Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Localized orthonormal virtual orbitals are crucial for accurate and efficient quantum chemical calculations.
• Existing methods for generating virtual orbitals can be computationally expensive and may lack desired localization properties.

Purpose of the Study:

• To develop a novel algorithm for computing stable, well-defined localized orthonormal virtual orbitals.
• To ensure these orbitals depend smoothly on nuclear coordinates for molecular dynamics simulations.
• To achieve computational efficiency and reduced storage requirements.

Main Methods:

• Decomposition of the atomic-orbital (AO) vector space into a minimal basis space and a hard-virtual (HV) space.
• Utilizing standard methods for valence virtual space localization.
• Constructing the HV space to be atom-centered and automatically local.

Main Results:

• The algorithm is very fast, with computational cost limited by matrix diagonalization.
• Storage requirements are quadratic in the number of electrons.
• The computed orbitals are orthonormal, stable, and depend smoothly on nuclear coordinates.
• The orbitals exhibit near-optimal localization, comparable to projected atomic orbitals.

Conclusions:

• The developed algorithm provides an efficient and accurate method for generating localized orthonormal virtual orbitals.
• This approach is expected to significantly benefit local-correlation methods in computational chemistry.
• The method offers a balance between computational speed, storage efficiency, and orbital quality.