Category:Electronic minimization: Difference between revisions

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Steps 2-4 are repeated until the change in the total energy from one cycle to the next drops below a specific threshold ({{TAG|EDIFF}}).
Steps 2-4 are repeated until the change in the total energy from one cycle to the next drops below a specific threshold ({{TAG|EDIFF}}).
When starting from scratch ({{TAG|ISTART}} = 0), the self-consistency cycle procedure of {{VASP}} always begins with several ({{TAG|NELMDL}}) cycles where the density is kept fixed at the initial approximation (overlapping atomic charge densities).
This ensures that the wave functions that are initialised with random numbers have converged to a something sensible before they are used to construct a new charge density.


=== Direct optimisation ===
=== 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.
Similar to the SCC procedure described above, when starting from scratch ({{TAG|ISTART}} = 0), the direct optimisation procedures in {{VASP}} always begin with several ({{TAG|NELMDL}}) self-consistency cycles where the density is kept fixed at the initial approximation (overlapping atomic charge densities).
This ensures that the wave functions that are initialised with random numbers have converged to reasonable starting point for the actual direct optimisation.
 
The direct optimisation of the orbitals uses 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.


After every change of the orbitals, the total energy and electronic density are recomputed.
After every change of the orbitals, the total energy and electronic density are recomputed.

Revision as of 11:48, 17 October 2023

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).

When starting from scratch (ISTART = 0), the self-consistency cycle procedure of VASP always begins with several (NELMDL) cycles where the density is kept fixed at the initial approximation (overlapping atomic charge densities). This ensures that the wave functions that are initialised with random numbers have converged to a something sensible before they are used to construct a new charge density.

Direct optimisation

Similar to the SCC procedure described above, when starting from scratch (ISTART = 0), the direct optimisation procedures in VASP always begin with several (NELMDL) self-consistency cycles where the density is kept fixed at the initial approximation (overlapping atomic charge densities). This ensures that the wave functions that are initialised with random numbers have converged to reasonable starting point for the actual direct optimisation.

The direct optimisation of the orbitals uses 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.

After every change of the orbitals, the total energy and electronic density are recomputed. 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.

Similar to the SCC described above, the direct optimisation of the orbitals stops when the change of the total energy drops below EDIFF.


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