Implementation of Occupied and Virtual Edmiston-Ruedenberg Orbitals Using Cholesky Decomposed Integrals.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Orbital localization is crucial for simplifying electronic structure calculations.
• The Edmiston-Ruedenberg method maximizes orbital self-repulsion energy for localization.
• Previous methods primarily focused on occupied orbitals.

Purpose of the Study:

• To implement and evaluate a trust-region optimization for the Edmiston-Ruedenberg orbital localization function.
• To demonstrate the general localization of virtual orbitals using this method.
• To compare the computational cost and efficiency with existing methods.

Main Methods:

• Trust-region optimization algorithm applied to the Edmiston-Ruedenberg function.
• Cholesky decomposition to reduce the cost of electron repulsion integrals.
• Optimization performed in the molecular orbital basis.

Main Results:

• Successful localization of both occupied and virtual orbitals.
• Occupied orbital localization shows linear scaling and is often cheaper than SCF optimization.
• Virtual orbital localization is computationally more expensive than SCF optimization.
• Resulting virtual Edmiston-Ruedenberg orbitals have larger spreads compared to other methods.

Conclusions:

• The Edmiston-Ruedenberg method is demonstrated for virtual orbital localization.
• Linear scaling achieved for occupied orbital localization offers computational advantages.
• Higher computational cost for virtual orbital localization suggests alternative methods are preferable for certain applications like local post-Hartree-Fock calculations.