Bethe-Salpeter-equations calculations - Revision history

Tal: /* Bethe-Salpeter equation calculation */

2025-04-11T12:51:33Z

Bethe-Salpeter equation calculation

← Older revision		Revision as of 12:51, 11 April 2025
Line 17:		Line 17:
	WFULL0001.tmp, WFULL0002.tmp, ..., WFULL{NKPTS}.tmp.		WFULL0001.tmp, WFULL0002.tmp, ..., WFULL{NKPTS}.tmp.

	The files {{FILE\|Wxxxx.tmp}} store only the diagonal terms of the kernel and are fairly small, whereas the files {{TAG\|WFULLxxxx.tmp}} store the full matrix. It is important to make sure in the ''GW'' step that the flag {{TAG\|LWAVE}} = .TRUE. is set, so that the {{FILE\|WAVECAR}} stores the one-electron ''GW'' energies and the one-electron orbitals, if the ''GW'' calculation is self-consistent.		The files {{FILE\|Wxxxx.tmp}} store only the diagonal terms of the kernel and are fairly small, whereas the files {{TAG\|WFULLxxxx.tmp}} store the full matrix. It is important to make sure in the ''GW'' step that the flag {{TAG\|LWAVE}} = .TRUE. is set, so that the {{FILE\|WAVECAR}} stores the one-electron ''GW'' energies and the one-electron orbitals, if the ''GW'' calculation is self-consistent. In the low-scaling ''GW'' algorithm use the {{TAG\|NOMEGA_DUMP}} tag to produce the {{TAG\|WFULLxxxx.tmp}} files.

	For the self-consistent ''GW'' calculations the following flags should be added		For the self-consistent ''GW'' calculations the following flags should be added

Tal: /* Calculations at finite wavevectors */

2025-01-29T14:54:47Z

Calculations at finite wavevectors

← Older revision		Revision as of 14:54, 29 January 2025
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	{{TAG\|NBANDSV}} = 8		{{TAG\|NBANDSV}} = 8

	The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP 6 (in VASP 5 the feature can be enabled, but the results are erroneous).		The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP 6 (in VASP 5 the feature can be enabled, but the results are erroneous).
			{{NB\|mind\|In the limit of infinitesimal momentum <math>\bf q</math>, <math>\varepsilon_{\alpha\beta}(q \to 0)</math> is a <math>3\times 3</math> tensor, where <math>\alpha=\{x,y,z\}</math> and <math>\beta=\{x,y,z\}</math>. However, at a finite momentum <math>\varepsilon(\bf q \neq 0)</math> is a scalar, i.e., has a single component.}}

	== Consistency tests ==		== Consistency tests ==

Tal at 14:39, 29 January 2025

2025-01-29T14:39:21Z

← Older revision		Revision as of 14:39, 29 January 2025
Line 112:		Line 112:
	{{TAG\|NBANDSV}} = 8		{{TAG\|NBANDSV}} = 8

	The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP.6 (in VASP.5 the feature can be enabled, but the results are erroneous).		The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP 6 (in VASP 5 the feature can be enabled, but the results are erroneous).

	== Consistency tests ==		== Consistency tests ==

Tal at 17:34, 7 February 2024

2024-02-07T17:34:25Z

← Older revision		Revision as of 17:34, 7 February 2024
Line 7:		Line 7:

	In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.		In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.


	== Bethe-Salpeter equation calculation ==		== Bethe-Salpeter equation calculation ==

Tal: /* Time-dependent Hartree-Fock */

2024-02-07T17:33:35Z

Time-dependent Hartree-Fock

← Older revision		Revision as of 17:33, 7 February 2024
Line 46:		Line 46:
	Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.		Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.

	== ~~Time-dependent Hartree-Fock~~ ==		== Model BSE (mBSE) ==
	~~The TDHF~~ calculations can be performed ~~in two~~ steps: ~~the~~ ground-state calculation ~~and the~~ optical absorption calculation. For example, an optical absorption calculation of bulk Si can be performed using a dielectric~~-dependent hybrid-functional~~ described in Ref. {{cite\|~~chen2018nonempirical~~}}.		BSE calculations can be performed using a model dielectric function{{cite\|bokdam:scr:2016}}{{cite\|tal:prr:2020}}. In this approach the calculation of the screened Coulomb potential is not required. Instead, the model dielectric function can be used to describe the screening of the Coulomb potential by setting the tag {{TAG\|LMODELHF}} with parameters {{TAG\|AEXX}} and {{TAG\|HFSCREEN}}.

			Model BSE calculation can be performed the following steps:
			# ground-state calculation
			# GW calculation (optional in model BSE calculation)
			# optical absorption calculation via model BSE

			For example, an optical absorption calculation of bulk Si can be performed using a model dielectric function as described in Ref. {{cite\|tal:prr:2020}}.

	{{TAG\|SYSTEM}} = Si		{{TAG\|SYSTEM}} = Si
Line 72:		Line 79:
	{{TAG\|LHARTREE}} = .TRUE.		{{TAG\|LHARTREE}} = .TRUE.
	{{TAG\|LADDER}} = .TRUE.		{{TAG\|LADDER}} = .TRUE.
	{{TAG\|LFXC}} = .~~TRUE~~.		{{TAG\|LFXC}} = .FALSE. ! local xc kernel is disabled in mBSE
	{{TAG\|LMODELHF}} = .TRUE.		{{TAG\|LMODELHF}} = .TRUE.
	{{TAG\|AEXX}} = 0.083		{{TAG\|AEXX}} = 0.083

Tal at 16:56, 7 February 2024

2024-02-07T16:56:07Z

@@ Line 8: / Line 8: @@
 In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.
 == Bethe-Salpeter equation calculation ==
@@ Line 82: / Line 45: @@
 Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG|vasprun.xml}} file.
 == Calculations beyond Tamm-Dancoff approximation ==

Tal at 15:01, 17 October 2023

2023-10-17T15:01:59Z

← Older revision		Revision as of 15:01, 17 October 2023
Line 1:		Line 1:
	VASP offers a powerful module for solving ~~time-dependent DFT (TD-DFT) and time-dependent Hartree-Fock equations (TDHF) (the Casida equation) or~~ the Bethe-Salpeter (BSE) equation{{cite\|albrecht:prl:98}}{{cite\|rohlfing:prl:98}}. ~~These approaches are~~ used for obtaining the frequency-dependent dielectric function with the excitonic effects and can be based on the ground-state electronic structure in the DFT, hybrid-functional or ~~[[Practical guide to GW calculations\|~~''GW'' ]] approximations.		VASP offers a powerful module for solving the Bethe-Salpeter (BSE) equation{{cite\|albrecht:prl:98}}{{cite\|rohlfing:prl:98}}. The BSE can be used for obtaining the frequency-dependent dielectric function with the excitonic effects and can be based on the ground-state electronic structure in the DFT, hybrid-functional or ''GW'' approximations.

	__TOC__		__TOC__

	== Solving Bethe-Salpeter ~~and Casida equations~~ ==		== Solving Bethe-Salpeter equation ==
	To take into account the excitonic effects or the electron-hole interaction, one has to use approximations beyond the independent-particle (IP) and the random-phase approximations ([[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|RPA]]). In VASP, it is done via the algorithm selected by {{TAG\|ALGO}} = BSE ~~or {{TAG\|ALGO}} = TDHF~~. These essentially solves the same equations (Casida/Bethe-Salpeter) but differ in the way the screening of the Coulomb potential is treated. The TDHF approach uses the exact-correlation kernel <math>f_{\rm xc}</math>, whereas BSE requires the <math>W(\omega \to 0)</math> from a preceding ''GW '' calculation. Thus, in order to perform TDHF or BSE calculations, one has to provide the ground-state orbitals ({{FILE\|WAVECAR}}) and the derivatives of the orbitals with respect to <math>k</math> ({{FILE\|WAVEDER}}). In addition, the BSE calculation requires files storing the screened Coulomb kernel produced in a ''GW'' calculation, i.e., {{FILE\|Wxxxx.tmp}}.		To take into account the excitonic effects or the electron-hole interaction, one has to use approximations beyond the independent-particle (IP) and the random-phase approximations ([[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|RPA]]). In VASP, it is done via the algorithm selected by {{TAG\|ALGO}} = BSE. These essentially solves the same equations (Casida/Bethe-Salpeter) but differ in the way the screening of the Coulomb potential is treated. The TDHF approach uses the exact-correlation kernel <math>f_{\rm xc}</math>, whereas BSE requires the <math>W(\omega \to 0)</math> from a preceding ''GW '' calculation. Thus, in order to perform TDHF or BSE calculations, one has to provide the ground-state orbitals ({{FILE\|WAVECAR}}) and the derivatives of the orbitals with respect to <math>k</math> ({{FILE\|WAVEDER}}). In addition, the BSE calculation requires files storing the screened Coulomb kernel produced in a ''GW'' calculation, i.e., {{FILE\|Wxxxx.tmp}}.

	In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.		In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.

Tal at 15:26, 16 October 2023

2023-10-16T15:26:48Z

← Older revision		Revision as of 15:26, 16 October 2023
Line 113:		Line 113:

	The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP.6 (in VASP.5 the feature can be enabled, but the results are erroneous).		The tag {{TAG\|KPOINT_BSE}} sets the <math>{\bf q}</math>-point and the shift at which the dielectric function is calculated. The first integer specifies the index of the <math>{\bf q}</math>-point and the other three values shift the provided <math>{\bf q}</math>-point by an arbitrary reciprocal vector <math> \bf G</math>. The reciprocal lattice vector is supplied by three integer values <math> n_i</math> with <math> {\bf G}= n_1 {\bf G}_1+n_2 {\bf G}_2+n_3 {\bf G}_3</math>. This feature is only supported as of VASP.6 (in VASP.5 the feature can be enabled, but the results are erroneous).

	~~== Scaling of the Bethe-Salpeter equation ==~~
	~~The scaling of the BSE/Casida equation strongly limits its application for large systems. The main limiting factor is the diagonalization of the BSE/TDHF Hamiltonian. The rank of the Hamiltonian is~~

	~~:<math>N_{\rm rank} = N_k\times N_c\times N_v</math>,~~

	where <math>N_k</math> is the number of k-points in the Brillouin zone and <math>N_c</math> and <math>N_v</math> are the number of conduction and valence bands, respectively. The diagonalization of the matrix scales cubically with the matrix rank, i.e., <math>N_{\rm rank}^3</math>. Despite the fact that this matrix diagonalization is usually the bottleneck for bigger systems, the construction of the BSE Hamiltonian also scales unfavorably and can play a dominant role in big systems, i.e.,

	~~:<math>N_k\times N_q\times (N_v\times N_v\times N_G\times N_c\times N_c)</math>,~~

	~~where <math>N_q</math> is the number of q-points and <math>N_G</math> number of G-vectors.~~

	== Consistency tests ==		== Consistency tests ==

Tal at 08:00, 20 July 2022

2022-07-20T08:00:10Z

← Older revision		Revision as of 08:00, 20 July 2022
Line 4:		Line 4:

	== Solving Bethe-Salpeter and Casida equations ==		== Solving Bethe-Salpeter and Casida equations ==
	To take into account the excitonic effects or the electron-hole interaction, one has to use approximations beyond the independent-particle (IP) and the random-phase approximations ([[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|RPA]]). In VASP, it is done via the algorithm selected by {{TAG\|ALGO}} = BSE or {{TAG\|ALGO}} = TDHF. These essentially solves the same equations (Casida/Bethe-Salpeter) but differ in the way the screening of the Coulomb potential is treated. The TDHF approach uses the exact-correlation kernel <math>f_{\rm xc}</math>, whereas BSE requires the <math>W(\omega \to 0)</math> from a preceding ''GW '' calculation. Thus, in order to perform TDHF or BSE calculations, one has to provide the ground-state orbitals ({{FILE\|WAVECAR}}) and the derivatives of the orbitals with respect to <math>k</math> ({{FILE\|WAVEDER}}). In addition, the BSE calculation requires files storing the screened Coulomb kernel produced in a ''GW'' calculation, i.e., {{FILE\|~~WXXXX~~.tmp}}.		To take into account the excitonic effects or the electron-hole interaction, one has to use approximations beyond the independent-particle (IP) and the random-phase approximations ([[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|RPA]]). In VASP, it is done via the algorithm selected by {{TAG\|ALGO}} = BSE or {{TAG\|ALGO}} = TDHF. These essentially solves the same equations (Casida/Bethe-Salpeter) but differ in the way the screening of the Coulomb potential is treated. The TDHF approach uses the exact-correlation kernel <math>f_{\rm xc}</math>, whereas BSE requires the <math>W(\omega \to 0)</math> from a preceding ''GW '' calculation. Thus, in order to perform TDHF or BSE calculations, one has to provide the ground-state orbitals ({{FILE\|WAVECAR}}) and the derivatives of the orbitals with respect to <math>k</math> ({{FILE\|WAVEDER}}). In addition, the BSE calculation requires files storing the screened Coulomb kernel produced in a ''GW'' calculation, i.e., {{FILE\|Wxxxx.tmp}}.

	In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.		In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.
Line 55:		Line 55:
	WFULL0001.tmp, WFULL0002.tmp, ..., WFULL{NKPTS}.tmp.		WFULL0001.tmp, WFULL0002.tmp, ..., WFULL{NKPTS}.tmp.

	The files {{FILE\|~~W000?~~}}~~.tmp~~ store only the diagonal terms of the kernel and are fairly small, whereas the files {{TAG\|~~WFULL000~~}}~~?.tmp~~ store the full matrix. It is important to make sure in the ''GW'' step that the flag {{TAG\|LWAVE}} = .TRUE. is set, so that the {{FILE\|WAVECAR}} stores the one-electron ''GW'' energies and the one-electron orbitals, if the ''GW'' calculation is self-consistent.		The files {{FILE\|Wxxxx.tmp}} store only the diagonal terms of the kernel and are fairly small, whereas the files {{TAG\|WFULLxxxx.tmp}} store the full matrix. It is important to make sure in the ''GW'' step that the flag {{TAG\|LWAVE}} = .TRUE. is set, so that the {{FILE\|WAVECAR}} stores the one-electron ''GW'' energies and the one-electron orbitals, if the ''GW'' calculation is self-consistent.

	For the self-consistent ''GW'' calculations the following flags should be added		For the self-consistent ''GW'' calculations the following flags should be added
Line 79:		Line 79:
	VASP tries to use sensible defaults, but it is highly recommended to check the {{FILE\|OUTCAR}} file and make sure that the right bands are included. The tag {{TAG\|OMEGAMAX}} specifies the maximum excitation energy of included electron-hole pairs and the pairs with the one-electron energy difference beyond this limit are not included in the BSE Hamiltonian. Hint: The convergence with respect to {{TAG\|NBANDSV}} and {{TAG\|OMEGAMAX}} should be thoroughly checked as the real part of the dielectric function, as well as the correlation energy, is usually very sensitive to these values, whereas the imaginary part of the dielectric function converges quickly.		VASP tries to use sensible defaults, but it is highly recommended to check the {{FILE\|OUTCAR}} file and make sure that the right bands are included. The tag {{TAG\|OMEGAMAX}} specifies the maximum excitation energy of included electron-hole pairs and the pairs with the one-electron energy difference beyond this limit are not included in the BSE Hamiltonian. Hint: The convergence with respect to {{TAG\|NBANDSV}} and {{TAG\|OMEGAMAX}} should be thoroughly checked as the real part of the dielectric function, as well as the correlation energy, is usually very sensitive to these values, whereas the imaginary part of the dielectric function converges quickly.

	At the beginning of the BSE calculation, VASP will try to read the {{FILE\|~~WFULL000?~~.tmp}} files and if these files are not found, VASP will read the {{FILE\|~~W000?~~.tmp}} files. For small isotropic bulk systems, the diagonal approximation of the dielectric screening may be sufficient and yields results very similar to the calculation with the full dielectric tensor {{TAG\|~~WFULL000?~~.tmp}}. Nevertheless, for molecules and atoms as well as surfaces, the full-screened Coulomb kernel is strictly required.		At the beginning of the BSE calculation, VASP will try to read the {{FILE\|WFULLxxxx.tmp}} files and if these files are not found, VASP will read the {{FILE\|Wxxxx.tmp}} files. For small isotropic bulk systems, the diagonal approximation of the dielectric screening may be sufficient and yields results very similar to the calculation with the full dielectric tensor {{TAG\|WFULLxxxx.tmp}}. Nevertheless, for molecules and atoms as well as surfaces, the full-screened Coulomb kernel is strictly required.

	Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.		Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.

Tal: /* Related tags and articles */

2022-07-20T07:51:52Z

← Older revision		Revision as of 17:33, 7 February 2024
Line 46:		Line 46:
	Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.		Both TDHF and BSE approaches write the calculated frequency-dependent dielectric function as well as the excitonic energies in the {{TAG\|vasprun.xml}} file.

	== ~~Time-dependent Hartree-Fock~~ ==		== Model BSE (mBSE) ==
	~~The TDHF~~ calculations can be performed ~~in two~~ steps: ~~the~~ ground-state calculation ~~and the~~ optical absorption calculation. For example, an optical absorption calculation of bulk Si can be performed using a dielectric~~-dependent hybrid-functional~~ described in Ref. {{cite\|~~chen2018nonempirical~~}}.		BSE calculations can be performed using a model dielectric function{{cite\|bokdam:scr:2016}}{{cite\|tal:prr:2020}}. In this approach the calculation of the screened Coulomb potential is not required. Instead, the model dielectric function can be used to describe the screening of the Coulomb potential by setting the tag {{TAG\|LMODELHF}} with parameters {{TAG\|AEXX}} and {{TAG\|HFSCREEN}}.

			Model BSE calculation can be performed the following steps:
			# ground-state calculation
			# GW calculation (optional in model BSE calculation)
			# optical absorption calculation via model BSE

			For example, an optical absorption calculation of bulk Si can be performed using a model dielectric function as described in Ref. {{cite\|tal:prr:2020}}.

	{{TAG\|SYSTEM}} = Si		{{TAG\|SYSTEM}} = Si
Line 72:		Line 79:
	{{TAG\|LHARTREE}} = .TRUE.		{{TAG\|LHARTREE}} = .TRUE.
	{{TAG\|LADDER}} = .TRUE.		{{TAG\|LADDER}} = .TRUE.
	{{TAG\|LFXC}} = .~~TRUE~~.		{{TAG\|LFXC}} = .FALSE. ! local xc kernel is disabled in mBSE
	{{TAG\|LMODELHF}} = .TRUE.		{{TAG\|LMODELHF}} = .TRUE.
	{{TAG\|AEXX}} = 0.083		{{TAG\|AEXX}} = 0.083

← Older revision		Revision as of 07:51, 20 July 2022
Line 184:		Line 184:
	{{TAG\|ALGO}},		{{TAG\|ALGO}},
	{{TAG\|LOPTICS}},		{{TAG\|LOPTICS}},
			{{TAG\|LPEAD}},
	{{TAG\|LHFCALC}},		{{TAG\|LHFCALC}},
	{{TAG\|LRPA}},		{{TAG\|LRPA}},