A combined model of electron density and lattice dynamics refined against elastic diffraction data. Thermodynamic properties of crystalline L-alanine

Thermodynamic stability is an essential property of crystalline materials, and its accurate calculation requires a reliable description of the thermal motion – phonons – in the crystal. Such information can be obtained from periodic density functional theory (DFT) calculations, but these are costly and in some cases insufficiently accurate for molecular crystals. This deficiency is addressed here by refining a lattice-dynamics model, derived from DFT calculations, against accurate high-resolution X-ray diffraction data. For the first time, a normal-mode refinement is combined with the refinement of aspherical atomic form factors, allowing a comprehensive description and physically meaningful deconvolution of thermal motion and static charge density in the crystal. The small and well diffracting L-alanine system was used. Different lattice-dynamics models, with or without phonon dispersion, and derived from different levels of theory, were tested, and models using spherical and aspherical form factors were compared. The refinements indicate that the vibrational information content in the 23 K data is too small to study lattice dynamics, whereas the 123 K data appear to hold information on the acoustic and lowest-frequency optical phonons. These normal-mode models show slightly larger refinement residuals than their counterparts using atomic displacement parameters, and these features are not removed by considering phonon dispersion in the model. The models refined against the 123 K data, regardless of their sophistication, give calculated heat capacities for L-alanine within less than 1 cal mol⁻¹ K⁻¹ of the calorimetric measurements, in the temperature range 10–300 K. The findings show that the normal-mode refinement method can be combined with an elaborate description of the electron density. It appears to be a promising technique for free-energy determination for crystalline materials at the expense of performing a single-crystal elastic X-ray diffraction determination combined with periodic DFT calculations.

Computing details

Program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014) for shelx, shelx_NoMoRe_dispersion, shelx_NoMoRe_gamma; Volkov et al., (2006) for xd, xd_dispersion, xd_gamma. Molecular graphics: ORTEP for Windows (Farrugia, 2012) for shelx, shelx_NoMoRe_dispersion, shelx_NoMoRe_gamma; Volkov et al., (2006) for xd, xd_dispersion, xd_gamma. Software used to prepare material for publication: WinGX publication routines (Farrugia, 2012) for shelx, shelx_NoMoRe_dispersion, shelx_NoMoRe_gamma; Volkov et al., (2006) for xd, xd_dispersion, xd_gamma.

(shelx)

Crystal data

C3H7NO2	F(000) = 192
Mr = 89.1	Dx = 1.399 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Hydrogen site location: difference Fourier map
Least-squares matrix: full	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.023	w = 1/[σ^2(Fo^2) + (0.0321P)^2 + 0.0037P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.063	(Δ/σ)max = 0.050
S = 1.14	Δρmax = 0.38 e Å^−3
5997 reflections	Δρmin = −0.27 e Å^−3
84 parameters	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.20 (2)
0 constraints	Absolute structure: Flack x determined using 2425 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.11 (8)
Secondary atom site location: difference Fourier map

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
O1	0.72762 (4)	0.08389 (2)	0.62535 (4)	0.01353 (4)
O2	0.44356 (4)	0.18436 (2)	0.76128 (4)	0.01348 (3)
N1	0.64927 (4)	0.13772 (2)	0.18384 (4)	0.01018 (3)
C1	0.55587 (4)	0.14091 (2)	0.60041 (4)	0.00878 (3)
C2	0.46905 (4)	0.16119 (2)	0.35471 (4)	0.00891 (3)
C3	0.26391 (5)	0.09093 (3)	0.30329 (6)	0.01419 (4)
H11	0.6983 (18)	0.0665 (10)	0.191 (2)	0.022 (2)*
H12	0.7633 (17)	0.1801 (8)	0.2048 (18)	0.018 (2)*
H13	0.5906 (18)	0.1470 (10)	0.036 (2)	0.031 (3)*
H21	0.4318 (18)	0.2363 (8)	0.3409 (19)	0.019 (2)*
H31	0.2032 (17)	0.1075 (8)	0.148 (2)	0.023 (2)*
H32	0.1475 (16)	0.1035 (8)	0.416 (2)	0.024 (2)*
H33	0.3016 (17)	0.0136 (9)	0.3037 (18)	0.020 (2)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.01495 (7)	0.01396 (7)	0.01167 (7)	0.00518 (5)	−0.00208 (6)	0.00126 (5)
O2	0.01730 (8)	0.01584 (7)	0.00731 (6)	0.00438 (6)	0.00087 (5)	−0.00116 (5)
N1	0.01185 (6)	0.01127 (6)	0.00742 (6)	0.00057 (5)	0.00046 (5)	0.00000 (5)
C1	0.01136 (6)	0.00815 (6)	0.00684 (6)	0.00047 (5)	−0.00085 (5)	0.00004 (5)
C2	0.01080 (6)	0.00894 (6)	0.00699 (6)	0.00117 (5)	−0.00059 (5)	−0.00008 (5)
C3	0.01277 (8)	0.01829 (10)	0.01150 (8)	−0.00304 (7)	−0.00139 (7)	−0.00064 (7)

Geometric parameters (Å, º)

O1—C1	1.2475 (3)	C1—C2	1.5335 (3)
O2—C1	1.2644 (3)	C2—C3	1.5246 (4)
N1—C2	1.4874 (3)	C2—H21	0.952 (10)
N1—H11	0.923 (11)	C3—H31	0.989 (11)
N1—H12	0.864 (11)	C3—H32	0.965 (11)
N1—H13	0.929 (13)	C3—H33	0.976 (11)
C2—N1—H11	112.4 (7)	C3—C2—C1	111.05 (2)
C2—N1—H12	110.9 (7)	N1—C2—H21	107.4 (6)
H11—N1—H12	108.4 (10)	C3—C2—H21	110.2 (7)
C2—N1—H13	108.4 (7)	C1—C2—H21	108.3 (7)
H11—N1—H13	106.1 (10)	C2—C3—H31	110.7 (6)
H12—N1—H13	110.5 (10)	C2—C3—H32	110.7 (6)
O1—C1—O2	125.80 (2)	H31—C3—H32	108.6 (9)
O1—C1—C2	118.34 (2)	C2—C3—H33	111.5 (6)
O2—C1—C2	115.86 (2)	H31—C3—H33	106.6 (9)
N1—C2—C3	109.78 (2)	H32—C3—H33	108.6 (9)
N1—C2—C1	110.00 (2)
O1—C1—C2—N1	−18.27 (3)	O1—C1—C2—C3	103.46 (3)
O2—C1—C2—N1	161.89 (2)	O2—C1—C2—C3	−76.38 (3)

(shelx_NoMoRe_dispersion)

Crystal data

C3H7NO2	Dx = 1.399 Mg m^−3
Mr = 89.1	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, P212121	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm
F(000) = 192

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Hydrogen site location: difference Fourier map
Least-squares matrix: full	Only H-atom coordinates refined
R[F^2 > 2σ(F^2)] = 0.031	w = 1/[σ^2(Fo^2)] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.082	(Δ/σ)max < 0.001
S = 2.29	Δρmax = 0.54 e Å^−3
5997 reflections	Δρmin = −0.69 e Å^−3
41 parameters	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.27 (3)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack x determined using 2417 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
Secondary atom site location: difference Fourier map	Absolute structure parameter: −0.10 (9)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
O1	0.72759 (5)	0.08386 (2)	0.62538 (5)	0.014
O2	0.44356 (6)	0.18437 (2)	0.76126 (5)	0.014
N1	0.64928 (5)	0.13768 (2)	0.18380 (5)	0.010
C1	0.55584 (5)	0.14092 (2)	0.60034 (5)	0.009
C2	0.46904 (5)	0.16119 (2)	0.35465 (5)	0.009
C3	0.26383 (6)	0.09090 (3)	0.30328 (7)	0.014
H11	0.698 (2)	0.0665 (11)	0.191 (2)	0.024
H12	0.765 (2)	0.1812 (10)	0.205 (2)	0.023
H13	0.5912 (18)	0.1485 (10)	0.030 (2)	0.022
H21	0.431 (2)	0.2360 (9)	0.345 (2)	0.022
H31	0.203 (2)	0.1090 (11)	0.149 (2)	0.032
H32	0.1475 (18)	0.1060 (11)	0.417 (3)	0.031
H33	0.302 (2)	0.0134 (11)	0.306 (3)	0.030

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.016	0.015	0.012	0.006	−0.001	0.002
O2	0.018	0.016	0.007	0.005	0.001	−0.001
N1	0.012	0.011	0.008	0.001	0.001	0.000
C1	0.012	0.008	0.007	0.001	−0.001	0.000
C2	0.011	0.010	0.007	0.001	−0.001	0.000
C3	0.012	0.018	0.011	−0.002	−0.002	0.000
H11	0.026	0.019	0.026	0.006	0.003	0.001
H12	0.020	0.025	0.022	−0.005	0.001	−0.001
H13	0.026	0.026	0.013	0.001	−0.001	0.000
H21	0.028	0.016	0.022	0.005	0.000	0.001
H31	0.032	0.044	0.021	−0.005	−0.011	0.005
H32	0.022	0.044	0.027	−0.002	0.006	−0.001
H33	0.034	0.020	0.037	−0.004	−0.004	−0.001

Geometric parameters (Å, º)

O1—C1	1.2479 (4)	C1—C2	1.5334 (4)
O2—C1	1.2645 (4)	C2—C3	1.5250 (5)
N1—C2	1.4875 (4)	C2—H21	0.947 (11)
N1—H11	0.922 (13)	C3—H31	0.991 (12)
N1—H12	0.881 (12)	C3—H32	0.975 (13)
N1—H13	0.962 (11)	C3—H33	0.978 (14)
C2—N1—H11	112.5 (9)	C3—C2—C1	111.04 (3)
C2—N1—H12	110.9 (8)	N1—C2—H21	108.6 (7)
H11—N1—H12	108.7 (11)	C3—C2—H21	110.4 (8)
C2—N1—H13	109.1 (7)	C1—C2—H21	107.1 (8)
H11—N1—H13	106.5 (11)	C2—C3—H31	109.9 (8)
H12—N1—H13	108.9 (10)	C2—C3—H32	109.2 (8)
O1—C1—O2	125.76 (3)	H31—C3—H32	108.1 (12)
O1—C1—C2	118.36 (3)	C2—C3—H33	111.2 (8)
O2—C1—C2	115.88 (3)	H31—C3—H33	108.4 (12)
N1—C2—C3	109.79 (3)	H32—C3—H33	109.9 (12)
N1—C2—C1	110.00 (3)
O1—C1—C2—N1	−18.29 (4)	O1—C1—C2—C3	103.44 (4)
O2—C1—C2—N1	161.90 (3)	O2—C1—C2—C3	−76.38 (4)

(shelx_NoMoRe_gamma)

Crystal data

C3H7NO2	Dx = 1.399 Mg m^−3
Mr = 89.1	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, P212121	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm
F(000) = 192

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Hydrogen site location: difference Fourier map
Least-squares matrix: full	Only H-atom coordinates refined
R[F^2 > 2σ(F^2)] = 0.029	w = 1/[σ^2(Fo^2) + (0.0321P)^2 + 0.0037P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.080	(Δ/σ)max = 0.001
S = 1.44	Δρmax = 0.60 e Å^−3
5997 reflections	Δρmin = −0.39 e Å^−3
41 parameters	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.17 (2)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack x determined using 2422 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
Secondary atom site location: difference Fourier map	Absolute structure parameter: −0.11 (8)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
O1	0.72766 (5)	0.08390 (2)	0.62537 (5)	0.013
O2	0.44354 (5)	0.18436 (2)	0.76130 (5)	0.013
N1	0.64928 (5)	0.13770 (2)	0.18385 (5)	0.010
C1	0.55582 (5)	0.14090 (2)	0.60037 (5)	0.009
C2	0.46902 (5)	0.16118 (2)	0.35471 (5)	0.009
C3	0.26388 (7)	0.09094 (4)	0.30331 (7)	0.014
H11	0.699 (2)	0.0659 (12)	0.191 (3)	0.022
H12	0.762 (2)	0.1794 (12)	0.207 (2)	0.022
H13	0.594 (2)	0.1490 (11)	0.033 (2)	0.021
H21	0.429 (2)	0.2369 (10)	0.343 (3)	0.022
H31	0.202 (2)	0.1084 (13)	0.150 (3)	0.035
H32	0.147 (2)	0.1049 (12)	0.415 (3)	0.032
H33	0.301 (3)	0.0126 (13)	0.303 (3)	0.032

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.015	0.015	0.011	0.005	−0.002	0.001
O2	0.016	0.016	0.007	0.005	0.000	−0.001
N1	0.012	0.010	0.007	0.000	0.000	0.000
C1	0.011	0.009	0.007	0.001	−0.001	0.000
C2	0.011	0.009	0.007	0.001	−0.001	0.000
C3	0.013	0.018	0.011	−0.003	−0.002	−0.001
H11	0.024	0.018	0.026	0.005	0.003	0.002
H12	0.022	0.024	0.020	−0.006	0.001	−0.001
H13	0.026	0.025	0.013	0.000	−0.001	0.000
H21	0.028	0.016	0.022	0.005	−0.001	0.001
H31	0.035	0.047	0.022	−0.006	−0.013	0.003
H32	0.022	0.044	0.030	−0.004	0.007	−0.005
H33	0.036	0.021	0.039	−0.004	−0.003	−0.004

Geometric parameters (Å, º)

O1—C1	1.2479 (4)	C1—C2	1.5333 (4)
O2—C1	1.2646 (4)	C2—C3	1.5244 (5)
N1—C2	1.4876 (4)	C2—H21	0.961 (13)
N1—H11	0.932 (14)	C3—H31	0.984 (14)
N1—H12	0.853 (14)	C3—H32	0.964 (15)
N1—H13	0.943 (13)	C3—H33	0.987 (16)
C2—N1—H11	112.6 (9)	C3—C2—C1	111.05 (3)
C2—N1—H12	110.3 (9)	N1—C2—H21	108.7 (8)
H11—N1—H12	108.1 (13)	C3—C2—H21	109.6 (9)
C2—N1—H13	109.6 (8)	C1—C2—H21	107.7 (9)
H11—N1—H13	106.9 (12)	C2—C3—H31	110.6 (9)
H12—N1—H13	109.3 (12)	C2—C3—H32	110.2 (8)
O1—C1—O2	125.77 (3)	H31—C3—H32	107.3 (14)
O1—C1—C2	118.35 (3)	C2—C3—H33	111.9 (9)
O2—C1—C2	115.88 (3)	H31—C3—H33	107.0 (13)
N1—C2—C3	109.79 (3)	H32—C3—H33	109.7 (13)
N1—C2—C1	109.99 (2)
O1—C1—C2—N1	−18.25 (4)	O1—C1—C2—C3	103.49 (4)
O2—C1—C2—N1	161.88 (3)	O2—C1—C2—C3	−76.38 (4)

(xd)

Crystal data

C3H7NO2	F(000) = 192
Mr = 89.1	Dx = 1.399 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.018	All H-atom parameters refined
wR(F^2) = 0.038	w2 = 1/[s^2(Fo^2)]
S = 1.15	(Δ/σ)max = 0.00003
6000 reflections	Δρmax = 0.15 e Å^−3
130 parameters	Δρmin = −0.13 e Å^−3
0 restraints	Extinction correction: Becker-Coppens type 1 Lorentzian isotropic, Becker, P.J. & Coppens, P. (1974) Acta Cryst., A30, 129-153.
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 1.03 (3)

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

	x	y	z	Uiso*/Ueq
O1	0.72759 (3)	0.084002 (13)	0.62528 (3)	0.013
O2	0.44363 (3)	0.184278 (14)	0.76120 (3)	0.013
N1	0.64930 (2)	0.137732 (11)	0.18381 (2)	0.01
C1	0.55587 (2)	0.140907 (10)	0.60035 (2)	0.009
C2	0.46911 (2)	0.161203 (10)	0.35465 (2)	0.009
C3	0.26393 (3)	0.090927 (15)	0.30334 (3)	0.014
H11	0.705077	0.056861	0.192042	0.025
H12	0.787683	0.189123	0.209166	0.026
H13	0.583041	0.148176	0.017539	0.024
H21	0.426191	0.247773	0.338709	0.023
H31	0.196398	0.109259	0.131151	0.038
H32	0.131319	0.105266	0.431619	0.04
H33	0.306342	0.00389	0.303717	0.038

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.014892	0.014033	0.011326	0.005312	−0.002135	0.001247
O2	0.017233	0.015778	0.007055	0.004584	0.000693	−0.001078
N1	0.011703	0.011089	0.007347	0.000504	0.000421	0.000014
C1	0.011157	0.008147	0.006641	0.000787	−0.000787	−0.000036
C2	0.010635	0.008658	0.006966	0.001122	−0.000689	−0.000063
C3	0.012582	0.018015	0.01143	−0.002893	−0.001423	−0.000579
H11	0.030712	0.018633	0.025665	0.008978	0.002906	−0.00132
H12	0.021219	0.030759	0.025662	−0.009567	0.001608	−0.001302
H13	0.029298	0.031441	0.012051	0.001778	−0.002763	0.000883
H21	0.032208	0.014223	0.023559	0.006776	−0.002186	0.000954
H31	0.036926	0.053619	0.023725	−0.009291	−0.01309	0.005389
H32	0.02515	0.061251	0.033939	−0.007467	0.010465	−0.009091
H33	0.041021	0.021719	0.05107	−0.00647	−0.005241	−0.001956

Geometric parameters (Å, º)

O1—C1	1.2466 (2)	C2—C3	1.5247 (2)
O2—C1	1.2637 (2)	C2—H21	1.0970 (1)
N1—H11	1.0480 (1)	C3—H31	1.0980 (2)
N1—H12	1.0480 (1)	C3—H32	1.0980 (2)
N1—H13	1.0480 (1)	C3—H33	1.0980 (2)
C1—C2	1.5335 (2)
H11—N1—H12	108.357 (11)	C3—C2—H21	110.200 (12)
H11—N1—H13	106.077 (11)	C2—C3—H31	110.742 (14)
H12—N1—H13	110.539 (11)	C2—C3—H32	110.707 (14)
O1—C1—O2	125.770 (15)	C2—C3—H33	111.475 (14)
O1—C1—C2	118.335 (13)	H31—C3—H32	108.523 (15)
O2—C1—C2	115.895 (13)	H31—C3—H33	106.589 (14)
C1—C2—C3	111.012 (11)	H32—C3—H33	108.665 (15)
C1—C2—H21	108.293 (10)
O1—C1—C2—C3	103.531 (17)	C1—C2—C3—H32	56.204 (13)
O1—C1—C2—H21	−135.368 (17)	C1—C2—C3—H33	−64.885 (14)
O2—C1—C2—C3	−76.344 (15)	H21—C2—C3—H31	56.650 (14)
O2—C1—C2—H21	44.757 (13)	H21—C2—C3—H32	−63.769 (14)
C1—C2—C3—H31	176.623 (18)	H21—C2—C3—H33	175.143 (18)

(xd_dispersion)

Crystal data

C3H7NO2	F(000) = 192
Mr = 89.1	Dx = 1.399 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.021	All H-atom parameters refined
wR(F^2) = 0.048	w2 = 1/[s^2(Fo^2)]
S = 1.44	(Δ/σ)max = 0.00001
6000 reflections	Δρmax = 0.32 e Å^−3
130 parameters	Δρmin = −0.18 e Å^−3
0 restraints	Extinction correction: Becker-Coppens type 1 Lorentzian isotropic, Becker, P.J. & Coppens, P. (1974) Acta Cryst., A30, 129-153.
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 1.04 (4)

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

	x	y	z	Uiso*/Ueq
O1	0.72757 (4)	0.083980 (17)	0.62520 (4)	0.014
O2	0.44364 (4)	0.184298 (17)	0.76117 (3)	0.013
N1	0.64931 (3)	0.137740 (13)	0.18379 (3)	0.01
C1	0.55587 (3)	0.140895 (12)	0.60033 (3)	0.009
C2	0.46912 (3)	0.161199 (13)	0.35461 (3)	0.009
C3	0.26392 (3)	0.090938 (19)	0.30334 (4)	0.014
H11	0.705075	0.056868	0.192042	0.023
H12	0.787687	0.189128	0.209161	0.022
H13	0.583031	0.148176	0.017518	0.021
H21	0.426193	0.247769	0.338711	0.022
H31	0.196392	0.109259	0.131149	0.033
H32	0.131311	0.105266	0.431625	0.031
H33	0.306345	0.003902	0.303718	0.031

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.01545	0.01454	0.01122	0.00573	−0.00146	0.0018
O2	0.01767	0.01565	0.00701	0.00491	0.00072	−0.00064
N1	0.01195	0.01046	0.00726	0.00065	0.00043	−0.00024
C1	0.0111	0.00798	0.00656	0.00065	−0.00074	−0.00005
C2	0.01063	0.00911	0.00677	0.00119	−0.00074	−0.00017
C3	0.01175	0.01774	0.01167	−0.0022	−0.00218	−0.00026
H11	0.02511	0.01809	0.0257	0.00618	0.00263	0.00119
H12	0.02008	0.02474	0.02182	−0.005	0.00123	−0.0015
H13	0.02581	0.02539	0.01264	0.00076	−0.00108	0.00021
H21	0.0277	0.01565	0.02166	0.00557	−0.00037	0.00097
H31	0.03149	0.04497	0.02169	−0.00466	−0.01165	0.004
H32	0.02093	0.04426	0.02801	−0.0023	0.00586	−0.00185
H33	0.03356	0.02033	0.03891	−0.0041	−0.00433	−0.00215

Geometric parameters (Å, º)

O1—C1	1.2465 (2)	C2—C3	1.5246 (3)
O2—C1	1.2638 (2)	C2—H21	1.0970 (1)
N1—H11	1.0480 (2)	C3—H31	1.0980 (2)
N1—H12	1.0480 (2)	C3—H32	1.0980 (2)
N1—H13	1.0480 (1)	C3—H33	1.0980 (2)
C1—C2	1.5335 (2)
H11—N1—H12	108.356 (14)	C3—C2—H21	110.192 (15)
H11—N1—H13	106.080 (14)	C2—C3—H31	110.743 (17)
H12—N1—H13	110.553 (14)	C2—C3—H32	110.723 (17)
O1—C1—O2	125.795 (19)	C2—C3—H33	111.464 (17)
O1—C1—C2	118.319 (16)	H31—C3—H32	108.528 (18)
O2—C1—C2	115.886 (16)	H31—C3—H33	106.582 (18)
C1—C2—C3	111.003 (14)	H32—C3—H33	108.660 (19)
C1—C2—H21	108.286 (13)
O1—C1—C2—C3	103.54 (2)	C1—C2—C3—H32	56.194 (17)
O1—C1—C2—H21	−135.38 (2)	C1—C2—C3—H33	−64.892 (17)
O2—C1—C2—C3	−76.352 (19)	H21—C2—C3—H31	56.676 (17)
O2—C1—C2—H21	44.730 (17)	H21—C2—C3—H32	−63.760 (17)
C1—C2—C3—H31	176.63 (2)	H21—C2—C3—H33	175.15 (2)

(xd_gamma)

Crystal data

C3H7NO2	F(000) = 192
Mr = 89.1	Dx = 1.399 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 5997 reflections
a = 5.9534 (5) Å	θ = 3.3–58.0°
b = 12.2772 (10) Å	µ = 0.12 mm^−1
c = 5.7882 (5) Å	T = 123 K
V = 423.07 (6) Å^3	Rhombic, colorless
Z = 4	0.33 × 0.26 × 0.18 mm

Data collection

Bruker Nonius X8 APEXII CCD area-detector diffractometer	5997 independent reflections
Radiation source: fine-focus sealed tube	5719 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
ω and φ scans	θmax = 58.0°, θmin = 3.3°
Absorption correction: multi-scan SADABS, Bruker(2001)	h = 0→14
Tmin = 0.645, Tmax = 0.751	k = 0→29
5997 measured reflections	l = 0→13

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.022	w2 = 1/[s^2(Fo^2)]
wR(F^2) = 0.049	(Δ/σ)max = 0.0001
S = 1.48	Δρmax = 0.25 e Å^−3
6000 reflections	Δρmin = −0.27 e Å^−3
130 parameters	Extinction correction: Becker-Coppens type 1 Lorentzian isotropic, Becker, P.J. & Coppens, P. (1974) Acta Cryst., A30, 129-153.
0 restraints	Extinction coefficient: 1.03 (4)
Primary atom site location: structure-invariant direct methods

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

	x	y	z	Uiso*/Ueq
O1	0.72758 (4)	0.083979 (18)	0.62526 (4)	0.014
O2	0.44362 (4)	0.184293 (18)	0.76121 (3)	0.013
N1	0.64931 (3)	0.137733 (13)	0.18379 (3)	0.01
C1	0.55586 (3)	0.140893 (13)	0.60033 (3)	0.009
C2	0.46909 (3)	0.161207 (13)	0.35466 (3)	0.009
C3	0.26394 (4)	0.090932 (19)	0.30336 (4)	0.014
H11	0.70508	0.056862	0.192042	0.022
H12	0.78768	0.189125	0.209167	0.022
H13	0.583037	0.148178	0.017521	0.021
H21	0.426186	0.247778	0.338707	0.022
H31	0.19641	0.109258	0.131168	0.034
H32	0.131314	0.105266	0.431627	0.032
H33	0.306338	0.003893	0.303717	0.032

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.01451	0.01512	0.01097	0.00546	−0.00146	0.00106
O2	0.01639	0.01595	0.00722	0.00501	0.00014	−0.00103
N1	0.01231	0.01026	0.00718	0.0001	0.00029	−0.00008
C1	0.01063	0.00835	0.00681	0.00066	−0.00077	−0.00026
C2	0.01106	0.00886	0.00694	0.00106	−0.00076	−0.0002
C3	0.01274	0.01796	0.01125	−0.0027	−0.00213	−0.00109
H11	0.02411	0.01774	0.02537	0.0052	0.00278	0.00155
H12	0.02132	0.02466	0.02006	−0.00607	0.00099	−0.00096
H13	0.02567	0.02497	0.01304	0.00026	−0.00137	0.00002
H21	0.02869	0.01542	0.02183	0.00559	−0.00059	0.00079
H31	0.03433	0.04694	0.022	−0.00593	−0.01285	0.00384
H32	0.02193	0.0447	0.02935	−0.00359	0.00661	−0.00408
H33	0.03651	0.02038	0.03819	−0.00452	−0.0032	−0.00314

Geometric parameters (Å, º)

O1—C1	1.2467 (2)	C2—C3	1.5246 (3)
O2—C1	1.2640 (3)	C2—H21	1.0970 (2)
N1—H11	1.0480 (2)	C3—H31	1.0980 (2)
N1—H12	1.0480 (2)	C3—H32	1.0980 (2)
N1—H13	1.0480 (2)	C3—H33	1.0980 (2)
C1—C2	1.5333 (2)
H11—N1—H12	108.357 (15)	C3—C2—H21	110.204 (15)
H11—N1—H13	106.085 (14)	C2—C3—H31	110.743 (18)
H12—N1—H13	110.547 (14)	C2—C3—H32	110.712 (17)
O1—C1—O2	125.770 (19)	C2—C3—H33	111.483 (18)
O1—C1—C2	118.344 (17)	H31—C3—H32	108.521 (19)
O2—C1—C2	115.885 (16)	H31—C3—H33	106.577 (18)
C1—C2—C3	111.008 (15)	H32—C3—H33	108.664 (19)
C1—C2—H21	108.307 (13)
O1—C1—C2—C3	103.52 (2)	C1—C2—C3—H32	56.218 (17)
O1—C1—C2—H21	−135.37 (2)	C1—C2—C3—H33	−64.879 (18)
O2—C1—C2—C3	−76.37 (2)	H21—C2—C3—H31	56.647 (18)
O2—C1—C2—H21	44.746 (17)	H21—C2—C3—H32	−63.773 (18)
C1—C2—C3—H31	176.64 (2)	H21—C2—C3—H33	175.13 (2)