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

• Received 30 July 1997

DOI:https://doi.org/10.1103/PhysRevB.56.14380