ANALYTICAL EVALUATION OF ENERGY DERIVATIVES IN EXTENDED SYSTEMS - I -FORMALISM

A method is developed to analytically evaluate energy derivatives for extended systems. Linear dependence among basis functions, which almos t always occurs in extended systems and brings instability to the coup led-perturbed equations, is automatically eliminated in this method. T he remaining independent basis functions are transformed into semiorth ogonal orbitals. The derivatives of the orbitals and the overlap matri x over them are obtained via a set of coupled-perturbed equations, sim ilar to those of the coupled-perturbed Hartree-Fock (CPHF) equations w hich are used to calculate the derivatives of the Hartree-Fock (HF) or bitals and the orbital energies. By introducing symmetrized coordinate s. these coupled-perturbed equations can be easily solved. Explicit ex pressions for calculating gradients and Hessians of the HF energy for extended systems are given. With this method, we can calculate energy derivatives with respect to displacements of the nuclei, including tho se which break the translational symmetry. Therefore, the method not o nly provides an efficient and accurate approach to calculate energy de rivatives of any order, but also enables us to determine the force con stants for individual nuclei, the interatomic force constants, and pho non dispersion curves in the whole Brillouin zone. With this method, t he computational cost to calculate phonon spectrum with k not equal 0 in the Brillouin zone is the same as that needed for the spectrum at k = 0. (C) 1998 American Institute of Physics.