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High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics
Roya Moghaddasi Fereidani1, Jiří J L Vaníček1
1Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
The Journal of Chemical Physics
|January 29, 2024
Summary
Efficient geometric integrators improve variational Gaussian wavepacket dynamics for quantum simulations. These methods reduce computational cost for high-dimensional systems, enhancing accuracy in semiclassical approximations.
Area of Science:
- Quantum mechanics
- Computational chemistry
- Applied mathematics
Background:
- Gaussian wavepacket dynamics is a semiclassical approximation for quantum simulations.
- Variational Gaussian wavepacket dynamics offers improved accuracy over local harmonic methods.
- Evaluating expectation values of potential energy, gradient, and Hessian presents computational challenges.
Purpose of the Study:
- To reduce the computational cost of local cubic variational Gaussian wavepacket dynamics.
- To introduce efficient high-order geometric integrators for quantum simulations.
- To enhance the practical applicability of accurate semiclassical methods.
Main Methods:
- Development of efficient high-order geometric integrators.
- Application of integrators to local cubic approximation of potential energy surfaces.
- Numerical demonstration on multidimensional, nonseparable coupled Morse potential.
Main Results:
- The proposed integrators are symplectic, time-reversible, and norm-conserving.
- Effective energy conservation is achieved for small time steps.
- Demonstrated efficiency and geometric properties of the integrators.
Conclusions:
- Efficient geometric integrators significantly reduce the cost of variational Gaussian wavepacket dynamics.
- These methods provide a more practical and accurate approach for quantum simulations.
- The developed integrators are suitable for complex, multidimensional systems.
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