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The atomic and molecular interactions in a crystal of dinitrogen tetraoxide, α-N2O4, have been studied in terms of the quantum topological theory of molecular structure using high-resolution, low-temperature X-ray diffraction data. The experimental electron density and electrostatic potential have been reconstructed with the Hansen–Coppens multipole model. In addition, the three-dimensional periodic electron density of crystalline α-N2O4 has been calculated at the B3LYP/cc-pVDZ level of theory with and without the geometry optimization. The application of the quantum theory of atoms in molecules and crystals (QTAIMC) recovered the two types of intermolecular bond paths between O atoms in crystalline α-N2O4, one measuring 3.094, the other 3.116 Å. The three-dimensional distribution of the Laplacian of the electron density around the O atoms showed that the lumps in the negative Laplacian fit the holes on the O atoms in the adjacent molecules, both atoms being linked by the intermolecular bond paths. This shows that the Lewis-type molecular complementarity contributes significantly to intermolecular bonding in crystalline N2O4. Partial overlap of atomic-like basins created by zero-flux surfaces in both the electron density and the electrostatic potential show that attractive electrostatic interaction exists between O atoms even though they carry the same net formal charge. The exchange and correlation contributions to the potential energy density were also computed by means of the model functionals, which use the experimental electron density and its derivatives. It was found that the intermolecular interactions in α-N2O4 are accompanied by the correlation energy-density `bridges' lowering the local potential energy along the intermolecular O...O bond paths in the electron density, while the exchange energy density governs the shape of bounded molecules.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768109028821/so5026sup1.cif
Contains datablocks I, Imult

fcf

Structure factor file (CIF format) https://doi.org/10.1107/S0108768109028821/so5026Isup2.fcf
Corrected version supplied by the author on 22 September 2009

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108768109028821/so5026sup3.pdf
Electron density maps and multipole parameters

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768109028821/so5026Isup4.hkl
Original version

Computing details top

Data collection: SMART (Siemens, 1993) for (I). Cell refinement: SAINT (Siemens ,1995) for (I). Data reduction: SAINT (Siemens ,1995) for (I). Program(s) used to solve structure: SHELXS 86 (Sheldrick, 1986) for (I). Program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003) for (I); Protas, J. (1997). MOLDOS97/MOLLY IBM PC-DOS for Imult. Molecular graphics: CAMERON (Watkin et al., 1996) for (I). Software used to prepare material for publication: CRYSTALS (Betteridge et al., 2003) for (I).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
(I) top
Crystal data top
N2O4Mo Kα radiation, λ = 0.71073 Å
Mr = 92.01Cell parameters from 6613 reflections
Cubic, Im3θ = 2.5–52.5°
a = 7.7529 (1) ŵ = 0.22 mm1
V = 466.01 (1) Å3T = 100 K
Z = 6Cylinder, colourless
F(000) = 2761.00 × 0.40 × 0.40 mm
Dx = 1.967 Mg m3
Data collection top
Area
diffractometer
476 reflections with I > 2.0σ(I)
Graphite monochromatorRint = 0.025
ω scansθmax = 52.3°, θmin = 3.7°
Absorption correction: multi-scan
SADABS (Siemens, 1996)
h = 117
Tmin = 0.72, Tmax = 0.92k = 017
11365 measured reflectionsl = 09
516 independent reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: charge flipping
R[F2 > 2σ(F2)] = 0.028 Method = Modified Sheldrick w = 1/[σ2(F2) + ( 0.05P)2 + 0.04P] ,
where P = (max(Fo2,0) + 2Fc2)/3
wR(F2) = 0.076(Δ/σ)max = 0.001
S = 1.03Δρmax = 0.26 e Å3
508 reflectionsΔρmin = 0.21 e Å3
11 parameters
Crystal data top
N2O4Z = 6
Mr = 92.01Mo Kα radiation
Cubic, Im3µ = 0.22 mm1
a = 7.7529 (1) ÅT = 100 K
V = 466.01 (1) Å31.00 × 0.40 × 0.40 mm
Data collection top
Area
diffractometer
516 independent reflections
Absorption correction: multi-scan
SADABS (Siemens, 1996)
476 reflections with I > 2.0σ(I)
Tmin = 0.72, Tmax = 0.92Rint = 0.025
11365 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.02811 parameters
wR(F2) = 0.0760 restraints
S = 1.03Δρmax = 0.26 e Å3
508 reflectionsΔρmin = 0.21 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O0.82717 (4)0.64186 (4)0.50000.0196
N0.88661 (5)0.50000.50000.0137
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O0.02012 (11)0.01743 (10)0.02111 (11)0.00580 (7)0.00000.0000
N0.01461 (11)0.01414 (11)0.01245 (10)0.00000.00000.0000
Geometric parameters (Å, º) top
O1—N21.1924 (3)N2—N2i1.7582 (8)
Ni—N—O112.73 (2)O—N—Oii134.54 (4)
Ni—N—Oii112.73 (2)
Symmetry codes: (i) x+2, y+1, z+1; (ii) x, y+1, z.
(Imult) top
Crystal data top
?β = ?°
Mr = ?γ = ?°
?, ?V = ? Å3
a = ? ÅZ = ?
b = ? Å? radiation, λ = ? Å
c = ? Å × × mm
α = ?°
Data collection top
h = ??l = ??
k = ??
Refinement top
Refinement on F469 reflections
Least-squares matrix: full14 parameters
R[F2 > 2σ(F2)] = 0.0150 restraints
wR(F2) = 0.023 w2 = q/[s2(Fo2) + (0.05 P)2 + 0.50 P + 0.00 + 0.00 sin(th)]
where P = (0.3333 Fo2 + 0.6667 Fc2) q = 4.5
S = 1.44
Crystal data top
?β = ?°
Mr = ?γ = ?°
?, ?V = ? Å3
a = ? ÅZ = ?
b = ? Å? radiation, λ = ? Å
c = ? Å × × mm
α = ?°
Data collection top
Refinement top
R[F2 > 2σ(F2)] = 0.015469 reflections
wR(F2) = 0.02314 parameters
S = 1.440 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
O0.82717 (3)0.64158 (3)0.50.01920.5
N0.88658 (3)0.50.50.01340.25
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O0.01918 (6)0.01720 (5)0.02128 (6)0.0053 (4)00
N0.01437 (6)0.01337 (5)0.01239 (5)000

Experimental details

(I)(Imult)
Crystal data
Chemical formulaN2O4?
Mr92.01?
Crystal system, space groupCubic, Im3?, ?
Temperature (K)100?
a (Å)7.7529 (1) ?
V3)466.01 (1)?
Z6?
Radiation typeMo Kα?, λ = ? Å
µ (mm1)0.22?
Crystal size (mm)1.00 × 0.40 × 0.40 × ×
Data collection
DiffractometerArea
diffractometer
?
Absorption correctionMulti-scan
SADABS (Siemens, 1996)
?
Tmin, Tmax0.72, 0.92?, ?
No. of measured, independent and
observed reflections
11365, 516, 476 [I > 2.0σ(I)]?, ?, ? (?)
Rint0.025?
(sin θ/λ)max1)1.113
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.028, 0.076, 1.03 0.015, 0.023, 1.44
No. of reflections508469
No. of parameters1114
Δρmax, Δρmin (e Å3)0.26, 0.21?, ?

Computer programs: SMART (Siemens, 1993), SAINT (Siemens ,1995), SHELXS 86 (Sheldrick, 1986), CRYSTALS (Betteridge et al., 2003), Protas, J. (1997). MOLDOS97/MOLLY IBM PC-DOS, CAMERON (Watkin et al., 1996).

Selected geometric parameters (Å, º) for (I) top
O1—N21.1924 (3)N2—N2i1.7582 (8)
Ni—N—O112.73 (2)O—N—Oii134.54 (4)
Ni—N—Oii112.73 (2)
Symmetry codes: (i) x+2, y+1, z+1; (ii) x, y+1, z.
 

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