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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Linear optical properties are crucial for understanding material behavior.
  • Time-dependent density functional theory (TD-DFT) is a key method for their calculation.
  • Two primary TD-DFT approaches exist: Casida equation and time evolution.

Purpose of the Study:

  • To compare the accuracy and computational performance of the Casida equation and time evolution methods within the projector augmented wave framework.
  • To identify the conditions under which each method is more efficient.

Main Methods:

  • Solving time-dependent density functional theory equations.
  • Linearizing equations of motion to form the Casida equation.
  • Simulating the system's response to a short electric field pulse (time evolution).
  • Applying corrections in the frequency domain for the time evolution method.
  • Utilizing the projector augmented wave (PAW) method.

Main Results:

  • Both methods yield virtually indistinguishable results for linear optical properties.
  • The time evolution approach is computationally superior for standard density functionals.
  • The Casida equation is more efficient for functionals with nonlocal exchange, despite its scaling.

Conclusions:

  • The choice of method depends on the specific density functional used.
  • Computational efficiency can be significantly impacted by the inclusion of nonlocal exchange terms.
  • Both TD-DFT approaches are reliable for predicting optical properties.