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Numerical density-to-potential inversions in time-dependent density functional theory.

Daniel S Jensen1, Adam Wasserman2

  • 1Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA. awasser@purdue.edu.

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Summary

We developed an optimization method to solve the inverse problem in time-dependent density functional theory. This approach efficiently recovers the potential from a target density, applicable to various systems.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Time-dependent density functional theory (TDDFT) is crucial for understanding electronic dynamics.
  • The density-to-potential inverse problem in TDDFT is computationally challenging.
  • Accurate potential reconstruction is vital for reliable TDDFT simulations.

Purpose of the Study:

  • To present a novel optimization framework for the TDDFT density-to-potential inverse problem.
  • To efficiently recover the external potential from a given electron density.
  • To demonstrate the method's applicability and robustness on model systems.

Main Methods:

  • Formulating the inverse problem as a partial differential equation-constrained optimization.
  • Utilizing a multilevel optimization strategy guided by error estimates.
  • Employing a classical optimization routine with gradients from the discrete adjoint method.
  • Inverting potentials with real and imaginary components to mitigate numerical artifacts.

Main Results:

  • Successfully recovered the target potential for model one-dimensional systems.
  • Demonstrated efficient gradient computation using the discrete adjoint method.
  • Showcased the effectiveness of the multilevel optimization approach.
  • Validated the use of complex potentials for reducing boundary reflections.

Conclusions:

  • The developed method provides an efficient and robust solution for the TDDFT inverse problem.
  • The approach is adaptable to different numerical solvers and higher-dimensional systems.
  • This work advances the capabilities of computational electronic structure calculations.
  • The technique holds promise for more accurate simulations of molecular and material dynamics.