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Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters
Sergiy Bubin1, Ludwik Adamowicz
1Department of Physics, University of Arizona, Tucson, Arizona 85721, USA. bubin@email.arizona.edu
The Journal of Chemical Physics
|June 21, 2006
Summary
This study introduces new analytical expressions for calculating atomic properties using explicitly correlated Gaussian basis functions. These methods enable precise calculations of atomic states without the Born-Oppenheimer approximation.
Area of Science:
- Quantum chemistry
- Computational physics
Background:
- Accurate calculation of atomic properties is crucial for understanding chemical and physical phenomena.
- Existing methods often rely on approximations like the Born-Oppenheimer approximation, limiting their precision.
Purpose of the Study:
- To develop novel analytical expressions for Hamiltonian matrix elements and energy gradients.
- To enable precise calculations of atomic systems using explicitly correlated Gaussian basis functions.
- To implement a method that bypasses the Born-Oppenheimer approximation.
Main Methods:
- Derivation of analytical expressions using matrix differential calculus.
- Formulation of energy gradient expressions for variational optimization.
- Implementation of formulas for numerical computation.
Main Results:
- Analytical expressions for Hamiltonian matrix elements and energy gradients were derived.
- The developed method was successfully applied to calculate ground and excited states of the Helium atom.
- The approach demonstrated accuracy without employing the Born-Oppenheimer approximation.
Conclusions:
- The presented analytical expressions and methods provide a robust framework for accurate quantum mechanical calculations.
- This work offers a significant advancement in the computational treatment of atomic systems, particularly for those where the Born-Oppenheimer approximation is inadequate.