Sc_0.43(2)Rb₂Mo₁₅S₁₉, a partially Sc-filled variant of Rb₂Mo₁₅S₁₉

The structure of scandium dirubidium penta­deca­molybdenum nona­deca­sulfide, Sc_0.43 (2)Rb₂Mo₁₅S₁₉, constitutes a partially Sc-filled variant of Rb₂Mo₁₅S₁₉ [Picard, Saillard, Gougeon, Noel & Potel (2000), J. Solid State Chem. 155, 417-426]. In the two compounds, which both crystallize in the Rc space group, the structural motif is characterized by a mixture of Mo₆Sⁱ₈S^a₆ and Mo₉Sⁱ₁₁S^a₆ cluster units (`i' is inner and `a' is apical) in a 1:1 ratio. The two components are inter­connected through inter­unit Mo-S bonds. The cluster units are centred at Wyckoff positions 6b and 6a (point-group symmetries and 32, respectively). The Rb⁺ cations occupy large voids between the different cluster units. The Rb and the two inner S atoms lie on sites with 3. symmetry (Wyckoff site 12c), and the Mo and S atoms of the median plane of the Mo₉S₁₁S₆ cluster unit lie on sites with .2 symmetry (Wyckoff site 18e). A unique feature of the structure is a partially filled octa­hedral Sc site with symmetry. Extended Hückel tight-binding calculations provide an understanding of the variation in the Mo-Mo distances within the Mo clusters induced by the increase in the cationic charge transfer due to the insertion of Sc.

S1. Comment

In₂Mo₁₅Se₁₉ (Potel et al., 1981) and In₃Mo₁₅Se₁₉ (Grüttner et al., 1979), which crystallize in the R3c and P6₃/m space groups, respectively, were the first compounds containing a molybdenum cluster with a nuclearity greater than 6. Indeed, their crystal structures contain an equal mixture of octahedral Mo₆ and bioctahedral Mo₉ clusters. Subsequently, compounds isotopic with In₂Mo₁₅Se₁₉, such as Alc₂Mo₁₅S₁₉ (Alc = K, Rb or Cs; Picard et al., 2002, 2000, 2004) or Ba₂Mo₁₅Se₁₉ (Gougeon et al., 1989), as well as compounds isotopic with In₃Mo₁₅Se₁₉, such as In_1.6Rb₂Mo₁₅S₁₉ and ScTl₂Mo₁₅S₁₉ (Salloum et al., 2004), have been obtained. Among the latter compounds, Rb₂Mo₁₅S₁₉ appears to be the first member of the series of compounds Rb_2nMo₉S₁₁Mo_6nS_6n+2 (n = 1, 2, 3 and 4; Picard et al., 2000). In addition to their interesting crystal structures, the Rb_2nMo₉S₁₁Mo_6nS_6n+2 compounds become superconducting at low temperature. In an attempt to replace Tl with Rb in ScTl₂Mo₁₅S₁₉ (In₃Mo₁₅Se₁₉-type), we obtained the title new quaternary compound Sc_0.4Rb₂Mo₁₅S₁₉ belonging to the In₂Mo₁₅Se₁₉ structure type and constituting a partially Sc-filled variant of Rb₂Mo₁₅S₁₉.

The Sc insertion in Rb₂Mo₁₅S₁₉ is evident from the variations in the unit-cell parameters. Indeed, the a axis increases by ca 0.08 Å while the c axis decreases by about 0.27 Å. A view of the crystal structure of Sc_0.43Rb₂Mo₁₅S₁₉ is shown in Fig. 1. The Mo—S framework is similar to that of Rb₂Mo₁₅S₁₉ and is based on an equal mixture of Mo₆Sⁱ₈S^a₆ and Mo₉Sⁱ₁₁S^a₆ cluster units interconnected through Mo—S bonds (Fig. 2) [for details of the i- and a-type ligand notation, see Schäfer & von Schnering (1964)]. The first unit can be described as an Mo₆ octahedron surrounded by eight face-capping inner Sⁱ (six S3 and two S5) and six apical S^a (S1) ligands. The Mo₉ core of the second unit results from the face-sharing of two octahedral Mo₆ clusters. The Mo₉ cluster is surrounded by 11 Sⁱ atoms (six S1, three S2 and two S4) capping the faces of the bioctahedron and six apical S^a ligands (S3) above the outer Mo atoms. The Mo₆Sⁱ₈S^a₆ and Mo₉Sⁱ₁₁S^a₆ units are centred at 6b and 6a positions and have point-group symmetries 3. and 32, respectively.

The Mo—Mo distances within the Mo₆ clusters are 2.6783 (6) Å for the intratriangle distances (distances within the Mo₃ triangles formed by atoms Mo3 related through the threefold axis) and 2.7393 (6) Å for the intertriangle distances. In Rb₂Mo₁₅S₁₉, the latter two values are 2.676 (2) and 2.767 (2) Å, respectively. These variations reflect the different cationic charge transfer towards the Mo₆ clusters in the two parent compounds.

The Mo—Mo distances within the Mo₉ clusters are 2.6658 (5) and 2.6910 (8) Å for the distances in the triangles formed by atoms Mo1 and Mo2, respectively. In Rb₂Mo₁₅S₁₉, the corresponding distances are 2.680 (2) and 2.688 (3) Å. The distances between the triangles formed by atoms Mo1 and Mo2 are 2.6958 (4) and 2.7663 (4) Å, respectively, in Sc_0.4Rb₂Mo₁₅S₁₉ compared with 2.719 (1) and 2.785 (2) Å, respectively, in Rb₂Mo₁₅S₁₉.

Although the structural response of the Mo₉ cluster with respect to the increase in charge transfer is more complex, we observe that the Mo1—Mo1 and two Mo1—Mo2 intertriangle distances are shorter in the Sc-filled compound. On the other hand, a slight increase in the Mo2—Mo2 bonds occurs in the median Mo₃ triangle [2.688 (3) Å in Rb₂Mo₁₅S₁₉]. In order to explain these variations, we performed extended Hückel tight-binding (EHTB) calculations on Rb₂Mo₁₅S₁₉ using the program YaEHMOP (Landrum, 1997). The Mo and S extended Hückel parameters used by Picard et al. (2000) were considered. Total Mo₆- and Mo₉-projected DOS (density of states) and COOP (crystal orbital overlap population) curves for the different bonds discussed above and obtained from 36 k points [define k?] are sketched in Figs. 3 and 4, respectively.

Assuming an ionic interaction between the inserted Sc atoms and the host material, the three electrons of the 3d transition metal should be transferred to the clusters. Assuming a rigid-band model, the Fermi level corresponding to the electron count of the title compound is slightly higher in energy (ca 0.02 eV) than that for Rb₂Mo₁₅S₁₉. The DOS at the Fermi level is mainly centred on Mo atoms belonging to both Mo₆ and Mo₉ clusters (Fig. 3). Therefore, both clusters should be affected by an increase in the anionic charge of the Mo–S network. As shown by the COOP curves of the Mo3—Mo3 intratriangle (solid line) and Mo3—Mo3 intertriangle (dotted line) bonds within the Mo₆ cluster, the increase in the metal electron count due to the insertion of Sc foresees a weak lengthening and a shortening of the Mo3—Mo3 bonds within the Mo₃ triangles and between the triangles, respectively. Such an evolution is in fact observed in Sc_0.4Rb₂Mo₁₅S₁₉, as mentioned above.

Regarding the Mo₉ cluster (Fig. 4), the lengthening of the Mo2—Mo2 bonds and the shortening of the Mo1—Mo1 and Mo1—Mo2 bonds can be envisioned theoretically when extra electrons are added, and this is what is observed experimentally in Sc_0.43Rb₂Mo₁₅S₁₉. The Mo—S distances are almost unaffected by the cationic charge, and range between 2.4207 (12) and 2.475 (1) Å within the Mo₆Sⁱ₈S^a₆ unit and between 2.4110 (9) and 2.6069 (7) Å within the Mo₉Sⁱ₁₁S^a₆ unit, as usual.

Finally, the three-dimensional packing arises from the interconnection of the Mo₆Sⁱ₈S^a₆ and Mo₉Sⁱ₁₁S^a₆ cluster units through Mo—S bonds. Indeed, each Mo₆Sⁱ₈S^a₆ unit is interconnected to six Mo₉Sⁱ₁₁S^a₆ units (and vice versa) via Mo3—S1 and Mo1—S3 bonds, respectively, to form the three-dimensional Mo–Se framework, the connective formula of which is Mo₉Sⁱ₅S^i-a_6/2S^a-i_6/2, Mo₆Sⁱ₂S^i-a_6/2S^a-i_6/2. The result of this arrangement is that the shortest intercluster Mo1—Mo3 distance between the Mo₆ and Mo₉ clusters is 3.2995 (4) Å, compared with 3.246 (2) Å in Rb₂Mo₁₅S₁₉, indicating only weak metal–metal interaction. This variation is consistent with the Mo–Mo intercluster antibonding nature of the bands that lie in the vicinity of the Fermi level.

The Sc atoms occupy highly flattened octahedral sites [2.172 (1) (× 2), 2.7983 (3) (× 2) and 2.920 (1) Å (× 2)] located near the Rb1 sites around the threefold axes. The alkali metal cation occupies a pentacapped trigonal prismatic site of S atoms, similar to that observed in Rb₂Mo₁₅S₁₉ (Fig. 5). The Rb—S distances are spread over the wide range 3.2512 (10)–3.7554 (11) Å, while in Rb₂Mo₁₅S₁₉ they are in the range 3.222 (3)–3.730 (3) Å. Thus, the insertion of Sc only leads to a slight decrease (ca 0.020 Å) of the Rb1—S4 and Rb1—S5 distances along the threefold axis, while the other distances are slightly decreased [increased?] (ca 0.027 Å).

Related literature

For related literature, see: Gougeon et al. (1989); Grüttner et al. (1979); Landrum (1997); Liang et al. (2009); Picard et al. (2000, 2002, 2004); Potel et al. (1981); Salloum et al. (2004); Schäfer & von Schnering (1964); Solodovnikova & Solodovnikov (2006); Zhao et al. (2011).

S2. Experimental

Single crystals of Sc_0.43Rb₂Mo₁₅S₁₉ were prepared from a mixture of Sc₂S₃, Rb₂MoS₄, MoS₂ and Mo with the nominal composition ScRb₂Mo₁₅S₁₉. Rubidium thiomolybdate was obtained by sulfuration of Rb₂MoO₄ at 723 K for 2 d under CS₂ gas carried by flowing argon. The molybdate Rb₂MoO₄ was synthesized by heating an equimolar ratio of Rb₂CO₃ and MoO₃ in an alumina vessel at 1073 K in air over a period of 2 d. Sc₂S₃ was prepared from the elements heated in a sealed evacuated silica tube at 1073 K for 2 d. All handling of materials was carried out in an argon-filled glove-box. The initial mixture (ca 5 g) was cold pressed and loaded into a molybdenum crucible, which was sealed under a low argon pressure using an arc-welding system. The charge was heated at a rate of 300 K h^-1 to 1773 K and the temperature held for 48 h. The charge was then cooled at a rate of 100 K h^-1 to 1373 K before finally being furnace cooled.

S3. Refinement

The site-occupancy factor of the Sc1 atom was refined freely. Because the U_eq parameter of atom Rb1 was larger than that of the other atoms, the site-occupancy factor of Rb1 was also refined. It converged to 1.011 (5) and was consequently fixed to unity in the final refinement. It is interesting to note that Rb atoms often present large U_eq (see, for example, Picard et al., 2000; Solodovnikova & Solodovnikov, 2006; Liang et al., 2009; Zhao et al., 2011).

Computing details

Data collection: COLLECT (Nonius, 1998); cell refinement: COLLECT (Nonius, 1998); data reduction: EVALCCD (Duisenberg et al., 2003); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1996); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

	Fig. 1. A view of Sc0.43Rb2Mo15S19 along [110].
	Fig. 2. A plot showing the atom-numbering scheme and the inter-unit linkage of the Mo9S11S6 and Mo6S8S6 cluster units. Displacement ellipsoids are drawn at the 97% probability level.
	Fig. 3. EHTB calculations for Rb2Mo15S19. (a) Total (solid line) and Mo6-projected (dotted line) DOS. (b) Total (solid line) and Mo9-projected (dotted line) DOS.
	Fig. 4. EHTB calculations for Rb2Mo15S19. (a) Mo3—Mo3 COOPs for interatomic distances within the Mo3 triangle (solid line) and between triangles (dotted line) of the Mo6 cluster. (b) COOPs for the intratriangle Mo1—Mo1 (solid line) and Mo2—Mo2 (dotted line) bonds in the Mo9 cluster. (c) COOPs for the intertriangle Mo1—Mo2 bonds of 2.719 (solid line) and 2.785 Å (dotted line).
	Fig. 5. A view of the environment of the Rb^+ and Sc^3+ cations. Displacement ellipsoids are drawn at the 97% probability level. [Two S4 atoms present - one should have a symmetry code]

scandium dirubidium pentadecamolybdenum nonadecasulfide

Crystal data

Sc0.43(2)Rb2Mo15S19	Dx = 5.076 Mg m^−3
Mr = 2238.37	Mo Kα radiation, λ = 0.71069 Å
Trigonal, R3c	Cell parameters from 22338 reflections
a = 9.5173 (1) Å	θ = 2.2–39.8°
c = 56.0061 (9) Å	µ = 10.92 mm^−1
V = 4393.33 (10) Å^3	T = 293 K
Z = 6	Multi-faceted, black
F(000) = 6102	0.13 × 0.12 × 0.09 mm

Data collection

Nonius KappaCCD area-detector diffractometer	1431 independent reflections
Radiation source: fine-focus sealed tube	1383 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.069
ϕ scans (κ = 0) + additional ω scans	θmax = 30.0°, θmin = 2.2°
Absorption correction: analytical (de Meulenaer & Tompa, 1965)	h = −13→13
Tmin = 0.298, Tmax = 0.463	k = −13→13
13057 measured reflections	l = −77→78

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.029	w = 1/[σ^2(Fo^2) + (0.P)^2 + 69.769P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.062	(Δ/σ)max < 0.001
S = 1.25	Δρmax = 1.09 e Å^−3
1431 reflections	Δρmin = −0.88 e Å^−3
64 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.000087 (11)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2sigma(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0.0000	0.0000	0.112814 (16)	0.0309 (2)
Sc1	−0.1667	0.1667	0.1667	0.025 (3)	0.142 (6)
Mo1	−0.34200 (4)	0.16746 (4)	0.123521 (6)	0.01226 (10)
Mo2	−0.17009 (5)	0.3333	0.0833	0.01165 (11)
Mo3	−0.49608 (4)	−0.18041 (4)	0.186855 (6)	0.01349 (10)
S1	−0.04693 (12)	0.31317 (12)	0.119858 (19)	0.01637 (19)
S2	−0.3333	0.03388 (14)	0.0833	0.0154 (3)
S3	−0.35297 (12)	−0.05314 (12)	0.149673 (19)	0.0169 (2)
S4	−0.3333	0.3333	0.15718 (3)	0.0179 (3)
S5	−0.6667	−0.3333	0.22009 (3)	0.0184 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0310 (3)	0.0310 (3)	0.0306 (4)	0.01549 (13)	0.000	0.000
Sc1	0.025 (4)	0.027 (4)	0.027 (5)	0.015 (4)	−0.010 (3)	−0.011 (4)
Mo1	0.01478 (16)	0.01464 (16)	0.00824 (16)	0.00800 (12)	−0.00071 (11)	0.00080 (11)
Mo2	0.01339 (16)	0.0131 (2)	0.0083 (2)	0.00656 (10)	−0.00095 (8)	−0.00189 (15)
Mo3	0.01728 (17)	0.01515 (16)	0.00806 (17)	0.00813 (13)	0.00061 (11)	0.00071 (11)
S1	0.0167 (4)	0.0174 (4)	0.0148 (4)	0.0084 (3)	−0.0030 (3)	−0.0039 (3)
S2	0.0195 (6)	0.0149 (4)	0.0134 (6)	0.0098 (3)	−0.0033 (5)	−0.0017 (2)
S3	0.0161 (4)	0.0184 (4)	0.0155 (4)	0.0080 (4)	0.0020 (3)	0.0059 (4)
S4	0.0229 (5)	0.0229 (5)	0.0079 (7)	0.0115 (2)	0.000	0.000
S5	0.0241 (5)	0.0241 (5)	0.0069 (7)	0.0121 (2)	0.000	0.000

Geometric parameters (Å, º)

Rb1—S1^i	3.2512 (10)	Mo2—Mo2^v	2.6910 (8)
Rb1—S1^ii	3.2512 (10)	Mo2—Mo2^vi	2.6910 (8)
Rb1—S1	3.2512 (10)	Mo2—Mo1^vi	2.6958 (4)
Rb1—S5^iii	3.3263 (19)	Mo2—Mo1^viii	2.6960 (4)
Rb1—S4^iv	3.5475 (19)	Mo2—Mo1^vii	2.7664 (4)
Rb1—S2^i	3.7306 (8)	Mo3—S5	2.4198 (13)
Rb1—S2	3.7306 (8)	Mo3—S3	2.4513 (10)
Rb1—S2^ii	3.7306 (8)	Mo3—S1^iv	2.4577 (10)
Rb1—S3^ii	3.7554 (11)	Mo3—S3^ix	2.4641 (10)
Rb1—S3	3.7554 (11)	Mo3—S3^x	2.4736 (10)
Rb1—S3^i	3.7554 (11)	Mo3—Mo3^xi	2.6783 (6)
Sc1—S3	2.1718 (10)	Mo3—Mo3^xii	2.6783 (6)
Sc1—S3^iv	2.1719 (11)	Mo3—Mo3^x	2.7393 (6)
Sc1—S4^iv	2.7983 (3)	Mo3—Mo3^ix	2.7394 (6)
Sc1—S4	2.7983 (3)	S1—Mo3^iv	2.4577 (10)
Sc1—S1	2.9200 (11)	S1—Mo1^vi	2.4786 (10)
Sc1—S1^iv	2.9201 (11)	S2—Mo2^v	2.4715 (11)
Mo1—S4	2.4336 (14)	S2—Mo1^viii	2.6066 (7)
Mo1—S1	2.4408 (10)	S2—Rb1^xiii	3.7307 (8)
Mo1—S1^v	2.4786 (10)	S3—Mo3^x	2.4641 (10)
Mo1—S3	2.5189 (10)	S3—Mo3^ix	2.4737 (10)
Mo1—S2	2.6065 (7)	S4—Mo1^vi	2.4336 (14)
Mo1—Mo1^vi	2.6658 (5)	S4—Mo1^v	2.4336 (14)
Mo1—Mo1^v	2.6658 (5)	S4—Sc1^vi	2.7983 (3)
Mo1—Mo2^v	2.6958 (4)	S4—Sc1^v	2.7983 (3)
Mo1—Mo2	2.7663 (4)	S4—Rb1^iv	3.5475 (19)
Mo2—S1	2.4125 (10)	S5—Mo3^xii	2.4198 (13)
Mo2—S1^vii	2.4126 (10)	S5—Mo3^xi	2.4198 (13)
Mo2—S2	2.4715 (11)	S5—Rb1^xiv	3.3263 (19)
Mo2—S2^vi	2.4715 (11)
S1^i—Rb1—S1^ii	118.549 (10)	S2^vi—Mo2—Mo2^vi	57.017 (19)
S1^i—Rb1—S1	118.549 (10)	Mo2^v—Mo2—Mo2^vi	60.0
S1^ii—Rb1—S1	118.549 (10)	S1—Mo2—Mo1^vi	57.73 (2)
S1^i—Rb1—S5^iii	96.97 (2)	S1^vii—Mo2—Mo1^vi	144.67 (3)
S1^ii—Rb1—S5^iii	96.97 (2)	S2—Mo2—Mo1^vi	117.777 (10)
S1—Rb1—S5^iii	96.97 (2)	S2^vi—Mo2—Mo1^vi	60.400 (8)
S1^i—Rb1—S4^iv	83.03 (2)	Mo2^v—Mo2—Mo1^vi	90.461 (10)
S1^ii—Rb1—S4^iv	83.03 (2)	Mo2^vi—Mo2—Mo1^vi	61.798 (10)
S1—Rb1—S4^iv	83.03 (2)	S1—Mo2—Mo1^viii	144.67 (3)
S5^iii—Rb1—S4^iv	180.0	S1^vii—Mo2—Mo1^viii	57.73 (2)
S1^i—Rb1—S2^i	57.45 (2)	S2—Mo2—Mo1^viii	60.401 (8)
S1^ii—Rb1—S2^i	76.93 (2)	S2^vi—Mo2—Mo1^viii	117.776 (10)
S1—Rb1—S2^i	157.73 (3)	Mo2^v—Mo2—Mo1^viii	61.800 (10)
S5^iii—Rb1—S2^i	63.732 (13)	Mo2^vi—Mo2—Mo1^viii	90.462 (10)
S4^iv—Rb1—S2^i	116.269 (13)	Mo1^vi—Mo2—Mo1^viii	148.89 (2)
S1^i—Rb1—S2	76.93 (2)	S1—Mo2—Mo1	55.73 (3)
S1^ii—Rb1—S2	157.73 (3)	S1^vii—Mo2—Mo1	152.23 (3)
S1—Rb1—S2	57.45 (2)	S2—Mo2—Mo1	59.370 (9)
S5^iii—Rb1—S2	63.731 (13)	S2^vi—Mo2—Mo1	118.531 (11)
S4^iv—Rb1—S2	116.268 (13)	Mo2^v—Mo2—Mo1	59.188 (10)
S2^i—Rb1—S2	101.899 (16)	Mo2^vi—Mo2—Mo1	88.969 (10)
S1^i—Rb1—S2^ii	157.73 (3)	Mo1^vi—Mo2—Mo1	58.408 (13)
S1^ii—Rb1—S2^ii	57.45 (2)	Mo1^viii—Mo2—Mo1	111.081 (13)
S1—Rb1—S2^ii	76.93 (2)	S1—Mo2—Mo1^vii	152.23 (3)
S5^iii—Rb1—S2^ii	63.731 (13)	S1^vii—Mo2—Mo1^vii	55.73 (3)
S4^iv—Rb1—S2^ii	116.269 (13)	S2—Mo2—Mo1^vii	118.530 (11)
S2^i—Rb1—S2^ii	101.899 (16)	S2^vi—Mo2—Mo1^vii	59.371 (9)
S2—Rb1—S2^ii	101.899 (16)	Mo2^v—Mo2—Mo1^vii	88.970 (10)
S1^i—Rb1—S3^ii	139.67 (4)	Mo2^vi—Mo2—Mo1^vii	59.190 (10)
S1^ii—Rb1—S3^ii	62.17 (2)	Mo1^vi—Mo2—Mo1^vii	111.082 (13)
S1—Rb1—S3^ii	60.30 (2)	Mo1^viii—Mo2—Mo1^vii	58.405 (13)
S5^iii—Rb1—S3^ii	123.35 (2)	Mo1—Mo2—Mo1^vii	144.35 (2)
S4^iv—Rb1—S3^ii	56.65 (2)	S5—Mo3—S3	172.12 (4)
S2^i—Rb1—S3^ii	138.80 (2)	S5—Mo3—S1^iv	92.32 (4)
S2—Rb1—S3^ii	117.69 (2)	S3—Mo3—S1^iv	95.56 (4)
S2^ii—Rb1—S3^ii	60.846 (16)	S5—Mo3—S3^ix	91.43 (3)
S1^i—Rb1—S3	60.30 (2)	S3—Mo3—S3^ix	88.13 (3)
S1^ii—Rb1—S3	139.67 (4)	S1^iv—Mo3—S3^ix	92.18 (3)
S1—Rb1—S3	62.17 (2)	S5—Mo3—S3^x	91.20 (3)
S5^iii—Rb1—S3	123.35 (2)	S3—Mo3—S3^x	87.92 (3)
S4^iv—Rb1—S3	56.65 (2)	S1^iv—Mo3—S3^x	97.54 (3)
S2^i—Rb1—S3	117.69 (2)	S3^ix—Mo3—S3^x	169.82 (4)
S2—Rb1—S3	60.846 (16)	S5—Mo3—Mo3^xi	56.40 (2)
S2^ii—Rb1—S3	138.80 (2)	S3—Mo3—Mo3^xi	117.07 (3)
S3^ii—Rb1—S3	92.68 (3)	S1^iv—Mo3—Mo3^xi	135.20 (3)
S1^i—Rb1—S3^i	62.17 (2)	S3^ix—Mo3—Mo3^xi	117.15 (3)
S1^ii—Rb1—S3^i	60.30 (2)	S3^x—Mo3—Mo3^xi	56.98 (3)
S1—Rb1—S3^i	139.67 (4)	S5—Mo3—Mo3^xii	56.40 (2)
S5^iii—Rb1—S3^i	123.35 (2)	S3—Mo3—Mo3^xii	117.30 (3)
S4^iv—Rb1—S3^i	56.65 (2)	S1^iv—Mo3—Mo3^xii	131.69 (3)
S2^i—Rb1—S3^i	60.846 (16)	S3^ix—Mo3—Mo3^xii	57.32 (3)
S2—Rb1—S3^i	138.80 (2)	S3^x—Mo3—Mo3^xii	116.81 (3)
S2^ii—Rb1—S3^i	117.69 (2)	Mo3^xi—Mo3—Mo3^xii	60.0
S3^ii—Rb1—S3^i	92.68 (3)	S5—Mo3—Mo3^x	117.03 (2)
S3—Rb1—S3^i	92.68 (3)	S3—Mo3—Mo3^x	56.35 (3)
S3—Sc1—S3^iv	180.0	S1^iv—Mo3—Mo3^x	138.29 (3)
S3—Sc1—S4^iv	87.61 (3)	S3^ix—Mo3—Mo3^x	114.42 (3)
S3^iv—Sc1—S4^iv	92.39 (3)	S3^x—Mo3—Mo3^x	55.82 (3)
S3—Sc1—S4	92.39 (3)	Mo3^xi—Mo3—Mo3^x	60.734 (8)
S3^iv—Sc1—S4	87.61 (3)	Mo3^xii—Mo3—Mo3^x	90.0
S4^iv—Sc1—S4	180.0	S5—Mo3—Mo3^ix	117.03 (2)
S3—Sc1—S1	90.13 (3)	S3—Mo3—Mo3^ix	56.60 (3)
S3^iv—Sc1—S1	89.87 (3)	S1^iv—Mo3—Mo3^ix	134.68 (3)
S4^iv—Sc1—S1	104.16 (4)	S3^ix—Mo3—Mo3^ix	55.91 (3)
S4—Sc1—S1	75.84 (4)	S3^x—Mo3—Mo3^ix	114.32 (3)
S3—Sc1—S1^iv	89.87 (3)	Mo3^xi—Mo3—Mo3^ix	90.0
S3^iv—Sc1—S1^iv	90.12 (3)	Mo3^xii—Mo3—Mo3^ix	60.734 (8)
S4^iv—Sc1—S1^iv	75.84 (4)	Mo3^x—Mo3—Mo3^ix	58.532 (15)
S4—Sc1—S1^iv	104.16 (4)	Mo2—S1—Mo1	69.50 (3)
S1—Sc1—S1^iv	180.0	Mo2—S1—Mo3^iv	133.69 (4)
S4—Mo1—S1	92.31 (3)	Mo1—S1—Mo3^iv	130.32 (5)
S4—Mo1—S1^v	91.39 (3)	Mo2—S1—Mo1^vi	66.88 (3)
S1—Mo1—S1^v	168.77 (5)	Mo1—S1—Mo1^vi	65.62 (3)
S4—Mo1—S3	93.68 (4)	Mo3^iv—S1—Mo1^vi	83.88 (3)
S1—Mo1—S3	94.52 (3)	Mo2—S2—Mo2^v	65.97 (4)
S1^v—Mo1—S3	95.81 (3)	Mo2—S2—Mo1	65.95 (3)
S4—Mo1—S2	170.48 (4)	Mo2^v—S2—Mo1	64.07 (3)
S1—Mo1—S2	84.06 (3)	Mo2—S2—Mo1^viii	64.07 (3)
S1^v—Mo1—S2	90.61 (3)	Mo2^v—S2—Mo1^viii	65.95 (3)
S3—Mo1—S2	95.38 (4)	Mo1—S2—Mo1^viii	119.53 (5)
S4—Mo1—Mo1^vi	56.79 (2)	Mo2^v—S2—Rb1	146.11 (3)
S1—Mo1—Mo1^vi	57.87 (3)	Mo1—S2—Rb1	84.011 (14)
S1^v—Mo1—Mo1^vi	116.28 (3)	Mo1^viii—S2—Rb1	128.288 (13)
S3—Mo1—Mo1^vi	134.72 (3)	Mo2—S2—Rb1^xiii	146.11 (3)
S2—Mo1—Mo1^vi	114.15 (2)	Mo1—S2—Rb1^xiii	128.291 (13)
S4—Mo1—Mo1^v	56.79 (2)	Mo1^viii—S2—Rb1^xiii	84.008 (14)
S1—Mo1—Mo1^v	117.64 (3)	Rb1—S2—Rb1^xiii	118.46 (4)
S1^v—Mo1—Mo1^v	56.51 (3)	Sc1—S3—Mo3^x	151.43 (5)
S3—Mo1—Mo1^v	134.87 (3)	Mo3—S3—Mo3^x	67.74 (3)
S2—Mo1—Mo1^v	117.38 (2)	Sc1—S3—Mo3^ix	130.32 (5)
Mo1^vi—Mo1—Mo1^v	60.0	Mo3—S3—Mo3^ix	67.59 (3)
S4—Mo1—Mo2^v	118.84 (2)	Mo3^x—S3—Mo3^ix	65.70 (3)
S1—Mo1—Mo2^v	113.75 (3)	Sc1—S3—Mo1	77.19 (3)
S1^v—Mo1—Mo2^v	55.39 (3)	Mo3—S3—Mo1	133.40 (4)
S3—Mo1—Mo2^v	134.25 (3)	Mo3^x—S3—Mo1	131.28 (5)
S2—Mo1—Mo2^v	55.53 (2)	Mo3^ix—S3—Mo1	82.72 (3)
Mo1^vi—Mo1—Mo2^v	91.004 (10)	Sc1—S3—Rb1	82.34 (3)
Mo1^v—Mo1—Mo2^v	62.117 (9)	Mo3—S3—Rb1	140.54 (4)
S4—Mo1—Mo2	116.20 (2)	Mo3^x—S3—Rb1	96.56 (3)
S1—Mo1—Mo2	54.77 (3)	Mo3^ix—S3—Rb1	140.41 (4)
S1^v—Mo1—Mo2	114.21 (3)	Mo1—S3—Rb1	84.64 (3)
S3—Mo1—Mo2	135.64 (3)	Mo1—S4—Mo1^vi	66.42 (4)
S2—Mo1—Mo2	54.68 (2)	Mo1—S4—Mo1^v	66.42 (4)
Mo1^vi—Mo1—Mo2	59.475 (9)	Mo1^vi—S4—Mo1^v	66.42 (4)
Mo1^v—Mo1—Mo2	89.484 (10)	Mo1^v—S4—Sc1	134.32 (5)
Mo2^v—Mo1—Mo2	59.014 (17)	Mo1—S4—Sc1^vi	134.32 (5)
S1—Mo2—S1^vii	116.58 (5)	Sc1—S4—Sc1^vi	116.48 (2)
S1—Mo2—S2	87.63 (3)	Sc1—S4—Sc1^v	116.48 (2)
S1^vii—Mo2—S2	95.52 (3)	Sc1^vi—S4—Sc1^v	116.48 (2)
S1—Mo2—S2^vi	95.52 (3)	Mo1—S4—Rb1^iv	140.77 (3)
S1^vii—Mo2—S2^vi	87.63 (3)	Mo1^vi—S4—Rb1^iv	140.77 (3)
S2—Mo2—S2^vi	174.03 (4)	Mo1^v—S4—Rb1^iv	140.77 (3)
S1—Mo2—Mo2^v	114.88 (3)	Mo3^xii—S5—Mo3	67.21 (4)
S1^vii—Mo2—Mo2^v	119.32 (2)	Mo3^xii—S5—Mo3^xi	67.21 (4)
S2—Mo2—Mo2^v	57.017 (19)	Mo3—S5—Mo3^xi	67.21 (4)
S2^vi—Mo2—Mo2^v	117.017 (19)	Mo3^xii—S5—Rb1^xiv	140.28 (3)
S1—Mo2—Mo2^vi	119.32 (2)	Mo3—S5—Rb1^xiv	140.28 (3)
S1^vii—Mo2—Mo2^vi	114.88 (3)	Mo3^xi—S5—Rb1^xiv	140.28 (3)
S2—Mo2—Mo2^vi	117.017 (19)

Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) −x+y−1/3, y+1/3, z−1/6; (iv) −x−1/3, −y+1/3, −z+1/3; (v) −x+y−1, −x, z; (vi) −y, x−y+1, z; (vii) x−y+1/3, −y+2/3, −z+1/6; (viii) −x−2/3, −x+y−1/3, −z+1/6; (ix) x−y−1/3, x+1/3, −z+1/3; (x) y−1/3, −x+y−2/3, −z+1/3; (xi) −x+y−1, −x−1, z; (xii) −y−1, x−y, z; (xiii) x−y−2/3, −y−1/3, −z+1/6; (xiv) −x+y−2/3, y−1/3, z+1/6.