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A Gauss-Radau-Laguerre Discrete Variable Representation for Use in Continuum Electron Dynamics
F L Yip1,2, R R Lucchese3, C W McCurdy3,4
1Department of Oceanography and Natural Science, California Polytechnic State University-Maritime Academy, Vallejo, California 94590, United States.
The Journal of Physical Chemistry. A
|June 8, 2026
Summary
This study introduces an enhanced computational method for highly correlated ionizing systems. The modified finite element discrete variable representation (FE-DVR) with exterior complex scaling (ECS) accurately models continuum electrons and highly correlated states.
Area of Science:
- Computational Quantum Chemistry
- Atomic and Molecular Physics
Background:
- Highly correlated ionizing systems require advanced computational methods to accurately model continuum electrons.
- Standard methods can suffer from reflections and inaccuracies when dealing with outgoing wave boundary conditions.
Purpose of the Study:
- To develop and validate a modified finite element discrete variable representation (FE-DVR) method for highly correlated ionizing systems.
- To incorporate exterior complex scaling (ECS) with a Gauss-Radau-Laguerre element for improved boundary condition treatment.
- To address the accurate computation of two-electron integrals within this framework.
Main Methods:
- Implementation of a modified FE-DVR with an appended Gauss-Radau-Laguerre element.
- Application of exterior complex scaling (ECS) with an "infinite range" (irECS) approach to impose outgoing wave boundary conditions.
- Detailed examination of boundary terms in Poisson's equation solutions for accurate two-electron integral computation.
Main Results:
- The irECS approach avoids reflections from grid boundaries by using Laguerre-weighted exponentially decaying tails.
- Accurate two-electron integrals are found to be essential for highly correlated systems.
- A necessary boundary term correction in the Radau-Laguerre DVR allows for accurate description of doubly excited states in helium.
Conclusions:
- The modified FE-DVR with irECS and Radau-Laguerre basis provides an accurate method for studying highly correlated ionizing systems.
- The inclusion of boundary term corrections is crucial for precise calculations of two-electron integrals over the ECS contour.
- This method shows promise for accurately describing complex atomic and molecular states involving continuum electrons.
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