Unphysical divergences in response theory

Area of Science:

• Theoretical Chemistry
• Quantum Mechanics
• Spectroscopy

Background:

• Transition densities between excited states are vital for nonlinear spectroscopy and multi-state non-adiabatic molecular dynamics (NAMD).
• These densities are typically calculated via poles of the quadratic response function within response theory.
• Previous studies identified unphysical divergences in time-dependent Hartree-Fock (TDHF) and adiabatic time-dependent density functional theory (TDDFT) transition densities.

Purpose of the Study:

• To investigate the origin and prevalence of unphysical divergences in transition densities calculated using approximate many-electron response theories.
• To determine the impact of these divergences on computational simulations, particularly NAMD and frequency-dependent response properties.

Main Methods:

• Analysis of the quadratic response function and its poles.
• Examination of various approximate many-electron response theories, including coupled cluster and multiconfigurational self-consistent field response theory.
• Tracing the source of divergences to the instantaneous time-dependence of the effective Hamiltonian.

Main Results:

• Unphysical divergences in transition densities are not limited to TDHF and adiabatic TDDFT but are present in a wide range of approximate response theories.
• These divergences occur on potential energy surfaces where the ground state is well-behaved and are frequently observed in NAMD simulations.
• The root cause is identified as an incorrect instantaneous time-dependence in the effective Hamiltonian.

Conclusions:

• The identified divergences pose significant challenges for accurate theoretical spectroscopy and NAMD simulations.
• The findings question the validity of conventional approximate many-electron response theories beyond linear response.
• Further development of theoretical frameworks is needed to address these unphysical behaviors in excited-state calculations.