# Converging SCF

As in any non-linear systems, numerical instabilities during SCF iterations may lead to nonconvergence. In ABACUS, we offer the following options to facilitate SCF convergence.

## Charge Mixing

By mixing the electron density with that obtained from previous steps, numerical instabilities can be ameliorated. ABACUS offers several mixing schemes, and users may make a selection by adjusting the mixing_type keyword in INPUT file.

For each of the mixing types, we also provide variables for controlling relevant parameters, including mixing_beta, mixing_ndim, and mixing_gg0.

The default choice is pulay, which should work fine in most cases. If convergence issue arises in metallic systems, inclusion of Kerker preconditioning may be helpful, which can be achieved by setting mixing_gg0 to be a positive number. For the default pulay method, a choice of 1.5 might be a good start.

A large mixing_beta means a larger change in electron density for each SCF step. For well-behaved systems, a larger mixing_beta leads to faster convergence. However, for some difficult cases, a smaller mixing_beta is preferred to avoid numerical instabilities.

An example showcasing different charge mixing methods can be found in our repository. Four INPUT files are provided, with description given in README.

## Smearing

Thermal smearing is an efficient tool for accelerating SCF convergence by allowing fractional occupation of molecular orbitals near the band edge. It is important for metallic systems.

In ABACUS, we provide a few smearing methods, which can be controlled using the keyword smearing_method. We also provide keyword smearing_sigma or smearing_sigma_temp to control the energy range of smearing. A larger value of smearing sigma leads to a more diffused occupation curve.

Note : The two keywords smearing_sigma and smearing_sigma_temp should not be used concurrently.

We provide an example showing the importance of smearing in our repository. Two INPUT fiels rae provided, with description given in README.