Delta self-consistent field - Revision history

Huebsch: /* Step 3 */

2025-10-17T10:41:48Z

Step 3

← Older revision		Revision as of 10:41, 17 October 2025
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	=== Step 3 ===		=== Step 3 ===
	To calculate ZPL, perform a full atomic relaxation of this excited state. After the convergence was achieved, make sure that the excited state was preserved and the converged configuration is correct.		To calculate ZPL, perform a full [[structure optimization\|atomic relaxation]] of this excited state. After the convergence was achieved, make sure that the excited state was preserved and the converged configuration is correct.
	Spin up Spin down		Spin up Spin down
	...		...

Huebsch at 10:37, 17 October 2025

2025-10-17T10:37:35Z

← Older revision		Revision as of 10:37, 17 October 2025
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	# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.		# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.
			# Perform a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.
	# ~~Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform~~ a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.

	# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>		# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>

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	state configuration. The ZPL calculation can be performed in three steps:		state configuration. The ZPL calculation can be performed in three steps:

	~~=== Step 1 ===~~		# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math display="inline">E_{gs}</math>.
	Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math display="inline">E_{gs}</math>.		# Set up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]] and perform a full [[Structure optimization\|atomic relaxation]] to obtain the total energy of the system in its excited-state configuration at relaxed atomic positions, <math display="inline">E_{ex}^*</math>
			# The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>
	~~=== Step 2 ===~~
	Set ~~the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags, i.e. set~~ up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]]~~. Then,~~ perform a full [[Structure optimization\|atomic relaxation]] to obtain the total energy of the system in its excited-state configuration at relaxed atomic positions, <math display="inline">E_{ex}^*</math>

	~~=== Step 3 ===~~
	The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>

	== Vertical emission energies (VEE) ==		== Vertical emission energies (VEE) ==
	The VEE calculation can be performed in three steps:		The VEE calculation can be performed in three steps:

	~~=== Step 1 ===~~		# Set up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]] to represent the excited state and perform a full [[Structure optimization\|atomic relaxation]] of the excited state to obtain the total energy <math>E_{ex}^*</math>.
	Set ~~the occupations of the bands~~ to represent the excited state ~~via {{TAG\|FERWE}}~~ and ~~{{TAG\|FERDO}} tags. Perform~~ a full [[Structure optimization\|atomic relaxation]] of the excited state to obtain the total energy <math>E_{ex}</math>.		# Remove the occupation constraints and perform a full [[Setting up an electronic minimization\|SCF calculation]] to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.
			# The VEE is then given by the difference between the total energies of the excited state and the ground state: <math display="inline">\mathrm{VEE} = E_{ex}^* - E_{gs}^*.</math>
	~~=== Step 2 ===~~
	Remove the occupation constraints and perform a full SCF calculation to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.

	~~=== Step 3 ===~~
	The VEE is then given by the difference between the total energies of the excited and ground ~~states~~: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}^*.</math>

	== Electronic minimization with constrained electronic occupation ==		== Electronic minimization with constrained electronic occupation ==
	[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]		[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]
	When ~~using constrained occupation calculations~~, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.		Identify the band index of the states involved in the excitation based on a ground-state calculation. Then, set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited state via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags.

			When constraining the electronic occupancies, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.

	To improve convergence, it is recommended to restart the calculation from the converged {{FILE\|WAVECAR}}.		To improve convergence, it is recommended to restart the calculation from the converged {{FILE\|WAVECAR}} file of a preceding calculation without constraints.
	{{NB\|mind\|{{TAG\|ALGO}}{{=}}Normal,Fast,VeryFast are not recommended for constrained occupation calculations as they may lead to state reordering.}}		{{NB\|mind\|{{TAG\|ALGO}}{{=}}Normal, Fast, VeryFast are not recommended for constrained occupation calculations as they may lead to state reordering.}}
	{{NB\|warning\|In versions of VASP between VASP 5.4.1 and VASP 6.4, the {{TAG\|LDIAG}}{{=}}.FALSE. was broken and did not preserve the order of states between ionic iterations.}}		{{NB\|warning\|In versions of VASP between VASP 5.4.1 and VASP 6.4, the {{TAG\|LDIAG}}{{=}}.FALSE. was broken and did not preserve the order of states between ionic iterations.}}

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	To simulate the excitation, we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:		To simulate the excitation, we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:

	{{~~TAG~~\|FERWE}} = 1281 640		{{TAGBL\|FERWE}} = 1281 640
	{{~~TAG~~\|FERDO}} = 1251 10 11 650		{{TAGBL\|FERDO}} = 1251 10 11 650

	Here, the first number is a multiplicity and the second number is the occupation, e.g., 128*1 means that the first 128 states are fully occupied. The occupations must be provided for all {{TAG\|NBANDS}} and all k-points. Thus, for a 4x4x4 k-point mesh with 13 k-points in IBZ, we have:		Here, the first number is a multiplicity and the second number is the occupation, e.g., 128*1 means that the first 128 states are fully occupied. The occupations must be provided for all {{TAG\|NBANDS}} and all k-points. Thus, for a 4x4x4 k-point mesh with 13 k-points in IBZ, we have:

	{{~~TAG~~\|FERWE}} = 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640		{{TAGBL\|FERWE}} = 1281 640 1281 640 1281 640 1281 640 \
	{{~~TAG~~\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650		1281 640 1281 640 1281 640 1281 640 \
			1281 640 1281 640 1281 640 1281 640 \
			1281 640
			{{TAGBL\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650

	=== Step 2 ===		=== Step 2 ===

Huebsch at 10:11, 17 October 2025

2025-10-17T10:11:50Z

← Older revision		Revision as of 10:11, 17 October 2025
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	The VAE can be calculated by performing a full SCF calculation of the system in its excited-state configuration following three steps:		The VAE can be calculated by performing a full SCF calculation of the system in its excited-state configuration following three steps:

	~~=== Step 1 ===~~		# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.
	Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.

	~~=== Step 2 ===~~		# Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.
	Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.

	~~=== Step 3 ===~~		# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>
	The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>

	== Zero-phonon lines (ZPL) ==		== Zero-phonon lines (ZPL) ==

Huebsch: /* Step 3 */

2025-10-17T10:11:03Z

Step 3

← Older revision		Revision as of 10:11, 17 October 2025
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	=== Step 3 ===		=== Step 3 ===
	The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{~~VEE~~} = E_{ex} - E_{gs}.</math>		The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>

	== Zero-phonon lines (ZPL) ==		== Zero-phonon lines (ZPL) ==

Huebsch at 10:08, 17 October 2025

2025-10-17T10:08:38Z

← Older revision		Revision as of 10:08, 17 October 2025
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	=== Step 2 ===		=== Step 2 ===
	Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full SCF calculation to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.		Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.

	=== Step 3 ===		=== Step 3 ===
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	The ZPL calculation requires performing a full atomic relaxation in the excited		The ZPL calculation requires performing a full atomic relaxation in the excited
	state configuration. The ZPL calculation can be performed in three steps:		state configuration. The ZPL calculation can be performed in three steps:
	# Perform a ground state calculation to obtain the total energy of the system in its ground state configuration, <math display="inline">E_{gs}</math>.
	# Set the occupations of the Kohn-Sham states to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full atomic relaxation to obtain the total energy of the system in its ~~relaxed~~ excited-state configuration, <math display="inline">E_{ex}^*</math>		=== Step 1 ===
	# The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>		Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math display="inline">E_{gs}</math>.

			=== Step 2 ===
			Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags, i.e. set up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]]. Then, perform a full [[Structure optimization\|atomic relaxation]] to obtain the total energy of the system in its excited-state configuration at relaxed atomic positions, <math display="inline">E_{ex}^*</math>

			=== Step 3 ===
			The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>

	== Vertical emission energies (VEE) ==		== Vertical emission energies (VEE) ==
	The VEE calculation can be performed in three steps:		The VEE calculation can be performed in three steps:
	# Set the occupations of the bands to represent the excited state via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Perform a full atomic relaxation of the excited state to obtain the total energy <math>E_{ex}</math>.
	~~# Remove the occupation constraints and perform a full SCF calculation to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.~~
	~~# The VEE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}^*.</math>~~

	== Electronic minimization ==		=== Step 1 ===
			Set the occupations of the bands to represent the excited state via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Perform a full [[Structure optimization\|atomic relaxation]] of the excited state to obtain the total energy <math>E_{ex}</math>.

			=== Step 2 ===
			Remove the occupation constraints and perform a full SCF calculation to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.

			=== Step 3 ===
			The VEE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}^*.</math>

			== Electronic minimization with constrained electronic occupation ==
	[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]		[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]
	When using constrained occupation calculations, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.		When using constrained occupation calculations, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.
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	[[Image:Diamond_nv.png\|200px\|thumb\|<math display="inline">\mathrm{NV}^-</math> center in		[[Image:Diamond_nv.png\|200px\|thumb\|<math display="inline">\mathrm{NV}^-</math> center in
	64-atom diamond supercell.]]		64-atom diamond supercell.]]
	We consider a negatively charged point defect in diamond, so called <math display="inline">\mathrm{NV}^-</math> which ~~consist~~ of a N substitution and a vacancy. This is a well studied point defect in diamond which can be used here for illustrating the principle of the ZPL calculations {{cite\|Lofgren2018}}.		We consider a negatively charged point defect in diamond, so-called <math display="inline">\mathrm{NV}^-</math>, which consists of an N substitution and a vacancy. This is a well-studied point defect in diamond, which can be used here for illustrating the principle of the ZPL calculations {{cite\|Lofgren2018}}.
	In this example, we consider a single <math display="inline">\mathrm{NV}^-</math> in a 64-atom supercell.		In this example, we consider a single <math display="inline">\mathrm{NV}^-</math> in a 64-atom supercell.

	=== Step 1 ===		=== Step 1 ===
	Perform a full atomic relaxation of the <math display="inline">\mathrm{NV}^-</math> center in its ground state.		Perform a full [[Structure optimization\|atomic relaxation]] of the <math display="inline">\mathrm{NV}^-</math> center in its ground state.
	Identify the band index of the states involved in the excitation.		Identify the band index of the states involved in the excitation.

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	...		...

	To simulate the excitation we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:		To simulate the excitation, we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:

	{{TAG\|FERWE}} = 1281 640		{{TAG\|FERWE}} = 1281 640
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	...		...

	By subtracting the ground-state energy from the excited state we find the VAE of 1.77 eV.		By subtracting the ground-state energy from the excited state, we find the VAE of 1.77 eV.

	=== Step 3 ===		=== Step 3 ===
	To calculate ZPL, perform a full atomic relaxation of this excited state. After the convergence was achieved make sure that the excited state was ~~presevred~~ and the converged configuration is correct.		To calculate ZPL, perform a full atomic relaxation of this excited state. After the convergence was achieved, make sure that the excited state was preserved and the converged configuration is correct.
	Spin up Spin down		Spin up Spin down
	...		...

Huebsch at 09:10, 17 October 2025

2025-10-17T09:10:33Z

← Older revision		Revision as of 09:10, 17 October 2025
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	<math display="inline">\Delta</math>SCF is a method that allows to calculate energies of neutral excitation within DFT by constraining occupations. Within the Franck-Condon approximation, the electronic excitation is much faster than the nuclear motion. Thus, <math display="inline">\Delta</math>SCF can be used for calculating excited-state properties such as vertical absorption (VAE) and vertical emission energy (VEE). Furthermore, this method can be used to calculate the zero-phonon lines (ZPL) by performing a full atomic relaxation in the excited-state configuration and thus account for the Stockes shifts.		<math display="inline">\Delta</math>SCF is a method that allows to calculate energies of neutral excitation within DFT by constraining occupations. Within the Franck-Condon approximation, the electronic excitation is much faster than the nuclear motion. Thus, <math display="inline">\Delta</math>SCF can be used for calculating excited-state properties such as vertical absorption (VAE) and vertical emission energy (VEE). Furthermore, this method can be used to calculate the zero-phonon lines (ZPL) by performing a full atomic relaxation in the excited-state configuration and thus account for the Stockes shifts.
	This method is commonly used for calculating the optical properties of point defects in semiconductors and insulators {{cite\|Freysoldt2014}}.		This method is commonly used for calculating the [[:Category:Dielectric properties\|optical properties]] of point defects in semiconductors and insulators {{cite\|Freysoldt2014}}.

	== Vertical absorption energies (VAE) ==		== Vertical absorption energies (VAE) ==
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	The VAE can be calculated by performing a full SCF calculation of the system in its excited-state configuration following three steps:		The VAE can be calculated by performing a full SCF calculation of the system in its excited-state configuration following three steps:

	# Perform a ground state calculation to obtain the total energy of the system in its ground state configuration, <math>E_{gs}</math>.		=== Step 1 ===
	# Set the occupations of the Kohn-Sham states to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full SCF calculation to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.		Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.
	# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}.</math>
			=== Step 2 ===
			Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full SCF calculation to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.

			=== Step 3 ===
			The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}.</math>

	== Zero-phonon lines (ZPL) ==		== Zero-phonon lines (ZPL) ==

Huebsch: Huebsch moved page Delta Self-Consistent Field to Delta self-consistent field

2025-10-17T09:03:33Z

Huebsch moved page Delta Self-Consistent Field to Delta self-consistent field

← Older revision	Revision as of 09:03, 17 October 2025
(No difference)

Tal: /* Example: ZPL of \mathrm{NV}^- center in diamond */

2025-10-17T08:34:58Z

Example: ZPL of \mathrm{NV}^- center in diamond

← Older revision		Revision as of 08:34, 17 October 2025
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	In this example, we consider a single <math display="inline">\mathrm{NV}^-</math> in a 64-atom supercell.		In this example, we consider a single <math display="inline">\mathrm{NV}^-</math> in a 64-atom supercell.

	1. Perform a full atomic relaxation of the <math display="inline">\mathrm{NV}^-</math> center in its ground state.		=== Step 1 ===
			Perform a full atomic relaxation of the <math display="inline">\mathrm{NV}^-</math> center in its ground state.
	Identify the band index of the states involved in the excitation.		Identify the band index of the states involved in the excitation.

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	{{TAG\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650		{{TAG\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650

	2. Perform a full SCF calculation with the above occupations to obtain the total		=== Step 2 ===
			Perform a full SCF calculation with the above occupations to obtain the total
	energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>. Make sure that the correct excited state is preserved throughout the calculation.		energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>. Make sure that the correct excited state is preserved throughout the calculation.
	Spin up Spin down		Spin up Spin down
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	By subtracting the ground-state energy from the excited state we find the VAE of 1.77 eV.		By subtracting the ground-state energy from the excited state we find the VAE of 1.77 eV.

	3. To calculate ZPL, perform a full atomic relaxation of this excited state. After the convergence was achieved make sure that the excited state was presevred and the converged configuration is correct.		=== Step 3 ===
			To calculate ZPL, perform a full atomic relaxation of this excited state. After the convergence was achieved make sure that the excited state was presevred and the converged configuration is correct.
	Spin up Spin down		Spin up Spin down
	...		...

Tal: /* Zero-phonon lines (ZPL) */

2025-10-16T16:01:16Z

Zero-phonon lines (ZPL)

← Older revision		Revision as of 16:01, 16 October 2025
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	The ZPL calculation requires performing a full atomic relaxation in the excited		The ZPL calculation requires performing a full atomic relaxation in the excited
	state configuration. The ZPL calculation can be performed in three steps:		state configuration. The ZPL calculation can be performed in three steps:
	# Perform a ground state calculation to obtain the total energy of the system in its ground state configuration, <math display="inline">~~E_gs~~</math>.		# Perform a ground state calculation to obtain the total energy of the system in its ground state configuration, <math display="inline">E_{gs}</math>.
	# Set the occupations of the Kohn-Sham states to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full atomic relaxation to obtain the total energy of the system in its relaxed excited-state configuration, <math display="inline">E_{ex}^*</math>		# Set the occupations of the Kohn-Sham states to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform a full atomic relaxation to obtain the total energy of the system in its relaxed excited-state configuration, <math display="inline">E_{ex}^*</math>
	# The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>		# The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>

Tal: Tal moved page Construction:Deltascf to Delta Self-Consistent Field

2025-10-16T15:54:44Z

Tal moved page Construction:Deltascf to Delta Self-Consistent Field

← Older revision	Revision as of 15:54, 16 October 2025
(No difference)

← Older revision		Revision as of 10:37, 17 October 2025
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	# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.		# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math>E_{gs}</math>.
			# Perform a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.
	# ~~Set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags. Then, perform~~ a full [[#Electronic minimization with constrained electronic occupation\|SCF calculation with constrained electronic occupancies]] to obtain the total energy of the system in its excited-state configuration, <math display="inline">E_{ex}</math>.

	# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>		# The VAE is then given by the difference between the total energies of the excited and ground states: <math display="inline">\mathrm{VAE} = E_{ex} - E_{gs}.</math>

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	state configuration. The ZPL calculation can be performed in three steps:		state configuration. The ZPL calculation can be performed in three steps:

	~~=== Step 1 ===~~		# Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math display="inline">E_{gs}</math>.
	Perform a [[Setting up an electronic minimization\|ground-state calculation]] to obtain the total energy of the system in its ground-state configuration, <math display="inline">E_{gs}</math>.		# Set up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]] and perform a full [[Structure optimization\|atomic relaxation]] to obtain the total energy of the system in its excited-state configuration at relaxed atomic positions, <math display="inline">E_{ex}^*</math>
			# The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>
	~~=== Step 2 ===~~
	Set ~~the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags, i.e. set~~ up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]]~~. Then,~~ perform a full [[Structure optimization\|atomic relaxation]] to obtain the total energy of the system in its excited-state configuration at relaxed atomic positions, <math display="inline">E_{ex}^*</math>

	~~=== Step 3 ===~~
	The ZPL is then given by the difference between the total energies of the relaxed excited and ground states: <math display="inline">\mathrm{ZPL} = E_{ex}^* - E_{gs}</math>

	== Vertical emission energies (VEE) ==		== Vertical emission energies (VEE) ==
	The VEE calculation can be performed in three steps:		The VEE calculation can be performed in three steps:

	~~=== Step 1 ===~~		# Set up a [[#Electronic minimization with constrained electronic occupation\|constrained occupation calculation]] to represent the excited state and perform a full [[Structure optimization\|atomic relaxation]] of the excited state to obtain the total energy <math>E_{ex}^*</math>.
	Set ~~the occupations of the bands~~ to represent the excited state ~~via {{TAG\|FERWE}}~~ and ~~{{TAG\|FERDO}} tags. Perform~~ a full [[Structure optimization\|atomic relaxation]] of the excited state to obtain the total energy <math>E_{ex}</math>.		# Remove the occupation constraints and perform a full [[Setting up an electronic minimization\|SCF calculation]] to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.
			# The VEE is then given by the difference between the total energies of the excited state and the ground state: <math display="inline">\mathrm{VEE} = E_{ex}^* - E_{gs}^*.</math>
	~~=== Step 2 ===~~
	Remove the occupation constraints and perform a full SCF calculation to obtain the total energy of the system in this atomic configuration, <math display="inline">E_{gs}^*</math>.

	~~=== Step 3 ===~~
	The VEE is then given by the difference between the total energies of the excited and ground ~~states~~: <math display="inline">\mathrm{VEE} = E_{ex} - E_{gs}^*.</math>

	== Electronic minimization with constrained electronic occupation ==		== Electronic minimization with constrained electronic occupation ==
	[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]		[[Image:Diagram_delta_scf.png\|200px\|thumb\|Scheme of how states order might change upon SCF calculation of the excited state.]]
	When ~~using constrained occupation calculations~~, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.		Identify the band index of the states involved in the excitation based on a ground-state calculation. Then, set the [[:Category:Electronic occupancy\|occupations of the Kohn-Sham states]] to represent the excited state via {{TAG\|FERWE}} and {{TAG\|FERDO}} tags.

			When constraining the electronic occupancies, it is important to ensure that the order of the states is preserved throughout the calculation. This can be achieved by setting {{TAG\|LDIAG}}=.FALSE. in {{TAG\|ALGO}}=Damped or {{TAG\|ALGO}}=All.

	To improve convergence, it is recommended to restart the calculation from the converged {{FILE\|WAVECAR}}.		To improve convergence, it is recommended to restart the calculation from the converged {{FILE\|WAVECAR}} file of a preceding calculation without constraints.
	{{NB\|mind\|{{TAG\|ALGO}}{{=}}Normal,Fast,VeryFast are not recommended for constrained occupation calculations as they may lead to state reordering.}}		{{NB\|mind\|{{TAG\|ALGO}}{{=}}Normal, Fast, VeryFast are not recommended for constrained occupation calculations as they may lead to state reordering.}}
	{{NB\|warning\|In versions of VASP between VASP 5.4.1 and VASP 6.4, the {{TAG\|LDIAG}}{{=}}.FALSE. was broken and did not preserve the order of states between ionic iterations.}}		{{NB\|warning\|In versions of VASP between VASP 5.4.1 and VASP 6.4, the {{TAG\|LDIAG}}{{=}}.FALSE. was broken and did not preserve the order of states between ionic iterations.}}

Line 67:		Line 57:
	To simulate the excitation, we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:		To simulate the excitation, we promote an electron from the highest occupied state in the spin-down channel (126) to the lowest unoccupied state in the same channel (127). Thus, we need to provide the following occupations:

	{{~~TAG~~\|FERWE}} = 1281 640		{{TAGBL\|FERWE}} = 1281 640
	{{~~TAG~~\|FERDO}} = 1251 10 11 650		{{TAGBL\|FERDO}} = 1251 10 11 650

	Here, the first number is a multiplicity and the second number is the occupation, e.g., 128*1 means that the first 128 states are fully occupied. The occupations must be provided for all {{TAG\|NBANDS}} and all k-points. Thus, for a 4x4x4 k-point mesh with 13 k-points in IBZ, we have:		Here, the first number is a multiplicity and the second number is the occupation, e.g., 128*1 means that the first 128 states are fully occupied. The occupations must be provided for all {{TAG\|NBANDS}} and all k-points. Thus, for a 4x4x4 k-point mesh with 13 k-points in IBZ, we have:

	{{~~TAG~~\|FERWE}} = 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640 1281 640		{{TAGBL\|FERWE}} = 1281 640 1281 640 1281 640 1281 640 \
	{{~~TAG~~\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650		1281 640 1281 640 1281 640 1281 640 \
			1281 640 1281 640 1281 640 1281 640 \
			1281 640
			{{TAGBL\|FERDO}} = 1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650 1251 10 11 650 1251 10 11 650 1251 10 11 650 \
			1251 10 11 650

	=== Step 2 ===		=== Step 2 ===