Carlo calculation of the exchange energy

In recent generalized Kohn-Sham (GKS) schemes for density functional theory (DFT) HartreeFock type exchange is important. In plane waves and grid approaches the high cost of exchange energy calculations makes these GKS considerably more expensive than Kohn-Sham DFT calculations. We develop a stochastic approach for speeding up the calculation of exchange for large systems. We show that stochastic error per particle does not grow and can even decrease with system size (at a given number of iterations). We discuss several alternative approaches and explain how these ideas can be included in the GKS framework. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4743959]