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Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals.

Ziling Luo¹, Rustam Z Khaliullin¹

¹Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec QC H3A 0B8, Canada.

Journal of Chemical Theory and Computation

|April 23, 2020

Summary

This study introduces a novel orbital localization method that balances orthogonality and locality. It simplifies calculations in electronic structure theory for molecules and materials.

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Area of Science:

Computational chemistry
Electronic structure theory

Background:

Spatially localized one-electron orbitals are crucial for describing chemical bonds and accelerating electronic structure calculations.
Existing methods for orbital localization often impose constraints like unitary transformations or fixed centers to prevent linear dependencies.

Purpose of the Study:

To develop a more flexible and straightforward approach to orbital localization.
To enable a tunable balance between orbital orthogonality and spatial localization.

Main Methods:

A new orbital localization method is proposed, replacing strict orthogonality or fixed-center constraints with a maximum allowed deviation from orthogonality.
This approach allows for unconstrained optimization of non-orthogonal orbital centers.
The method utilizes Berghold and Pipek-Mezey localization functions.

Main Results:

The developed method successfully produces well-localized orthogonal and non-orthogonal orbitals.
It is effective for diverse systems, including large molecules and periodic materials with complex bonding.
The approach simplifies calculations by avoiding unitary transformations.

Conclusions:

The new method offers a generalized and practical approach to orbital localization.
It provides a flexible way to control the trade-off between orthogonality and locality in electronic structure calculations.
This technique enhances the efficiency and applicability of electronic structure theory for various chemical systems.