Analyzing Grid-Based Direct Quantum Molecular Dynamics Using Non-Linear Dimensionality Reduction

Area of Science:

• Quantum dynamics simulations
• Computational chemistry
• Molecular dynamics

Background:

• Grid-based quantum dynamics simulations, such as the multi-configuration time-dependent Hartree (MCTDH) method, accurately predict molecular system dynamics.
• Analyzing complex, multi-dimensional wavepacket motion in non-adiabatic simulations is challenging.
• Extracting physical insight beyond expectation values from these simulations requires advanced techniques.

Purpose of the Study:

• To adapt non-linear dimensionality reduction (NLDR) methods for analyzing grid-based quantum dynamics simulations.
• To extract key nuclear motions that explain observed molecular dynamics.
• To provide alternative views of wavefunction dynamics in complex molecular systems.

Main Methods:

• Application of non-linear dimensionality reduction (NLDR) techniques, specifically diffusion maps.
• Analysis of grid-based wavefunction dynamics data from simulations.
• Demonstration on models of proton transfer in salicylaldimine and cis-trans isomerization in ethene.

Main Results:

• NLDR methods successfully extract meaningful information from complex quantum dynamics simulations.
• Diffusion maps reveal key nuclear motions governing proton transfer and isomerization dynamics.
• The approach provides novel perspectives on wavefunction evolution in multi-dimensional systems.

Conclusions:

• NLDR, particularly diffusion maps, offers a powerful tool for interpreting complex quantum dynamics.
• This method enhances the understanding of nuclear-electronic coupling and molecular reaction mechanisms.
• Future developments can further leverage NLDR for advanced molecular dynamics analysis.