Gradient equivalent crystal theory

This paper presents an extension of the formalism of equivalent crystal theory (ECT) by introducing an electron density gradient term so that the total model density becomes a more accurate representation of the real local density. Specifically, we allow for the electron density around a lattice site to have directionality, in addition to an average value, as assumed in ECT. We propose that an atom senses its neighbouring density as a weighted sum-the weights given by the its own electronic probability. As a benchmark, the method is used to compute vacancy migration energy curves of iron. These energies are in good agreement with previously published results.