  The various approximations used in the construction of a first-principles
effective Hamiltonian for BaTiO3, and their effects on the calculated
transition temperatures, are discussed. An effective Hamiltonian for BaTiO3 is
constructed not from first-principles calculations, but from the structural
energetics of an atomistic shell model for BaTiO3 of Tinte et al. This allows
the elimination of certain uncontrolled approximations that arise in the
comparison of first-principles effective Hamiltonian results with experimental
values and the quantification of errors associated with the selection of the
effective Hamiltonian subspace and subsequent projection. The discrepancies in
transition temperatures computed in classical simulations for this effective
Hamiltonian and for the atomistic shell model are shown to be associated
primarily with a poor description of the thermal expansion in the former case.
This leads to specific proposals for refinements to the first-principles
effective Hamiltonian method. Our results suggest that there are at least two
significant sources of error in the effective-Hamiltonian treatment of BaTiO3
in the literature, i.e., the improper treatment of thermal expansion, and the
errors inherent in the first-principles approach itself.
