  The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ)
are typically used in calculations of lattice vibrational and transport
properties as they contain the smallest number of degrees of freedom and thus
have the cheapest computational cost. However, in complex materials, the FBZ
can take on irregular shapes where lattice symmetries are not apparent. Thus,
conventional cells (with more atoms and regular shapes) are often used to
describe materials, though dynamical and transport calculations are more
expensive. Here we discuss an efficient anharmonic lattice dynamic method that
maps conventional cell dynamics to primitive cell dynamics based on
translational symmetries. This leads to phase interference conditions that act
like conserved quantum numbers and a conservation rule for phonon scattering
that is hidden in conventional dynamics which significantly reduces
computational cost. We demonstrate this method for phonon transport in a
variety of materials with inputs from first-principles calculations and
attribute its efficiency to reduced scattering phase space and fewer summations
in scattering matrix element calculations.
