The experimental and theoretical QTAIMC study of the atomic and molecular interactions in dinitrogen tetroxide

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.

Computing details

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

(I)

Crystal data

N2O4	Mo Kα radiation, λ = 0.71073 Å
Mr = 92.01	Cell parameters from 6613 reflections
Cubic, Im3	θ = 2.5–52.5°
a = 7.7529 (1) Å	µ = 0.22 mm^−1
V = 466.01 (1) Å^3	T = 100 K
Z = 6	Cylinder, colourless
F(000) = 276	1.00 × 0.40 × 0.40 mm
Dx = 1.967 Mg m^−3

Data collection

Area diffractometer	476 reflections with I > 2.0σ(I)
Graphite monochromator	Rint = 0.025
ω scans	θmax = 52.3°, θmin = 3.7°
Absorption correction: multi-scan SADABS (Siemens, 1996)	h = 1→17
Tmin = 0.72, Tmax = 0.92	k = 0→17
11365 measured reflections	l = 0→9
516 independent reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: charge flipping
R[F^2 > 2σ(F^2)] = 0.028	Method = Modified Sheldrick w = 1/[σ^2(F^2) + ( 0.05P)^2 + 0.04P] , where P = (max(Fo^2,0) + 2Fc^2)/3
wR(F^2) = 0.076	(Δ/σ)max = 0.001
S = 1.03	Δρmax = 0.26 e Å^−3
508 reflections	Δρmin = −0.21 e Å^−3
11 parameters

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

	x	y	z	Uiso*/Ueq
O	0.82717 (4)	0.64186 (4)	0.5000	0.0196
N	0.88661 (5)	0.5000	0.5000	0.0137

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O	0.02012 (11)	0.01743 (10)	0.02111 (11)	0.00580 (7)	0.0000	0.0000
N	0.01461 (11)	0.01414 (11)	0.01245 (10)	0.0000	0.0000	0.0000

Geometric parameters (Å, º)

O1—N2	1.1924 (3)	N2—N2^i	1.7582 (8)
N^i—N—O	112.73 (2)	O—N—O^ii	134.54 (4)
N^i—N—O^ii	112.73 (2)

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

(Imult)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	× × mm
α = ?°

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Refinement on F	469 reflections
Least-squares matrix: full	14 parameters
R[F^2 > 2σ(F^2)] = 0.015	0 restraints
wR(F^2) = 0.023	w2 = q/[s^2(Fo^2) + (0.05 P)^2 + 0.50 P + 0.00 + 0.00 sin(th)] where P = (0.3333 Fo^2 + 0.6667 Fc^2) q = 4.5
S = 1.44

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
O	0.82717 (3)	0.64158 (3)	0.5	0.0192	0.5
N	0.88658 (3)	0.5	0.5	0.0134	0.25

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O	0.01918 (6)	0.01720 (5)	0.02128 (6)	0.0053 (4)	0	0
N	0.01437 (6)	0.01337 (5)	0.01239 (5)	0	0	0