Localizing the exchange hole

Upon an appropriate coordinate transformation one can write the exchange energy in terms of an exchange hole that is more local than usually considered. The most local holes correspond to complex transformations, but a simpler one leads to only slightly less local exchange holes. This transformation is directly related to the Weyl correspondence between classical and quantum mechanics and has close connections with the intra- and extracule densities that are useful when studying electron–electron interactions. The main disadvantage is that the local exchange hole is not normalized, but it offers an optimal starting point for developing approximate density functionals.