Anharmonicity of potentials of atoms in potassium hydrogensulfide (KDS) determined by neutron single-crystal diffraction

Potassium hydrogensulfide (KHS) is an ionic compound with an anionic molecular group HS. The fast reorientational disorder of the anions was determined for the ambient temperature modification [; Jeffrey (1974). Can. J. Phys. 52, 2370-2378]. Single crystals are available now as protonated or deuterated specimens. With neutron single-crystal diffraction at room temperature, a considerable anharmonicity of the atom potential of the H or D atoms was observed. Even the thermal motions of K and S atoms show small deviations from an isotropic probability density function, which can be modelled using anharmonic temperature factors. The temperature factors of the atoms were expanded into a Gram-Charlier series [Kuhs (1992). Acta Cryst. A48, 80-98] in order to evaluate the anharmonicity quantitatively. Parameters up to a fourth-order approximation are relevant for the D atoms. Results from neutron single-crystal diffraction are compared with split-atom models extracted from neutron powder diffraction patterns of fully deuterated samples.

S1. Comment

Single-crystal neutron diffraction has clearly shown, that the pdf of deuterium atoms in the hydrogensulfide of potassium is strongly anharmonic. This is due to the repulsive forces between cations and deuterium atoms, which influence the librational motion of the anions. A deviation from an isotropic pdf of sulfur and potassium atoms is visible in Fourier sections but cannot be quantified by the measurement.

Qualitative information about the anharmonicity of deuterium atoms in KDS was already obtained by powder diffraction data (Haarmann et al., 2000). Reflection profile decomposition using the Rietveld method is required to extract more quantitative information from powder data, but current computer programs do not include the Gram-Chalier series expansion.

Rather than powder diffraction, which is impaired by peak overlap, single-crystal diffraction yields unambiguous quantitative information about the density distribution.

S2. Experimental

Single crystals of the potassium and the rubidium compound can be synthesized by recrystallization of the samples from liquid ammonia at ambient temperature and 7 bar pressure of the solvent. Carefully handled glass containers were used to grow the crystals by slow evaporation of the solvent. The temperature was controlled by a thermostat during the process. For details see Haarmann, (2000). Protonated and deuterated crystals can be obtained by the choice of the solvent NH₃ or ND₃ respectively. Single-crystals of NaHS/DS are not available by this method. A reaction of the salt with the solvent gives NaNH₂ and NH₄HS as the main products.

S3. Refinement

The crystal structure, including the positions of deuterium was known (Jacobs et al., 1991). The data were analyzed and refined with the computer program package JANA98 (Petricek, V. & Dusek, M., 1998). A numerical correction for absorption was applied. For extinction correction an isotropic Zachariasen model with Gaussian mosaic spread was applied. The refinement of the g-value of extinction resulted in a value close to zero not significantly larger then its standard deviation. Therefore this correction has been dropped. Thermal diffuse scattering (TDS) corrections were not taken into account.

Computing details

(kds)

Crystal data

DKS	Dx = 1.692 Mg m^−3
Mr = 73.16	Neutron radiation, λ = 0.912 Å
Trigonal, R3m	Cell parameters from 110 reflections
Hall symbol: -R 3 2"	θ = 6–52°
a = 4.988 (3) Å	µ = 0.001887 mm^−1
c = 9.997 (7) Å	T = 298 K
V = 215.4 (3) Å^3	Rhombohedral, colourless
Z = 3	3.2 × 2.6 × 1.5 mm
F(000) = 39.684

Data collection

Four-circle diffractometer	Rint = 0.067
ω–2θ scans	θmax = 52.0°, θmin = 6.6°
Absorption correction: gaussian Petricek, and Dusek (1998)	h = −8→7
Tmin = 0.946, Tmax = 0.968	k = −7→8
659 measured reflections	l = −17→9
161 independent reflections	1 standard reflections every 20 reflections
100 reflections with > 3σ(I)	intensity decay: none

Refinement

Refinement on F	12 parameters
R[F^2 > 2σ(F^2)] = 0.058	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.031	(Δ/σ)max = 0.0001
S = 2.24	Δρmax = 0.76 e Å^−3
659 reflections	Δρmin = −0.91 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K	0	0	0	0.0406 (2)
S	0	0	0.5	0.0324 (2)
D	0	0	0.3735 (2)	0.1032 (7)	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
D	0.1207 (7)	0.1207 (7)	0.068 (2)	0.0604 (4)	0	0

Geometric parameters (Å, º)

K—D	2.9077 (3)	D—K^v	2.9077 (3)
K—D	2.9077 (3)	D—K^vi	2.9077 (3)
K—D	2.9077 (3)	D—K^vii	2.9077 (3)
K—D^i	2.9077 (3)	D—S	1.264 (2)
K—D^ii	2.9077 (3)	D—D^iv	2.529 (3)
K—D^iii	2.9077 (3)	D—D	2.9899 (7)
S—D	1.264 (2)	D—D	2.9899 (7)
S—D^iv	1.264 (2)	D—D	2.9899 (7)
D—K—D	118.12 (1)	K^v—D—D^iv	97.95 (4)
D—K—D	118.12 (1)	K^v—D—D	59.06 (1)
D—K—D^i	61.88 (1)	K^v—D—D	59.06 (1)
D—K—D^ii	61.88 (1)	K^v—D—D	156.46 (8)
D—K—D^iii	180	K^vi—D—K^v	118.12 (2)
D—K—D	118.12 (1)	K^vi—D—K^vii	118.12 (2)
D—K—D	118.12 (1)	K^vi—D—S	97.95 (4)
D—K—D^i	61.88 (1)	K^vi—D—D^iv	97.95 (4)
D—K—D^ii	180	K^vi—D—D	59.06 (1)
D—K—D^iii	61.88 (1)	K^vi—D—D	156.46 (8)
D—K—D	118.12 (1)	K^vi—D—D	59.06 (1)
D—K—D	118.12 (1)	K^vii—D—K^v	118.12 (2)
D—K—D^i	180	K^vii—D—K^vi	118.12 (2)
D—K—D^ii	61.88 (1)	K^vii—D—S	97.95 (4)
D—K—D^iii	61.88 (1)	K^vii—D—D^iv	97.95 (4)
D^i—K—D	61.88 (1)	K^vii—D—D	156.46 (8)
D^i—K—D	61.88 (1)	K^vii—D—D	59.06 (1)
D^i—K—D	180	K^vii—D—D	59.06 (1)
D^i—K—D^ii	118.12 (1)	S—D—D^iv	0
D^i—K—D^iii	118.12 (1)	S—D—D	105.60 (5)
D^ii—K—D	61.88 (1)	S—D—D	105.60 (5)
D^ii—K—D	180	S—D—D	105.60 (5)
D^ii—K—D	61.88 (1)	D^iv—D—D	105.60 (5)
D^ii—K—D^i	118.12 (1)	D^iv—D—D	105.60 (5)
D^ii—K—D^iii	118.12 (1)	D^iv—D—D	105.60 (5)
D^iii—K—D	180	D—D—D^iv	105.60 (5)
D^iii—K—D	61.88 (1)	D—D—D	113.05 (4)
D^iii—K—D	61.88 (1)	D—D—D	113.05 (4)
D^iii—K—D^i	118.12 (1)	D—D—D^iv	105.60 (5)
D^iii—K—D^ii	118.12 (1)	D—D—D	113.05 (4)
D—S—D^iv	180	D—D—D	113.05 (4)
D^iv—S—D	180	D—D—D^iv	105.60 (5)
K^v—D—K^vi	118.12 (2)	D—D—D	113.05 (4)
K^v—D—K^vii	118.12 (2)	D—D—D	113.05 (4)
K^v—D—S	97.95 (4)

Symmetry codes: (i) x−2/3, y−1/3, z+2/3; (ii) x−2/3, y+2/3, z+2/3; (iii) x+1/3, y+2/3, z+2/3; (iv) −x, −y, −z+1; (v) −x−1/3, −y−2/3, −z+1/3; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3.