Category talk:Electronic minimization - Revision history

Vaspmaster at 15:16, 5 August 2024

2024-08-05T15:16:25Z

← Older revision		Revision as of 15:16, 5 August 2024
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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).		* 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.		*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>~~

Vaspmaster at 10:09, 15 July 2024

2024-07-15T10:09:57Z

← Older revision		Revision as of 10:09, 15 July 2024
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	*Do not use the TAG template to link to non-tag related articles.		*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>

Vaspmaster at 12:56, 2 July 2024

2024-07-02T12:56:29Z

← Older revision		Revision as of 12:56, 2 July 2024
Line 1:		Line 1:
			* 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).		* 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).

Huebsch: Huebsch moved page Talk:Electronic minimization to Category talk:Electronic minimization

2022-04-06T09:55:41Z

Huebsch moved page Talk:Electronic minimization to Category talk:Electronic minimization

← Older revision	Revision as of 09:55, 6 April 2022
(No difference)

Huebsch: Huebsch moved page Category talk:Electronic Minimization to Talk:Electronic minimization without leaving a redirect

2022-04-06T09:55:17Z

Huebsch moved page Category talk:Electronic Minimization to Talk:Electronic minimization without leaving a redirect

← Older revision	Revision as of 09:55, 6 April 2022
(No difference)

Karsai at 16:12, 9 February 2021

2021-02-09T16:12:15Z

← Older revision		Revision as of 16:12, 9 February 2021
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	*Several "Theory" pages mentioned here are off-topic:		*Several "Theory" pages mentioned here are off-topic:
	** Move "PAW method" elsewhere (e.g. to the "Theoretical Background section")
	** Move "k-point integration" elsewhere		** Move "k-point integration" elsewhere
	** Move "Wrap-around errors" elsewhere		** Move "Wrap-around errors" elsewhere

Vaspmaster at 10:26, 16 April 2019

2019-04-16T10:26:37Z

← Older revision		Revision as of 10:26, 16 April 2019
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			* 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:		*Several "Theory" pages mentioned here are off-topic:
	** Move "PAW method" elsewhere (e.g. to the "Theoretical Background section")		** Move "PAW method" elsewhere (e.g. to the "Theoretical Background section")

Vaspmaster: Created page with "*Several "Theory" pages mentioned here are off-topic: Move "PAW method" elsewhere (e.g. to the "Theoretical Background section") Move "k-point integration" elsewhere **..."

2019-04-16T10:18:43Z

Created page with "*Several "Theory" pages mentioned here are off-topic: ** Move "PAW method" elsewhere (e.g. to the "Theoretical Background section") ** Move "k-point integration" elsewhere **..."

New page

*Several "Theory" pages mentioned here are off-topic:
** Move "PAW method" elsewhere (e.g. to the "Theoretical Background section")
** 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.