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Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation.

Jian Liu¹, William H Miller

¹Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA.

The Journal of Chemical Physics

|December 3, 2008

Summary

The maximum entropy analytic continuation (MEAC) method enhances the accuracy of linearized semiclassical methods for real-time correlation functions. This combined approach significantly improves results for nonlinear systems, especially at low temperatures.

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Area of Science:

Quantum Chemistry
Chemical Physics
Computational Chemistry

Background:

Linearized semiclassical initial value representation (LSC-IVR) is effective for real-time correlation functions but less accurate at low temperatures.
Classical Wigner approximation has limitations for highly nonlinear systems.
Accurate calculation of real-time correlation functions is crucial for understanding chemical dynamics.

Purpose of the Study:

To enhance the accuracy of the LSC-IVR/classical Wigner approximation for real-time correlation functions.
To apply the combined Maximum Entropy Analytic Continuation (MEAC)+LSC-IVR method to nonlinear dynamical systems.
To assess the performance of the MEAC+LSC-IVR approach at different temperatures and for various operators.

Main Methods:

The Maximum Entropy Analytic Continuation (MEAC) method was employed.
The LSC-IVR approximation was used as a "prior" for the MEAC procedure.
The combined MEAC+LSC-IVR method was applied to a 1D quartic potential and liquid para-hydrogen.

Main Results:

The MEAC procedure significantly enhanced the accuracy of LSC-IVR for both linear and nonlinear operators, particularly at low temperatures.
For liquid para-hydrogen, MEAC provided significant corrections at 14 K, where LSC-IVR was already excellent at 25 K.
The MEAC method demonstrated its ability to correct other trajectory-based dynamical approximations.

Conclusions:

The MEAC+LSC-IVR approach is a powerful tool for extending the accuracy of semiclassical methods for real-time correlation functions.
This method shows particular promise for studying complex molecular systems at low temperatures.
MEAC offers a significant improvement over standard LSC-IVR for nonlinear dynamics.