An experimental (120 K) and theoretical electron-density study of KMnO₄ and KClO₄

The experimental electron density ρ(r) of the two isomorphic salts KMnO₄ and KClO₄ was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules was applied to ρ(r) and to its Laplacian ∇²ρ(r). The bonds were characterized using the topological parameters at the bond critical points of the density ρ(r), ∇²ρ(r), G(r) (kinetic energy density), V(r) (potential energy density) and H(r) (total energy density). According to the classification recently proposed by Espinosa, Alkorta, Elguero & Molins [J. Chem. Phys. (2002), 117, 5529–5542], the K—O and Cl—O bonds have a pure ionic and covalent character, respectively, while the Mn—O bonds show an intermediate behaviour. The results of the topological analysis of the experimental and theoretical (fully periodic Hartree–Fock and density functional calculations) electron density are in good agreement, even on a quantitative level. The atomic charges, determined by performing an integration over the topological basins, are about +2 e for Mn and Cl atoms. The ionic radius, estimated with the distance of the bond critical point from the nucleus, is in agreement with a charge of +2 e for the Mn atom.

Computing details

For both compounds, data collection: SMART; cell refinement: SAINT; data reduction: SAINT; program(s) used to refine structure: VALRAY (Stewart, Spackman, 1983).

Figures

(KMnO4)

Crystal data

?	Z = 4
Mr = ?	F(000) = 304
?, Pnma	Dx = 2.796 Mg m^−3
a = 9.0509 (7) Å	Mo Kα radiation, λ = 0.71073 Å
b = 5.6381 (4) Å	Cell parameters from 12606 reflections
c = 7.3582 (5) Å	θ = 2.3–46.7°
α = 90°	µ = 4.47 mm^−1
β = 90°	T = 120 K
γ = 90°	Prism, dark violet
V = 375.49 (5) Å^3	0.17 × 0.22 × 0.28 mm

Data collection

Siemens P4 with Apex detector diffractometer	1791 independent reflections
Radiation source: fine-focus sealed tube	1704 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.032
phiscan	θmax = 46.8°, θmin = 2.3°
Absorption correction: multi-scan ?	h = −11→11
Tmin = 0.833, Tmax = 1.000	k = −15→15
18417 measured reflections	l = −18→18

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
wR(F^2) = 0.018	Weighting scheme based on measured s.u.'s w = 1/σ2
S = 0.94	(Δ/σ)max = 0.01
1791 reflections	Extinction correction: isotropic
97 parameters	Extinction coefficient: 0.941

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

	x	y	z	Biso*/Beq
K	0.31877	0.250000	0.65798
Mn	0.43748	0.250000	0.19264
O1	0.3107	0.250000	0.0385
O2	0.5998	0.250000	0.1022
O3	0.41857	0.0164	0.3186

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K	0.01121	0.02346	0.01366	0.00000	−0.00015	0.00000
Mn	0.01008	0.01238	0.00980	0.00000	0.00009	0.00000
O1	0.0254	0.0277	0.0159	0.00000	−0.0110	0.00000
O2	0.0174	0.0365	0.0289	0.00000	0.0124	0.00000
O3	0.0191	0.0133	0.0196	−0.0004	−0.0019	−0.0050

Geometric parameters (Å, º)

K—O3	2.9643	K—O2^iv	2.755
K—O1^i	2.801	Mn—O1	1.613
K—O3^ii	2.8173	Mn—O2	1.613
K—O3^iii	2.8753	Mn—O3	1.6195
O3—K—O1^i	148.22	O3^ii—K—O3^iii	109.07
O3—K—O3^ii	63.74	O3^ii—K—O2^iv	130.50
O3—K—O3^iii	109.99	O3^iii—K—O2^iv	75.41
O3—K—O2^iv	68.53	O1—Mn—O2	110.95
O1^i—K—O3^ii	87.75	O1—Mn—O3	109.10
O1^i—K—O3^iii	64.51	O2—Mn—O3	109.42
O1^i—K—O2^iv	132.51	O3—Mn—O3^v	108.82

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

(KClO4)

Crystal data

?	Z = 4
Mr = ?	F(000) = 272
?, Pnma	Dx = 2.591 Mg m^−3
a = 8.7684 (3) Å	Mo Kα radiation, λ = 0.71073 Å
b = 5.6237 (2) Å	Cell parameters from 13489 reflections
c = 7.2039 (3) Å	θ = 2.3–45.6°
α = 90°	µ = 2.09 mm^−1
β = 90°	T = 120 K
γ = 90°	Prism, incolor
V = 355.23 (2) Å^3	0.22 × 0.30 × 0.34 mm

Data collection

Siemens P4 with Apex detector diffractometer	1604 independent reflections
Radiation source: fine-focus sealed tube	1518 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.025
phiscan	θmax = 45.6°, θmin = 2.3°
Absorption correction: multi-scan ?	h = −17→17
Tmin = 0.865, Tmax = 1.000	k = −9→11
15985 measured reflections	l = −14→12

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
wR(F^2) = 0.015	Weighting scheme based on measured s.u.'s w = 1/σ2
S = 1.02	(Δ/σ)max = 0.01
1604 reflections	Extinction correction: isotropic
92 parameters	Extinction coefficient: 0.846

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

	x	y	z	Biso*/Beq
K	0.31965	0.250000	0.66139
Cl	0.43049	0.250000	0.18838
O1	0.3060	0.250000	0.0571
O2	0.5746	0.250000	0.0939
O3	0.41911	0.0406	0.3056

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K	0.01024	0.01461	0.01239	0.00000	−0.00033	0.00000
Cl	0.00852	0.00966	0.00890	0.00000	0.00012	0.00000
O1	0.0127	0.0241	0.0207	0.00000	−0.0082	0.00000
O2	0.0152	0.0180	0.0125	0.00000	−0.0057	0.00000
O3	0.0159	0.0112	0.0144	−0.0001	−0.0012	0.0036

Geometric parameters (Å, º)

K—O3	2.9525	K—O2^iv	2.829
K—O1^i	2.853	Cl—O1	1.4445
K—O3^ii	2.8239	Cl—O2	1.435
K—O3^iii	2.8518	Cl—O3	1.4524
O3—K—O1^i	151.62	O3^ii—K—O3^iii	103.48
O3—K—O3^ii	66.59	O3^ii—K—O2^iv	132.15
O3—K—O3^iii	107.73	O3^iii—K—O2^iv	71.28
O3—K—O2^iv	70.12	O1—Cl—O2	110.79
O1^i—K—O3^ii	87.13	O1—Cl—O3	109.19
O1^i—K—O3^iii	66.75	O2—Cl—O3	109.64
O1^i—K—O2^iv	128.15	O3—Cl—O3^v	108.34

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