Location of the H atoms in ammonium persulphate by deuteron NMR. Verification by X-ray diffraction

It is demonstrated that H atoms can be located by the spectroscopic method of deuteron NMR. The requirement is that the `heavy-atom' positions are known from diffraction studies. The technique allows an accuracy of the order of 0.01 Å. The compound studied is ammonium persulphate (APS), (NH)SO. APS crystallizes in space group P2/ with lattice parameters  (2),  (3),  (3) Å and  (1)° at  K. In perdeuterated crystals of APS, only one of the deuterons of every ND ion becomes localized at low temperatures. Therefore, most of this work uses samples with 9% deuteration. In such crystals, most of the ammonium ions containing deuterons come in the form of NDH ions. At  K, the single deuteron of these ions becomes localized in one of four equilibrium sites. The deuteron site occupancies differ from each other and are measured at 17 K. The deuterons are located in three steps. (i) The deuteron quadrupole-coupling (QC) tensors are measured at 17 K. Their unique principal directions are identified, as is well justified, with the N-D bond directions. (ii) The fine structure of a deuteron NMR line is analyzed in terms of the magnetic dipole-dipole interactions between all nuclei in an NDH ion to obtain the N-D and D-H internuclear distances. (iii) An empirical relation between deuteron QC constants and DO distances in N-DO hydrogen bonds is exploited to assign the N-D bond vectors to the appropriate N atom of which there are four in the unit cell. The results are highly relevant for an understanding of the complex tunnelling and stochastic reorientation dynamics of the ammonium ions in APS. They are verified by a complementary X-ray diffraction study.

Computing details

Data collection: Collect Package, BRUKER NONIUS B.V. 1999; cell refinement: Collect Package, BRUKER NONIUS B.V. 1999; data reduction: Collect Package, BRUKER NONIUS B.V. 1999; program(s) used to solve structure: SHELXS97, Sheldrick 1990; program(s) used to refine structure: SHELXL97, Sheldrick 1997; molecular graphics: SCHAKAL 99, Keller 1999.

Figures

ammonium persulfate-d8

Crystal data

(SO4)2(NH4)2	F(000) = 236
Mr = 228.20	Dx = 2.016 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
a = 6.1340 (2) Å	Cell parameters from 786 reflections
b = 7.9324 (3) Å	θ = 1.0–27.9°
c = 7.7541 (3) Å	µ = 0.73 mm^−1
β = 94.966 (1)°	T = 118 K
V = 375.88 (2) Å^3	Fragment, colourless
Z = 2	0.32 × 0.20 × 0.20 mm

Data collection

NONIUS KappaCCD diffraktometer diffractometer	768 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.024
Graphite monochromator	θmax = 27.9°, θmin = 5.1°
phi– and ω scans	h = −8→8
1393 measured reflections	k = −10→10
791 independent reflections	l = −10→10

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)] = 0.028	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.069	Refined isotropic
S = 1.07	w = 1/[σ^2(Fo^2) + (0.0151P)^2 + 0.2285P] where P = (Fo^2 + 2Fc^2)/3
791 reflections	(Δ/σ)max = 0.002
71 parameters	Δρmax = 0.25 e Å^−3
0 restraints	Δρmin = −0.30 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s 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 > σ(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
S1	0.21386 (5)	0.85461 (4)	0.63745 (4)	0.01348 (16)
O3	0.11829 (13)	1.01867 (13)	0.52348 (13)	0.0213 (3)
O1	0.18431 (17)	0.71093 (13)	0.52550 (13)	0.0242 (3)
O4	0.08329 (16)	0.84816 (12)	0.78417 (12)	0.0191 (2)
O2	0.43508 (14)	0.91084 (13)	0.67523 (13)	0.0198 (2)
N1	0.2287 (2)	0.88530 (17)	0.14819 (16)	0.0172 (3)
D1	0.217 (4)	0.862 (2)	0.042 (3)	0.036 (6)*
D2	0.352 (4)	0.908 (3)	0.182 (3)	0.036 (5)*
D3	0.191 (4)	0.798 (3)	0.196 (3)	0.048 (7)*
D4	0.143 (3)	0.963 (3)	0.169 (2)	0.022 (4)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
S1	0.0126 (2)	0.0144 (2)	0.0133 (2)	0.00095 (10)	0.00006 (13)	−0.00041 (10)
O3	0.0098 (5)	0.0242 (5)	0.0285 (6)	−0.0041 (4)	−0.0056 (4)	0.0105 (4)
O1	0.0247 (5)	0.0233 (6)	0.0247 (5)	−0.0002 (4)	0.0030 (4)	−0.0107 (4)
O4	0.0188 (5)	0.0248 (5)	0.0141 (5)	0.0022 (4)	0.0028 (4)	0.0008 (3)
O2	0.0130 (4)	0.0217 (5)	0.0239 (5)	0.0003 (4)	−0.0028 (4)	0.0016 (4)
N1	0.0161 (6)	0.0173 (6)	0.0181 (6)	0.0005 (4)	0.0002 (5)	−0.0002 (4)

Geometric parameters (Å, º)

S1—O2	1.4344 (9)	N1—D1	0.84 (2)
S1—O1	1.4346 (10)	N1—D2	0.80 (2)
S1—O4	1.4478 (10)	N1—D3	0.83 (3)
S1—O3	1.6518 (10)	N1—D4	0.84 (2)
O3—O3^i	1.4949 (17)
O2—S1—O1	116.00 (6)	D1—N1—D2	112 (2)
O2—S1—O4	115.36 (6)	D1—N1—D3	104 (2)
O1—S1—O4	113.45 (6)	D2—N1—D3	110 (2)
O2—S1—O3	98.62 (5)	D1—N1—D4	110.0 (19)
O1—S1—O3	106.37 (6)	D2—N1—D4	111.2 (19)
O4—S1—O3	104.68 (5)	D3—N1—D4	109 (2)
O3^i—O3—S1	105.44 (9)
O2—S1—O3—O3^i	−178.60 (10)	O4—S1—O3—O3^i	−59.42 (11)
O1—S1—O3—O3^i	60.96 (11)

Symmetry code: (i) −x, −y+2, −z+1.