RECORD
Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting
Computational Physics · Submitted 27 Jan 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the Bethe-Salpeter Hamiltonian require at least $\O(N_e^5)$ operations, where $N_e$ is proportional to the number of electrons in the system, limiting its application to small systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to $\O(N_e^3)$ with a much smaller pre-constant. Here, we implement the ISDF method for the BSE calculations within the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. | contribution 0.89 | 0.88 | 0.11 | asserted 1.00 |
| s1 | Standard approaches to construct and diagonalize the Bethe-Salpeter Hamiltonian require at least $\O(N_e^5)$ operations, where $N_e$ is proportional to the number of electrons in the system, limiting its application to small systems. | background 0.94 | 0.07 | 0.04 | asserted 1.00 |
| s2 | Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. | method 0.94 | 0.72 | 0.06 | asserted 0.99 |
| s3 | This approach reduces the complexity of the Hamiltonian construction to $\O(N_e^3)$ with a much smaller pre-constant. | result 0.68 | 0.87 | 0.21 | asserted 1.00 |
| s4 | Here, we implement the ISDF method for the BSE calculations within the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. | method 0.78 | 0.94 | 0.04 | asserted 0.99 |
| s5 | We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost. | result 1.00 | 0.96 | 0.88 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the Bethe-Salpeter Hamiltonian require at least $\O(N_e^5)$ operations, where $N_e$ is proportional to the number of electrons in the system, limiting its application to small systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to $\O(N_e^3)$ with a much smaller pre-constant. Here, we implement the ISDF method for the BSE calculations within the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.
Human review
How the literature uses it
2 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 1 paper
-
The solution of the BSE as described is highly demanding; in recent years several methodological advancements have been introduced to lower the computational cost of performing such BSE calculations [ref] .
Koopmans Meets Bethe-Salpeter: Excitonic Optical Spectra without GW · Method · 0.84
What it cites · 1 sentence without a confident label
Uses the method or tool of 1 paper
-
In the future, we plan to replace the costly QRCP procedure with the centroidal Voronoi tessellation (CVT) method [ref] for selecting the interpolation points in the ISDF method.
Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation With Applications to Hybrid Functional Electronic Structure Calculations · Conclusion and outlook · 0.84
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.