Invariom-model refinement of L-valinol

The structure of L-valinol [(S)-(+)-2-amino-3-methyl­butan-1-ol or hydroxy­lated L-valine], C₅H₁₃NO, has been determined at 100 K by single-crystal X-ray diffraction. The independent atom model geometry, Flack parameter and figures of merit are compared with results from an invariom structure refinement. The latter provides H-atom positions free of independent atom model bias and therefore yields a more accurate hydrogen-bond pattern, and the geometry from invariom refinement shows an improved agreement with results from a quantum chemical geometry optimization.

S1. Comment

L-Valinol, the reduction product of L-valine, is not zwitterionic, as the carboxylate group is replaced by a CH₂OH group and the amino group is neutral. It occurs naturally, for example, in polypeptide peptaibol antibiotics (Chugh et al., 2002).

The invariom concept (Dittrich et al., 2004) provides a definition of a pseudoatom electron density employing the multipole formalism (Hansen & Coppens, 1978), where the pseudoatom is transferable from one molecule to another. In a conventional multipole refinement, the multipole model electron density parameters are freely refined against the experimental data and stringent requirements apply for data quality. In invariom refinement, the multipole parameters are predicted by a procedure involving theoretical calculations and can be described as providing aspherical scattering factors. Hence, the number of parameters to be refined in the least-squares procedure does not increase when compared with a standard independent atom model (IAM) refinement. In this paper we compare a refinement of the same intensity data using the invariom model and the IAM.

It has been demonstrated that the accuracy of molecular geometry determination by conventional X-ray single-crystal diffraction experiments of organic molecules can be improved by invariom modelling, with bond lengths involving H atoms benefiting in particular (Dittrich et al., 2005). When invariom-model aspherical scattering factors are employed to replace the spherical scattering factors of the conventional IAM, standard deviations and figures of merit also improve.

For both models the same intensity data and cutoff criteria were used. For invariom refinement of L-valinol the R-factor is reduced from 4.2 to 2.9%, the goodness of fit from 2.8 to 1.7 and the maximum residual density from 0.43 to 0.30 e Å⁻³ when compared with the IAM refinement. In the invariom refinement the Hirshfeld (1976) test fails only for the C3—C5 bond and the average for all bonds is 5.7 × 10 ⁻⁴ Ų; in the IAM additionally the C1—C2 bond fails and the average is 7.2 × 10 ⁻⁴ Ų. Therefore, the physical significance of the atomic displacement parameters improves with invariom scattering factors.

Table 2 compares the geometry from invariom and IAM refinements, as well as a quantum chemical (QC) geometry optimization for an isolated molecule with GAUSSIAN (Frisch et al., 2002) employing the basis set D95++(3df,3pd). In order to correctly show the improvements of the geometry obtained from invariom refinement, ideally a comparison should be made with the results of a neutron experiment rather than with the geometry of an isolated molecule of different conformation. However, neutron data are not available for the title molecule. Still, a comparison of bond distances is revealing and differences in conformation due to hydrogen bonding are discussed below. The most significant differences between IAM and invariom refinement occur for the C—O and the X—H bonds (X = C, N and O). The bond distances to H atoms from invariom refinement agree very well with results from the geometry optimization, whereas the IAM X—H bond distances are strongly affected by the well known systematic errors. We can conclude that X—H bonds can be observed free of promolecule bias with invarioms.

Fig. 1 compares an ORTEPIII (Burnett & Johnson, 1996) plot (Fig. 1a) of the molecular structure in the crystal with the conformation from the geometry optimization (Fig. 1b).

Table 3 provides the results of an analysis of the hydrogen-bond pattern. Both the amine N and the hydroxyl O atoms act as donors and acceptors simultaneously. An intramolecular N—H···O hydrogen bond, as well as intermolecular N—H···O and O—H···N hydrogen bonds, form one-dimensional zigzag chains, which are further extended into a two-dimensional network structure of sheets perpendicular to the c axis, as depicted in Fig. 2. A classification of the hydrogen bonds in terms of graph-set notation (Etter et al., 1990) reveals a first-level graph set N₁ = C¹₁(5)S¹₁(5)C¹₁(5) and a second-level graph set N₂ = C²₂(4), a product of the two C(5) chain motives. Graph-set assignments were confirmed using the GSET routine in RPLUTO (Motherwell et al. 1999).

The conformation of the CNO skeleton of the molecule as defined by the torsion angles, e.g. N1—C2—C3—C4, is similar in the observed X-ray and optimized geometry. The largest discrepancy is found for the C1—C2—C3—C5 torsion angle, which is 62.2 (1)° in the experiment and 55.0° in the calculation. Changes associated with the intra- or intermolecular hydrogen bonds affect the H1—O1—C1—C2, H2—N1—C2—C1 and H3—N1—C2—C1 torsion angles, as listed in Table 1. Values for the other torsion angles involving the hydrogen-bonded H atoms can be found in the supplementary information.

The fact that the aspherical electron density is available from invariom modelling allows calculation of the dipole moment of 1.9 Debye (with indiviual components x = −0.3, y = 1.9, z = 0.1) for the geometry found in the crystal. The result from a single point energy calculation of 1.1 Debye (x = −0.4, y = 0.6, z = −0.8) using GAUSSIAN (Frisch et al. 2002) and the experimental geometry agrees reasonably well with this value.

The Flack (1983) parameter obtained from the IAM refinement, 0.1 (10), has a high standard deviation of 1. Flack & Bernardinelli (2000) have pointed out that this is the physical range of the parameter. The value of the parameter is improved to 0.0 (6) when invariom scattering factors are used (Dittrich et al., 2006). This means that a definite conclusion on absolute structure and chirality of the molecule cannot be drawn, a result that is not surprising, considering that there is only one O atom in the structure and that Mo Kα radiation was used. For the inverted structure the IAM value was 0.9 (10) and the invariom value 1.0 (6). The chirality of the sample was known from the chemical synthesis.

It is common practice to merge Friedel pairs as recommended by IUCr journals. However, this and our recent study (Dittrich et al., 2006) show that extra information due to anomalous dispersion can be extracted for light-atom structures that contain O and F, even when Mo Kα radiation is used. In our opinion, even when the standard deviation of the Flack parameter is higher than the significance limit of 0.12 (Flack & Bernardinelli, 2000), invariom refinement including high-order data often gives a reliable indication of whether or not the absolute structure is correct (Dittrich et al., 2006) (although this statement is not supported by the data reported in this paper). We therefore recommend keeping Friedel pairs unmerged for high-resolution light-atom structures containing oxygen or slightly heavier elements.

S2. Experimental

A crystal of the title compound was grown by slow cooling of the pure liquid. Owing to the low melting point, a spherical crystal formed while mounting the crystal, which was ice-cooled before [before what?].

S3. Refinement

The 13 H atoms were found as the 13 highest peaks in the difference Fourier map. An IAM refinement with SHELXL97 (Sheldrick, 1997) provided starting values for IAM and aspherical atom refinements both performed with XDLSM of the XD package (Koritsánszky et al., 2003), which included reflections with F_o > 2σ(F_o). XD input files were prepared with the program INVARIOMTOOL (Hübschle & Dittrich, 2004). Aspherical valence scattering contributions for C, N and O atoms were obtained from theoretical calculations on model compounds that included nearest neighbours, whereas H-atom model compounds involved next-nearest neighbours. The basis set D95++(3df,3pd) was used to optimize the geometry of these model compounds. The deviation from electroneutrality was 0.17 electrons out of 44 valence electrons and electroneutrality was achieved by scaling H-atom monopoles only. Full details of the general modelling procedure will be published elsewhere (Hübschle et al., 2006). The relatively high goodness of fit of 1.71 is due to the weighting scheme (1/σ²) employed.

Computing details

Data collection: CrysAlis CCD (Oxford Diffraction, 2006); cell refinement: CrysAlis RED (Oxford Diffraction, 2006); data reduction: CrysAlis RED; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: XD (Koritsánszky et al., 2003); molecular graphics: PLATON (Spek, 2003); software used to prepare material for publication: enCIFer (Allen et al., 2004).

Figures

	Fig. 1. (a) An ORTEP (Burnett & Johnson, 1996) representation of the L-valinol molecular structure at 100 K after invariom refinement. Displacement ellipsoids are shown at the 50% probability level. (b) The conformation of the geometry optimized isolated molecule.
	Fig. 2. The hydrogen-bond pattern in L-valinol, generated with Mercury (Macrae et al., 2006).

(S)-(+)-2-Amino-3-methylbutan-1-ol

Crystal data

C5H13NO	Dx = 1.065 Mg m^−3
Mr = 103.17	Melting point: 32 K
Orthorhombic, P212121	Mo Kα radiation, λ = 0.7107 Å
Hall symbol: P 2ac 2ab	Cell parameters from 23916 reflections
a = 4.8154 (9) Å	θ = 2.7–40.1°
b = 8.518 (5) Å	µ = 0.07 mm^−1
c = 15.624 (5) Å	T = 100 K
V = 640.9 (5) Å^3	Spherical, colorless
Z = 4	0.59 × 0.59 × 0.59 mm
F(000) = 232.0

Data collection

Oxford Diffraction Xcalibur S diffractometer	4056 independent reflections
Radiation source: Enhance (Mo) X-ray Source	3015 reflections with F > 2σ(F)
Graphite monochromator	Rint = 0.030
Detector resolution: 16.0009 pixels mm^-1	θmax = 40.1°, θmin = 2.7°
ω scans	h = −8→8
Absorption correction: multi-scan (Blessing, 1995)	k = −15→15
Tmin = 0.911, Tmax = 0.960	l = −28→28
37777 measured reflections

Refinement

Refinement on F	All H-atom parameters refined
Least-squares matrix: full	w1 = 1/[σ^2(Fo)]
R[F^2 > 2σ(F^2)] = 0.028	(Δ/σ)max < 0.001
wR(F^2) = 0.018	Δρmax = 0.30 e Å^−3
S = 1.71	Δρmin = −0.13 e Å^−3
3015 reflections	Absolute structure: (Dittrich et al., 2006)
117 parameters	Absolute structure parameter: −0.0 (6)
0 restraints

Special details

Experimental. A nitrogen gas flow low temperature device was used. Due to the low melting point of the sample, the crystal melted partly and a spherical crystal formed.

Data collection was carried out on an Oxford Diffraction Xcalibur S diffractometer with Mo Kα radiation. The maximum resolution in sin θ / λ was 0.91 Å⁻¹ and each frame covered 1° in ω.

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

	x	y	z	Uiso*/Ueq
O1	0.23443 (9)	0.85871 (4)	0.71501 (2)	0.024 (3)
N1	0.2293 (1)	0.5396 (1)	0.7523 (1)	0.020 (3)
C2	0.2747 (1)	0.5923 (1)	0.6635 (1)	0.018 (3)
C1	0.1361 (1)	0.7520 (1)	0.6526 (1)	0.022 (3)
C3	0.1625 (1)	0.4714 (1)	0.5991 (1)	0.022 (3)
C4	0.2849 (1)	0.3082 (1)	0.6151 (1)	0.027 (3)
C5	0.2226 (2)	0.5204 (1)	0.5065 (1)	0.035 (3)
H1	0.104 (2)	0.926 (1)	0.728 (1)	0.028 (2)
H2	0.233 (2)	0.630 (1)	0.789 (1)	0.030 (1)
H3	0.376 (2)	0.470 (1)	0.770 (1)	0.041 (2)
H4	0.498 (2)	0.607 (1)	0.650 (1)	0.032 (2)
H5	0.173 (1)	0.797 (1)	0.589 (1)	0.034 (2)
H6	−0.084 (2)	0.738 (1)	0.658 (1)	0.044 (2)
H7	−0.069 (2)	0.464 (1)	0.609 (1)	0.038 (2)
H8	0.213 (2)	0.227 (1)	0.569 (1)	0.048 (2)
H9	0.250 (2)	0.271 (1)	0.677 (1)	0.047 (2)
H10	0.510 (2)	0.313 (1)	0.607 (1)	0.059 (2)
H11	0.136 (2)	0.627 (1)	0.489 (1)	0.053 (2)
H12	0.165 (2)	0.432 (1)	0.465 (1)	0.059 (2)
H13	0.455 (2)	0.537 (1)	0.498 (1)	0.064 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0161 (2)	0.0168 (1)	0.0388 (2)	−0.0002 (2)	−0.0024 (2)	−0.0036 (1)
N1	0.0161 (2)	0.0167 (2)	0.0263 (2)	−0.0011 (2)	−0.0011 (2)	0.0002 (2)
C2	0.0124 (2)	0.0150 (2)	0.0257 (2)	−0.0009 (2)	−0.0001 (2)	−0.0012 (2)
C1	0.0184 (2)	0.0166 (2)	0.0295 (3)	0.0014 (2)	−0.0021 (2)	0.0008 (2)
C3	0.0183 (3)	0.0197 (2)	0.0266 (2)	−0.0027 (2)	−0.0003 (2)	−0.0043 (2)
C4	0.0263 (3)	0.0186 (2)	0.0364 (3)	−0.0016 (2)	0.0013 (3)	−0.0073 (2)
C5	0.0474 (4)	0.0320 (3)	0.0270 (3)	−0.0059 (3)	0.0008 (3)	−0.0038 (2)

Geometric parameters (Å, º)

O1—C1	1.4146 (6)	C3—C4	1.5309 (8)
O1—H1	0.875 (9)	C3—C5	1.5327 (8)
N1—C2	1.4747 (7)	C3—H7	1.128 (8)
N1—H2	0.961 (7)	C4—H8	1.056 (8)
N1—H3	0.961 (9)	C4—H9	1.032 (8)
C2—C1	1.5244 (7)	C4—H10	1.095 (11)
C2—C3	1.5382 (7)	C5—H11	1.035 (9)
C2—H4	1.101 (8)	C5—H12	1.034 (10)
C1—H5	1.078 (7)	C5—H13	1.136 (12)
C1—H6	1.072 (9)
C1—O1—H1	110.3 (5)	C4—C3—H7	108.0 (4)
H2—N1—H3	107.9 (6)	C5—C3—H7	109.5 (3)
C1—C2—C3	111.74 (4)	C3—C4—H8	110.9 (4)
C1—C2—H4	107.8 (3)	C3—C4—H9	111.9 (4)
C3—C2—H4	107.1 (3)	C3—C4—H10	109.1 (5)
O1—C1—C2	110.48 (4)	H8—C4—H9	112.5 (6)
O1—C1—H5	110.6 (4)	H8—C4—H10	105.4 (7)
O1—C1—H6	110.5 (4)	H9—C4—H10	106.6 (7)
C2—C1—H5	110.3 (3)	C3—C5—H11	114.4 (5)
C2—C1—H6	108.9 (4)	C3—C5—H12	110.1 (5)
H5—C1—H6	106.0 (6)	C3—C5—H13	109.4 (5)
C2—C3—C4	111.46 (4)	H11—C5—H12	111.1 (7)
C2—C3—C5	111.64 (4)	H11—C5—H13	105.1 (8)
C2—C3—H7	106.9 (3)	H12—C5—H13	106.2 (8)
C4—C3—C5	109.20 (5)
N1—C2—C1—O1	54.9 (1)	H1—O1—C1—C2	−148.9 (9)
N1—C2—C3—C4	−54.4 (1)	H2—N1—C2—C1	−35.0 (6)
N1—C2—C3—C5	−176.9 (1)	H2—N1—C2—C3	−158.0 (6)
C3—C2—C1—O1	177.5 (1)	H3—N1—C2—C1	−153.1 (6)
C1—C2—C3—C4	−175.3 (1)	H3—N1—C2—C3	84.0 (6)
C1—C2—C3—C5	62.2 (1)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1···N1^i	0.87 (1)	1.90 (1)	2.7607 (6)	168 (1)
N1—H2···O1	0.96 (1)	2.27 (1)	2.7800 (3)	113 (1)
N1—H3···O1^ii	0.96 (1)	2.12 (1)	3.0502 (6)	164 (1)

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