Solving the Schrödinger equation of atoms and molecules without analytical integration based on the free...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Solving the Schrödinger equation (SE) for atoms and molecules is computationally intensive.
• Traditional methods often require difficult analytic integrations, limiting their applicability.
• The iterative-complement-interaction (ICI) wave function offers a potentially exact solution but poses integration challenges.

Purpose of the Study:

• To introduce a novel local Schrödinger equation (LSE) method.
• To overcome the difficulties of analytic integration in quantum chemistry calculations.
• To provide an accurate and efficient method for solving the SE for atoms and molecules.

Main Methods:

• Developed a local Schrödinger equation (LSE) method.
• Utilized free iterative-complement-interaction (ICI) wave functions.
• Assumed flatness of local energy due to the potentially exact nature of the free ICI wave function.
• Avoided analytic integrations over complement functions.

Main Results:

• Achieved high accuracy (10^-5 Hartree) in total energies for 2- to 5-electron systems.
• Precisely calculated potential energy curves for H2 and LiH molecules using the free ICI LSE method.
• Demonstrated the method's effectiveness for general atoms and molecules.

Conclusions:

• The proposed local Schrödinger equation (LSE) method is highly effective for solving the Schrödinger equation (SE).
• This method shows significant potential for developing accurate predictive quantum chemistry.
• It offers a viable alternative to traditional methods requiring complex analytic integrations.