Category:Bethe-Salpeter equations - Revision history

Csheldon: /* Additional resources */

2026-03-24T13:34:42Z

Additional resources

← Older revision		Revision as of 13:34, 24 March 2026
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	=== How to ===		=== How to ===
	* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]]		* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]].
	* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]		* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]].
	* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]		* Practical guide for using the [[Bethe-Salpeter equation for core excitations]].
	* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]		* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]].

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Csheldon: /* Additional resources */

2026-03-24T13:17:10Z

Additional resources

← Older revision		Revision as of 13:17, 24 March 2026
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	== Additional resources ==		== Additional resources ==
	=== Lectures ===		=== Lectures ===
	~~<!--*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].-->~~
	*Lecture on the {{Video\|bse:alexey:2026\|Bethe-Salpeter equation and optical excitations}}.		*Lecture on the {{Video\|bse:alexey:2026\|Bethe-Salpeter equation and optical excitations}}.

Csheldon at 13:16, 24 March 2026

2026-03-24T13:16:54Z

← Older revision		Revision as of 13:16, 24 March 2026
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	=== Tutorials ===		=== Tutorials ===
	*Tutorial calculating optical absorption of C diamond using {{Tutorial\|bse:e01\|G0W0}}, {{Tutorial\|bse:e02\|BSE}}, and {{Tutorial\|bse:e03\|TDDDH}}.		*Tutorial calculating optical absorption of C diamond using {{Tutorial\|bse:e01\|G0W0}}, {{Tutorial\|bse:e02\|BSE}}, and {{Tutorial\|bse:e03\|TDDDH}}.
	*Tutorial calculating optical absorption of LiF using ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part2/#BSE-~~e04 G0W0], the ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part2/#BSE-~~e05 independent particle approximation] (IPA), the ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part2/#BSE-~~e06 random phase approximation] (RPA), the ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part2/#BSE-~~e07 Tamm-Dancoff approximation] (TDA), and ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part2/#BSE-~~e08 beyond TDA].		*Tutorial calculating optical absorption of LiF using {{Tutorial\|bse:e04\|G0W0}}, the {{Tutorial\|bse:e05\|independent particle approximation (IPA)}}, the {{Tutorial\|bse:e06\|random phase approximation (RPA)}}, the {{Tutorial\|bse:e07\|Tamm-Dancoff approximation] (TDA)}}, and {{Tutorial\|bse:e08\|beyond TDA}}.
	*Tutorial on the ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part3/#BSE-~~e09 efficient Brillouin zone sampling] and ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part3/#BSE-~~e10 exciton analysis].		*Tutorial on the {{Tutorial\|bse:e09\|efficient Brillouin zone sampling}} and {{Tutorial\|bse:e10\|exciton analysis}}.
	*Tutorial for calculating x-ray adsorption spectroscopy ~~([https~~:~~//vasp.at/tutorials/latest/xas/~~part2 XAS calculations]) using the BSE.		*Tutorial for calculating x-ray adsorption spectroscopy {{Tutorial\|bse:part2\|XAS calculations}} using the BSE.

	=== How to ===		=== How to ===

Csheldon: /* Time evolution */

2026-03-18T16:52:08Z

Time evolution

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	* Calculating the dielectric function		* Calculating the dielectric function
	* Calculations beyond the Tamm-Dancoff approximation		* Calculations beyond the Tamm-Dancoff approximation


	==Lanczos algorithm==		==Lanczos algorithm==

Csheldon: /* Additional resources */

2026-03-18T16:51:54Z

Additional resources

← Older revision		Revision as of 16:51, 18 March 2026
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	=== Tutorials ===		=== Tutorials ===
	*Tutorial calculating optical absorption of C diamond using ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part1/#BSE-~~e01 G0W0], ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part1/#BSE-~~e02 BSE], and ~~[https~~:~~//www.vasp.at/tutorials/latest/bse/part1/#BSE-~~e03 TDDDH].		*Tutorial calculating optical absorption of C diamond using {{Tutorial\|bse:e01\|G0W0}}, {{Tutorial\|bse:e02\|BSE}}, and {{Tutorial\|bse:e03\|TDDDH}}.
	*Tutorial calculating optical absorption of LiF using [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e04 G0W0], the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e05 independent particle approximation] (IPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e06 random phase approximation] (RPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e07 Tamm-Dancoff approximation] (TDA), and [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e08 beyond TDA].		*Tutorial calculating optical absorption of LiF using [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e04 G0W0], the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e05 independent particle approximation] (IPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e06 random phase approximation] (RPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e07 Tamm-Dancoff approximation] (TDA), and [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e08 beyond TDA].
	*Tutorial on the [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e09 efficient Brillouin zone sampling] and [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e10 exciton analysis].		*Tutorial on the [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e09 efficient Brillouin zone sampling] and [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e10 exciton analysis].

Csheldon: /* Tutorials */

2026-03-18T14:19:01Z

Tutorials

← Older revision		Revision as of 14:19, 18 March 2026
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	*Tutorial calculating optical absorption of LiF using [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e04 G0W0], the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e05 independent particle approximation] (IPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e06 random phase approximation] (RPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e07 Tamm-Dancoff approximation] (TDA), and [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e08 beyond TDA].		*Tutorial calculating optical absorption of LiF using [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e04 G0W0], the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e05 independent particle approximation] (IPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e06 random phase approximation] (RPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e07 Tamm-Dancoff approximation] (TDA), and [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e08 beyond TDA].
	*Tutorial on the [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e09 efficient Brillouin zone sampling] and [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e10 exciton analysis].		*Tutorial on the [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e09 efficient Brillouin zone sampling] and [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e10 exciton analysis].
	~~<!--~~*Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE. ~~-->~~		*Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE.

	=== How to ===		=== How to ===

Csheldon: /* Additional resources */

2026-03-18T11:36:44Z

Additional resources

← Older revision		Revision as of 11:36, 18 March 2026
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	== Additional resources ==		== Additional resources ==
	=== Lectures ===		=== Lectures ===
	*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].		<!--*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].-->
			*Lecture on the {{Video\|bse:alexey:2026\|Bethe-Salpeter equation and optical excitations}}.

	=== Tutorials ===		=== Tutorials ===

Csheldon at 11:07, 12 February 2026

2026-02-12T11:07:59Z

← Older revision		Revision as of 11:07, 12 February 2026
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	{{NB\|mind\|When running BSE calculations on GPUs, we recommend not setting {{TAG\|OMEGAMAX}} or setting it to a larger value so that all the bands selected in {{TAG\|NBANDSV}} and {{TAG\|NBANDSO}} are included in the kernel. Otherwise, additional data transfers between CPU and GPU might be required, which leads to a serious performance degradation on GPUs.\|}}		{{NB\|mind\|When running BSE calculations on GPUs, we recommend not setting {{TAG\|OMEGAMAX}} or setting it to a larger value so that all the bands selected in {{TAG\|NBANDSV}} and {{TAG\|NBANDSO}} are included in the kernel. Otherwise, additional data transfers between CPU and GPU might be required, which leads to a serious performance degradation on GPUs.\|}}

	== ~~How to~~ ==		== Additional resources ==
			=== Lectures ===
			*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].

			=== Tutorials ===
			*Tutorial calculating optical absorption of C diamond using [https://www.vasp.at/tutorials/latest/bse/part1/#BSE-e01 G0W0], [https://www.vasp.at/tutorials/latest/bse/part1/#BSE-e02 BSE], and [https://www.vasp.at/tutorials/latest/bse/part1/#BSE-e03 TDDDH].
			*Tutorial calculating optical absorption of LiF using [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e04 G0W0], the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e05 independent particle approximation] (IPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e06 random phase approximation] (RPA), the [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e07 Tamm-Dancoff approximation] (TDA), and [https://www.vasp.at/tutorials/latest/bse/part2/#BSE-e08 beyond TDA].
			*Tutorial on the [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e09 efficient Brillouin zone sampling] and [https://www.vasp.at/tutorials/latest/bse/part3/#BSE-e10 exciton analysis].
			<!--*Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE. -->

			=== How to ===
	* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]]		* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]]
	* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]		* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]
	* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]		* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]
	* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]		* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]

	~~== Tutorials ==~~
	Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].<!--Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE. -->
	*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Csheldon: /* Tutorials */

2026-02-06T09:41:16Z

Tutorials

← Older revision		Revision as of 09:41, 6 February 2026
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	== Tutorials ==		== Tutorials ==
	*Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].		Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].<!--Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE. -->
	<!--		*Lecture on the [https://youtu.be/arTPHW28qNM Bethe-Salpeter equation and optical excitations].
	*Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE.
	-->

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Singraber at 08:15, 24 October 2025

2025-10-24T08:15:10Z

← Older revision		Revision as of 08:15, 24 October 2025
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	The steep scaling of BSE with the system size can be a limiting factor for its application in large systems. This should be considered when performing BSE calculations.		The steep scaling of BSE with the system size can be a limiting factor for its application in large systems. This should be considered when performing BSE calculations.
	=== Building matrix ===		=== Building matrix ===
	The {{~~TAGO~~\|ALGO\|BSE/TDHF}} algorithm as a first step, requires building the Hamiltonian of rank		The {{TAG\|ALGO\|BSE/TDHF}} algorithm as a first step, requires building the Hamiltonian of rank
	:<math>N_{\rm rank} = N_k\times N_c\times N_v</math>,		:<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 full Brillouin zone and <math>N_c</math> and <math>N_v</math> are the number of conduction and valence bands, respectively. This computation scales as		where <math>N_k</math> is the number of k-points in the full Brillouin zone and <math>N_c</math> and <math>N_v</math> are the number of conduction and valence bands, respectively. This computation scales as
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	In the second step, the equation has to be solved. VASP provides different methods for doing that.		In the second step, the equation has to be solved. VASP provides different methods for doing that.
	==== Exact diagonalization ====		==== Exact diagonalization ====
	The exact diagonalization algorithm ({{~~TAGO~~\|IBSE\|2}}) scales cubically with the matrix rank <math>N_{\rm rank}^3</math>		The exact diagonalization algorithm ({{TAG\|IBSE\|2}}) scales cubically with the matrix rank <math>N_{\rm rank}^3</math>
	or as <math>N^6</math> with the system size.		or as <math>N^6</math> with the system size.
	==== Iterative solution ====		==== Iterative solution ====
	The iterative solution, as in the time-evolution ({{~~TAGO~~\|IBSE\|1}}) or Lanczos		The iterative solution, as in the time-evolution ({{TAG\|IBSE\|1}}) or Lanczos
	({{~~TAGO~~\|IBSE\|3}}) algorithms, do not		({{TAG\|IBSE\|3}}) algorithms, do not
	require diagonalizaing the full matrix but instead, require computing the matrix-vector multiplication for a number of steps or iterations <math>m</math>. Thus, solving the equation via the time-evolution or Lanczos algorithms scales as <math>N_{\rm rank}^2\times m</math> or <math>N^4</math> with the system size. The number of iterations depends on the algorithm and the required precision, which can be selected via {{TAG\|BSEPREC}} .		require diagonalizaing the full matrix but instead, require computing the matrix-vector multiplication for a number of steps or iterations <math>m</math>. Thus, solving the equation via the time-evolution or Lanczos algorithms scales as <math>N_{\rm rank}^2\times m</math> or <math>N^4</math> with the system size. The number of iterations depends on the algorithm and the required precision, which can be selected via {{TAG\|BSEPREC}} .

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	The BSE/TDHF algorithm can also be used to model the X-ray absorption spectra (XAS), i.e., excitations from the core states into conduction bands. The detailed documentation of this method can be found in [[:Category:XAS]].		The BSE/TDHF algorithm can also be used to model the X-ray absorption spectra (XAS), i.e., excitations from the core states into conduction bands. The detailed documentation of this method can be found in [[:Category:XAS]].
	== Performing BSE calculations on GPU ==		== Performing BSE calculations on GPU ==
	As of VASP 6.5, the BSE/TDHF calculations with {{~~TAGO~~\|IBSE\|1}} or {{~~TAGO~~\|IBSE\|2}} can be fully run on NVIDIA GPUs.		As of VASP 6.5, the BSE/TDHF calculations with {{TAG\|IBSE\|1}} or {{TAG\|IBSE\|2}} can be fully run on NVIDIA GPUs.
	To be able to offload the BSE calculations to GPUs one has to compile VASP with the [https://docs.nvidia.com/cuda/cusolvermp cuSOLVERMp] and [https://docs.nvidia.com/cuda/cublasmp cuBLASMp] libraries provided with NVHPC-SDK 24.7 or newer.		To be able to offload the BSE calculations to GPUs one has to compile VASP with the [https://docs.nvidia.com/cuda/cusolvermp cuSOLVERMp] and [https://docs.nvidia.com/cuda/cublasmp cuBLASMp] libraries provided with NVHPC-SDK 24.7 or newer.
	To be able to use these libraries VASP has to be compiled with HPC-X (MPI shipped with NVHPC-SDK), which can be loaded via		To be able to use these libraries VASP has to be compiled with HPC-X (MPI shipped with NVHPC-SDK), which can be loaded via
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	LLIBS += -cudalib=cusolvermp,cublasmp -lnvhpcwrapcal		LLIBS += -cudalib=cusolvermp,cublasmp -lnvhpcwrapcal

	To be able to perform the BSE calculation on GPUs, VASP needs to store the full BSE Hamiltonian in the GPU memory, which is often the limiting factor. The memory required to store the BSE Hamiltonian can be estimated as <math>N_{\rm rank}^2\times 16\cdot 10^{-9}</math> in Gb for {{~~TAGO~~\|ANTIRES\|0}}. In the case of exact diagonalization {{~~TAGO~~\|IBSE\|2}}, the eigensolver requires an additional scratch space.		To be able to perform the BSE calculation on GPUs, VASP needs to store the full BSE Hamiltonian in the GPU memory, which is often the limiting factor. The memory required to store the BSE Hamiltonian can be estimated as <math>N_{\rm rank}^2\times 16\cdot 10^{-9}</math> in Gb for {{TAG\|ANTIRES\|0}}. In the case of exact diagonalization {{TAG\|IBSE\|2}}, the eigensolver requires an additional scratch space.
	{{NB\|mind\|When running BSE calculations on GPUs, we recommend not setting {{TAG\|OMEGAMAX}} or setting it to a larger value so that all the bands selected in {{TAG\|NBANDSV}} and {{TAG\|NBANDSO}} are included in the kernel. Otherwise, additional data transfers between CPU and GPU might be required, which leads to a serious performance degradation on GPUs.\|}}		{{NB\|mind\|When running BSE calculations on GPUs, we recommend not setting {{TAG\|OMEGAMAX}} or setting it to a larger value so that all the bands selected in {{TAG\|NBANDSV}} and {{TAG\|NBANDSO}} are included in the kernel. Otherwise, additional data transfers between CPU and GPU might be required, which leads to a serious performance degradation on GPUs.\|}}