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A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related
Jonathan R Mannouch1, Jeremy O Richardson1
1Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
The Journal of Chemical Physics
|November 21, 2020
Summary
The spin partially linearized density matrix (spin-PLDM) method improves upon fully linearized spin-mapping by including an extra term, reducing common errors. This approach allows for systematic improvement and accurate results in quantum dynamics simulations.
Area of Science:
- Quantum Chemistry
- Theoretical Chemistry
- Chemical Physics
Background:
- Introduces the spin partially linearized density matrix (spin-PLDM) method, a novel partially linearized mapping-based classical-trajectory technique.
- Builds upon previous work on spin-mapping methods for simulating nonadiabatic dynamics.
- Highlights the known accuracy of fully linearized spin-mapping for certain dynamical observables.
Purpose of the Study:
- To conduct a comprehensive comparison between spin-PLDM and fully linearized spin mapping.
- To analyze the underlying expressions for real-time quantum correlation functions for both methods.
- To ascertain the relative accuracy and identify sources of error reduction in spin-PLDM.
Main Methods:
- Detailed comparison of the mathematical expressions for real-time quantum correlation functions.
- Derivation of a systematic improvement scheme for spin-PLDM via re-sampling mapping variables.
- Implementation of focused initial conditions to enhance computational efficiency.
Main Results:
- Spin-PLDM incorporates an additional term in its correlation function, mitigating errors common in fully linearized methods.
- The re-sampling scheme enables numerically exact results for systems with classical nuclei using minimal 'jumps'.
- Focused initial conditions reduce the number of required classical trajectories for convergence without significant accuracy loss.
Conclusions:
- Spin-PLDM offers improved accuracy over fully linearized spin-mapping by addressing inherent errors.
- The derived schemes for spin-PLDM enhance its efficiency and potential for obtaining exact quantum dynamics.
- Spin-PLDM presents a promising advancement for accurate and efficient simulation of nonadiabatic dynamics.
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