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Dynamical second-order Bethe-Salpeter equation kernel: a method for electronic excitation beyond the adiabatic

Du Zhang1, Stephan N Steinmann, Weitao Yang

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We developed a new method for calculating electronic excitation energies using a dynamical second-order kernel for the Bethe-Salpeter equation. This approach improves accuracy beyond current approximations and matches experimental data.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Accurate calculation of electronic excitation energies is crucial for understanding material properties.
  • Existing methods like CIS and TDHF often lack sufficient accuracy.
  • The adiabatic approximation limits the scope of current density functional theory (DFT) approaches.

Purpose of the Study:

  • To introduce a novel dynamical second-order kernel for the Bethe-Salpeter equation (BSE).
  • To improve the calculation of electronic excitation energies by incorporating frequency dependence.
  • To provide a more accurate theoretical tool for predicting excited-state properties.

Main Methods:

  • Derivation of a dynamical second-order kernel by considering the functional derivative of the second-order self-energy.
  • Application of perturbative calculations within the Tamm-Dancoff approximation (TDA).
  • Utilizing configuration interaction singles (CIS) eigenvectors as a basis.

Main Results:

  • The new method demonstrates significant improvement over CIS, time-dependent Hartree-Fock (TDHF), and adiabatic time-dependent DFT (a-TDDFT).
  • Perturbative results show good agreement with more computationally intensive methods like equation-of-motion coupled-cluster (EOM-CC).
  • The calculated excitation energies align well with experimental data.

Conclusions:

  • The dynamical second-order kernel offers a more accurate and reliable approach for electronic excitation energy calculations.
  • This method overcomes limitations of the adiabatic approximation, providing frequency-dependent insights.
  • The improved accuracy holds promise for theoretical predictions in various fields, including chemistry and materials science.