3,5-Di­methyl-1,3,5-oxadi­azane-2,4,6-trione: short intermolecular contacts determining the crystal packing

In the title compound, C₅H₆N₂O₄, the mol­ecules lie across a crystallographic mirror plane. The compound lacks traditional hydrogen-bond donors, and hence crystals are held together by unusual C=O...O, O...C and weak C—H...O interactions, forming layers. Adjacent layers are arranged in an antiparallel manner, yielding an ABA layer sequence. The intermolecular contacts are quite short; a topological analysis of charge density based on density-functional-theory calculations was used for consideration of these short contacts and indicated a strong attractive bonding closed-shell interaction between these atoms in the crystal structure.

S1. Comment

Intermolecular interactions are the basis for crystal engineering, their nature and strength determining their competitive importance in forming different crystal packings (Desiraju, 1995). Among these intermolecular forces, hydrogen bonds are the most important in view of their higher energy and directionality. The three-dimensional network in a crystal is determined by other forces as well, such as multipolar electrostatic, donor–acceptor and van der Waals interactions (Dunitz, 1996). For the consideration of non-bonded interactions, for a long time, the van der Waals radii concept (Bondi, 1964; Zefirov & Zorky, 1989) has been a common approach, and more recently, mean statistical contacts (Rowland & Taylor, 1996) have been also suggested for this purpose. There is a somewhat arbitrary dividing line between what is or is not an interaction, and none of these approaches give a valid conclusion about the nature of these short contacts; furthermore, in general, attractive and repulsive interactions cannot be distinguished.

The structure of the molecule of the title compound, (I), is shown in Fig. 1. The molecule is a cyclic derivative of urea, containing an anhydride moiety. X-ray investigation has shown that the bond lengths in (I) do not differ considerably from standard values found in other anhydrides, as well as urea derivatives (Bolte & Bauch, 1999), and the structure is related to 1,3-dimethylbarbituric acid, (II), where the CH₂ fragment is replaced by an O atom (Bertolasi et al., 2001). The molecule lies across a crystallographic mirror plane passing through O1, O3 and C2. The geometric parameters for (I) can be depicted from Table 1.

The smallest subunit of the packing mode in (I) consists of a trimer arrangement of (I), shown in Fig. 2. Because (I) does not have traditional hydrogen-bond donor groups, molecules interact in the crystal by means of unsual short C═O···O and O···C contacts, and weak C—H···O hydrogen bonds. The units of (I) are linked into chains by a very short C═O···O [O1···O3ⁱⁱ = 2.842 (3) Å] interaction. These chains are, in turn, transformed into layers by further short contacts [C═O3···O1ⁱⁱⁱ = 3.106 (2) Å and O1ⁱⁱⁱ···C2ⁱⁱ = 3.257 (2) Å] and weak H3···O2ⁱⁱⁱ and H2ⁱⁱ···O2ⁱⁱⁱ hydrogen bonds, having distances of 2.78 (2) and 2.58 (3) Å, respectively [symmetry codes: (ii) − 1/2 + x, 1/2 − y, 3/2 − z; (iii) x, y, −1 + z]. The three contacts are comparable to the sum of the C and O van der Waals radii, of 3.04 Å (O/O) and 3.22 Å (C/O; Bondi, 1964), and are to be compared with an average of ca 3.4 Å and a minimum of 2.8 Å found for comparable types of interactions (Allen et al., 1998; Zacharias & Glusker, 1984). Adjacent layers are arranged in a reverse manner and there are no particularly strong interactions between these layers, indicating a simple close packing. The lateral packing of the layers arranged in an antiparallel manner (ABA layer sequence) is simply a consequence of the centrosymmetric nature of the space group Pnma.

The theory of atoms in molecules (Bader, 1990) can be used to analyze the chemical bonding in terms of shared (covalent) and closed shell interaction (van der Waals, ionic bonding etc.) with respect to the attractive bonding character of short contacts. This theory describes a molecule in terms of electron density, ρ(r), its gradient vector field, gradρ(r), Laplacian, grad²ρ(r), and bond critical points, CP. The type of interaction is characterized by the sign and magnitude of the Laplacian ρ(r_b) at the bond critical point. If electronic charge is concentrated in the bond CP [grad²ρ(r_b) < 0], this type of interaction is referred to as a shared interaction. Interactions that are dominated by contraction of charge away from the interatomic surface toward each nuclei [grad²ρ(r_b) > 0] are called closed-shell interactions. For closed shell interactions, ρ(r_b) is relatively low in value, and the value of grad²ρ(r_b) is positive. The sign of the Laplacian is determined by the positive curvature of ρ(r_b) along the interaction line, as the exclusion principle leads to relative depletion of charge in the atomic surface. Critical points of the (3,-1) type, so-called bond critical points, provide, according Bader (1990), a universal indicator of bonding between these atoms and are of prime importance from the chemical standpoint. It is believed that a bonding interaction occurs between the atoms if there is a line (bonding path) linking their nuclei along which the charge density has a maximum with respect to any lateral shift, and which has a minimum at the bond critical point (3,-1).

The trimer unit as shown in Fig. 2 was used for the analysis of the intermolecular interactions in (I) and every expected covalent bond has been characterized by a negative Laplacian at the bond CP. In addition to the expected path network, three (3,-1) unusual bond CPs have been found on the O1···O3ⁱⁱ (CP1), O3···O1ⁱⁱⁱ (CP2) and O1ⁱⁱⁱ···C2ⁱⁱ (CP3) lines (Table 2). Fig. 3 (left) shows the gradient lines of the electron density and the projection of the molecular graph onto the mirror plane O1···O1ⁱⁱⁱ···C2ⁱⁱⁱ containing CP1, CP2 and CP3. In Fig. 3 (right), a few of the gradient lines and the projection of the molecular graph onto the O1···O3ⁱⁱ···C3ⁱⁱ shows the origin of the strongest attractive interaction between the atoms O1 and O3ⁱⁱ (CP1).

The calculated positive Laplacian of the electron density [grad²ρ(r_b)] and the relatively low value of ρ(r_b) at the bond critical points (Table 2) indicate that the closest O1···O3ⁱⁱ (CP1), O3···O1ⁱⁱⁱ (CP2) and O1ⁱⁱⁱ···C2ⁱⁱ (CP3) contacts (Klapötke et al., 2005), as well as the weak hydrogen bonds H2ⁱⁱ···O2ⁱⁱⁱ (CP4) and H3···O2ⁱⁱⁱ (CP5), are dominated by bonding closed-shell interaction. The high values of the ratio G(r_b)/ρ(r_b) at the bond CPs (Table 2) and the ratio of the eigenvalues |λ₁|λ₃ << 1 supports this conclusion (Table 3; Bader & Essen, 1984). Additional information about chemical bond types is available from total electronic energy density Ee(r_b) = G(r_b) + V(r_b). Closed-shell interactions are dominated by the kinetic energy density, G(r_b), in the region of the bond CP, with G(r_b) being slightly greater than potential energy density |V(r_b)| and with the energy density [Ee(r_b) > 0] close to zero (Table 2).

The values found for ρ(r) in (I) at the critical points for intermolecular C—H···O contacts (CP4 and CP5; Table 2) are comparable to those reported for intermolecular hydrogen bonds studied previously (Koch & Popelier, 1995).

S2. Experimental

To a cooled (268 K) suspension of dry N,N'-dimethylurea (5, 57 mmol) in MeCN (20 ml) was added slowly chlorosulfonylisocyanate (9.8 ml, 114 mmol) under nitrogen. The solution was stirred for 4 h at room temperature and quenched with ice (80 g). The reaction mixture was reduced to one-third of its volume and cooled at 278 K overnight. The resulting colorless powder was recrystallized from acetone yielding (I) as colorless rods suitable for single-crystal X-ray diffraction (m.p. 524 K). IR: 1832 cm⁻¹ (C═O), 1766 cm⁻¹ (C═O), 1708 cm⁻¹ (C═O); ¹H NMR ([d6]-DMSO): δ 3.16 (3H, s); ¹³C NMR ([d6]-DMSO): δ 29.5 (CH₃), 144.7 (C), 148.6 (C).

S3. Refinement

All non-H atoms were refined with anisotropic displacement parameters, employing a rigid-bond restraint to U^ij of the two bonded atoms (Rollett, 1970). The quantum-chemical calculations for (I) were performed at the B3LYP/6–311+G(3d,2p) level using the GAUSSIAN98 package (Frisch et al., 1998). Single-point calculations at the experimental geometry of a subunit of the crystal structure were performed, with no geometry optimization. Wavefunction files suitable for direct reading by AIM2000 (Biegler-Koenig, 2002) were obtained using the `output=wfn' option. The topological analysis of the theoretical charge-density distribution was carried out using AIM2000 program package.

Computing details

Data collection: IPDS Software (Stoe & Cie, 1997); cell refinement: IPDS Software; data reduction: IPDS Software; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 2000); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. A view of the molecular structure of (I), showing the atom-labeling scheme. Displacement ellipsoids are drawn at the 50% probability level and H atoms are shown as small spheres of a arbitrary radii. [Symmetry code: (i) x, − y + 1/2, z.]
	Fig. 2. The molecular packing in (I), shown in a perspective view along the a axis. Thick dashed lines represent C═O···O and C···O closed-shell bonding contacts, while thin dashed lines represent C—H···O hydrogen bonds. The dot indicates the inversion centre located in the middle of the unit cell. [Symmetry codes: (ii) x − 1/2, −y + 1/2, − z + 3/2; (iii) x, y, z − 1.]
	Fig. 3. Left: Gradient lines of the electron density and the projection density of the molecular graph on to the O1—O1^iii—C2^ii plane. Right: Gradient lines of the electron density and the projection density of the molecular graph onto the O1—O3^ii—C3^ii plane. Each line represents a trajectory of gradρ, which is a line of steepest ascent through the charge density. Most trajectories are attracted to a nucleus and constitute an atomic basin. The bond CPs are shown as circles, the ring CPs as rectangles and the cage critical point as triangles.

3,5-Dimethyl-1,3,5-oxadiazane-2,4,6-trione

Crystal data

C5H6N2O4	Orthorhombic P (as derived from metrics)
Mr = 158.11	Dx = 1.650 Mg m^−3
Orthorhombic, Pnma	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2n	Cell parameters from 3141 reflections
a = 7.7406 (7) Å	θ = 2.7–28.0°
b = 14.9682 (14) Å	µ = 0.15 mm^−1
c = 5.4928 (7) Å	T = 200 K
V = 636.41 (12) Å^3	Rod, colourless
Z = 4	0.42 × 0.15 × 0.09 mm
F(000) = 328

Data collection

Stoe IPDS diffractometer	595 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.048
Graphite monochromator	θmax = 28.0°, θmin = 4.0°
ϕ or ω scans	h = −10→9
5084 measured reflections	k = −18→19
794 independent reflections	l = −7→7

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.033	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.092	All H-atom parameters refined
S = 0.96	w = 1/[σ^2(Fo^2) + (0.0647P)^2] where P = (Fo^2 + 2Fc^2)/3
794 reflections	(Δ/σ)max < 0.001
67 parameters	Δρmax = 0.18 e Å^−3
0 restraints	Δρmin = −0.21 e Å^−3

Special details

Refinement. 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	0.04642 (14)	0.2500	0.2444 (2)	0.0274 (3)
O2	0.03498 (13)	0.39692 (7)	0.25123 (18)	0.0413 (3)
O3	0.32724 (15)	0.2500	0.8405 (2)	0.0305 (3)
N1	0.18465 (11)	0.32814 (6)	0.55163 (16)	0.0206 (3)
C1	0.08625 (15)	0.33055 (8)	0.34690 (19)	0.0246 (3)
C2	0.23911 (17)	0.2500	0.6605 (3)	0.0193 (3)
C3	0.23222 (18)	0.41312 (9)	0.6666 (3)	0.0289 (3)
H1	0.147 (3)	0.4561 (15)	0.634 (4)	0.071 (6)*
H2	0.338 (3)	0.4320 (14)	0.614 (4)	0.068 (5)*
H3	0.233 (3)	0.4064 (15)	0.829 (5)	0.072 (6)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0314 (6)	0.0328 (7)	0.0179 (5)	0.000	−0.0034 (5)	0.000
O2	0.0517 (6)	0.0347 (6)	0.0375 (5)	0.0075 (4)	−0.0082 (4)	0.0133 (4)
O3	0.0294 (6)	0.0314 (7)	0.0307 (6)	0.000	−0.0123 (5)	0.000
N1	0.0199 (4)	0.0187 (5)	0.0233 (5)	−0.0011 (3)	0.0007 (3)	0.0007 (3)
C1	0.0248 (5)	0.0279 (7)	0.0211 (5)	0.0020 (5)	0.0022 (4)	0.0049 (5)
C2	0.0150 (6)	0.0204 (8)	0.0226 (7)	0.000	0.0009 (5)	0.000
C3	0.0334 (6)	0.0195 (6)	0.0338 (7)	−0.0037 (5)	0.0017 (5)	−0.0031 (5)

Geometric parameters (Å, º)

O1—C1	1.3658 (13)	N1—C3	1.4669 (15)
O1—C1^i	1.3658 (13)	C2—N1^i	1.3798 (12)
O2—C1	1.1919 (15)	C3—H1	0.94 (2)
O3—C2	1.2008 (18)	C3—H2	0.91 (2)
N1—C1	1.3587 (14)	C3—H3	0.90 (2)
N1—C2	1.3798 (12)
C1—O1—C1^i	123.95 (12)	O3—C2—N1	122.03 (6)
C1—N1—C2	123.55 (10)	N1^i—C2—N1	115.93 (13)
C1—N1—C3	118.29 (10)	N1—C3—H1	109.5 (12)
C2—N1—C3	118.14 (10)	N1—C3—H2	111.0 (13)
O2—C1—N1	125.01 (12)	H1—C3—H2	110.9 (18)
O2—C1—O1	118.61 (11)	N1—C3—H3	109.3 (14)
N1—C1—O1	116.38 (10)	H1—C3—H3	105.6 (19)
O3—C2—N1^i	122.03 (6)	H2—C3—H3	110.3 (19)
C2—N1—C1—O2	178.68 (12)	C1^i—O1—C1—N1	6.0 (2)
C3—N1—C1—O2	0.19 (17)	C1—N1—C2—O3	179.38 (12)
C2—N1—C1—O1	−2.16 (16)	C3—N1—C2—O3	−2.13 (19)
C3—N1—C1—O1	179.35 (11)	C1—N1—C2—N1^i	−1.27 (19)
C1^i—O1—C1—O2	−174.76 (8)	C3—N1—C2—N1^i	177.22 (9)

Symmetry code: (i) x, −y+1/2, z.