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Fourth-order complex time-dependent Redfield theory for absorption line shapes.

Andrius Gelzinis1,2, Leonas Valkunas1

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Summary
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A new fourth-order complex-time dependent Redfield (ctR4) theory was developed for molecular simulations. While offering improvements for certain spectral densities, the original second-order ctR theory remains preferable for practical calculations due to accuracy concerns.

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Area of Science:

  • Quantum chemistry
  • Theoretical spectroscopy
  • Computational physics

Background:

  • Simulations of molecular absorption line shapes are crucial for interpreting experimental data.
  • The second-order complex-time dependent Redfield (ctR) theory offers a balance of accuracy and efficiency.
  • Enhancements to existing theories are needed for specific molecular systems.

Purpose of the Study:

  • To develop and evaluate a fourth-order extension of the ctR theory (ctR4).
  • To assess the performance of ctR4 for different spectral densities and reorganization energies.
  • To compare ctR4 with the original ctR theory for accuracy and applicability.

Main Methods:

  • Developed a fourth-order extension of the complex-time dependent Redfield theory (ctR4).
  • Assumed exponential decomposition of the bath correlation function for analytical expressions.
  • Avoided numerical integration by deriving time-domain analytical solutions.
  • Simulated absorption line shapes for various spectral densities (Debye, Ohmic with cutoff, super-Ohmic).

Main Results:

  • The ctR4 approach showed higher quality results for the Debye spectral density.
  • For Ohmic spectral density with exponential cutoff, ctR4 accuracy was limited to small reorganization energies.
  • The original second-order ctR theory performed better for super-Ohmic spectral densities.
  • Negative features were observed in ctR4 line shapes for certain parameter values.

Conclusions:

  • The fourth-order ctR4 theory provides improvements for specific spectral densities like Debye.
  • Accuracy limitations and potential for negative features necessitate careful application of ctR4.
  • The original second-order ctR theory is recommended for general practical calculations due to its robustness and reliability.