FREE-ENERGY DERIVATIVES AND STRUCTURE OPTIMIZATION WITHIN QUASI-HARMONIC LATTICE-DYNAMICS

A method is presented for the calculation of the gradient of the free energy with respect to all the internal and external degrees of freedo m of a periodic crystal. This gradient can be used in conjunction with a static-energy Hessian for efficient geometrical optimization of sys tems with lar,ae unit cells. The free energy is calculated using latti ce statics and lattice dynamics in the quasiharmonic approximation. an d its derivatives by means of first-order perturbation theory. In the present application of the method, particles are assumed to interact v ia arbitrary short-ranged spherically-symmetric pair potentials and lo ng-ranged Coulomb forces, and polarizability effects are accounted for by use of the shell model. The method can be used directly as the bas is for a computer program which makes efficient use of both storage an d CPU time, especially for large unit cells. Detailed expressions for all the lattice sums are presented.