Post-Kohn-Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Post-Kohn-Sham (post-KS) random-phase approximation (RPA) is a widely used method for calculating interaction energies.
• Existing RPA methods often neglect certain theoretical corrections, potentially limiting their accuracy for complex systems.
• Accurate calculation of noncovalent interactions is crucial in chemistry and materials science.

Purpose of the Study:

• To develop and implement a series of corrections to the post-KS RPA energy.
• To improve the theoretical description of noncovalent interactions beyond standard RPA.
• To provide a computationally efficient method for accurate energy calculations.

Main Methods:

• Formulation of beyond-RPA corrections using expectation-value coupled-cluster theory and many-body perturbation theory (MBPT).
• Inclusion of non-Hartree-Fock reference contributions and coupled-cluster doubles non-ring contractions.
• Implementation utilizing a semicanonical orbital basis and low-rank tensor decomposition for efficient energy evaluation scaling as O(N^5).

Main Results:

• The proposed corrections, particularly the third-order doubles correction (E_c^2), recover accuracy lost by neglecting non-Hartree-Fock contributions.
• The new approach incorporates all terms from renormalized second-order perturbation theory (rPT2) plus additional third-order MBPT terms.
• Accurate results were achieved for noncovalent dimers of polar molecules and the complex (CH4)---(H2O)20 cluster.

Conclusions:

• The developed method offers a significant improvement over standard RPA for calculating noncovalent interaction energies.
• The approach provides a balance between high accuracy and computational feasibility, suitable for complex molecular systems.
• This work advances the theoretical toolkit for studying intermolecular forces and molecular aggregates.