Category talk:Electronic minimization: Difference between revisions

Latest revision as of 15:16, 5 August 2024

The page Algorithms used in VASP to calculate the electronic groundstate describes the class of minimizers based on a combination of the SCF cycle and density mixing. This, however, is not the only class of methods available (there's the direct minimizers as well).

Several "Theory" pages mentioned here are off-topic:
- Move "k-point integration" elsewhere
- Move "Wrap-around errors" elsewhere

Several (probably all) pages on electronic minimizers need to be reworked. In some of them references like "in the previous section" are used, which are meaningless in a wiki environment. Examples: Efficient single band eigenvalue-minimization and Conjugate gradient optimization.

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-* Add a more precise definition of "electronic minimization" (from the lecture).
 * The page [[Algorithms used in VASP to calculate the electronic groundstate]] describes the class of minimizers based on a combination of the SCF cycle and density mixing. This, however, is not the only class of methods available (there's the direct minimizers as well).
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 *Do not use the TAG template to link to non-tag related articles.
-We seek to minimize the Kohn-Sham free energy:
-<math>
-F = \sum_n f_n \epsilon_n -E_{\rm H}\left[ \rho \right] +
-E_{\rm xc} \left[ \rho \right] -\int V_{\rm xc}({\bf r})\rho({\bf r})d{\bf r} -
-\sum_n \sigma S \left( \frac{\epsilon_n - \mu}{\sigma} \right)
-</math>
-where the electronic density is given by:
-<math>
-\rho({\bf r})= \sum_n f_{n} |\psi_{n}({\bf r})|^2
-</math>
-and the Kohn-Sham orbitals and eigenenergies, <math>\{\psi_n, \epsilon_n \}</math> are solutions to the Kohn-Sham equations:
-<math>
-H \left[ \rho \right] \psi_n = \epsilon_n S \psi_n
-</math>
-under the constraint that the orbitals are ''S''-orthonormal:
-<math>
-\langle \psi_m | S | \psi_n \rangle = \delta_{mn}
-</math>