Category:Density mixing

Density mixing refers to the way of updating, e.g., the charge density with each iteration step in a self-consistent calculation within density-functional theory (DFT). In the case of magnetism and metaGGAs also the spin-magnetization density and kinetic-energy density are considered. Selecting the optimal procedure enhances the electronic convergence, and avoids problems such as charge sloshing. In many cases, VASP automatically selects suitable values and it is unnecessary to set the tags related to density mixing manually.

Theory

In each iteration of a DFT calculation, we start from a given charge density ${\displaystyle \rho_{in}}$ and obtain the corresponding Kohn-Sham (KS) Hamiltonian and its eigenstates, i.e., KS orbitals. From the occupied KS orbitals, we can compute a new charge density ${\displaystyle \rho_{out}}$. Thus, conceptionally VASP solves a multidimensional fixed-point problem. To solve this problem, VASP uses nonlinear solvers that work with the input vector ${\displaystyle \rho_{in}}$ and the residual ${\displaystyle R = \rho_{out} - \rho_{in}}$. In these methods, a subspace is built from the input vectors and the optimal solution within this subspace is obtained. The most efficient solutions are the Broyden^[1] and the Pulay^[2] mixing scheme (IMIX=4). In the Broyden^[1] mixing, an approximate of the Jacobian matrix is iteratively improved to find the optimal solution. In the Pulay^[2] mixing, the input vectors are combined assuming linearity to minimize the residual.

The implementation in VASP is based on the work of Johnson^[3]. Kresse and Furthmüller^[4] extended on it and demonstrated that the Broyden and Pulay schemes transform into each other for certain choices of weights for the previous iterations. They also introduced an efficient metric putting additional weight on the long-range components of the density (small ${\displaystyle \mathbf G}$ vectors) resulting in a more robust convergence. Furthermore, VASP uses a Kerker preconditioning^[5] to improve the choice of the input density for the next iteration.

How to

Improve the convergence

For most simple DFT calculations, the default choice of the convergence parameters is quite well suited to converge the calculation. As a first step, we suggest visualizing your structure or examining the output for warnings to check for very close atoms. This can occasionally happen during a relaxation if a too large ionic step is performed. If the structure is correct, we recommend increasing the number of steps NELM and only if that doesn't work starting to tweak the parameters AMIX or BMIX; preferably the latter.

Magnetic calculations

For magnetic materials, not only the charge density but also the spin-magnetization density needs to converge. Converge magnetic calculations

MetaGGAs

For the density mixing schemes to work reliably, the charge density mixer must be aware of all quantities that affect the total energy during the self-consistency cycle. For a standard DFT functional, this is solely the charge density. In case of meta-GGAs, however, the total energy depends on the kinetic energy density as well.

In many cases the density mixing scheme works well enough without passing the kinetic energy density through the mixer, which is why LMIXTAU=.FALSE., per default. However, when the selfconsistency cycle fails to converge for one of the density-mixing algorithms (for instance, IALGO=38 or 48), one may set LMIXTAU=.TRUE. to have VASP pass the kinetic energy density through the mixer as well. This sometimes helps to cure convergence problems in the selfconsistency cycle.

References