Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Molecular Dynamics

Background:

• Simulating large molecular systems and chemical reactions using quantum mechanics (QM) is computationally intensive due to exponential scaling.
• Current methods often use time-dependent basis functions to approximate nuclear wave functions, but assessing accuracy is challenging.
• Energy conservation is insufficient for verifying the accuracy of quantum dynamics simulations.

Purpose of the Study:

• To introduce a practical and reliable measure for assessing the accuracy of quantum dynamics simulations.
• To address the challenge of quantifying basis set completeness in quantum mechanical calculations.

Main Methods:

• Proposing the variance of the Hamiltonian's expectation value as a measure of basis completeness and simulation accuracy.
• Applying and evaluating time-dependent basis methods, including coupled and variational coherent states and quantum-trajectory guided adaptable Gaussians (QTAG).
• Introducing a novel semilocal definition for QTAG basis time-evolution to optimize basis function placement.

Main Results:

• The variance of the Hamiltonian is demonstrated as a suitable metric for evaluating the accuracy of quantum dynamics.
• Illustrative examples on chemistry-relevant systems validate the proposed measure.
• A new QTAG basis time-evolution method enhances the adaptability and accuracy of simulations.

Conclusions:

• The Hamiltonian variance provides a practical criterion for assessing the accuracy of quantum mechanical simulations of nuclear motion.
• Time-dependent basis methods, particularly QTAG with its improved evolution, offer efficient approaches for complex molecular systems.
• This work advances the computational accuracy and reliability of simulating chemical reactions and molecular isomerizations.