Weighted Density Functionals for Ferroelectric Materials

The weighted density approximation, its implementation and its application to ferroelectric materials is discussed. Calculations are presented for several perovskite oxides and related materials. In general the weighted density approximation is found to be superior to either the local density or generalized gradient approximation for the ground state. Electronic structures are little changed. The linear response of the weighted density approximation is calculated for the homogeneous electron gas, and found to be improved relative to the local density result, but not in full agreement with existing Monte Carlo data. It is shown that the agreement can be further improved by a simple modification. Calculations of the ferroelectric soft mode in KNbO$_3$ suggest that the low temperature distortion is approximately 20% smaller than indicated by existing experiments.