First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides

Abstract

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.