First-Principles Electronic Structure Calculations

Dacapo is a solid-state electronic structure package created by Nørskov and coworkers at CAMP .  The code has two principle components: an  electronic structure calculation module and a potential energy minimization module.  The electronic structure calculations are performed using density functional theory. The exchange-correlation energy and potential are described by the generalized gradient approximation (GGA). The self-consistent density is determined by iterative diagonalization of the Kohn-Sham Hamiltonian, Fermi population of the Kohn-Sham states, and Pulay mixing of the resulting electronic density. All ionic cores are described by ultrasoft pseudopotentials, and the Kohn-Sham one-electron valence states are expanded in a basis of plane waves with kinetic energy below a chosen energy cut- off. The surface Brillouin zone is generally sampled at several k points.

Using the above techniques, values of the potential energy and the potential energy gradient are calculated for fixed positions of the ions.  This information is then fed to the second major component of Dacapo, the potential energy minimization module. The ionic positions are adjusted using standard optimization algorithms to find local minima in the potential energy surface.  At low temperature, these local minima represent stable, equilibrium configurations of the system under consideration.  Using this approach, it is possible to determine the thermodynamics of systems at low temperature. By analyzing ionic configurations that do not correspond to local minima in the potential energy surface, it is possible to probe non-equilibrium, kinetic processes such as surface diffusion and adsorbate bond breaking and bond making.

All of the above calculations are performed with a periodic, slab geometry.  A unit cell (comprised of several layers of metal ions with adsorbate layers at the surface) is periodically repeated in three dimensions.  Several equivalent layers of vacuum are incorporated into the unit cell to ensure that successive metal slabs will not interact with one another. Dacapo performs calculations only on the electrons and ions of the unit cell itself; the periodic structure of the material is simulated through the use of periodic boundary conditions.