N2–N2 interaction potential from ab initio calculations, with application to the structure of (N2)2

The short range electrostatic and (first order) exchange contributions to the N2–N2 interaction energy have been calculated a b i n i t i o as a function of the N2 orientations and the distance (139 geometries). Using a numerical integration procedure, the results have been represented analytically in the form of a spherical expansion. At R=0.3 nm this expansion is accurate to better than 0.5% if we include the first 18 independent terms, to 2% if we truncate after L A =L B =4, and to 16% if we truncate after L A =L B =2. In combination with the long range multipole expansion results (electrostaticR −5, R −7, R −9 terms, dispersion R −6, R −8, R −10 terms) calculated by Mulder e t a l., this yields an anisotropic N2–N2 interaction potential in the region of the van der Waals minimum, which can be fairly well represented also by a site–site model. The potential is in good agreement with the available experimental data for the gas phase and for the ordered (α and γ) crystal phases of solid N2. The structure of the van der Waals molecule (N2)2 is discussed; its energy is lowest for the crossed structure: ΔE m =1.5 kJ/mol, R m =0.35 nm (for the isotropic potential the well characteristics are ΔE m =0.75 kJ/mol and R m =0.417 nm). The (staggered) parallel and the T‐shaped structures are slightly higher in energy. The internal N2 rotation barriers vary from 0.2 kJ/mol (17 cm−1) to values comparable with the dissociation energy.

[1]  G. Herzberg,et al.  Spectra of diatomic molecules , 1950 .

[2]  P. Wormer,et al.  Anisotropy of long range interactions between linear molecules: H2-H2 and H2-He , 1979 .

[3]  P. Wormer,et al.  Interaction potential for He-H2 in the region of the Van der Waals minimum , 1975 .

[4]  W. Meyer,et al.  Theoretical studies of H2–H2 collisions. I. Elastic scattering of ground state para‐ and ortho‐H2 in the rigid rotor approximation , 1979 .

[5]  T. Scott.  Solid and liquid nitrogen , 1976 .

[6]  W. Steele.  Statistical Mechanics of Nonspherical Molecules , 1963 .

[7]  A. Stone.  The description of bimolecular potentials, forces and torques: the S and V function expansions , 1978 .

[8]  G. A. Parker,et al.  Intermolecular potential energy surfaces from electron gas methods. III. Angle, distance, and vibrational dependence of the Ar–CO interaction , 1978 .

[9]  P. Wormer,et al.  Quantum theoretical calculations of van der Waals interactions between molecules. Anisotropic long range interactions , 1977 .

[10]  T. Kihara,et al.  Intermolecular forces for D2, N2, O2, F2 and CO2 , 1974 .

[11]  William Klemperer,et al.  Molecular beam studies of benzene dimer, hexafluorobenzene dimer, and benzene–hexafluorobenzene , 1979 .

[12]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[13]  K. Ng,et al.  Validity of the multipole results for first-order molecule-molecule interaction energies. , 1977 .

[14]  G. Ewing,et al.  The infrared spectrum of the (N2)2 van der waals molecule , 1973 .

[15]  P. W. Langhoff,et al.  Approximations to Hartree—Fock Perturbation Theory , 1966 .

[16]  C. F. Curtiss,et al.  Molecular Theory Of Gases And Liquids , 1954 .

[17]  T. Kihara,et al.  Intermolecular forces for hydrogen, nitrogen and acetylene , 1977 .

[18]  A. Avoird,et al.  Multipole moments, polarizabilities and anisotropic long range interaction coefficients for N2 , 1980 .

[19]  A. Avoird,et al.  Lattice dynamics of the ethylene crystal with interaction potentials from ab initio calculations , 1978 .

[20]  N. S. Gillis,et al.  The anisotropic interaction between nitrogen molecules from solid state data , 1977 .