Category:Electronic minimization

The algorithms VASP offers for electronic optimisation (i.e., determining the electronic ground state) can be divided in two categories:

• Iterative matrix diagonalisation + density mixing, aka the "Self-Consistency Cycle" (SCC).
• Direct optimisation of the orbitals.

The Self-Consistency Cycle

1. The SCC starts with an initial guess for the electronic density of the system under consideration: VASP uses the approximation of overlapping atomic charge densities. This density defines the initial Hamiltonian.
2. By means of iterative matrix diagonalisation techniques one obtains the N lowest lying eigenstates of the Hamiltonian (where N is of the order of the number of electrons in the unit cell). The iterative matrix diagonalisation algorithms implemented in VASP are the blocked-Davidson algorithm and the Residual Minimization Method with Direct Inversion in the Iterative Subspace (RMM-DIIS).
3. After the eigenstates and eigenvalues have been the determined with sufficient accuracy, they are used to to compute the total energy of the system, and to construct a new electronic density.
4. In principle, this new density could be taken to define a new Hamiltonian. However, in order to arrive at a stable algorithm this new density is not used as is, but is mixed with the old density. By default VASP uses a Broyden mixer. The resulting density then defines the new Hamiltonian for the next round of iterative metrix diagonalisation (step 2).

Steps 2-4 are repeated until the change in the total energy from one cycle to the next drops below a specific threshold (EDIFF).

Direct optimisation

The methods in this category of electronic optimisation use the gradient of the total energy with respect to the orbitals to move towards the ground state of the system: the orbitals are changed such that the total energy is lowered, using, e.g. the Conjugate Gradient Approximation, or Damped Molecular Dynamics. Per default, the electronic density is constructed directly from the orbitals at each step along the way, without any density mixing. Optionally, though, density mixing may be used to stabilise these optimisation procedures when charge sloshing occurs.

• Electronic minimization: Algorithms used in VASP to calculate the electronic groundstate.
  • Preconditioning of residuals: Preconditioning.
  • Simple Davidson iteration scheme: Davidson iteration scheme.
  • Single band steepest descent scheme: Single band steepest descent scheme.
  • Efficient single band eigenvalue-minimization: Efficient single band eigenvalue-minimization.
  • Conjugate gradient optimization: Conjugate gradient optimization.
  • Residual minimization scheme, direct inversion in the iterative subspace (RMM-DIIS): RMM-DIIS.
• Wrap-around errors in FFT meshes - convolutions: Wrap-around errors.
• Integration of k points: k-point integration.
• Theory of density mixing

How to

• A description to obtain band decomposed charge densities is given here: Band decomposed charge densities.
• k-point projection scheme: LKPROJ.