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Solving the Schrodinger equation for helium atom and its isoelectronic ions with the free iterative complement
Hiroyuki Nakashima1, Hiroshi Nakatsuji
1Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245, Japan.
The Journal of Chemical Physics
|December 18, 2007
Summary
The free iterative complement interaction (ICI) method accurately solves the Schrodinger equation for helium and its ions. This method achieves high precision, demonstrating its capability for desired accuracy in quantum mechanical calculations.
Area of Science:
- Quantum Chemistry
- Atomic Physics
- Computational Physics
Background:
- The Schrodinger equation is fundamental for describing atomic and molecular systems.
- Accurate solutions are crucial for understanding atomic properties and interactions.
- Previous methods faced challenges in achieving high precision for multi-particle systems.
Purpose of the Study:
- To accurately solve the Schrodinger equation for the helium atom and its isoelectronic ions (Z=1-10).
- To evaluate the efficacy of the free iterative complement interaction (ICI) method.
- To explore the impact of scaling and initial functions on computational accuracy.
Main Methods:
- Solving the Schrodinger equation using the free iterative complement interaction (ICI) method.
- Employing the variational principle to refine wave functions and energies.
- Investigating various scaling functions (g) and initial functions (psi(0)) within the ICI framework.
Main Results:
- Achieved highly accurate energies for the helium atom and isoelectronic ions, with over 40 digits of accuracy.
- Calculated energy for helium: -2.903... a.u.; for H(-): -0.527... a.u.
- Demonstrated that the free ICI method can achieve arbitrary accuracy.
Conclusions:
- The free ICI method provides a powerful tool for high-accuracy solutions to the Schrodinger equation.
- Logarithmic functions, particularly those incorporating inter-particle distances (r12), enhance computational performance.
- The study validates the free ICI method for precise quantum mechanical calculations.
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