Localized Resolution of Identity Approach to the Analytical Gradients of Random-Phase Approximation Ground-State...

Area of Science:

• Quantum Chemistry
• Computational Materials Science

Background:

• Accurate prediction of molecular geometries and energies is crucial for understanding chemical reactions and material properties.
• Particle-hole random-phase approximation (RPA) offers a promising route to correlated electronic energies but faces challenges in computational efficiency for geometry optimization.

Purpose of the Study:

• To develop and implement a formalism for calculating analytical gradients of the particle-hole RPA ground-state energy.
• To enable efficient molecular structure relaxation and geometry optimization at the RPA level within an atomic orbital basis set framework.

Main Methods:

• Utilized a localized resolution of identity (LRI) approximation for efficient evaluation of two-electron Coulomb integrals and their derivatives.
• Employed density functional perturbation theory to compute first-order derivatives of Kohn-Sham orbitals and energies.
• Implemented the formalism for both Gaussian-type orbitals (GTOs) and numerical atomic orbitals (NAOs).

Main Results:

• Achieved adequate numerical precision for RPA gradient evaluations, demonstrating the utility of the LRI approximation.
• Found that post-KS RPA systematically overestimates bond lengths in small molecules.
• Optimized geometries of water hexamer isomers and determined their energy hierarchy, showing good agreement with coupled cluster methods.

Conclusions:

• The developed formalism provides an efficient and accurate method for RPA-based geometry optimizations.
• Post-KS RPA requires corrections for accurate bond length predictions, but provides a reliable energy ordering for isomers.
• Renormalized single excitation corrections effectively address the underestimation of dissociation energies by RPA.