Mb. Taylor et al., FREE-ENERGY DERIVATIVES AND STRUCTURE OPTIMIZATION WITHIN QUASI-HARMONIC LATTICE-DYNAMICS, Physical review. B, Condensed matter, 56(22), 1997, pp. 14380-14390
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.