Category talk:Electronic minimization

• 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).

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

• All "How to" pages mentioned here are off-topic (should be moved elsewhere)

• Subcategory "density of states" is off-topic

• 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.

• Do not use the TAG template to link to non-tag related articles.

We seek to minimize the Kohn-Sham free energy:

$F=\sum _{n}f_{n}\epsilon _{n}-E_{\rm {H}}\left[\rho \right]+E_{\rm {xc}}\left[\rho \right]-\int V_{\rm {xc}}({\bf {r}})\rho ({\bf {r}})d{\bf {r}}-\sum _{n}\sigma S\left({\frac {\epsilon _{n}-\mu }{\sigma }}\right)$

where the electronic density is given by:

$\rho ({\bf {r}})=\sum _{n}f_{n}|\psi _{n}({\bf {r}})|^{2}$

and the Kohn-Sham orbitals and eigenenergies, $\{\psi _{n},\epsilon _{n}\}$ are solutions to the Kohn-Sham equations:

$H\left[\rho \right]\psi _{n}=\epsilon _{n}S\psi _{n}$

under the constraint that the orbitals are S-orthonormal:

$\langle \psi _{m}|S|\psi _{n}\rangle =\delta _{mn}$