The dimer interaction and lattice energy of ethylene and pyrazine in the multipole expansion; a comparison with atom-atom potentials

The long-range interactions between ethylene (C2H4) and between pyrazine (C4N2H4) molecules have been calculated in the multipole expansion from LCAO-SCF wave functions on the monomers. In first-order perturbation theory, the R-5 and R-7dependent terms have been considered. The second-order energy has been calculated in a new (non-empirical) application of Unsold’s approximation up to R-10terms inclusive. The electrostatic interactions appear to be relatively large for the dimers. Their contributions to the lattice energies of the crystals and, similarly, the contributions of the so-called dispersion cross terms are much less important, however, because these anisotropic interactions cancel to a large extent. The quadratic dispersion terms, which behave more isotropically, yield the major part of the lattice energy. The induction energy is very small. Difficulties appear in the calculations of the lattice energies because of the non-convergence of the multipole expansion. A comparison is made between the multipole expansion results and results obtained with the aid of empirical non-bonded atom-atom potentials. For the dispersion interactions the agreement is satisfactory; the results for the electrostatic energy disagree