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The charge density of urea is studied using very high precision single-crystal synchrotron-radiation diffraction data collected at the Swiss–Norwegian Beam Lines at ESRF. An unprecedented resolution of 1.44 Å
−1 in sinθ
λ is obtained at 123 K. The optimization of the experiment for charge-density studies is discussed. The high precision of the data allowed the refinement of a multipole model extending to hexadecapoles and quadrupoles on the heavy and H atoms, respectively, as well as a liberal treatment of radial functions. The topological properties of the resulting electron density are analysed and compared with earlier experimental results as well as with periodic Hartree–Fock calculations. The properties of the strongly polarized C—O bond agree with trends derived from previous experimental results while the
ab initio calculations differ significantly. The results indicate that the description of the C—O bond requires more flexible basis sets in the theoretical calculations. The calculated integrated atomic charges are much larger than the observed ones. It is suggested that the present experimental results provide new target values for validation of future
ab initio calculations. The molecular dipole moment derived from the integrated atomic properties is the same as the one obtained from the multipole model even though the individual atomic contributions differ. Comparison with literature data for urea in solution and the gas phase yields a dipole enhancement in the solid of about 1.5 D. The thermal expansion of urea is determined using synchrotron powder diffraction data. With decreasing temperature, an increasing anisotropic strain is observed.
Supporting information
CCDC reference: 1047783
Data collection: KM6-CH software; cell refinement: KM6-CH software; data reduction: XD_RED; program(s) used to refine structure: VALRAY.
Crystal data top
CH4N2O | F(000) = 64 |
Mr = 60.06 | Dx = 1.368 Mg m−3 |
Tetragonal, P421m | Synchrotron radiation, λ = 0.5996 (1) Å |
Hall symbol: P -4 2ab | Cell parameters from 17 reflections |
a = 5.5780 (6) Å | T = 123 K |
c = 4.6860 (7) Å | Block, colourless |
V = 145.80 (3) Å3 | 0.23 × 0.13 × 0.09 mm |
Z = 2 | |
Data collection top
KM6-CH six-circle κ diffractometer operated as standard four-circle
κ diffractometer with detector circle in the vertical plane to profit
from the linear polarization of the synchrotron beam. | 817 reflections with I > 2σ(I) |
Radiation source: bending magnet | Rint = 0.014 |
Si(111) double crystal monochromator | θmax = 59.8°, θmin = 3.7° |
ω–scan | h = −15→15 |
3942 measured reflections | k = −15→0 |
1045 independent reflections | l = −13→0 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
wR(F2) = 0.010 | Hydrogen site location: inferred from neighbouring sites |
S = 1.17 | All H-atom parameters refined |
1045 reflections | w = 1/[σ2(Fo2] |
77 parameters | (Δ/σ)max < 0.001 |
0 restraints | |
Crystal data top
CH4N2O | V = 145.80 (3) Å3 |
Mr = 60.06 | Z = 2 |
Tetragonal, P421m | Synchrotron radiation, λ = 0.5996 (1) Å |
a = 5.5780 (6) Å | T = 123 K |
c = 4.6860 (7) Å | 0.23 × 0.13 × 0.09 mm |
Data collection top
KM6-CH six-circle κ diffractometer operated as standard four-circle
κ diffractometer with detector circle in the vertical plane to profit
from the linear polarization of the synchrotron beam. | 817 reflections with I > 2σ(I) |
3942 measured reflections | Rint = 0.014 |
1045 independent reflections | |
Refinement top
wR(F2) = 0.010 | 77 parameters |
S = 1.17 | 0 restraints |
1045 reflections | All H-atom parameters refined |
Special details top
Refinement. Charge density refinement. H positional and displacement parameters fixed at
values from neutron study (Swaminathan et al. (1984) Acta Cryst. B40,
300–306. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
C | 0.0 | 0.5 | 0.32821 (3) | 0.01238 (2) | |
O | 0.0 | 0.5 | 0.59634 (10) | 0.01527 (2) | |
N | 0.14468 (7) | 0.64468 (7) | 0.17901 (10) | 0.02273 (3) | |
H1 | 0.2557 (4) | 0.7557 (4) | 0.2841 (4) | 0.0365 (6) | |
H2 | 0.1431 (4) | 0.6431 (4) | −0.0348 (3) | 0.0333 (5) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
O | 0.01958 (4) | 0.01958 (4) | 0.00665 (3) | 0.00164 (8) | 0.000 | 0.000 |
C | 0.01519 (4) | 0.01519 (4) | 0.00675 (4) | −0.00035 (6) | 0.000 | 0.000 |
N | 0.02931 (6) | 0.02931 (6) | 0.00956 (4) | −0.01570 (7) | 0.00002 (3) | 0.00002 (3) |
H1 | 0.0440 (11) | 0.0440 (11) | 0.0216 (7) | −0.0222 (8) | −0.0031 (9) | −0.0031 (9) |
H2 | 0.0430 (10) | 0.0430 (10) | 0.0140 (6) | −0.0158 (8) | 0.0019 (8) | 0.0019 (8) |
Geometric parameters (Å, º) top
O—C | 1.2565 (5) | N—H1 | 1.005 (2) |
C—N | 1.3384 (4) | N—H2 | 1.0020 (15) |
| | | |
O—C—N | 121.49 (2) | C—N—H2 | 120.78 (13) |
C—N—H1 | 119.16 (12) | H1—N—H2 | 120.06 (17) |
Experimental details
Crystal data |
Chemical formula | CH4N2O |
Mr | 60.06 |
Crystal system, space group | Tetragonal, P421m |
Temperature (K) | 123 |
a, c (Å) | 5.5780 (6), 4.6860 (7) |
V (Å3) | 145.80 (3) |
Z | 2 |
Radiation type | Synchrotron, λ = 0.5996 (1) Å |
µ (mm−1) | ? |
Crystal size (mm) | 0.23 × 0.13 × 0.09 |
|
Data collection |
Diffractometer | KM6-CH six-circle κ diffractometer operated as standard four-circle
κ diffractometer with detector circle in the vertical plane to profit
from the linear polarization of the synchrotron beam. |
Absorption correction | – |
No. of measured, independent and observed [I > 2σ(I)] reflections | 3942, 1045, 817 |
Rint | 0.014 |
(sin θ/λ)max (Å−1) | 1.442 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | ?, 0.010, 1.17 |
No. of reflections | 1045 |
No. of parameters | 77 |
H-atom treatment | All H-atom parameters refined |
Δρmax, Δρmin (e Å−3) | ?, ? |
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