CRYSTAL PACKING WITHOUT SYMMETRY CONSTRAINTS .1. TESTS OF A NEW ALGORITHM FOR DETERMINING CRYSTAL-STRUCTURES BY ENERGY MINIMIZATION

We describe an efficient algorithm for determining crystal structures of rigid molecules by energy minimization, in which no constraint is imposed except for the existence of a fully variable lattice. The algorithm makes use of advances in secant methods for minimization, and in techniques for computing analytical derivatives of empirical potentials, to achieve both speed and accuracy of convergence. Tests of the algorithm with crystals of 25 organic molecules, in which the number of independent variables varied from 12 to 114 and energy minimization was started from an experimentally observed crystal structure, showed that (1) the final energies and lattice parameters were independent of the starring lattice (centered or primitive). (?) the final space group symmetry, determined by mathematical superposition of the molecules in the unit cell, was identical to the initial space group symmetry within close tolerances, and (3) in most cases, some or all symmetry was lost during energy minimization and regained before convergence. Varying the limits at which energetic contributions from nonbonded interactions were cut off, from values adopted frequently in the literature out to larger distances, had little effect on the final lattice parameters but could result in changes in total energy of as much as 10%. Tests with three different potentials, in which the pairwise interatomic contributions to the energy had the same mathematical form but different parameterization, indicated that, for full accuracy in reproducing crystal structures, changes might have to be made in the mathematical form as well as the parametrization of these potentials.