Nitrogen solid lattice dynamics

In most cases, the crystal potential is not known a priori. The usual procedure is to introduce some model potential containing several parameters, which are subsequently found by fitting the calculated crystal properties to the observed data available. This procedure has the drawback that the empirical potential thus obtained includes the effects of the approximations made in the lattice dynamics model, which is mostly the harmonic model. It is very useful to have independent and detailed information about the potential from quantum-chemical ab initio calculations. Such information is available for nitrogen (Berns and van der Avoird, 1980) and oxygen (Wormer and van der Avoird, 1984), and we have chosen the results calculated for solid nitrogen and solid oxygen to illustrate in Sections V and VI, respectively, the lattice dynamics methods described in Sections III and IV. Nitrogen is the simplest typical molecular crystal as such it has received much attention from theorists and... 

The ab initio potentials used in solid nitrogen are from Refs. [31] and [32]. They have been respresented by a spherical expansion, Eq. (3), with coefficients up to = 6 and Lg = 6 inclusive, which describe the anisotropic short-range repulsion, the multipole-multipole interactions and the anisotropic dispersion interactions. They have also been fitted by a site-site model potential, Eq. (5), with force centers shifted away from the atoms, optimized for each interaction contribution. In the most advanced lattice dynamics model used, the TDH or RPA model, the libra-tions are expanded in spherical harmonics up to / = 12 and the translational vibrations in harmonic oscillator functions up to = 4, inclusive. 

---