hamilton population curves (COHP) for selected averaged interactions, respectively. (c, d) Same electronic properties for a BaLiCd₃Ge₂ model.

Solid and dashed colored curves denote COHP curves and their integrals, respectively.

From the above, it is evident that the unexpected high DOS at the Fermi level in BaLi₂Cd₂Ge₂ is related to the 3-fold coordination of the Cd atoms by Ge. This bonding environment makes the application of the Zintl concept somewhat ambiguous, as was previously noted in our presentation, and has also been discussed for some other phases with trigonally coordinated metal species [27]. However the perceived electron deficiency in BaLi₂Cd₂Ge₂ also indicates that the electronic structure is likely to be stabilized, subject to a suitable electron doping. A possible way to inject electrons in the system is via the substitution of Li by Cd, in a manner similar to the Li → In exchange in BaLi_2−x In_2+x Ge₂ [1], provided that Cd will exhibit cationic character upon such substitution. There is a hint from the single-crystal work that this might be the case, since the SOF of the Li site was freely refined as 25% “overoccupied”, but the exact reasons for this experimental observations are still unclear (more systematic studies will be necessary to discern two likely scenarios, BaLi_2−x Cd_2+x Ge₂ or BaLi_2−x Cd₂Ge_2+x ). Our first-principle calculations on yet another hypothetical model, BaLiCd₃Ge₂, with half of the Li atoms replaced by Cd in an ordered manner, confirm this scenario (Figure 3(c)). The Ba–Ge and Ba–Cd bonding states that were crossed by the Fermi level in the original BaLi₂Cd₂Ge₂ structure are occupied in the BaLiCd₃Ge₂ model (Figure 3(d)). The Li–Ge and Li–Cd interactions are almost unaffected by electron doping due to the small number of the respective hybridized electronic states in the vicinity of the Fermi level. Due to the extension of the bonding states for the Cd–Ge contacts above E _F in BaLi₂Cd₂Ge₂, electron doping has a weakly stabilizing effect on the covalent Cd–Ge interactions. Therefore, the main effect of electron doping is optimization of Ba–Ge and Ba–Cd interactions in the structure. It is worth noting that the somewhat too small anisotropic displacement parameters of Li in the refined BaLi₂Cd₂Ge₂ structure may point toward small substitution of Li by Cd, as such substitution would be favorable based on our calculations.