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Multidimensional quantum trajectories: applications of the derivative propagation method.
Corey J Trahan1, Robert E Wyatt, Bill Poirier
1Department of Chemistry and Biochemistry, Texas Tech University, Box 41061 Lubbock, Texas 79409-1061, USA. corey.trahan@ttu.edu
The Journal of Chemical Physics
|June 11, 2005
Summary
The derivative propagation method (DPM) now calculates quantum wave packet transmission probabilities in 2D and 3D. This quantum hydrodynamics approach avoids fitting and basis sets, enabling parallel trajectory propagation for complex systems.
Area of Science:
- Quantum mechanics
- Computational chemistry
- Physical chemistry
Background:
- The quantum hydrodynamic equations of motion (QHEM) describe wave packet evolution.
- Previous QHEM solutions used ensemble propagation with fitting techniques for derivatives.
- The derivative propagation method (DPM) was previously introduced for 1D QHEM.
Purpose of the Study:
- Extend the DPM to calculate transmission probabilities in 2D and 3D.
- Evaluate the DPM's performance on coupled potential energy surfaces.
- Assess the DPM's scalability for systems with more degrees of freedom.
Main Methods:
- Developed equations of motion for derivatives within the DPM.
- Integrated these derivative equations alongside QHEM for C and S.
- Propagated single, uncoupled quantum trajectories concurrently.
- Calculated transmission probabilities for 2D and 3D wave packet evolution.
Main Results:
- Successfully extended DPM to 2D and 3D wave packet dynamics.
- Computed transmission probabilities on coupled Eckart barrier/harmonic oscillator surfaces.
- Compared DPM results for a 2D system against time-dependent Schrödinger equation solutions.
Conclusions:
- The DPM is a viable method for calculating quantum wave packet transmission probabilities in higher dimensions.
- DPM avoids spatial fitting and basis set expansions, simplifying calculations.
- The method shows promise for studying complex chemical systems with multiple degrees of freedom.