Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

Area of Science:

• Quantum Dynamics
• Physical Chemistry
• Computational Chemistry

Background:

• Understanding quantum dynamics in dissipative systems is crucial for molecular processes.
• Classical models like the generalized Langevin equation describe dissipative system dynamics.
• Accurate computation of quantum thermal correlation functions is computationally challenging.

Purpose of the Study:

• To apply the newly formulated continuum limit semiclassical initial value series representation (SCIVR) to vibrational relaxation.
• To investigate the quantum dynamics of model harmonic and anharmonic oscillator systems.
• To assess the convergence and accuracy of the SCIVR method for dissipative systems.

Main Methods:

• Utilized Langevin trajectories with quantum noise as input for the continuum limit SCIVR.
• Combined SCIVR with a prefactor-free propagator for computing quantum thermal correlation functions.
• Implemented and tested the SCIVR method on dissipative harmonic and Morse oscillators.

Main Results:

• The SCIVR series demonstrated rapid convergence for the dissipative harmonic oscillator, needing only the first two terms.
• For the dissipative Morse oscillator, the SCIVR series also converged quickly, achieving accuracy within a few percent.
• Results were compared with the classical Wigner approximation for vibrational relaxation dynamics.

Conclusions:

• The continuum limit SCIVR is an effective and rapidly converging method for studying quantum vibrational relaxation.
• The SCIVR method provides accurate quantum mechanical results for both harmonic and anharmonic dissipative systems.
• This approach offers a tractable scheme for computing quantum thermal correlation functions in complex systems.