Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Accurate calculation of molecular properties is crucial in chemistry and physics.
• Random Phase Approximation (RPA) methods are valuable for describing electron correlation, but can be computationally demanding.
• Existing methods often struggle with self-consistency or computational scaling for large systems.

Purpose of the Study:

• To develop an efficient and self-consistent Random Phase Approximation (RPA) method in atomic orbital (AO) space.
• To overcome limitations of existing RPA methods, including computational cost and accuracy for specific interactions.
• To enable accurate calculations for larger molecular systems.

Main Methods:

• Minimization of RPA energy with respect to the one-particle density matrix in AO space.
• Approximation of the RPA Hamiltonian using the Hartree-Fock Hamiltonian for parameter-free, self-consistent calculations.
• Introduction of Cholesky decomposed projectors to manage computational prefactors in AO-based methods.
• Exploitation of orbital locality for asymptotically quadratic scaling.

Main Results:

• The developed self-consistent RPA method is parameter-free.
• The method outperforms post-Kohn-Sham RPA for noncovalent interactions.
• Accurate dipole moments were obtained, indicating high-quality electron densities.
• The method achieves asymptotically quadratic scaling, overcoming the prefactor drawback of AO-based methods.

Conclusions:

• The new self-consistent RPA method provides an efficient and accurate approach for electronic structure calculations.
• The method's scalability opens possibilities for studying large molecular systems.
• This work advances the application of RPA in computational chemistry and materials science.