Sr(Hg_1–xSn_x)₄: variations of the EuIn₄-type structure

2.1 Preparation and phase analysis

The synthesis of the title compounds of the series Sr(Hg_1–xSn_x)₄ was generally performed starting from the elements strontium, mercury and tin as obtained from commercial sources (Sr: Metallhandelsgesellschaft Maassen, Bonn, Germany, 99 %; Hg: Merck, p.A.; Sn: Shots, ABCR Karlsruhe, 99.9 %). The elements were filled into tantalum crucibles in a glovebox under an argon atmosphere and the sealed containers were heated up to a maximum temperature of 800–1000 °C. Subsequently, the crystallization was performed by a slow cooling rate of 5–20 K/h. The details of the temperature programs can be found in Table 1, together with the weighed sample compositions, which were restricted to the stoichiometric 1:4 (for Sr:Hg/Sn) element ratio. After the syntheses, representative parts of the reguli were ground in the glovebox and sealed in capillaries with a diameter of 0.3 mm. Powder X-ray diffraction diagrams were collected on transmission powder diffraction systems (STADI-P, linear PSD, Stoe & Cie, Darmstadt, Germany, MoK_α radiation, graphite monochromator). The exactly stoichiometric compound SrHg₂Sn₂ forms over a wide composition range at Sn proportions x in Sr(Hg_1–xSn_x)₄ between 0.85 and 0.47, where the tin-rich samples contain in addition the known binary stannide SrSn₄ [27]. According to our single crystal data, the latter compound does not take up any mercury. From a series of single crystal data and also from the positions of characteristic reflections of the EuIn₄-I-type structure of SrHg₂Sn₂ in the powder patterns, no phase width could be observed for this compound. At a tin content x of 0.43 (SrHg_2.28Sn_1.72), the powder diagrams of the samples change and additional reflections appear, which clearly indicate the larger unit cell of a superstructure. Several data sets collected from crystals taken from samples around the composition SrHg_2.5Sn_1.5 show a small phase width of the superstructure compound not larger than from SrHg_2.48Sn_1.52 to SrHg_2.52Sn_1.48. A further decreased tin content in samples of compositions like SrHg_2.75Sn_1.25 and SrHg₃Sn yielded only the distorted EuIn₄-II-type structure. Again, from several single crystal data sets a small phase width ranging from SrHg_2.56Sn_1.44 to SrHg_3.22Sn_0.77 has been obtained for the electron-poor form II of the EuIn₄ structure.

2.2 Crystal structure determination

For the crystal structure determinations, irregularly shaped single crystals of silver metallic luster were selected using a stereo microscope and mounted in glass capillaries (diameter 0.1 mm) under dried paraffine oil. The crystals were centered on diffractometers equipped with an image plate (Stoe IPDS, sealed tube) or a CCD (Bruker Apex-II Quazar, microfocus source) detector.

The reflections of the border compound SrHg₂Sn₂ could be indexed using a C-centered monoclinic lattice. Due to the lack of further absence conditions (and thus C2/m as a possible space group) and the similarities of the lattice parameters with the indide SrIn₄ [3], the latter model has been used for the structure refinement (program Shelxs-2013 [28]). The refinement of the Hg/Sn site occupation factors of the four original indium positions easily showed the fully ordered Hg/Sn distribution in SrHg₂Sn₂. This also holds for all four data sets collected from crystals of different samples (see the section 2.1 Preparation and phase analysis).

Crystals isolated from the most Hg-rich samples of the series Sr(Hg_1–xSn_x)₄ also exhibit the monoclinic C-centered EuIn₄-type unit cell, but the ratios of the lattice parameters are significantly different: While the a axis is decreased from 1258 (Sn-rich EuIn₄-I-type) to 1173 pm, the c axis increases from 998 to 1010 pm. As expected from the slightly smaller metallic radius of mercury (r = 157.3 pm) compared to tin (r = 162.3 pm), the unit cell is about 5 % smaller at the Hg-rich border of the series. Nevertheless, the structure of SrHg_3.2Sn_0.8 could be refined starting from the atomic coordinates of SrIn₄. The statistically occupied Hg/Sn positions M(2), M(3) and M(4) were refined with constrained positional and thermal parameters. The significant shifting of the atomic parameters (see the differences of the related x and z parameter values in Table 2, top and bottom) results in a distorted EuIn₄ variant (hereafter referred to as EuIn₄-II-type). The distortion is associated with the formation of additional, primarily Hg–Hg, bonds (see section 3 Results and discussion). Similar electronically driven structural changes have already been observed for the related series Sr(Hg_1–xIn_x)₄ [24].

The reflections of the crystals of the “intermediate” compounds (SrHg_2.5Sn_1.5) could likewise be indexed using a C-centered monoclinic lattice. In this case, however, only the length of the lattice parameter b fits the EuIn₄-type structure. A closer inspection of the precession photographs calculated from the image plate data revealed the presence of a superstructure of the original EuIn₄ unit cell, which is connected with a tripling of the monoclinic a–c basis. Also in this case, the lack of further absence conditions reduced the possible space groups to C2/m, C2 and Cm. The structure was solved using Direct Methods (program Shelxs-2013 [28]) in the centrosymmetric space group C2/m. This solution already yielded the three strontium and 10 of the 12 Hg/Sn atomic positions. After the completion of the model, the assignment of the pure Hg and Sn positions and the refinement of the Hg/Sn occupation for five mixed M positions, all displacement parameters converged to plausible values and the data refined to a low R1 value of 0.0475. The residual difference electron density maxima of 2.8 e^– × 10^–6 pm^–3 are located in the vicinity of the M atoms.

The crystallographic data and the refined atomic parameters of the three compounds are summarized in Tables 2 and 3, respectively [31]. Selected interatomic distances are collected in Table 4 (EuIn₄-type structures I and II) and 6 (tripled superstructure of SrHg_2.5Sn_1.5).

2.3 Band structure calculations

DFT calculations of the electronic band structures were performed using the FP-LAPW method (program Wien2k [32]). Whereas the fully ordered compound SrHg₂Sn₂ could be calculated directly, ‘SrHg₃Sn’ and ‘SrHg₄’ were set up as model compounds for the second electron-poor variant of the EuIn₄-type structure using the crystal data of SrHg_3.2Sn_0.8. For the Sn-containing model, the position M(2), which shows the highest tin content, was treated as a pure Sn site. In all calculations, the exchange-correlation contribution was described by the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof [33]. Muffin-tin radii were chosen as 127.0 pm (2.4 a.u.) for all atoms. Cutoff energies used are Emaxpot = 190 eV (potential) and Emaxwf = 170 eV (interstitial plane waves). Electron densities and Fermi surfaces were calculated and visualized using the programs XCrysDen [34] and DrawXTL [35]. A Bader [36] analysis of the electron density map was performed to evaluate the charge distribution between the atoms, the bond critical points (3, –1; BCP) and the volumes of the Bader basins (V_BB). Details and selected results of the calculations are summarized in Table 5. The total and partial Sr, Hg, and Sn densities of states are depicted in Fig. 1.

Fig. 1:

Calculated total density of states (gray) together with partial Sr/Hg/Sn DOS of SrHg₂Sn₂ (above) and SrHg₃Sn (below, together with ‘SrHg₄’) in the range between –10.5 and 2 eV relative to E_F (hatched bar: electronic stability region of the Hg-rich compounds).

3.1 Description of the crystal structure of SrHg₂Sn₂ (EuIn₄-I)

SrHg₂Sn₂ crystallizes with a fully ordered variant of the EuIn₄-type structure. This very rare monoclinic structure type occurs only for the isoelectronic (14 v.e./f.u.) binary indides EuIn₄ and SrIn₄ [3, 4], the latter with a very small substitution of In by Hg [24]. The structure has nevertheless been repeatedly described in the literature emphazising different structural elements [3, 4, 24]. For the ordered phase SrHg₂Sn₂ (I), the mercury-rich variant (II) and also the superstructure (S) reported herein, a description of the structures is given following, which focusses on the Hg/Sn distribution and the similarities with the structure elements found in SrHgSn [25] (LiGaGe type) and in binary and ternary Hg-rich alkaline-earth mercurides [16, 17, 19].

For the structure description and comparison, the shorter M–M distances are denoted by the bold characters a to e. They are found in the range 280–300 pm and, thus, vary around the Hg–Sn bond length observed in the electron precise compound SrHgSn (d_Hg–Sn = 290.1 pm). These distances are well separated from those of the multicenter/metallic bonds above 315 pm. This gap in the bond length distribution has been similarly reported for the binary alkaline-earth indides [1, 4], as well as for the corresponding mercurides [8, 16]. The distances f,g, and h alternate between the shorter and longer group of contacts within the different structure variants. The longer contacts u and v (314–335 pm) still have bond critical points in the calculated electron densities (see following). In Tables 4 and 6 the coordination numbers of Hg/Sn are designated (N + M) for the N shorter (280–300 pm) and the M longer/“secondary” (314–335 pm) bonds.

The left-hand side of Fig. 2 shows the unit cell of the fully ordered compound SrHg₂Sn₂ (x = 0.5) forming the “usual” (I) EuIn₄-type structure. As in the other variants of this structure, all atoms are located at y = 0 and 12, i.e., on the mirror planes perpendicular to the short b axis. In SrHg₂Sn₂, the atoms Hg(2) and Sn(3) at the one hand, and Hg(1) and Sn(4), on the other hand, are alternatingly forming zig-zag chains running along the b axis. These two types of chains are interconnected (via Hg–Sn bonds only) to form folded ladders like in the TiNiSi/KHg₂-type structures. In Fig. 3a these two types of zig-zag ladders A [formed by Sn(2) and Hg(3)] and B [Sn(1)/Hg(4)] are indicated by medium gray (A) and transparent light gray (B) planes. The Hg–Sn bonds d (A) and c (B) along the zig-zag chains are strong with interatomic distances of 287.0 and 282.0 pm, respectively (Table 4). In contrast, the rungs of the folded ladders, the Hg–Sn contacts f/u (for ladders A/B), are elongated significantly (317.6/323.3 pm). The square planar rings of the ladders B are only slightly distorted forming a rectangle with angles of 96.5/83.5° at the Hg/Sn corners, whereas the ladders A are strongly distorted toward rhombs (107.2/72.8° for Hg/Sn). Similar to the situation in the KHg₂ structure, both ladder types A and B are further connected along [100] via the Sn–Sn bonds a/h (d_Sn–Sn = 289.8/285.0 pm). In the resulting layers, six-membered rings are formed between the ladders, which are nearly planar between the ladders A and heavily puckered (chair conformation) between the ladders B (see dashed boxes in Fig. 2a). The two layers are further connected by strong Hg–Sn bonds b and e (285.0 and 289.1 pm) resulting in five-membered rings on the mirror planes (see Fig. 4a). The Sr cations are interspersed between two such pentagons exhibiting an overall coordination by (10 + 5) Hg/Sn and 2 Sr cations. The coordination number of Sn(1) amounts to 4 + 1 (with the neighbor atoms forming a trigonal-bipyramidal arrangement), whereas Sn(2), Hg(3) and Hg(4) show a distorted tetrahedral 3 + 1 coordination (Table 4). With the exception of the increased coordination number of Sn(1), the structure of SrHg₂Sn₂ can be described as a network of tetrahedra with four-, five- and six-membered rings similar to the nets observed in SrHgSn (LiGaGe-type [25]), SrIn₂ (CaIn₂-type [1]) (both with six-membered rings only) and SrHg₂ (KHg₂-type [37], four-, six- and eight-membered rings). Also related to the situation in SrHgSn, Hg–Sn bonds with a small polarity dominate the complex polyanion. The only exception are the two strong Sn–Sn bonds a and h, which connect the folded ladders to layers. Neglecting the weaker M–M bonds longer than 300 pm, the characteristic building blocks of the structure of SrHg₂Sn₂ are double tubes of connected cages consisting of five- and six-membered Hg/Sn rings. These structural elements are located around the b axis (0, y, 0) and are marked by ellipses in Figs. 2 and 5. The tubes are connected by the Sn(2)–Sn(2) bonds a resulting in complex layers in the b–c plane. Very similar layers (in this case formed by connected triple tubes) are found in the structure of the electron precise compound SiAs [38]. The Si positions are taken by the similarly four-bonded Sn atoms, which form Sn–Sn dumbbells inside [Sn(1)] and between [Sn(2)] the tubes. The As positions are occupied by the likewise three-bonded Hg(3,4) atoms. Compared to the electron precise compound SiAs (^3bAs and ^4bSi) with 9 v.e./f.u., all Hg/Sn atoms in the 7 v.e. unit [HgSn]^– of SrHg₂Sn₂ are additionally connected to the neigboring layers via the longer secondary Hg/Sn contacts of the folded ladders as described. This compensates for the two electron difference resulting also in an electron precise bonding situation for SrHg₂Sn₂ (see section Electronic structure and chemical bonding, following).

Fig. 2:

Crystal structure of SrHg₂Sn₂ (a) and SrHg_3.2Sn_0.8 (b), representing the EuIn₄-I and -II-type structure (cf. Table 4 for interatomic distances; dark spheres: Hg; light gray spheres: Sn; medium gray spheres: mixed Hg/Sn positions M; small gray spheres: Sr [35]).

Fig. 3:

Comparison of the crystal structures of the electron-rich SrHg₂Sn₂ (a), the electron-poor SrHg_3.4Sn_0.6 (b) (cf. Table 4 for interatomic distances) and the superstructure of the intermediate compounds SrHg_2.5Sn_1.5 (c) (black (pure Hg) to light gray (pure Sn) spheres: M; small gray spheres: Sr [35]).

Fig. 4:

Crystal structures of the EuIn₄ variants observed in the compound series Sr(Hg_1–xSn_x)₄ shown in a projection along [010]. a: SrHg₂Sn₂ (I); b: SrHg_3.2Sn_0.8 (II); c: SrHg_2.5Sn_1.5 (S) (black (pure Hg) to light gray (pure Sn) spheres: M; small gray spheres: Sr [35]).

Fig. 5:

Crystal structure of SrHg_2.5Sn_1.5 (cf. Table 6 for interatomic distances; black (pure Hg) to light gray (pure Sn) spheres: M; small spheres: Sr [35]).

3.2 Comparison with the electron-poor EuIn₄-II-type of SrHg_3.2Sn_0.8

As expected from the slightly smaller metallic radius of mercury relative to tin, the unit cell volume of the Hg-rich compound decreased by 5 % compared to SrHg₂Sn₂. Whereas the a and the b lattice parameter are also decreased, c unexpectedly increases from 998 to 1010 pm, indicating a significant change of the bonding situation in the two variants of the EuIn₄-type structure. The interchanged Hg/Sn distribution also points to significant differences between the two structure variants: The pure tin position Sn(1) of SrHg₂Sn₂ is fully occupied by Hg in SrHg_3.2Sn_0.8 and vice versa Hg(3) is the site occupied by the highest Sn content in the Hg-richer compound. Initially, the folded ladders A and B appear to be similar. Admittedly, the bonds f of the ladders A are significantly decreased from 317.6 to 297.7 pm. In addition, the distortion of the folded ladders is inverted: In SrHg₂Sn₂, the meshes of the ladders A are strongly sheared to give paralellograms, whereas in SrHg_3.2Sn_0.8 the four-membered rings of the ladders B are those which deviate significantly from rectangularity [77.5/102.5° at Hg(4)/Hg(1)]. Here, the ladders A are with 87.7/92.4° [M(2)/M(3)] next to rectangular. The reduced distortion of the ladders A not only decreases the bonds f but results in the formation of the new contacts v and additionally decreases the bonds g. In return, the strong bond h between two Sn(1) atoms (285.0 pm) is elongated to a secondary contact of lengths 329.9 pm between the two Hg(1) atoms. These modifications of the bond lengths are associated with a change of the ultimately resulting structural elements located around the b axis: Whereas SrHg₂Sn₂ exhibits the SiAs-like tubes formed by five- and six-membered rings as described, the Hg-rich derivative SrHg_3.2Sn_0.8 exhibits M₈ rhombohedra as characteristic building blocks in this part of the structure, which are similarily found in elemental mercury and Hg-rich mercurides [7, 16, 17]. The rhombohedra, which are depicted as dark polyhedra in Fig. 3, are connected via common edges to form rods along [010].

The differences of the two EuIn₄-type structure variants also lead to different coordination numbers, especially of the positions M(1) and M(4) forming the ladders B (Table 4). Due to the formation of the new contacts g and v at a higher Hg content, the coordination number of the very Hg-rich position M(4) is clearly increased from (3 + 1) to (4 + 3). As expected for a reduced v.e. number, the average connectivity of the atoms increases and, thus, the averaged coordination numbers (M + N) increase from (3.5 + 1) in the more electron rich compound SrHg₂Sn₂ to (4 + 1.75) in the Hg-rich derivative. With a value of 15 in SrHg₂Sn₂ and 16 in SrHg_3.2Sn_0.8 (Sr–M distances of 346–410 pm) the M coordination of the Sr cations is also slightly increased.

3.3 The superstructure of the EuIn₄-type in SrHg_2.5Sn_1.5

The compound SrHg_2.5Sn_1.5 with an intermediate Sn-content crystallizes in an isomorphous superstructure of index 3 of the EuIn₄-type structure (C2/m; Pearson code mS60, Figs. 3c and 5). The tripled unit cell is crystallographically achieved by the transformation matrix 1 0 –2, 0 1 0, 1 0 1 (see dotted small unit cell in Fig. 4c). Conversely, the corresponding small unit cell dimensions are a = 1195.2, b = 493.9, c = 991.1 pm, and β = 114.38°. Its volume V_u.c. of 532.9 × 10⁶ pm³ is consequently of intermediate size compared to those of the Sn-richer (545.2 × 10⁶pm³, I) and the Hg-richer (516.6 × 10⁶ pm³, II) EuIn₄-type structures. According to this tripling, the structure exhibits three Sr and 12 Hg/Sn sites. Two of the M sites, Sn(12) and Sn(22), are pure tin positions, five are pure mercury sites, and the other five are statistically occupied by the two elements (Table 2, middle). The atom labels of the M atoms, in general M(ij), are chosen in such a way, that i (with i = 1–4) corresponds to the label of the atom in the simple EuIn₄-type structures as discussed. The second part of the label, j (with j = 1–3), has been selected so that atoms with the same j form the zig-zag chains running along [010]. Bond labels (bold numbers) are also chosen to match the labeling in the simple structure type (e.g., a splits into a, a′ and a″, Table 6).

Similar to the two EuIn₄ variants, atoms M(1j) alternating with M(4j) and likewise M(2j) alternating with M(3j) form zig-zag chains running along the b axis. Two chains are again connected via bonds u and f to form the characteristic folded ladders A [two chains M(21)/M(31)], A′ [chains Sn(22)/Hg(32) and M(23)/Hg(33)], B [2 × Hg(11)/M(41)], and B′ [M(12)/Hg(42) + Sn(13)-Hg(43)]. The folded ladders A/A′ are connected to sheets forming flat six-membered rings in between the ladders. In contrast, the six-membered rings between the ladders B/B′ are again heavily puckered. The sheets formed by the ladders A/A′ are very similar in the two variants of the two EuIn₄-type structure; therefore, it is not surprising that they are also equal in the superstructure. In the sheets formed by the ladders B and B′ the building blocks of the variants I (SiAs-like double tubes, solid gray ellipses in Fig. 5) and II (rods of rhombohedra, dashed ellipses) of the two EuIn₄-derivatives alternate in a 1:2 ratio. The distribution of Hg and Sn also corresponds to the two more simple structure variants: The tubes of the “original” EuIn₄-type I are built up by the Hg/Sn atoms Sn(13), Sn(22), Hg(32) and Hg(43), which are–with the exception of the Sn(13)–Sn(13) bond h″–alternately connected. Comparable with the Hg-rich EuIn₄ variant II, the remaining mixed Hg-rich/pure Hg atoms Hg(11), M(12), M(21), M(31), Hg(33), M(41), and Hg(42) form rods of edge-sharing rhombohedra (black polyhedra in Fig. 3c), dashed ellipses in Fig. 5). In this mercury-rich region of the structure, additional longer M–M bonds are formed, which are missing in the open tubes: The bond v [M(12)– M(41)] newly appears, and the bond u between Hg(11) and M(41) is strengthened from a secondary to a short M–M contact.

According to this 1:2 structure relation, the Sr cations also exhibit the two coordination numbers of the EuIn₄ type variants, 16 (1×) and 15 (2×), in parallel.

Figure 4 shows the three variants of the EuIn₄-type structure observed in the title compounds Sr(Hg_1–xSn_x)₄ in a projection along b, which is also a useful description to compare the structures with related compounds like BaIn₄ (BaAl₄ type), Sr₃In₁₁ (La₃Al₁₁) or several Hg-rich mercurides (see figures and discussion in [3, 24]). These projections, in which the short (long) bonds below (above) 300 pm are depicted with thick (thin) sticks, easily show the different connection of the double pentagons inside the layers of similar y parameters (bold/thin atoms and bonds). In the original EuIn₄-I-type (Fig. 4a) the double pentagons are connected via the short Sn–Sn bond h along the diagonal [101] of the monoclinic unit cell. In contrast, this strong bond h is elongated in the mercury richer compound, some longer bonds appear and the new short Hg(4)–Hg(4) bond g connects the double pentagons to form ribbons running along [001] (Fig. 4b). Consequently, the connection of the pentagon dimers in the superstructure (Fig. 4c) is a combination of both the EuIn₄-I- and the -II-type structure, resulting in very wide (lengths of the large a lattice parameter) ribbons running along the [001] direction of the superstructure cell.

3.4 Comparison of the two series Sr(Hg_1–xSn_x)₄ and Sr(Hg_1–xIn_x)₄

The series of the mixed mercuride indides Sr(Hg_1–xIn_x)₄ [24] and the mixed stannides Sr(Hg_1–xSn_x)₄ examined herein, show some similarities but also some distinct differences. At first, the electron-rich EuIn₄-type structure exists for the binary tetraindide (v.e./M = 3.5), as well as for the isoelectronic mixed stannide SrHg₂Sn₂. In the case of the indide, a small phase width due to In to Hg exchange is observed reaching down to a valence electron concentration of 3.36 in SrHg_0.56In_3.44. In contrast, no additional Hg incorporation is observed for SrHg₂Sn₂. A partial occupation of the Sn positions by Hg in this coumpound would result in a loss of the strong Sn–Sn bonds. Second, the EuIn₄-II-type occurs in both series at significantly reduced v.e. concentrations. In the case of the indides, this structure type is found in the v.e./M range 2.82 to 2.74, and for the tin compounds at somewhat larger values of v.e./M from 3.22 to 2.88. Also similar for both compound series, the stability range of the two different EuIn₄-type structures is interrupted by the occurence of an alternative structure: In constrast to the superstructure found for the stannides at v.e./M = 3.25, the common BaAl₄-type is observed in the indium system at intermediate v.e. concentrations from v.e./M 3.26 to the stoichiometric compound SrHg₂In₂ with v.e./M = 3.0. The composition of the isoelectronic hypothetic tin compound would be SrHg₃Sn, which already lies in the stability region of the EuIn₄-II variant. The absence of a BaAl₄-type structure in the Sr/Hg/Sn system is presumably caused by the smaller radius of tin (and the high content of likewise small mercury atoms). The geometric stability range of the BaAl₄ structure, which is observed for larger A and smaller M atoms only, is already exceeded for this composition.

3.5 Electronic structures and chemical bonding

For the band structure calculations of the title compounds, the fully ordered electron-rich compound SrHg₂Sn₂ and, as model systems for the electron-poor compounds, ‘SrHg₄’ and ‘SrHg₃Sn’ with the crystal data taken from SrHg_3.2Sn_0.8 were used. For the latter model compound, the statistically occupied M(3) position was treated as a pure tin site (see the Experimental section).

In the calculated valence electron density of all compounds, distinct bond critical points of heights 0.21–0.33 e^– × 10^–6 pm^–3 (Table 5) are located on each short Hg–Sn bond up to 300 pm. The short Sn–Sn bonds a and h (in SrHg₂Sn₂) are found at the upper end of this range (ρ_BCP = 0.30–0.33 e^– × 10^–6 pm^–3). In accordance with the electronegativities of Hg (χ = 1.9) and Sn (χ = 1.8), the bond critical points at the Hg–Sn bonds are slightly (approximately 10 pm) shifted toward the less electronegative tin atom. The reduced Bader charges of tin (0 to –0.18) compared to the charges of mercury of –0.57 to –0.60 are also in agreement with this observation. Thus, the always higher charge of mercury also leads to very similar volumes of the Bader basins for both M elements: Even though mercury has a smaller metallic radius (157.3 pm compared to tin (162.3 pm) (see the trends in the unit cell volumes along with the tin-content x), the smaller radius of mercury is “compensated” by the increased negative charge. The longer contacts f, h, and u, which are found inside the Hg-rich rhombohedra, still exhibit bond critical points with reduced electron densities. These weaker bonds, which are clearly separated by their lengths, as well as by their ρ_BCP values from the purely covalent 2e2c bonds, are a very characteristic feature in most of the electron-poor polar intermetallics of mercury and the heavier p block elements Sn, Pb, In, and Tl.

For SrHg₂Sn₂ and both Hg-rich model compounds the calculated total density of states (DOS) and the partial DOS (pDOS) of the different Hg/Sn and Sr sites are plotted in Fig. 1 in the range between –10.5 and +2 eV relative to the Fermi level. The electronic stability range of the Hg-rich EuIn₄-II-type structure is marked by a hatched bar, numbers indicate v.e./M. As expected, the occupied bands are primarily of Hg and Sn character. The s and p states of all M atoms (not shown) are extensivly mixed, resulting in broad bands typical for an extended three-dimensional polyanion. The Hg d states are mainly situated between –9 and –5 eV below E_F, but they also spread out to higher energy and show a pronounced mixing in particular with the Hg- s states. This corresponds to a considerable contribution of Hg- d states to the covalent bonding. The Sr pDOS found below the Fermi level is mainly composed of d states. The contribution of these Sr states to the chemical bonding, which indicates an incomplete electron transfer from Sr towards M, is in the same order of magnitude as in electron precise Zintl phases with pseudo band gaps. The Bader charges of the Sr atoms, which are +1.35 and +1.40 in the calculated compounds (Table 5) are also similar to those in electron precise Sr indides [1].

The tDOS of SrHg₂Sn₂, similar to the observation for the isoelectronic indide [1, 3, 4, 24], exhibits a very pronounced pseudo band gap (Fig. 1, top). However, the distinct local minimum of the tDOS is located slightly below the Fermi energy (see discussion for the “hypoelectronic” SrIn₄ on the basis of a Hückel calculation [3]). In contrast to the related Hg/In tetrametallides [24], no phase width toward this slightly decreased v.e. concentration of 3.45 v.e./M is observed. The tDOS of ‘SrHg₃Sn’ (Fig. 1, bottom), which serves as a model compound for the Hg-rich version of the EuIn₄-type structure, shows that the structural distortion leads to a new, though not too pronounced, broad minimum of the tDOS around E_F, which nicely corresponds with the compositions of the observed variants of the Hg-rich EuIn4-II type (see hatched bar in Fig. 1, bottom). Although simple electron counting rules cannot be applied for both variants of the EuIn₄ type (i.e., due to the larger secondary bonds found inside the folded ladders and the Hg-rich parts of the structures), the results of the bandstructure calculations prove that the structural distorsions are governed by electronic factors.