A neutron diffraction study of xylitol: derivation of mean square internal vibrations for H atoms from a rigid-body description

Madsen, A.Ø.; Mason, S.; Larsen, S.

doi:10.1107/S010876810301557X

A neutron diffraction study of xylitol: derivation of mean square internal vibrations for H atoms from a rigid-body description

A neutron diffraction study of xylitol (C₅O₅H₁₂) is presented. The nuclear anisotropic displacement parameters have been analysed showing that the carbon-oxygen skeleton conforms to a rigid-body (TLS) description. Applying this TLS model to the xylitol H atoms allows characterization of the internal molecular displacements of the H nuclei, assuming that the observed H nuclear mean-square displacements are a sum of the internal displacements and rigid-body displacements. These internal molecular displacements are very similar for chemically equivalent H atoms and in good agreement with the values obtained by other methods. In all cases the smallest eigenvector of the residual mean-square displacement tensor is almost parallel to the X-H bond. The use of ab initio calculations to obtain the internal vibrations in xylitol is discouraging. Another 12 structures extracted from the literature which have been investigated by neutron diffraction were subjected to a similar analysis. The results for the nine compounds investigated at low temperature conform to the results from xylitol and provide estimates of the internal vibrations of H atoms in a range of chemical environments.

Keywords: neutron diffraction; internal vibrations; rigid-body description.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S010876810301557X/bs5000sup1.cif Contains datablocks global, anders
	Portable Document Format (PDF) file https://doi.org/10.1107/S010876810301557X/bs5000sup2.pdf Supplementary material
	Structure factor file (CIF format) https://doi.org/10.1107/S010876810301557X/bs5000sup3.hkl Contains datablock anders

CCDC reference: 223330

Computing details top

Cell refinement: rafd9; data reduction: racer; program(s) used to solve structure: SHELXL; program(s) used to refine structure: VALRAY (Stewart et al., 2000); molecular graphics: ORTEP; software used to prepare material for publication: PLATON (Spek, 1990).

Figures top

(anders) top

Crystal data top

C₅H₁₂O₅	D_x = 1.540 Mg m⁻³
M_r = 152.15	Melting point = 93–94.9 K
Orthorhombic, P2₁2₁2₁	Neutron radiation, λ = 0.83950 Å
Hall symbol: P 2ac 2ab	Cell parameters from 2917 reflections
a = 8.2660 (4) Å	θ = 3.8–45.3°
b = 8.8977 (4) Å	µ = 0.27 mm⁻¹
c = 8.9116 (4) Å	T = 122 K
V = 655.43 (5) Å³	Prism, colourless
Z = 4	2.5 × 2.0 × 0.9 mm
F(000) = 328

Data collection top

Four-circle diffractometer	R_int = 0.041
Cu 220 transmission geometry monochromator	θ_max = 45.3°, θ_min = 3.8°
%T Coupled ${\w}–x\q$–scans with scan width between 1.2 and 4.5$^{^χ^{irc}$ and $1}^λ^{eq x}^λ^{eq 2$.}	h = ⁻¹³^→³
Absorption correction: integration datap	k = ⁻³^→¹⁵
T_min = 0.132, T_max = 0.223	l = ⁻¹⁵^→¹⁰
2917 measured reflections	2 standard reflections every 100 reflections
1911 independent reflections	intensity decay: none
1831 reflections with I > 2^σ^(I)

Refinement top

Refinement on F²	Hydrogen site location: structure-invariant direct methods
Least-squares matrix: full	All H-atom parameters refined
wR(F²) = 0.054	Weighting scheme based on measured s.u.'s w = 1/σ²(F_o²)
S = 1.47	(Δ/σ)_max < 0.001
1911 reflections	Δρ_max = 1.81 e Å⁻³
200 parameters	Δρ_min = −1.23 e Å⁻³
0 restraints	Extinction correction: Becker-Coppens type 1 isotropic Lorentzian., Spackman, M. A.. (1987), Journal of Applied Crystallography, 20:256-258
0 constraints	Extinction coefficient: 12892 (154)
Primary atom site location: structure-invariant direct methods

Crystal data top

C₅H₁₂O₅	V = 655.43 (5) Å³
M_r = 152.15	Z = 4
Orthorhombic, P2₁2₁2₁	Neutron radiation, λ = 0.83950 Å
a = 8.2660 (4) Å	µ = 0.27 mm⁻¹
b = 8.8977 (4) Å	T = 122 K
c = 8.9116 (4) Å	2.5 × 2.0 × 0.9 mm

Data collection top

Four-circle diffractometer	1831 reflections with I > 2σ(I)
Absorption correction: integration datap	R_int = 0.041
T_min = 0.132, T_max = 0.223	2 standard reflections every 100 reflections
2917 measured reflections	intensity decay: none
1911 independent reflections

Refinement top

wR(F²) = 0.054	0 restraints
S = 1.47	All H-atom parameters refined
1911 reflections	Δρ_max = 1.81 e Å⁻³
200 parameters	Δρ_min = −1.23 e Å⁻³

Special details top

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All e.s.d.'s are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement on F^{2 for ALL reflections. Weighted R-factors wR and all goodnesses of fit S are based on F}2, conventional R-factors R are based on F, with F set to zero for negative F^2.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
O1	0.67826 (10)	0.22884 (10)	0.42178 (9)	0.0099 (2)
O2	0.61461 (10)	0.43594 (10)	0.18273 (10)	0.0100 (2)
O3	0.31823 (11)	0.43108 (10)	0.04011 (10)	0.0096 (2)
O4	0.22887 (10)	0.12960 (10)	0.10839 (10)	0.0096 (2)
O5	−0.08866 (10)	0.20517 (11)	0.21646 (10)	0.0114 (2)
C1	0.52470 (9)	0.29389 (9)	0.39045 (8)	0.0092 (1)
C2	0.50050 (8)	0.32283 (8)	0.22439 (7)	0.0074 (1)
C3	0.32774 (8)	0.37534 (8)	0.18980 (8)	0.0078 (1)
C4	0.20081 (8)	0.25179 (8)	0.20983 (8)	0.0075 (1)
C5	0.03186 (8)	0.31486 (9)	0.18585 (9)	0.0101 (2)
H1A	0.5127 (3)	0.4016 (2)	0.4520 (2)	0.0271 (5)
H1B	0.4318 (2)	0.2168 (3)	0.4333 (2)	0.0275 (5)
H2	0.5262 (2)	0.2190 (2)	0.1611 (2)	0.0205 (4)
H3	0.2979 (2)	0.46794 (19)	0.26822 (19)	0.0201 (4)
H4	0.2073 (2)	0.2095 (2)	0.32600 (18)	0.0212 (4)
H5A	0.0131 (3)	0.4103 (2)	0.2618 (3)	0.0314 (5)
H5B	0.0197 (2)	0.3565 (2)	0.0695 (2)	0.0265 (5)
H11	0.7560 (2)	0.2432 (2)	0.3376 (2)	0.0216 (4)
H12	0.6521 (2)	0.4163 (2)	0.0805 (2)	0.0249 (5)
H13	0.3268 (2)	0.54153 (19)	0.0450 (2)	0.0220 (4)
H14	0.2766 (2)	0.0490 (2)	0.1667 (2)	0.0248 (4)
H15	−0.1183 (2)	0.1567 (2)	0.1209 (2)	0.0240 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0086 (3)	0.0138 (4)	0.0073 (3)	0.0010 (3)	−0.0003 (3)	0.0003 (3)
O2	0.0097 (3)	0.0118 (3)	0.0086 (3)	−0.0032 (3)	−0.0003 (3)	−0.0007 (3)
O3	0.0119 (3)	0.0103 (3)	0.0065 (3)	0.0004 (3)	−0.0001 (3)	0.0006 (3)
O4	0.0101 (3)	0.0091 (3)	0.0097 (3)	0.0016 (3)	−0.0020 (3)	−0.0015 (3)
O5	0.0080 (3)	0.0154 (4)	0.0108 (3)	−0.0015 (3)	0.0016 (3)	−0.0016 (3)
C1	0.0079 (2)	0.0128 (3)	0.0068 (2)	0.0002 (2)	0.0004 (2)	0.0000 (2)
C2	0.0077 (2)	0.0083 (2)	0.0062 (2)	−0.0001 (2)	−0.0001 (2)	−0.0012 (2)
C3	0.0072 (2)	0.0085 (2)	0.0076 (2)	0.0004 (2)	−0.0002 (2)	−0.0009 (2)
C4	0.0068 (2)	0.0097 (3)	0.0060 (2)	0.0001 (2)	−0.0006 (2)	−0.0008 (2)
C5	0.0073 (2)	0.0105 (3)	0.0125 (3)	0.0010 (2)	−0.0001 (2)	−0.0013 (2)
H1A	0.0316 (8)	0.0253 (8)	0.0243 (8)	0.0081 (7)	−0.0024 (8)	−0.0112 (7)
H1B	0.0184 (7)	0.0379 (10)	0.0262 (8)	−0.0070 (7)	0.0017 (6)	0.0123 (8)
H2	0.0190 (6)	0.0181 (6)	0.0244 (7)	0.0013 (6)	0.0011 (6)	−0.0072 (6)
H3	0.0226 (7)	0.0175 (6)	0.0203 (7)	0.0023 (6)	−0.0004 (6)	−0.0066 (6)
H4	0.0230 (7)	0.0266 (8)	0.0139 (6)	−0.0004 (6)	−0.0008 (6)	0.0048 (6)
H5A	0.0240 (8)	0.0246 (8)	0.0457 (11)	0.0024 (7)	0.0037 (8)	−0.0181 (8)
H5B	0.0228 (7)	0.0304 (9)	0.0264 (8)	−0.0001 (7)	−0.0053 (7)	0.0112 (7)
H11	0.0160 (6)	0.0297 (8)	0.0192 (7)	−0.0012 (6)	0.0045 (6)	0.0034 (7)
H12	0.0265 (8)	0.0282 (8)	0.0199 (8)	−0.0047 (7)	0.0071 (6)	−0.0019 (7)
H13	0.0297 (8)	0.0155 (6)	0.0207 (7)	−0.0010 (6)	0.0010 (7)	0.0023 (6)
H14	0.0313 (8)	0.0174 (7)	0.0258 (8)	0.0086 (7)	−0.0030 (7)	0.0014 (6)
H15	0.0255 (8)	0.0258 (8)	0.0206 (7)	−0.0064 (7)	0.0002 (6)	−0.0070 (7)

Geometric parameters (Å, º) top

O1—C1	1.4227 (11)	C2—C3	1.5338 (9)
O2—C2	1.4284 (11)	C3—C4	1.5301 (10)
O3—C3	1.4254 (11)	C4—C5	1.5202 (10)
O4—C4	1.4328 (11)	C1—H1A	1.109 (2)
O5—C5	1.4211 (12)	C1—H1B	1.098 (2)
O1—H11	0.9960 (19)	C2—H2	1.1031 (19)
O2—H12	0.978 (2)	C3—H3	1.1082 (18)
O3—H13	0.9863 (19)	C4—H4	1.1028 (18)
O4—H14	0.970 (2)	C5—H5A	1.097 (2)
O5—H15	0.986 (2)	C5—H5B	1.106 (2)
C1—C2	1.5154 (10)

O1···O2	2.8654 (12)	H1A···H14^v	2.423 (3)
O1···O5ⁱ	2.6654 (12)	H1B···C4	2.7764 (19)
O1···C1ⁱⁱ	3.3229 (11)	H1B···H4	2.089 (2)
O1···C4ⁱⁱ	3.2927 (11)	H1B···O1^x	2.5088 (19)
O1···C3ⁱⁱⁱ	3.2991 (11)	H1B···H11^x	2.531 (2)
O1···O3ⁱⁱⁱ	2.6712 (13)	H1B···O2ⁱⁱⁱ	2.732 (3)
O2···O5ⁱ	3.2129 (12)	H1B···H13ⁱⁱⁱ	2.540 (3)
O2···O3	2.7603 (12)	H2···O4	2.6256 (19)
O2···O4^iv	2.8218 (13)	H2···H11	2.476 (2)
O2···O4^v	2.8475 (12)	H2···H14	2.559 (2)
O2···O1	2.8654 (12)	H2···H5B^iv	2.163 (3)
O2···C4^v	3.3381 (11)	H3···H1A	2.487 (3)
O3···O5^iv	2.7000 (13)	H3···H5A	2.410 (3)
O3···O1^v	2.6712 (13)	H3···O3^xi	2.7567 (19)
O3···O2	2.7603 (12)	H3···O1^v	2.8801 (19)
O3···O4	2.8481 (13)	H3···O5^xii	2.7323 (19)
O4···O5	2.8755 (12)	H3···H15^xii	2.450 (2)
O4···O2^vi	2.8218 (13)	H4···C1	2.7887 (18)
O4···O3	2.8481 (13)	H4···H1B	2.089 (2)
O4···O2ⁱⁱⁱ	2.8475 (12)	H4···O1^x	2.3261 (18)
O5···O3^vi	2.7000 (13)	H4···C1^x	2.9435 (18)
O5···O1^vii	2.6654 (12)	H4···O2ⁱⁱⁱ	2.846 (2)
O5···O4	2.8755 (12)	H5A···H3	2.410 (3)
O5···O2^vii	3.2129 (12)	H5A···O5^xii	2.704 (2)
O1···H1Bⁱⁱ	2.5088 (19)	H5A···H15^xii	2.580 (3)
O1···H13ⁱⁱⁱ	1.6932 (19)	H5B···O3	2.5687 (19)
O1···H4ⁱⁱ	2.3261 (18)	H5B···H1A^viii	2.408 (3)
O1···H3ⁱⁱⁱ	2.8801 (19)	H5B···O4^vi	2.8823 (19)
O2···H11	2.492 (2)	H5B···C2^vi	3.0709 (19)
O2···H4^v	2.846 (2)	H5B···H2^vi	2.163 (3)
O2···H14^v	1.903 (2)	H11···O2	2.492 (2)
O2···H1B^v	2.732 (3)	H11···O5ⁱ	1.7113 (19)
O2···H13	2.8371 (19)	H11···C5ⁱ	2.7267 (18)
O3···H3^viii	2.7567 (19)	H11···H2	2.476 (2)
O3···H12	2.7862 (19)	H11···H15ⁱ	2.324 (2)
O3···H5B	2.5687 (19)	H11···H1Bⁱⁱ	2.531 (2)
O3···H15^iv	1.716 (2)	H11···H13ⁱⁱⁱ	2.187 (2)
O4···H12^vi	1.845 (2)	H12···O3	2.7862 (19)
O4···H2	2.6256 (19)	H12···O4^iv	1.845 (2)
O4···H15	2.8820 (19)	H12···C4^iv	3.0155 (19)
O4···H5B^iv	2.8823 (19)	H12···H14^iv	2.451 (2)
O5···H11^vii	1.7113 (19)	H13···O2	2.8371 (19)
O5···H3^ix	2.7323 (19)	H13···H15^iv	2.346 (2)
O5···H5A^ix	2.704 (2)	H13···O1^v	1.6932 (19)
C1···O1^x	3.3229 (11)	H13···C1^v	2.6229 (19)
C3···O1^v	3.2991 (11)	H13···H1B^v	2.540 (3)
C4···O1^x	3.2927 (11)	H13···H11^v	2.187 (2)
C4···O2ⁱⁱⁱ	3.3381 (11)	H14···H2	2.559 (2)
C1···H4	2.7887 (18)	H14···H12^vi	2.451 (2)
C1···H14^v	2.8477 (19)	H14···O2ⁱⁱⁱ	1.903 (2)
C1···H13ⁱⁱⁱ	2.6229 (19)	H14···C1ⁱⁱⁱ	2.8477 (19)
C1···H4ⁱⁱ	2.9435 (18)	H14···C2ⁱⁱⁱ	2.8959 (19)
C2···H14^v	2.8959 (19)	H14···H1Aⁱⁱⁱ	2.423 (3)
C2···H5B^iv	3.0709 (19)	H15···O4	2.8820 (19)
C3···H15^iv	2.8190 (19)	H15···H11^vii	2.324 (2)
C4···H12^vi	3.0155 (19)	H15···O3^vi	1.716 (2)
C4···H1B	2.7764 (19)	H15···C3^vi	2.8190 (19)
C5···H11^vii	2.7267 (18)	H15···H13^vi	2.346 (2)
H1A···H3	2.487 (3)	H15···H3^ix	2.450 (2)
H1A···H5B^xi	2.408 (3)	H15···H5A^ix	2.580 (3)

C1—O1—H11	112.06 (12)	C2—C1—H1A	108.93 (11)
C2—O2—H12	108.99 (13)	C2—C1—H1B	110.70 (11)
C3—O3—H13	107.54 (13)	H1A—C1—H1B	107.78 (18)
C4—O4—H14	106.80 (13)	O2—C2—H2	109.27 (11)
C5—O5—H15	108.00 (13)	C1—C2—H2	109.37 (11)
O1—C1—C2	112.24 (6)	C3—C2—H2	109.37 (10)
O2—C2—C3	110.36 (6)	O3—C3—H3	108.62 (11)
C1—C2—C3	111.77 (6)	C2—C3—H3	107.88 (10)
O2—C2—C1	106.64 (6)	C4—C3—H3	107.94 (10)
O3—C3—C4	108.74 (6)	O4—C4—H4	109.00 (11)
C2—C3—C4	113.34 (6)	C3—C4—H4	108.74 (11)
O3—C3—C2	110.21 (6)	C5—C4—H4	107.61 (10)
C3—C4—C5	110.38 (6)	O5—C5—H5A	108.31 (14)
O4—C4—C3	111.13 (6)	O5—C5—H5B	110.27 (11)
O4—C4—C5	109.88 (6)	C4—C5—H5A	109.20 (14)
O5—C5—C4	111.32 (7)	C4—C5—H5B	109.82 (10)
O1—C1—H1A	109.54 (14)	H5A—C5—H5B	107.84 (17)
O1—C1—H1B	107.55 (13)

O1—C1—C2—O2	−66.06 (8)	O3—C3—C4—O4	60.62 (8)
O1—C1—C2—C3	173.25 (7)	O3—C3—C4—C5	−61.57 (8)
O2—C2—C3—O3	49.43 (8)	C2—C3—C4—O4	−62.32 (8)
O2—C2—C3—C4	171.56 (6)	C2—C3—C4—C5	175.50 (6)
C1—C2—C3—O3	167.93 (7)	O4—C4—C5—O5	62.08 (9)
C1—C2—C3—C4	−69.94 (8)	C3—C4—C5—O5	−175.00 (7)

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

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O1—H11···O2	0.9960 (19)	2.492 (2)	2.8654 (12)	101.70 (12)
O1—H11···O5ⁱ	0.9960 (19)	1.7113 (19)	2.6654 (12)	159.04 (17)
O2—H12···O4^iv	0.978 (2)	1.845 (2)	2.8218 (13)	176.90 (17)
O3—H13···O1^v	0.9863 (19)	1.6932 (19)	2.6712 (13)	170.66 (17)
O4—H14···O2ⁱⁱⁱ	0.970 (2)	1.903 (2)	2.8475 (12)	164.00 (17)
O5—H15···O3^vi	0.986 (2)	1.716 (2)	2.7000 (13)	176.22 (17)
C1—H1B···O1^x	1.098 (2)	2.5088 (19)	3.3229 (11)	129.99 (18)
C4—H4···O1^x	1.1028 (18)	2.3261 (18)	3.2927 (11)	145.24 (14)

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

Experimental details

Crystal data
Chemical formula	C₅H₁₂O₅
M_r	152.15
Crystal system, space group	Orthorhombic, P2₁2₁2₁
Temperature (K)	122
a, b, c (Å)	8.2660 (4), 8.8977 (4), 8.9116 (4)
V (Å³)	655.43 (5)
Z	4
Radiation type	Neutron, λ = 0.83950 Å
µ (mm⁻¹)	0.27
Crystal size (mm)	2.5 × 2.0 × 0.9

Data collection
Diffractometer	Four-circle diffractometer
Absorption correction	Integration datap
T_min, T_max	0.132, 0.223
No. of measured, independent and observed [I > 2σ(I)] reflections	2917, 1911, 1831
R_int	0.041
(sin θ/λ)_max (Å⁻¹)	0.847

Refinement
R[F² > 2σ(F²)], wR(F²), S	?, 0.054, 1.47
No. of reflections	1911
No. of parameters	200
H-atom treatment	All H-atom parameters refined
Δρ_max, Δρ_min (e Å⁻³)	1.81, −1.23

Computer programs: rafd9, racer, SHELXL, VALRAY (Stewart et al., 2000), ORTEP, PLATON (Spek, 1990).

Selected geometric parameters (Å, º) top

O1—C1	1.4227 (11)	O4—C4	1.4328 (11)
O2—C2	1.4284 (11)	O5—C5	1.4211 (12)
O3—C3	1.4254 (11)

O1—C1—C2	112.24 (6)	O3—C3—C2	110.21 (6)
O2—C2—C3	110.36 (6)	O4—C4—C3	111.13 (6)
O2—C2—C1	106.64 (6)	O4—C4—C5	109.88 (6)
O3—C3—C4	108.74 (6)	O5—C5—C4	111.32 (7)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O1—H11···O2	0.9960 (19)	2.492 (2)	2.8654 (12)	101.70 (12)
O1—H11···O5ⁱ	0.9960 (19)	1.7113 (19)	2.6654 (12)	159.04 (17)
O2—H12···O4ⁱⁱ	0.978 (2)	1.845 (2)	2.8218 (13)	176.90 (17)
O3—H13···O1ⁱⁱⁱ	0.9863 (19)	1.6932 (19)	2.6712 (13)	170.66 (17)
O4—H14···O2^iv	0.970 (2)	1.903 (2)	2.8475 (12)	164.00 (17)
O5—H15···O3^v	0.986 (2)	1.716 (2)	2.7000 (13)	176.22 (17)
C1—H1B···O1^vi	1.098 (2)	2.5088 (19)	3.3229 (11)	129.99 (18)
C4—H4···O1^vi	1.1028 (18)	2.3261 (18)	3.2927 (11)	145.24 (14)

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

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