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

In ABACUS, KS-DFT is solved by self-consistent field (SCF) iteration method. By mixing the electron density with that obtained from previous steps, numerical instabilities can be ameliorated while also accelerating convergence. 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_ndim, mixing_type, mixing_beta, mixing_gg0, mixing_beta_mag, mixing_gg0_mag, mixing_gg0_min, mixing_angle.

mixing_ndim is the mixing dimensions in DIIS (broyden or pulay) mixing. Gerenally, a larger mixing_ndim leads to a better convergence. the default choice mixing_ndim=8 should work fine in most cases. For mixing_type, the default choice is broyden, which is slightly better than Pulay typically. Besides that, 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.

For non-spin-polarized calculations, the default choices usually achieve convergence. If convergence issue arises in metallic systems, you can try different value of Kerker preconditioning mixing_gg0 and mixing_gg0_min, and try to reduce mixing_beta, which is 0.8 defaultly for nspin=1.

For magnetic calculations, mixing_beta_mag and mixing_gg0_mag are activated. Considering collinear calculations, you can rely on the default value for most cases. If convergence issue arises, you can try to reduce mixing_beta and mixing_beta_mag together. For non-collinear calculations, tradtional broyden usually works, especially for a given magnetic configuration. If one is not interested in the energies of a given magnetic configuration but wants to determine the ground state by relaxing the magnetic moments’ directions, the standard Broyden mixing algorithm sometimes fails to find the correct magnetic configuration. If so, we can set mixing_angle=1.0, which is a promising mixing method proposed by J. Phys. Soc. Jpn. 82 (2013) 114706.

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


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.