The atomic orbitals of the topological atom

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Traditional atomic orbital basis sets can be computationally expensive and redundant.
• Quantum Theory of Atoms in Molecules (QTAIM) provides a rigorous partitioning of molecular properties to atoms.
• Developing efficient and accurate atomic orbital representations is crucial for computational chemistry.

Purpose of the Study:

• To develop a method for generating effective atomic orbitals (EAOs) from general wavefunctions.
• To demonstrate that EAOs can accurately represent molecular orbitals and QTAIM atomic populations.
• To explore the reduction of basis set size while maintaining high accuracy.

Main Methods:

• Implementation of EAOs within the framework of Bader's atoms in molecules theory.
• Utilizing singular value decomposition (SVD) for basis set reduction.
• Comparison of EAO-based Mulliken population analysis with QTAIM atomic populations.

Main Results:

• A general formalism for deriving orthonormalized numerical atomic orbitals with QTAIM occupation numbers was established.
• A limited set of EAOs with significant occupation numbers accurately represents core and valence atomic shells.
• Molecular orbitals can be exactly expressed as linear combinations of EAOs, and Mulliken analysis on this basis reproduces QTAIM populations.

Conclusions:

• Effective atomic orbitals offer a compact and accurate representation of atomic and molecular orbitals.
• This method provides a robust way to obtain physically meaningful atomic basis sets from any quantum chemical calculation.
• Basis set reduction using EAOs and SVD is highly effective, paving the way for more efficient computational chemistry studies.