Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum.

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Physics

Background:

• Accurate quantum-mechanical calculations are crucial for understanding atomic and molecular properties.
• Existing methods may face challenges with arbitrary angular momentum and explicit electron correlation.

Purpose of the Study:

• To introduce a new algorithm for calculating Hamiltonian matrix elements.
• To enable high-accuracy quantum-mechanical calculations for atoms with arbitrary angular momentum.
• To provide a unified framework for studying small atoms and molecules.

Main Methods:

• Development of a new algorithm for Hamiltonian matrix element calculation.
• Utilizing all-electron explicitly correlated Gaussian functions.
• Application to excited states of three- and four-electron systems.

Main Results:

• The algorithm successfully calculates Hamiltonian matrix elements for atoms with arbitrary angular momentum.
• Validation performed on excited states of three- and four-electron systems.
• Demonstrated the feasibility and accuracy of the new computational approach.

Conclusions:

• The presented algorithm offers a robust method for quantum-mechanical calculations.
• The formalism serves as a unified framework for high-accuracy atomic and molecular property calculations.
• This work advances computational methods in atomic and molecular physics.