A well-scaling natural orbital theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Accurate ground-state electronic structure calculations are crucial for understanding molecular and material properties.
• Existing methods like density-functional theory (DFT) face challenges with accuracy for certain systems.
• The development of computationally efficient and accurate electronic structure methods remains an active research area.

Purpose of the Study:

• To introduce a novel energy functional for ground-state electronic structure calculations.
• To explore the use of natural spin-orbitals and approximations to the two-particle density matrix as variables.
• To evaluate the performance of the proposed functional against established high-accuracy methods.

Main Methods:

• Developed an energy functional based on natural spin-orbitals and occupation probabilities.
• Employed controlled approximations to the two-particle density matrix.
• Implemented a seniority-zero version yielding Hartree-Fock scaling.
• Compared results for small molecular systems with full configuration interaction (FCI) and doubly occupied configuration interaction (DOCI).

Main Results:

• The proposed functional yields energies above FCI and close to DOCI calculations.
• Demonstrated algebraic and Hartree-Fock scaling properties for computational efficiency.
• Achieved considerably greater accuracy compared to current DFT approximations.
• Outperformed current functionals of the one-particle density matrix.

Conclusions:

• The new energy functional provides a promising balance of accuracy and computational efficiency.
• It represents a significant improvement over existing DFT methods for ground-state electronic structure.
• The method holds potential for applications in quantum chemistry and materials science.