D. Steiger et al., CRYSTAL-POTENTIAL FORMULA FOR THE CALCULATION OF CRYSTAL-LATTICE SUMS, JOURNAL OF PHYSICAL CHEMISTRY B, 102(22), 1998, pp. 4257-4260
A new formula is derived for the determination of the potential energy
of the central unit cell of a finite crystal; this formula is called
the crystal potential formula. The crystal potential formula is based
on a two-center Cartesian multipole expansion. The key feature of the
crystal potential formula is that it achieves a separation of the latt
ice geometry and multipole moments. This feature allows one to compute
in a highly effective way the crystal energies as a function of the m
olecules contained in the unit cell. Numerical implementation is discu
ssed, and a numerical example is given. The example mimics an organic
crystal composed of dipolar molecules. It is found that the crystal en
vironment may create local minima and that the effects of the environm
ent might be well-approximated by consideration of the proximate unit
cells only. Both of these effects have important implications for the
crystal engineering of molecular organic materials.