On Chemical Bonding in ht-Ga3Rh and Its Effect on Structural Organization and Thermoelectric Behavior

In the course of systematic studies of intermetallic compounds Ga3TM (TM—transition metal), the compound Ga3Rh is synthesized by direct reaction of the elements at 700 °C. The material obtained is characterized as a high-temperature modification of Ga3Rh. Powder and single-crystal X-ray diffraction analyses reveal tetragonal symmetry (space group P42/mnm, No. 146) with a = 6.4808(2) Å and c = 6.5267(2) Å. Large values and strong anisotropy of the atomic displacement parameters of Ga atoms indicate essential disorder in the crystal structure. A split-position technique is applied to describe the real crystal structure of ht-Ga3Rh. Bonding analysis in ht-Ga3Rh performed on ordered models with the space groups P1̅, P42nm, and P42212 shows, besides the omnipresent heteroatomic Ga–Rh bonds in the rhombic prisms ∞3[Ga8/2Rh2], the formation of homoatomic Ga–Ga bonds bridging the Rh–Rh contacts and the absence of significant Rh–Rh bonding. These features are essential reasons for the experimentally observed disorder in the lattice. In agreement with the calculated electronic density of states, ht-Ga3Rh shows temperature-dependent electrical resistivity of a “bad metal”. The very low lattice thermal conductivity of less than 0.5 W m–1 K–1 at 300 K, being lower than those for most other Ga3TM compounds, correlates with the enhanced bonding complexity.


Table of contents
Table S1.Ordered models of ht-Ga3Rh used for bonding analysis.
Table S2.Crystallographic data for ht-Ga3Rh in the space groups P42nm and P4 n2.

Space group P42nm
Space group P n2 x/a 0.15731(5) 1/2 0.8572(5) 0.8489(4) 0.34263(5) 0 0.6487(3)    Table S5.Selected interatomic distances in the models P1 _1, P1 _2, P42nm and P42212 of the crystal structure of ht-Ga3Rh.Lattice parameters a = 6.4808(2)Å, c = 6.5267(2)Å obtained from least-squares refinement of powder X-ray diffraction data were used in all models.Quantitative analysis of the surfaces for the QTAIM Rh atoms: with 1.79 Å 2 or 3.6% of the total surface (49.84 Å 2 ) in the P42nm model and 1.83 Å 2 or 3.6% of the total surface (51.36Å 2 ) in the P1 _2 model, the common Rh-Rh surfaces are clearly smaller than 2.43 Å 2 or 5.2% of the total surface (46.96Å 2 ) in the P42/mnm model.participates in all heteroatomic bonds as a minor partner.The characteristic difference to the P42/mnm model, is the absence of the dedicated bond basin between the Rh atoms.It is only included in the 4a-Rh-Rh-Ga2-Ga2 bond basin (red basin in the bottom panels of Figure 7), but here the Ga2 contributions are the majority ones (72% of the bond population).This means that these two Ga2-Ga2 contacts within the TCRP should be included into the conceptual electron counting (2-electron bonds).That gives 19 bonds, which is not realizable with 36 available valence electrons.But it can be realized, if the one topologically absent Rh-Rh bond would be excluded (18 bonds).This agrees well with the ELI-D picture of the bonding (Figure 7, bottom panels).
Another way to describe the split in the difference electron density leads to a model with the space group P42nm and trapezium-like shape of the middle quadrilateral plane of the TCRP (Figure 5, top, cf. also Experimental for atomic coordinates).Here, the number of different bond types -ten -is also larger than in the P42/mnm one (Figure 7, top).The P42nm model is similar to the P1 _2 one with respect to (i) the presence in several variations of all heteroatomic bond basins, known from the P42/mnm model and (ii) the rhodium participation in all heteroatomic bonds as a minority partner.A dedicated bond basin between the Rh atoms is here also absent.In the bottom region of the unit cell, the original 4a-Rh-Rh-Ga2-Ga2 bond (P42/mnm model, red basin in the middle panel of Figure 7) splits topologically into two 4-atomic parts (light red and green basins in the top panel of Figure 7) with one of them (green basin) having more than 90% of the Ga22 contribution.On the conceptual level, the shorter Ga22-Ga22 contact and the Rh-Rh one in the TCRP should be included into electron counting.That gives 18 bonds, which can be realized with 36 available valence electrons, i.e. it agrees well with the ELI-D picture of the bonding (Figure 7, top panel).Similar results are obtained for the models P1 _2 and P42212 (Figure S10).

Figure S2 .
Figure S2.Ordered models of the crystal structure of ht-RhGa3.

Figure S3 .
Figure S3.QTAIM atoms' basins and populations in the ordered models of ht-RhGa3.

Figure S4 .
Figure S4.ELI-D distribution in the (001) and (110) planes in three models of the crystal structure of ht-Ga3Rh.

Figure S5 .
Figure S5.Bond basins, their atomicity and electron populations in low-symmetrical models.

Figure S2 .
Figure S2.Ordered models of the crystal structure of ht-RhGa3.

Figure S3 .
Figure S3.QTAIM atoms' basins and populations in the ordered models of ht-Ga3Rh in

Figure S6 .
Figure S6.Specific heat CP versus temperature for ht-Ga3Rh in comparison with the temperature

Table S2 .
Crystallographic data for ht-Ga3Rh in the space groups P42nm and P4 n2.Lattice parameter are obtained from powder x-ray diffraction data, chemical composition from WDXS analysis.

Table S4 .
Interatomic distances in the crystal structure of ht-RhGa3 in the space group P42/mnm ideal IrIn3-type model and split model.Lattice parameters a = 6.4808(2)Å, c = 6.5267(2)Å obtained from powder x-ray diffraction data were used in all models.