Accelerating Optical Absorption Spectra and Exciton Energy Computation via Interpolative Separable Density Fitting

  • Wei Hu
  • Meiyue Shao
  • Andrea Cepellotti
  • Felipe H. da Jornada
  • Lin Lin
  • Kyle Thicke
  • Chao YangEmail author
  • Steven G. Louie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10861)


We present an efficient way to solve the Bethe–Salpeter equation (BSE), a method for the computation of optical absorption spectra in molecules and solids that includes electron–hole interactions. Standard approaches to construct and diagonalize the Bethe–Salpeter Hamiltonian require at least \(\mathcal {O}(N_e^5)\) operations, where \(N_e\) is the number of electrons in the system, limiting its application to smaller systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare exchange and screened direct operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to \(\mathcal {O}(N_e^3)\) with a much smaller pre-constant, and allows for a faster solution of the BSE. Here, we implement the ISDF method for BSE calculations within the Tamm–Dancoff approximation (TDA) in the BerkeleyGW software package. We show that this novel approach accurately reproduces exciton energies and optical absorption spectra in molecules and solids with a significantly reduced computational cost.



This work is supported by the Center for Computational Study of Excited-State Phenomena in Energy Materials (C2SEPEM) at the Lawrence Berkeley National Laboratory, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-05CH11231, as part of the Computational Materials Sciences Program, which provided support for developing, implementing and testing ISDF for BSE in BerkeleyGW. The Center for Applied Mathematics for Energy Research Applications (CAMERA) (L. L. and C. Y.) provided support for the algorithm development and mathematical analysis of ISDF. Finally, the authors acknowledge the computational resources of the National Energy Research Scientific Computing (NERSC) center.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Wei Hu
    • 1
    • 2
  • Meiyue Shao
    • 1
  • Andrea Cepellotti
    • 3
    • 4
  • Felipe H. da Jornada
    • 3
    • 4
  • Lin Lin
    • 1
    • 5
  • Kyle Thicke
    • 6
  • Chao Yang
    • 1
    Email author
  • Steven G. Louie
    • 3
    • 4
  1. 1.Computational Research DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Hefei National Laboratory for Physical Sciences at MicroscaleUniversity of Science and Technology of ChinaHefeiChina
  3. 3.Department of PhysicsUniversity of California, BerkeleyBerkeleyUSA
  4. 4.Materials Sciences DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  5. 5.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA
  6. 6.Department of MathematicsDuke UniversityDurhamUSA

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