Modeling of the nuclear parameters for H atoms in X-ray charge-density studies

Extensive and precise X-ray diffraction data for xylitol have been used to test different approaches to estimate nuclear parameters for H atoms in charge-density studies. The parameters from a neutron diffraction study of the same compound were taken as a reference. The resulting static charge densities obtained for the different approaches based on a multipole model were subjected to a topological analysis. The comparative analysis led to the following results. The procedure of extending the X-H bond to match bond lengths from neutron diffraction studies provides the best agreement with the neutron positional parameters. An isotropic model for the atomic displacements of H atoms is highly unsatisfactory and leads to significant deviations for the properties of the bond critical points including those that only involve non-H atoms. Anisotropic displacement parameters for H atoms can be derived from the X-ray data that are in agreement with the values from the neutron study, and the resulting charge-density models are in good agreement with the reference model. The anisotropic displacement parameters for H atoms are derived from the X-ray data as a sum of the external (rigid-body) and internal vibrations. The external vibrations are obtained from a TLS analysis of the ADPs of the non-H atoms and the internal vibrations from analysis of neutron diffraction studies of related compounds. The results from the analysis of positional and thermal parameters were combined to devise a `best anisotropic' model, which was employed for three other systems where X-ray and neutron data were available. The results from the topological analysis of these systems confirm the success of the `best anisotropic' model in providing parameters for the H atoms that give charge densities in agreement with the reference models based on H-atom parameters derived from neutron diffraction.

Computing details

Data collection: Enraf-Nonius Express; cell refinement: Enraf-Nonius Express; data reduction: DREADD (Blessing, 1987); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: VALRAY (Stewart, 1998).

(xylitol-multipole-model)

Crystal data

C5H12O5	Dx = 1.540 Mg m^−3
Mr = 152.15	Melting point: 366 K
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
a = 8.264 (4) Å	Cell parameters from 20 reflections
b = 8.901 (2) Å	µ = 0.14 mm^−1
c = 8.9223 (14) Å	T = 122 K
V = 656.3 (4) Å^3	Prism, colourless
Z = 4	0.37 × 0.32 × 0.26 mm
F(000) = 328

Data collection

Enraf Nonius CAD4 diffractometer	θmax = 51.4°, θmin = 3.2°
Radiation source: fine-focus sealed tube	h = −18→18
Graphite monochromator	k = −19→19
ω 2θ scans	l = −19→19
33102 measured reflections	5 standard reflections every 100 reflections
7320 independent reflections	intensity decay: 10.4%
6651 reflections with I > 2σ(I)

Refinement

Refinement on F^2	H-atom parameters not refined
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.013	(Δ/σ)max = 0.0001
S = 0.65	Δρmax = 0.16 (6) e Å^−3
7320 reflections	Δρmin = −0.15 (6) e Å^−3
366 parameters	Extinction correction: Becker-Coppens
0 restraints	Extinction coefficient: 3931 (118)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
Secondary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.0 (2)
Hydrogen site location: from neutron diffraction study

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.

Refinement. NOTICE: Multipole refinement using VALRAY (Stewart et al., 2000). 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
O1	0.67854 (2)	0.22878 (2)	0.42170 (2)	0.0 (1)
O2	0.61485 (2)	0.43608 (2)	0.18251 (2)	0.0 (1)
O3	0.31808 (2)	0.43113 (2)	0.04008 (1)	0.0 (1)
O4	0.22908 (2)	0.12952 (2)	0.10845 (2)	0.0 (1)
O5	−0.08877 (2)	0.20499 (2)	0.21617 (2)	0.0 (1)
C1	0.52462 (1)	0.29375 (2)	0.39061 (1)	0.0 (1)
C2	0.50069 (1)	0.32292 (1)	0.22441 (1)	0.0 (1)
C3	0.32769 (1)	0.37544 (1)	0.18985 (1)	0.0 (1)
C4	0.20082 (1)	0.25170 (1)	0.21004 (1)	0.0 (1)
C5	0.03183 (1)	0.31477 (2)	0.18557 (2)	0.0 (1)
H1A	0.51269 (1)	0.40156 (1)	0.45202 (1)	0.0 (1)
H1B	0.43176 (1)	0.21677 (1)	0.43329 (1)	0.0 (1)
H2	0.52623 (1)	0.21900 (1)	0.16109 (1)	0.0 (1)
H3	0.29794 (1)	0.46794 (1)	0.26822 (1)	0.0 (1)
H4	0.20730 (1)	0.20947 (1)	0.32600 (1)	0.0 (1)
H5B	0.01970 (1)	0.35648 (1)	0.06950 (1)	0.0 (1)
H5A	0.01310 (1)	0.41026 (1)	0.26178 (1)	0.0 (1)
H11	0.75601 (1)	0.24315 (1)	0.33761 (1)	0.0 (1)
H12	0.65213 (1)	0.41634 (1)	0.08046 (1)	0.0 (1)
H13	0.32675 (1)	0.54153 (1)	0.04502 (1)	0.0 (1)
H14	0.27659 (1)	0.04897 (1)	0.16671 (1)	0.0 (1)
H15	−0.11834 (1)	0.15675 (1)	0.12088 (1)	0.0 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.00946 (5)	0.01627 (4)	0.00997 (4)	0.00067 (4)	−0.00081 (5)	0.00064 (4)
O2	0.01079 (4)	0.01418 (4)	0.01141 (4)	−0.00311 (4)	0.00084 (4)	−0.00058 (4)
O3	0.01331 (4)	0.01242 (4)	0.00941 (4)	0.00055 (3)	−0.00058 (4)	0.00053 (3)
O4	0.01202 (4)	0.01104 (4)	0.01144 (4)	0.00173 (4)	−0.00160 (4)	−0.00167 (4)
O5	0.00921 (5)	0.01774 (4)	0.01281 (4)	−0.00177 (4)	0.00148 (5)	−0.00174 (4)
C1	0.00931 (5)	0.01576 (4)	0.00890 (4)	0.00041 (4)	0.00020 (5)	−0.00037 (4)
C2	0.00833 (4)	0.01155 (3)	0.00866 (3)	−0.00036 (3)	−0.00018 (4)	−0.00099 (3)
C3	0.00876 (4)	0.01118 (3)	0.00882 (3)	0.00024 (3)	−0.00016 (4)	−0.00102 (3)
C4	0.00827 (4)	0.01189 (4)	0.00879 (4)	0.00019 (3)	−0.00029 (4)	−0.00056 (3)
C5	0.00872 (4)	0.01276 (5)	0.01514 (5)	0.00085 (4)	−0.00010 (4)	−0.00149 (4)
H1A	0.0336 (8)	0.0274 (7)	0.0264 (8)	0.0081 (7)	−0.0024 (9)	−0.0112 (8)
H1B	0.0205 (7)	0.0399 (7)	0.0283 (6)	−0.0070 (8)	0.00175 (1)	0.0123 (8)
H2	0.0210 (6)	0.0202 (6)	0.0264 (6)	0.0012 (7)	0.0011 (7)	−0.0072 (8)
H3	0.0247 (7)	0.0196 (6)	0.0224 (6)	0.0023 (5)	−0.0004 (6)	−0.0066 (7)
H4	0.0250 (7)	0.0287 (6)	0.0160 (6)	−0.0004 (5)	−0.0008 (8)	0.0049 (6)
H5B	0.0248 (7)	0.0325 (7)	0.0285 (7)	−0.0002 (7)	−0.0053 (9)	0.0112 (8)
H5A	0.0261 (8)	0.0267 (7)	0.0478 (8)	0.0024 (8)	0.0038 (8)	−0.01806 (13)
H11	0.0181 (6)	0.0317 (6)	0.0213 (6)	−0.0012 (7)	0.0045 (8)	0.0034 (7)
H12	0.0286 (8)	0.0302 (7)	0.0219 (7)	−0.0047 (7)	0.0071 (8)	−0.0019 (8)
H13	0.0318 (8)	0.0176 (6)	0.0228 (7)	−0.0010 (6)	0.0010 (6)	0.0023 (7)
H14	0.0334 (9)	0.0195 (7)	0.0278 (7)	0.0086 (6)	−0.0030 (7)	0.0014 (8)
H15	0.0275 (8)	0.0279 (7)	0.0226 (6)	−0.0064 (7)	0.0002 (8)	−0.0070 (7)