Electronic structure calculations with interpolating tensor product wavelet basis.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Solving the Schrödinger equation is fundamental for understanding atomic and molecular properties.
• Accurate and efficient computational methods are crucial for advancing quantum chemistry.
• Existing methods may face challenges with computational cost or accuracy for complex systems.

Purpose of the Study:

• To introduce a novel computational approach for solving the Schrödinger equations.
• To apply this method to various atomic and molecular systems, including excited states.
• To evaluate the performance and accuracy of the new method.

Main Methods:

• Utilized three-dimensional Deslauriers-Dubuc wavelets as a basis set.
• Employed Hartree-Fock and Density Functional Theory (DFT) for electronic structure calculations.
• Handled the Coulomb singularity using pseudopotentials and solved eigenvalue/Poisson equations with established numerical methods.

Main Results:

• Successfully solved the Schrödinger equations for hydrogen (H) and helium (He) atoms, and H2, H2+, and LiH molecules.
• Computed 2s and 2p excited states of hydrogen accurately.
• Demonstrated efficient computation of matrix elements via wavelet properties.

Conclusions:

• The Deslauriers-Dubuc wavelet basis set provides an effective numerical tool for quantum chemistry.
• The method shows competitive performance compared to established databases like CCCBDB and bigDFT.
• This approach offers a promising avenue for accurate and efficient electronic structure calculations.