Crystal structure, electronic structure, and optical properties of the novel Li₄CdGe₂S₇, a wide-bandgap quaternary sulfide with a polar structure derived from lonsdaleite

The novel quaternary thio­germanate Li₄CdGe₂S₇ (tetra­lithium cadmium di­ger­manium hepta­sulfide) was discovered from a solid-state reaction at 750 °C. Single-crystal X-ray diffraction data were collected and used to solve and refine the structure. Li₄CdGe₂S₇ is a member of the small, but growing, class of I₄–II–IV₂–VI₇ diamond-like materials. The com­pound adopts the Cu₅Si₂S₇ structure type, which is a derivative of lonsdaleite. Crystallizing in the polar space group Cc, Li₄CdGe₂S₇ contains 14 crystallographically unique ions, all residing on general positions. Like all diamond-like structures, the com­pound is built of corner-sharing tetra­hedral units that create a relatively dense three-dimensional assembly. The title com­pound is the major phase of the reaction product, as evidenced by powder X-ray diffraction and optical diffuse reflectance spectroscopy. While the com­pound exhibits a second-harmonic generation (SHG) response com­parable to that of the AgGaS₂ (AGS) reference material in the IR region, its laser-induced damage threshold (LIDT) is over an order of magnitude greater than AGS for λ = 1.064 µm and τ = 30 ps. Bond valence sums, global instability index, minimum bounding ellipsoid (MBE) analysis, and electronic structure calculations using density functional theory (DFT) were used to further evaluate the crystal structure and electronic structure of the com­pound and provide a com­parison with the analogous I₂–II–IV–VI₄ dia­mond-like com­pound Li₂CdGeS₄. Li₄CdGe₂S₇ appears to be a better IR nonlinear optical (NLO) candidate than Li₂CdGeS₄ and one of the most promising contenders to date. The exceptional LIDT is likely due, at least in part, to the wider optical bandgap of ∼3.6 eV.

Computing details

Data collection: APEX2 (Bruker, 2010); cell refinement: SMART (Bruker, 2010); data reduction: SMART (Bruker, 2010); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015b); molecular graphics: CrystalMaker (Palmer, 2019); software used to prepare material for publication: SHELXL2018 (Sheldrick, 2015b).

Tetralithium cadmium digermanium heptasulfide

Crystal data

Li4CdGe2S7	F(000) = 944
Mr = 509.76	Dx = 2.926 Mg m^−3
Monoclinic, Cc	Mo Kα radiation, λ = 0.71073 Å
a = 16.8354 (10) Å	Cell parameters from 7524 reflections
b = 6.7870 (4) Å	θ = 2.4–33.0°
c = 10.1499 (6) Å	µ = 8.18 mm^−1
β = 93.710 (3)°	T = 293 K
V = 1157.32 (12) Å^3	Polyhedra, colourless
Z = 4	0.21 × 0.12 × 0.11 mm

Data collection

Bruker SMART APEXII diffractometer	2612 reflections with I > 2σ(I)
φ and ω scan	Rint = 0.017
Absorption correction: multi-scan (SADABS; Sheldrick, 2002)	θmax = 27.5°, θmin = 2.4°
Tmin = 0.549, Tmax = 0.747	h = −21→21
7415 measured reflections	k = −8→8
2634 independent reflections	l = −13→13

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0097P)^2 + 0.0293P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.010	Δρmax = 0.27 e Å^−3
wR(F^2) = 0.024	Δρmin = −0.21 e Å^−3
S = 1.08	Extinction correction: SHELXL2018 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
2634 reflections	Extinction coefficient: 0.00183 (7)
129 parameters	Absolute structure: Refined as an inversion twin.
2 restraints	Absolute structure parameter: 0.001 (5)

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. Refined as a 2-component inversion twin.

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

	x	y	z	Uiso*/Ueq
Li1	0.3309 (6)	0.1842 (15)	0.5012 (10)	0.0224 (18)
Li2	0.1207 (8)	0.3276 (14)	0.4190 (13)	0.025 (2)
Li3	0.9764 (7)	0.3297 (11)	0.7180 (11)	0.0199 (19)
Li4	0.7674 (6)	0.1619 (14)	0.6423 (10)	0.025 (2)
Cd	0.54849 (2)	0.36329 (3)	0.56327 (4)	0.01770 (6)
Ge1	0.40538 (2)	0.33494 (7)	0.84280 (2)	0.01042 (11)
Ge2	0.19465 (2)	0.17688 (7)	0.77467 (2)	0.01045 (10)
S1	0.50089 (4)	0.29460 (12)	0.00091 (8)	0.01425 (15)
S2	0.43895 (5)	0.16838 (12)	0.66829 (7)	0.01398 (16)
S3	0.37399 (5)	0.35832 (12)	0.31017 (8)	0.01570 (17)
S4	0.30151 (5)	0.16992 (11)	0.92654 (7)	0.01258 (16)
S5	0.22120 (5)	0.33369 (13)	0.59790 (8)	0.01651 (18)
S6	0.66610 (5)	0.36507 (11)	0.73450 (8)	0.01491 (16)
S7	0.09614 (4)	0.32632 (13)	0.86708 (8)	0.01446 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li1	0.022 (4)	0.025 (4)	0.021 (3)	−0.001 (3)	0.006 (3)	−0.001 (3)
Li2	0.028 (4)	0.021 (4)	0.025 (4)	−0.002 (3)	0.000 (3)	0.001 (3)
Li3	0.021 (3)	0.023 (4)	0.016 (4)	0.000 (3)	0.004 (3)	0.002 (3)
Li4	0.026 (4)	0.025 (4)	0.024 (4)	0.003 (3)	−0.003 (3)	−0.001 (3)
Cd	0.01709 (9)	0.01891 (11)	0.01720 (9)	0.00053 (13)	0.00176 (6)	0.00054 (13)
Ge1	0.00954 (19)	0.0111 (2)	0.01056 (18)	−0.00010 (12)	0.00062 (14)	−0.00022 (12)
Ge2	0.00921 (18)	0.01191 (19)	0.01018 (18)	−0.00051 (13)	0.00025 (13)	−0.00008 (13)
S1	0.0124 (3)	0.0164 (4)	0.0135 (3)	−0.0005 (3)	−0.0020 (2)	0.0005 (3)
S2	0.0160 (3)	0.0138 (4)	0.0124 (3)	−0.0002 (3)	0.0032 (3)	−0.0021 (3)
S3	0.0179 (4)	0.0117 (4)	0.0175 (4)	−0.0012 (3)	0.0018 (3)	−0.0008 (3)
S4	0.0098 (3)	0.0163 (4)	0.0115 (3)	−0.0024 (3)	−0.0002 (3)	0.0023 (3)
S5	0.0173 (4)	0.0203 (4)	0.0120 (4)	−0.0021 (3)	0.0011 (3)	0.0036 (3)
S6	0.0150 (4)	0.0124 (4)	0.0171 (3)	−0.0010 (3)	−0.0013 (3)	−0.0017 (3)
S7	0.0130 (4)	0.0146 (4)	0.0161 (3)	0.0020 (3)	0.0035 (3)	−0.0005 (3)

Geometric parameters (Å, º)

Li1—S5	2.374 (10)	Li4—S6	2.428 (10)
Li1—S2	2.408 (10)	Li4—S4^ix	2.567 (11)
Li1—S3	2.421 (10)	Cd—S1^x	2.5235 (8)
Li1—S4^i	2.559 (10)	Cd—S7^ix	2.5441 (9)
Li2—S1^ii	2.380 (13)	Cd—S6	2.5487 (10)
Li2—S5	2.401 (13)	Cd—S2	2.5576 (9)
Li2—S7^iii	2.437 (10)	Ge1—S3^x	2.1680 (8)
Li2—S6^iv	2.447 (12)	Ge1—S2	2.2055 (9)
Li3—S3^v	2.385 (10)	Ge1—S1^xi	2.2141 (8)
Li3—S1^v	2.420 (12)	Ge1—S4	2.2862 (8)
Li3—S2^vi	2.428 (7)	Ge2—S5	2.1577 (8)
Li3—S7^vii	2.440 (12)	Ge2—S6^xii	2.2024 (10)
Li4—S5^viii	2.393 (9)	Ge2—S7	2.2045 (8)
Li4—S3^v	2.397 (10)	Ge2—S4	2.2926 (9)
S5—Li1—S2	107.5 (4)	Ge1^xiii—S1—Li2^ix	112.5 (3)
S5—Li1—S3	113.8 (4)	Ge1^xiii—S1—Li3^iv	123.0 (3)
S2—Li1—S3	109.5 (4)	Li2^ix—S1—Li3^iv	113.2 (4)
S5—Li1—S4^i	112.5 (4)	Ge1^xiii—S1—Cd^iii	105.78 (3)
S2—Li1—S4^i	106.8 (4)	Li2^ix—S1—Cd^iii	98.4 (3)
S3—Li1—S4^i	106.5 (4)	Li3^iv—S1—Cd^iii	99.34 (19)
S1^ii—Li2—S5	108.3 (5)	Ge1—S2—Li1	108.8 (2)
S1^ii—Li2—S7^iii	106.0 (5)	Ge1—S2—Li3^xii	113.3 (3)
S5—Li2—S7^iii	104.4 (4)	Li1—S2—Li3^xii	111.3 (4)
S1^ii—Li2—S6^iv	113.2 (4)	Ge1—S2—Cd	107.38 (3)
S5—Li2—S6^iv	110.4 (5)	Li1—S2—Cd	102.5 (2)
S7^iii—Li2—S6^iv	114.0 (5)	Li3^xii—S2—Cd	113.0 (3)
S3^v—Li3—S1^v	109.9 (4)	Ge1^iii—S3—Li3^iv	113.5 (2)
S3^v—Li3—S2^vi	113.8 (5)	Ge1^iii—S3—Li4^iv	109.1 (2)
S1^v—Li3—S2^vi	101.4 (3)	Li3^iv—S3—Li4^iv	102.6 (4)
S3^v—Li3—S7^vii	110.0 (4)	Ge1^iii—S3—Li1	115.4 (2)
S1^v—Li3—S7^vii	112.3 (5)	Li3^iv—S3—Li1	108.3 (3)
S2^vi—Li3—S7^vii	109.3 (4)	Li4^iv—S3—Li1	107.0 (4)
S5^viii—Li4—S3^v	107.5 (4)	Ge1—S4—Ge2	109.01 (3)
S5^viii—Li4—S6	111.9 (4)	Ge1—S4—Li1^xiv	115.6 (2)
S3^v—Li4—S6	105.7 (4)	Ge2—S4—Li1^xiv	110.3 (2)
S5^viii—Li4—S4^ix	110.0 (4)	Ge1—S4—Li4^ii	108.5 (2)
S3^v—Li4—S4^ix	115.7 (4)	Ge2—S4—Li4^ii	110.8 (2)
S6—Li4—S4^ix	106.1 (3)	Li1^xiv—S4—Li4^ii	102.4 (4)
S1^x—Cd—S7^ix	112.35 (3)	Ge2—S5—Li1	110.0 (2)
S1^x—Cd—S6	112.75 (3)	Ge2—S5—Li4^xv	112.6 (3)
S7^ix—Cd—S6	105.41 (3)	Li1—S5—Li4^xv	102.9 (4)
S1^x—Cd—S2	110.77 (3)	Ge2—S5—Li2	116.5 (3)
S7^ix—Cd—S2	109.70 (2)	Li1—S5—Li2	102.1 (4)
S6—Cd—S2	105.52 (3)	Li4^xv—S5—Li2	111.3 (3)
S3^x—Ge1—S2	116.24 (3)	Ge2^vi—S6—Li4	117.8 (2)
S3^x—Ge1—S1^xi	112.82 (3)	Ge2^vi—S6—Li2^v	116.6 (2)
S2—Ge1—S1^xi	107.87 (3)	Li4—S6—Li2^v	104.7 (3)
S3^x—Ge1—S4	110.03 (3)	Ge2^vi—S6—Cd	106.34 (3)
S2—Ge1—S4	106.82 (3)	Li4—S6—Cd	105.6 (2)
S1^xi—Ge1—S4	101.95 (3)	Li2^v—S6—Cd	104.6 (3)
S5—Ge2—S6^xii	111.99 (3)	Ge2—S7—Li2^x	114.4 (3)
S5—Ge2—S7	109.20 (3)	Ge2—S7—Li3^xvi	110.8 (3)
S6^xii—Ge2—S7	111.08 (3)	Li2^x—S7—Li3^xvi	104.3 (4)
S5—Ge2—S4	111.93 (3)	Ge2—S7—Cd^ii	112.60 (3)
S6^xii—Ge2—S4	104.90 (3)	Li2^x—S7—Cd^ii	112.1 (3)
S7—Ge2—S4	107.62 (3)	Li3^xvi—S7—Cd^ii	101.6 (2)

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