# Mean-field calculations

The BerkeleyGW software package uses many-body perturbation-theory formalisms; therefore, one needs to provide a reasonable mean-field starting point for the perturbation-theory calculations. For most application, density-functional theory (DFT) based on semilocal functionals provide a good starting point for GW and GW-BSE calculations.

The following mean-field codes are currently supported by BerkeleyGW:

In addition, we include a wrapper to convert mean-field quantities to the StochasticGW code.

We provide a library to easily write mean-field-related quantities in the format used by BerkeleyGW.

BerkeleyGW requires the following quantities from mean-field codes:

• Mean-field eigenvalues and eigenvectors, stored in WFN files, for arbitrary k-point grids.
• The mean-field exchange-correlation matrix elements, vxc.dat, or exchange-correlation matrix in reciprocal space, VXC.
• Ground-state charge density $\rho(G)$, stored in RHO -- only for calculations based on the generalized plasmon-pole (GPP) model.

For further information on how to use each mean-field code with the appropriate wrapper for BerkeleyGW, we refer to the BerkeleyGW tutorials.

## Pitfalls

There are some notorious cases where typical DFT calculations might not provide a good starting point for one-shot perturbation-theory calculations. Examples include:

• Germanium crystal, which is often predicted to be metallic at DFT. This issue can be remedied by either using another mean-field starting point, or performing some sort of self-consistent iteration, for instance, based on the static COHSEX approximation.

• Molecules such as silane (SiH4), in which semilocal DFT often yields a LUMO orbital that bound, where in reality it is unbound. These systems can also be remedied by using a different starting mean-field point, or performing self-consistent GW calculations. For molecules, another common approach is known as best $G$, best $W$, where one picks one mean-field starting point to write the Green's function $G$ in $\Sigma=iGW$, such as Hartree-Fock, and another one to compute the polarizability $\chi^0$ used to construct $W$, such as LDA.

• Some strongly correlated systems, especially those with partially filled $f$ orbitals. Systems such as transition-metal oxides are often tackled with a Hubbard-type of correction scheme, such as DFT+U.