  We present a scheme to construct model potentials, with parameters computed
from first principles, for large-scale lattice-dynamical simulations of
materials. Our method mimics the traditional solid-state approach to the
investigation of vibrational spectra, i.e., we start from a suitably chosen
reference configuration of the material and describe its energy as a function
of arbitrary atomic distortions by means of a Taylor series. Such a form of the
potential-energy surface is completely general, trivial to formulate for any
compound, and physically transparent. Further, the approximations involved in
our effective models are clear-cut, and the precision can be improved in a
systematic and well-defined fashion. Moreover, such a simple definition allows
for a straightforward determination of the parameters in the low-order terms of
the series, as they are the direct result of
density-functional-perturbation-theory calculations, which greatly simplifies
the model construction. Here we present such a scheme, discuss a practical and
versatile methodology for the calculation of the model parameters from first
principles, and describe our results for two challenging cases in which the
model potential is strongly anharmonic, namely, ferroic perovskite oxides
PbTiO3 and SrTiO3. The choice of test materials was partly motivated by
historical reasons, since our scheme can be viewed as a natural extension of
(and was initially inspired by) the so-called first-principles effective
Hamiltonian approach to the investigation of temperature-driven effects in
ferroelectric perovskite oxides. Thus, the study of these compounds allows us
to better describe the connections between the effective-Hamiltonian method and
ours.
