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Published on: May 27, 2020
Relativistic calculations using Monte Carlo methods: one-electron systems
1Department of Physics and Geology, University of Texas Pan American, Edinburg, Texas 78539, USA.
Summary
Accurate atomic and diatomic system energies are calculated using variance minimization and Monte Carlo integration to solve the four-component Dirac equation. This approach offers a simpler, more robust alternative to traditional computational methods.
Area of Science:
- Computational chemistry
- Quantum mechanics
Background:
- The four-component Dirac equation is essential for accurately describing relativistic effects in atomic and molecular systems.
- Traditional computational techniques for solving the Dirac equation can be complex and prone to numerical instabilities.
Purpose of the Study:
- To evaluate the four-component Dirac equation for one-electron atomic and diatomic systems.
- To present a computational approach that is accurate, simple to implement, and avoids common issues.
Main Methods:
- Utilizing variance minimization techniques.
- Employing Monte Carlo integration for numerical evaluation.
- Applying these methods to one-electron atomic and diatomic systems.
Main Results:
- Accurate energy calculations for the studied systems.
- Demonstration of the method's simplicity and ease of implementation.
- Identification of fewer numerical problems compared to conventional approaches.
Conclusions:
- The combination of variance minimization and Monte Carlo integration provides a powerful and practical tool for relativistic electronic structure calculations.
- This method offers a viable and improved alternative for studying atomic and diatomic systems.
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