Category:Electronic minimization - Revision history

Huebsch at 14:04, 20 March 2026

2026-03-20T14:04:36Z

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-By '''electronic minimization''' we denote the process of determining the electronic ground state. This is an integral part of the vast majority of VASP calculations. The '''electronic minimization''' in VASP is highly optimized, and different settings warrant the use of different algorithms or procedures. For instance, very elongated cells are prone to [[charge sloshing]], which hampers convergence and can be avoided by clever settings in the [[:Category:density mixing|density mixer]].
+By '''electronic minimization''' we denote the process of determining the electronic ground state. This is an integral part of the vast majority of VASP calculations. The '''electronic minimization''' in VASP is highly optimized, and different settings warrant the use of different algorithms or procedures. For instance, very elongated cells are prone to [[charge sloshing]], which hampers convergence and can be avoided by clever settings in the [[:Category:density mixing|density mixer]].To learn the basics of electronic minimization in practice, visit the following how-to pages:
 == Theoretical background ==
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 For more details on the direct optimization algorithms, see [[Direct optimization of the orbitals|direct optimization of the orbitals]].
 [[Category:VASP|Electronic minimization]]

Huebsch: Style fixes: remove how-to links from intro (→ Related tags); add Related tags and articles section; add References section; Tutorials → Additional resources/Lectures with {{Video}} template; "Per default" → "By default" (×2); diagonalisation → diagonalization; aka → also known as; {{TAG|ALGO}} = Normal → {{TAG|ALGO|Normal}}; {{TAG|ISTART}} = 0 → {{TAG|ISTART|0}}; wavefunctions → orbitals; remove stale commented-out block; prose tweaks

2026-03-20T13:58:15Z

Style fixes: remove how-to links from intro (→ Related tags); add Related tags and articles section; add References section; Tutorials → Additional resources/Lectures with {{Video}} template; "Per default" → "By default" (×2); diagonalisation → diagonalization; aka → also known as; {{TAG|ALGO}} = Normal → {{TAG|ALGO|Normal}}; {{TAG|ISTART}} = 0 → {{TAG|ISTART|0}}; wavefunctions → orbitals; remove stale commented-out block; prose tweaks

← Older revision		Revision as of 13:58, 20 March 2026
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	By '''electronic minimization''' we denote the process of determining the electronic ground state. This is an integral part of the vast majority of VASP calculations. The '''electronic minimization''' in VASP is highly optimized, and different settings warrant the use of different algorithms or procedures. For instance, very elongated cells are prone to [[charge sloshing]], which hampers convergence and can be avoided by clever settings in the [[:Category:density mixing\|density mixer]]. ~~To learn the basics of electronic minimization in practice, visit the following how-to pages:~~		By '''electronic minimization''' we denote the process of determining the electronic ground state. This is an integral part of the vast majority of VASP calculations. The '''electronic minimization''' in VASP is highly optimized, and different settings warrant the use of different algorithms or procedures. For instance, very elongated cells are prone to [[charge sloshing]], which hampers convergence and can be avoided by clever settings in the [[:Category:density mixing\|density mixer]].

	* [[Setting up an electronic minimization]]
	* [[Troubleshooting electronic convergence]]
	== Theoretical background ==		== Theoretical background ==
	Within the context of Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:		Within the context of Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:
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	</math>		</math>

	The various algorithms for '''electronic minimization''' {{VASP}} offers, can be roughly divided into two categories:		The various algorithms for '''electronic minimization''' {{VASP}} offers can be roughly divided into two categories:
	* Iterative matrix ~~diagonalisation~~ + density mixing, ~~''aka''~~ the [[Self-consistency cycle\|self-consistency cycle]] (SCC).		* Iterative matrix diagonalization + density mixing, also known as the [[Self-consistency cycle\|self-consistency cycle]] (SCC).
	* [[Direct optimization of the orbitals]].		* [[Direct optimization of the orbitals]].

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	# The SCC starts with an initial guess for the electronic density of the system. In particular, {{VASP}} uses the approximation of overlapping atomic charge densities. This density defines the initial Hamiltonian.		# The SCC starts with an initial guess for the electronic density of the system. In particular, {{VASP}} uses the approximation of overlapping atomic charge densities. This density defines the initial Hamiltonian.
	# By means of iterative matrix-diagonalization techniques, one obtains the {{TAG\|NBANDS}} lowest lying eigenstates of the Hamiltonian. The iterative matrix-diagonalization algorithms implemented in {{VASP}} are the [[Blocked-Davidson algorithm\|blocked-Davidson algorithm]] and the [[RMM-DIIS\|residual-minimization method with direct inversion in the iterative subspace (RMM-DIIS)]]. ~~Per~~ default {{VASP}} uses the blocked-Davidson algorithm ({{TAG\|ALGO}} ~~= Normal~~).		# By means of iterative matrix-diagonalization techniques, one obtains the {{TAG\|NBANDS}} lowest lying eigenstates of the Hamiltonian. The iterative matrix-diagonalization algorithms implemented in {{VASP}} are the [[Blocked-Davidson algorithm\|blocked-Davidson algorithm]] and the [[RMM-DIIS\|residual-minimization method with direct inversion in the iterative subspace (RMM-DIIS)]]. By default, VASP uses the blocked-Davidson algorithm ({{TAG\|ALGO\|Normal}}).
	# After the eigenstates and eigenvalues have been determined with sufficient accuracy, they are used ~~in order~~ to compute the total energy of the system and to construct a new electronic density.		# After the eigenstates and eigenvalues have been determined with sufficient accuracy, they are used to compute the total energy of the system and to construct a new electronic density.
	# In principle, this new density could be taken to define a new Hamiltonian. However, in order to obtain 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 matrix diagonalization (step 2).		# In principle, this new density could be taken to define a new Hamiltonian. However, in order to obtain 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 matrix diagonalization (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 set by {{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 set by {{TAG\|EDIFF}}.

	Note that when starting from scratch ({{TAG\|ISTART}} ~~= 0~~), the SCC procedure of {{VASP}} always begins with several ({{TAG\|NELMDL}}) cycles where the density is kept fixed at the initial approximation, i.e., overlapping atomic charge densities.		Note that when starting from scratch ({{TAG\|ISTART\|0}}), the SCC procedure of {{VASP}} always begins with several ({{TAG\|NELMDL}}) cycles where the density is kept fixed at the initial approximation, i.e., overlapping atomic charge densities.
	This ensures that the ~~wavefunctions~~ that are initialized with random numbers have converged to something sensible before they are used to construct a new charge density.		This ensures that the orbitals that are initialized with random numbers have converged to something sensible before they are used to construct a new charge density.

	For a more detailed description of the SCC ~~have a look at: the~~ [[Self-consistency cycle\|self-consistency cycle]].		For a more detailed description of the SCC, see [[Self-consistency cycle\|self-consistency cycle]].

	== Direct optimization ==		== Direct optimization ==

	Similar to the SCC procedure described above, when starting from scratch ({{TAG\|ISTART}} ~~= 0~~), the direct optimization 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).		Similar to the SCC procedure described above, when starting from scratch ({{TAG\|ISTART\|0}}), the direct optimization 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 ~~wavefunctions~~ that are initialized with random numbers have converged to a reasonable starting point for the subsequent direct optimization.		This ensures that the orbitals that are initialized with random numbers have converged to a reasonable starting point for the subsequent direct optimization.

	The direct optimization 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.		The direct optimization 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.
	~~Per~~ default, the electronic density is constructed directly from the orbitals at each step along the way, without any density mixing.		By 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 stabilize these optimization procedures when [[charge sloshing]] occurs.		Optionally, though, density mixing may be used to stabilize these optimization procedures when [[charge sloshing]] occurs.

	As for the SCC described above, the direct optimization of the orbitals stops when the change of the total energy drops below {{TAG\|EDIFF}}.		As for the SCC described above, the direct optimization of the orbitals stops when the change of the total energy drops below {{TAG\|EDIFF}}.

	For more details on the direct optimization algorithms, ~~please read:~~ [[Direct optimization of the orbitals\|direct optimization of the orbitals]].		For more details on the direct optimization algorithms, see [[Direct optimization of the orbitals\|direct optimization of the orbitals]].

	== ~~Tutorials~~ ==		== Related tags and articles ==
	*Lecture available on [~~https://youtu.be/WlYykovzyiA~~ electronic optimization].		[[Setting up an electronic minimization]], [[Troubleshooting electronic convergence]], [[Self-consistency cycle]], [[Direct optimization of the orbitals]], [[charge sloshing]]

	~~<!--~~		Tags: {{TAG\|ALGO}}, {{TAG\|IALGO}}, {{TAG\|EDIFF}}, {{TAG\|NELMDL}}, {{TAG\|ISTART}}, {{TAG\|NBANDS}}
	~~----~~

	*Electronic minimization: {{TAG\|Algorithms used in VASP to calculate the electronic groundstate}}.		== Additional resources ==
	**Preconditioning of residuals: {{TAG\|Preconditioning}}.		=== Lectures ===
	**Simple Davidson iteration scheme: {{~~TAG~~\|~~Davidson iteration scheme}}.~~		* {{Video\|electronic-minimization:vasp\|Electronic optimization}}
	**Single band steepest descent scheme: {{TAG\|Single band steepest descent scheme}}.
	**Efficient single band eigenvalue-minimization: ~~{{TAG~~\|~~Efficient single band eigenvalue-minimization}}.~~
	**Conjugate gradient optimization~~: {{TAG\|Conjugate gradient optimization}}.~~
	**Residual minimization scheme, direct inversion in the iterative subspace (RMM-DIIS): {{TAG\|RMM-DIIS}}.
	*Wrap-around errors in FFT meshes - convolutions: {{TAG\|Wrap-around errors}}.
	*Integration of k points: {{TAG\|k-point integration}}.
	*[[Density mixing\|Theory of density mixing]]

	== ~~How to~~ ==		== References ==
	* [[Setting up an electronic minimization]]		<references/>
	* A description to obtain band decomposed charge densities is given here: [[Band decomposed charge densities]].
	* k-point projection scheme: {{TAG\|LKPROJ}}.
	-->

	[[Category:VASP\|Electronic minimization]]		[[Category:VASP\|Electronic minimization]]

Csheldon at 13:09, 20 October 2025

2025-10-20T13:09:06Z

← Older revision		Revision as of 13:09, 20 October 2025
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	For more details on the direct optimization algorithms, please read: [[Direct optimization of the orbitals\|direct optimization of the orbitals]].		For more details on the direct optimization algorithms, please read: [[Direct optimization of the orbitals\|direct optimization of the orbitals]].

			== Tutorials ==
			*Lecture available on [https://youtu.be/WlYykovzyiA electronic optimization].

	<!--		<!--
	----		----

Huebsch at 07:02, 14 May 2025

2025-05-14T07:02:47Z

← Older revision		Revision as of 07:02, 14 May 2025
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	By '''electronic minimization''' we denote the process of determining the electronic ground state.		By '''electronic minimization''' we denote the process of determining the electronic ground state. This is an integral part of the vast majority of VASP calculations. The '''electronic minimization''' in VASP is highly optimized, and different settings warrant the use of different algorithms or procedures. For instance, very elongated cells are prone to [[charge sloshing]], which hampers convergence and can be avoided by clever settings in the [[:Category:density mixing\|density mixer]]. To learn the basics of electronic minimization in practice, visit the following how-to pages:

			* [[Setting up an electronic minimization]]
			* [[Troubleshooting electronic convergence]]
			== Theoretical background ==
	Within the context of Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:		Within the context of Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:

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	== How to ==		== How to ==
	*A description to obtain band decomposed charge densities is given here: ~~{{TAG\|~~Band decomposed charge densities}}.		* [[Setting up an electronic minimization]]
	*k-point projection scheme: {{TAG\|LKPROJ}}.		* A description to obtain band decomposed charge densities is given here: [[Band decomposed charge densities]].
			* k-point projection scheme: {{TAG\|LKPROJ}}.
	-->		-->

	[[Category:VASP\|Electronic minimization]]		[[Category:VASP\|Electronic minimization]]

Huebsch: /* Direct optimization */

2024-10-17T09:49:25Z

Direct optimization

← Older revision		Revision as of 09:49, 17 October 2024
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	For more details on the direct optimization algorithms, please read: [[Direct optimization of the orbitals\|direct optimization of the orbitals]].		For more details on the direct optimization algorithms, please read: [[Direct optimization of the orbitals\|direct optimization of the orbitals]].

	<!--		<!--
	----		----
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	*k-point projection scheme: {{TAG\|LKPROJ}}.		*k-point projection scheme: {{TAG\|LKPROJ}}.
	-->		-->

	~~----~~

	[[Category:VASP\|Electronic minimization]]		[[Category:VASP\|Electronic minimization]]

Vaspmaster at 06:39, 16 July 2024

2024-07-16T06:39:23Z

← Older revision		Revision as of 06:39, 16 July 2024
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	By '''electronic minimization''' we denote the process of determining the electronic ground state.		By '''electronic minimization''' we denote the process of determining the electronic ground state.
			Within the context of Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:
	In Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:

	<span id="KohnShamFreeEnergy">		<span id="KohnShamFreeEnergy">
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	\langle \psi_m \| S \| \psi_n \rangle = \delta_{mn}		\langle \psi_m \| S \| \psi_n \rangle = \delta_{mn}
	</math>		</math>


	The various algorithms for '''electronic minimization''' {{VASP}} offers, can be roughly divided into two categories:		The various algorithms for '''electronic minimization''' {{VASP}} offers, can be roughly divided into two categories:

Vaspmaster at 11:59, 15 July 2024

2024-07-15T11:59:48Z

← Older revision		Revision as of 11:59, 15 July 2024
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	In Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:		In Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:

			<span id="KohnShamFreeEnergy">
	:<math>		:<math>
	F = \sum_n f_n \epsilon_n -E_{\rm H}\left[ \rho \right] +		F = \sum_n f_n \epsilon_n -E_{\rm H}\left[ \rho \right] +
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	\sum_n \sigma S \left( \frac{\epsilon_n - \mu}{\sigma} \right)		\sum_n \sigma S \left( \frac{\epsilon_n - \mu}{\sigma} \right)
	</math>		</math>
			</span>

	where the electronic density is given by:		where the electronic density is given by:

Vaspmaster at 10:19, 15 July 2024

2024-07-15T10:19:28Z

← Older revision		Revision as of 10:19, 15 July 2024
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	By '''electronic minimization''' we denote the process of determining the electronic ground state.		By '''electronic minimization''' we denote the process of determining the electronic ground state.

	~~The groundstate~~ is that state of the system that minimizes the Kohn-Sham free energy:		In Hohenberg-Kohn-Sham density functional theory, the ground state is that state of the system that minimizes the Kohn-Sham free energy:

	:<math>		:<math>

Vaspmaster at 10:18, 15 July 2024

2024-07-15T10:18:39Z

← Older revision		Revision as of 10:18, 15 July 2024
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	By '''electronic minimization''' we denote the process of determining the electronic ground state~~, ''i~~.~~e.'',~~		By '''electronic minimization''' we denote the process of determining the electronic ground state.
	that state of the system that minimizes the Kohn-Sham free energy:
			The groundstate is that state of the system that minimizes the Kohn-Sham free energy:

	:<math>		:<math>

Vaspmaster at 10:18, 15 July 2024

2024-07-15T10:18:07Z

← Older revision		Revision as of 10:18, 15 July 2024
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	By '''electronic minimization''' we denote the process of determining the electronic ground state.		By '''electronic minimization''' we denote the process of determining the electronic ground state, ''i.e.'',
			that state of the system that minimizes the Kohn-Sham free energy:
	~~The groundstate is~~ that state of the system that minimizes the Kohn-Sham free energy:

	:<math>		:<math>