Plotting exciton wavefunction - Revision history

Tal: /* How to plot the exciton wavefunction */

2025-02-26T16:50:28Z

How to plot the exciton wavefunction

← Older revision		Revision as of 16:50, 26 February 2025
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	{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
	{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}		{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}
	{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction ~~was~~ not correctly calculated in <code>vasp_std</code> and <code>vasp_ncl</code> if the hole or electron is not fixed at the coordinate (0,0,0). This issue was resolved in VASP 6.5.0}}		{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction is not correctly calculated in <code>vasp_std</code> and <code>vasp_ncl</code> if the hole or electron is not fixed at the coordinate (0,0,0). This issue was resolved in VASP 6.5.0}}

	=== Degeneracy ===		=== Degeneracy ===

Tal: /* How to plot the exciton wavefunction */

2025-02-26T16:48:17Z

How to plot the exciton wavefunction

← Older revision		Revision as of 16:48, 26 February 2025
Line 16:		Line 16:
	{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
	{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}		{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}
	{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction was not correctly calculated in <code>vasp_std</code> and <code>vasp_ncl</code> if the hole or electron is not fixed at (0,0,0). This issue was resolved in VASP 6.5.0}}		{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction was not correctly calculated in <code>vasp_std</code> and <code>vasp_ncl</code> if the hole or electron is not fixed at the coordinate (0,0,0). This issue was resolved in VASP 6.5.0}}

	=== Degeneracy ===		=== Degeneracy ===

Tal: /* How to plot the exciton wavefunction */

2025-02-26T16:47:50Z

How to plot the exciton wavefunction

← Older revision		Revision as of 16:47, 26 February 2025
Line 16:		Line 16:
	{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
	{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}		{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}
	{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction was not correctly calculated if the hole or electron is not fixed at (0,0,0). This issue was resolved in VASP 6.5.0}}		{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction was not correctly calculated in <code>vasp_std</code> and <code>vasp_ncl</code> if the hole or electron is not fixed at (0,0,0). This issue was resolved in VASP 6.5.0}}

	=== Degeneracy ===		=== Degeneracy ===

Tal: /* How to plot the exciton wavefunction */

2025-02-26T16:45:09Z

How to plot the exciton wavefunction

← Older revision		Revision as of 16:45, 26 February 2025
Line 15:		Line 15:
	FFT grid for supercell:		FFT grid for supercell:
	{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
	{{NB\|~~warning~~\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}		{{NB\|mind\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}
			{{NB\|warning\|In VASP 6.4.3 the exciton wavefunction was not correctly calculated if the hole or electron is not fixed at (0,0,0). This issue was resolved in VASP 6.5.0}}

	=== Degeneracy ===		=== Degeneracy ===

Huebsch: Huebsch moved page Construction:Plotting exciton wavefunction to Plotting exciton wavefunction without leaving a redirect

2024-03-19T10:52:27Z

Huebsch moved page Construction:Plotting exciton wavefunction to Plotting exciton wavefunction without leaving a redirect

← Older revision	Revision as of 10:52, 19 March 2024
(No difference)

Tal at 13:38, 16 February 2024

2024-02-16T13:38:06Z

← Older revision		Revision as of 13:38, 16 February 2024
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	The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v^*(\mathbf{r}_h)\phi_c(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.		The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v^*(\mathbf{r}_h)\phi_c(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.

	=== How to fix the position of the particle ===		=== How to fix the position of the particle ===
	The position of the fixed particle is provided in direct (fractional) coordinates by the tags {{TAG\|BSEHOLE}} or {{TAG\|BSEELECTRON}} for a hole or an electron, respectively. The tag {{TAG\|NBSEEIG}} sets the number of exciton wavefunctions that need to be computed.		The position of the fixed particle is provided in direct (fractional) coordinates by the tags {{TAG\|BSEHOLE}} or {{TAG\|BSEELECTRON}} for a hole or an electron, respectively. The tag {{TAG\|NBSEEIG}} sets the number of exciton wavefunctions that need to be computed.

Tal at 13:37, 16 February 2024

2024-02-16T13:37:31Z

← Older revision		Revision as of 13:37, 16 February 2024
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	electron position is fixed at:		electron position is fixed at:
	=== How to plot the exciton wavefunction ===		=== How to plot the exciton wavefunction ===
	VASP computes the charge density of a particular excitonic state, i.e., <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(r_e,\mathbf{r}_h)\|^2</math> or <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(\mathbf{r}_e,r_h)\|^2</math>, and writes the resulting charge density into {{FILE\|~~CHGCAR~~}}.XX files, which can be visualized using standard tools like VESTA, ASE, etc. Here, XX stands for the index <math>\lambda</math> of the state. VASP computes the charge density by transforming the unit cell with k-points into a supercell. Thus, the exciton charge density is written for a supercell of dimensions <math>{\rm NKX}\times{\rm NKX}\times{\rm NKX}</math>.		VASP computes the charge density of a particular excitonic state, i.e., <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(r_e,\mathbf{r}_h)\|^2</math> or <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(\mathbf{r}_e,r_h)\|^2</math>, and writes the resulting charge density into {{FILE\|CHG}}.XX files, which can be visualized using standard tools like VESTA, ASE, etc. Here, XX stands for the index <math>\lambda</math> of the state. VASP computes the charge density by transforming the unit cell with k-points into a supercell. Thus, the exciton charge density is written for a supercell of dimensions <math>{\rm NKX}\times{\rm NKX}\times{\rm NKX}</math>.
	The size of the supercell is written in the {{FILE\|OUTCAR}} file		The size of the supercell is written in the {{FILE\|OUTCAR}} file
	FFT grid for supercell:		FFT grid for supercell:
Line 23:		Line 23:

	== Related tags and sections ==		== Related tags and sections ==
	{{FILE\|~~CHGCAR~~}}, {{TAG\|NBSEEIG}}, {{TAG\|BSEHOLE}}, {{TAG\|BSEELECTRON}}, [[Bethe-Salpeter-equations calculations\|BSE]]		{{FILE\|CHG}}, {{TAG\|NBSEEIG}}, {{TAG\|BSEHOLE}}, {{TAG\|BSEELECTRON}}, [[Bethe-Salpeter-equations calculations\|BSE]]
	== References ==		== References ==

	[[Category:VASP]][[Category:Many-body perturbation theory]][[Category:Bethe-Salpeter equations]]		[[Category:VASP]][[Category:Many-body perturbation theory]][[Category:Bethe-Salpeter equations]]

Tal at 13:35, 16 February 2024

2024-02-16T13:35:30Z

← Older revision		Revision as of 13:35, 16 February 2024
Line 2:		Line 2:
	Plotting the wavefunction or charge density corresponding to an exciton can be instrumental in analyzing the excitonic state's symmetry, position, and localization.		Plotting the wavefunction or charge density corresponding to an exciton can be instrumental in analyzing the excitonic state's symmetry, position, and localization.

	The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v(\mathbf{r}_h)\phi_c^*(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.		The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v^*(\mathbf{r}_h)\phi_c(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.

	=== How to fix the position of the particle ===		=== How to fix the position of the particle ===
Line 11:		Line 11:
	or		or
	electron position is fixed at:		electron position is fixed at:

	=== How to plot the exciton wavefunction ===		=== How to plot the exciton wavefunction ===
	VASP computes the charge density of a particular excitonic state, i.e., <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(r_e,\mathbf{r}_h)\|^2</math> or <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(\mathbf{r}_e,r_h)\|^2</math>, and writes the resulting charge density into {{FILE\|CHGCAR}}.XX files, which can be visualized using standard tools like VESTA, ASE, etc. Here, XX stands for the index <math>\lambda</math> of the state. VASP computes the charge density by transforming the unit cell with k-points into a supercell. Thus, the exciton charge density is written for a supercell of dimensions <math>{\rm NKX}\times{\rm NKX}\times{\rm NKX}</math>.		VASP computes the charge density of a particular excitonic state, i.e., <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(r_e,\mathbf{r}_h)\|^2</math> or <math>\rho_\lambda(\mathbf{r})=\|\psi_\lambda(\mathbf{r}_e,r_h)\|^2</math>, and writes the resulting charge density into {{FILE\|CHGCAR}}.XX files, which can be visualized using standard tools like VESTA, ASE, etc. Here, XX stands for the index <math>\lambda</math> of the state. VASP computes the charge density by transforming the unit cell with k-points into a supercell. Thus, the exciton charge density is written for a supercell of dimensions <math>{\rm NKX}\times{\rm NKX}\times{\rm NKX}</math>.
	The size of the supercell is written in the {{FILE\|OUTCAR}} file		The size of the supercell is written in the {{FILE\|OUTCAR}} file
	FFT grid for supercell:		FFT grid for supercell:
	{{NB\|mind\| The size of {{FILE\|~~CHGCAR~~}}.XX files can get very large. Estimate the {{FILE\|~~CHGCAR~~}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})18</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHG}}.XX files can get very large. Estimate the {{FILE\|CHG}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})12</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
	{{NB\|warning\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}		{{NB\|warning\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}

Tal: Tal moved page Construction:Plot exciton wavefunction to Construction:Plotting exciton wavefunction

2024-02-12T09:24:33Z

Tal moved page Construction:Plot exciton wavefunction to Construction:Plotting exciton wavefunction

← Older revision	Revision as of 09:24, 12 February 2024
(No difference)

Huebsch at 12:22, 9 February 2024

2024-02-09T12:22:26Z

← Older revision		Revision as of 12:22, 9 February 2024
Line 1:		Line 1:
	[[File:HBN exciton.png\|400px\|thumb\|Charge density of the first bright exciton in hBN.]]		[[File:HBN exciton.png\|400px\|thumb\|Charge density of the first bright exciton in hBN.]]
	Plotting the wavefunction or charge density corresponding to an exciton can be instrumental ~~for~~ analyzing the symmetry, position, and localization ~~of the excitonic state~~.		Plotting the wavefunction or charge density corresponding to an exciton can be instrumental in analyzing the excitonic state's symmetry, position, and localization.

			The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v(\mathbf{r}_h)\phi_c^*(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.
	The exciton wavefunction is written as a function of coordinates of two particles (one hole and one electron) <math>\psi_\lambda(\mathbf{r}_e,\mathbf{r}_h)=\sum_{vc} A_{vc}^\lambda \phi_v(\mathbf{r}_h)\phi_c^*(\mathbf{r}_e)</math> {{cite\|gatti:prb:2013}}. In order to visualize such a function in 3D space, we need to "fix" one of the coordinates: the position of the electron <math>\psi_\lambda(r_e,\mathbf{r}_h)</math> or the position of the hole <math>\psi_\lambda(\mathbf{r}_e,r_h)</math>.

	=== How to fix the position of the particle ===		=== How to fix the position of the particle ===
	The position of the fixed particle is provided in direct (fractional) coordinates by the tags {{TAG\|BSEHOLE}} or {{TAG\|BSEELECTRON}} for a hole or an electron, respectively. The tag {{TAG\|NBSEEIG}} sets the number of exciton wavefunctions that ~~needs~~ to be computed.		The position of the fixed particle is provided in direct (fractional) coordinates by the tags {{TAG\|BSEHOLE}} or {{TAG\|BSEELECTRON}} for a hole or an electron, respectively. The tag {{TAG\|NBSEEIG}} sets the number of exciton wavefunctions that need to be computed.

	When fixing the position of the particle, ~~it is important to make sure~~ that it is not fixed exactly at the center of an atom or ~~coincide~~ with a node of the wavefunction. To avoid that, ~~make sure to~~ shift the fixed coordinate slightly away from the center of the atom. Furthermore, the wavefunction of the fixed particle is taken at the nearest <math>\mathbf{G}</math>-vector, whose exact position is written in the {{FILE\|OUTCAR}} file		When fixing the position of the particle, ensure that it is not fixed exactly at the center of an atom or coincides with a node of the wavefunction. To avoid that, shift the fixed coordinate slightly away from the center of the atom. Furthermore, the wavefunction of the fixed particle is taken at the nearest <math>\mathbf{G}</math>-vector, whose exact position is written in the {{FILE\|OUTCAR}} file
	hole position is fixed at:		hole position is fixed at:
	or		or
Line 17:		Line 16:
	The size of the supercell is written in the {{FILE\|OUTCAR}} file		The size of the supercell is written in the {{FILE\|OUTCAR}} file
	FFT grid for supercell:		FFT grid for supercell:

	{{NB\|mind\| The size of {{FILE\|CHGCAR}}.XX files can get very large. Estimate the {{FILE\|CHGCAR}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})18</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}		{{NB\|mind\| The size of {{FILE\|CHGCAR}}.XX files can get very large. Estimate the {{FILE\|CHGCAR}}.XX file size as follows <math>(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})\times(\mathrm{NGXNKX})18</math> bytes. Here, NG{X,Y,Z} is the number of grid points and NK{X,Y,Z} is the number of k-points along the axis.}}
			{{NB\|warning\|The exciton charge density only accounts for the plane-wave part of the wavefunction, and the augmentation terms are neglected.}}
	{{NB\|warning\|The exciton charge density only accounts for the plane-wave part of the ~~wave function~~ and the augmentation terms are neglected.}}

	=== Degeneracy ===		=== Degeneracy ===
	The calculated excitonic states can be degenerate, i.e., multiple eigenvectors have the same energy. For the correct analysis, the degenerate states should be added together.		The calculated excitonic states can be degenerate, i.e., multiple eigenvectors have the same energy. For the correct analysis, the degenerate states should be added together.

	{{NB\|mind\|Calculation of the exciton wavefunction is only supported with {{TAG\|IBSE}}{{=}}0 and {{TAG\|ANTIRES}}{{=}}0.}}		{{NB\|mind\|Calculation of the exciton wavefunction is only supported with {{TAG\|IBSE}}{{=}}0 and {{TAG\|ANTIRES}}{{=}}0.}}