Controlling energy conservation in quantum dynamics with independently moving basis functions: Application to...

Area of Science:

• Quantum dynamics
• Computational chemistry
• Theoretical physics

Background:

• The time-dependent variational principle (TDVP) with frozen-width Gaussians conserves total energy but requires serial computation.
• Simplified independent Gaussian trajectories accelerate computation but violate energy conservation in practical applications.
• Existing methods struggle to balance computational efficiency with the accurate conservation of energy and norm.

Purpose of the Study:

• To develop a computational method that ensures energy and norm conservation in quantum dynamics.
• To enable parallelization and acceleration of simulations involving Gaussian wavepackets.
• To address the limitations of simplified trajectory methods in accurately representing nuclear dynamics.

Main Methods:

• Application of the time-dependent variational principle to Gaussian wavefunctions.
• Introduction of Lagrange multipliers to enforce energy and norm conservation.
• Implementation within the multi-configurational Ehrenfest (MCE) method.
• Testing on a linear vibronic coupling model.

Main Results:

• The proposed method successfully conserves both energy and norm.
• Lagrange multipliers ensure conservation irrespective of basis function complexity or completeness.
• The approach allows for parallel computation, significantly accelerating simulations.
• Accurate energy conservation is maintained even with simplified Gaussian trajectories.

Conclusions:

• Lagrange multipliers provide a robust solution for energy and norm conservation in TDVP-based quantum dynamics.
• This method enhances the efficiency and accuracy of computational simulations for nuclear wavepacket dynamics.
• The developed formalism is applicable to various quantum mechanical systems, including those with vibronic coupling.