Modelling of crystal structure of cis-1,2,3,6 and 3,4,5,6-tetrahydrophthalic anhydrides using lattice energy calculations

Lattice energy calculations using a model potential were performed to model the crystal structures of cis-1,2,3,6- and 3,4,5,6-tetrahydrophthalic (THP) anhydrides. The optimized molecular models using the DFT method at the B3LYP/6-31G** level were found consistent with the available experimental evidence and allowed all differences observed in crystal packing between cis-1,2,3,6- and 3,4,5,6-THP anhydrides to be reproduced. Calculations provide evidence for the presence of dipole-dipole C= O center dot center dot center dot C= O intermolecular interactions and support the idea that the molecules distort from their ideal geometries, improving packing in both crystals. The search for minima in the lattice energy of both crystals amongst the more common space groups with Z'= 1, using a simulated annealing crystal structure prediction procedure followed by lattice energy minimization showed that the observed structure of 3,4,5, 6-THP anhydride (Z'= 2) is the thermodynamically most stable, and allowed us to justify why 3,4,5,6-THP anhydride crystallizes in such a complex structure with 16 molecules in the unit cell. The computational model was successful in predicting the second observed form at 173 K for cis-1,2,3, 6-THP anhydride as a polymorph, and could predict several hypothetical structures with Z'= 1 that appear competitive with the observed structures. The results of phonon estimates of zero point intermolecular vibrational energy and entropy suggest that crystal structures of cis-1,2,3,6-THP anhydride cannot be predicted solely on the basis of lattice energy; factors other than thermodynamics favor the observed structures.