# Exact exchange¶

Inclusion of the non-local Fock operator as an exchange-correclation functional is an experimental feature in gpaw.

The current implementation lacks the following features:

• Support for periodic systems. Actually, the code won’t complain, but the results have not been tested.
• Support for k-point sampling. No consideration has been made as to multiple k-points, or even comlplex wave functions, so this definitely won’t work.
• Forces. Force evaluations when including (a fraction of -) the fock operator in the xc-functional has been implemented, but has not been tested.
• Fractional occupations. For technical reasons, we had to decouple occupied and unoccupied states. This makes fractional occupations imposible. (Warning: the code will not raise an exception, but probably won’t converge).
• Speed. Inclusion of Fock exchange is exceedingly slow. The bottleneck is solving the poisson integrals of the Fock operator, which is currently done using an iterative real-space solver with a zero initial guess for the potential at each SCF cycle. This should be optimized.

One way to speed up an exact-exchange (or hybrid) calculation is to use the coarse grid (used for wave functions) instead of the finegrid (used for for densities) for the Fock potentials. This should give a speed-up factor of 8. This can be specified in the xc keyword like in this example coarse.py

Parallelization using domain decomposition is fully supported.

The Fock operator can be used to do the hybrid functional PBE0, and of course, Hartree-Fock type EXX. These are accessed by setting the xc keyword to PBE0 or EXX respectively.

A thesis on the implementation of EXX in the PAW framework, and the specifics of the GPAW project can be seen on the literature page.

A comparison of the atomization energies of the g2-1 test-set calculated in VASP, Gaussian03, and GPAW is shown in the below two figures for the PBE and the PBE0 functional respectively.

In the last figure, the curve marked GPAW (nonself.) is a non-selfconsistent PBE0 calculation using self-consistent PBE orbitals.