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This study derives analytical expressions for response functions, crucial for understanding nuclear and electronic dynamics in molecular and solid-state systems. The findings validate a theoretical approach for calculating these functions, essential for spectroscopy.

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Area of Science:

  • Quantum chemistry
  • Spectroscopy
  • Theoretical physics

Background:

  • Nuclear and electronic dynamics are key to multidimensional electronic spectra.
  • Response functions theoretically describe the interplay of these dynamics.

Purpose of the Study:

  • Derive analytical expressions for response functions in model systems.
  • Investigate the impact of electronic-vibrational coupling and nonadiabatic effects.
  • Apply the method to third-order response functions for spectroscopic processes.

Main Methods:

  • Utilize Dyson expansion of propagators with respect to nonadiabatic couplings.
  • Expand propagators concerning displacements of harmonic oscillators.
  • Derive analytical expressions for time integrals contributing to response functions.

Main Results:

  • Analytical expressions for linear response functions are obtained.
  • Third-order response functions for ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence are derived.
  • Convergence of the Dyson expansion series is demonstrated through comparison with numerical calculations.

Conclusions:

  • The developed theoretical framework provides accurate analytical expressions for response functions.
  • This method is applicable to various spectroscopic phenomena.
  • The study confirms the convergence and utility of the Dyson expansion approach.