Analytical Gradients of Random-Phase Approximation Plus Corrections from Renormalized Single Excitations.

Area of Science:

• Quantum chemistry
• Computational materials science

Background:

• The random-phase approximation (RPA) is a robust method for calculating molecular and material properties.
• The renormalized single excitation (rSE) correction improves RPA's underbinding tendency.
• Analytical gradients for RPA enable geometry optimizations, but rSE gradients were missing.

Purpose of the Study:

• To formulate and implement analytical gradients for the rSE correction within an atomic-orbital basis set.
• To enable geometry optimizations and assess the performance of RPA+rSE for molecular structures and energies.

Main Methods:

• Derivation of analytical gradients for the rSE energy with respect to nuclear coordinates.
• Implementation within an atomic-orbital basis set framework.
• Application to small molecules, water clusters, and the WATER27 dataset.

Main Results:

• The rSE correction strengthens RPA's overestimation for covalent bonds but corrects it for dispersion-bound interactions.
• rSE gradients minimally impact water hexamer isomer energy differences.
• Using RPA+rSE geometries reduces the mean absolute error for the WATER27 dataset.

Conclusions:

• The developed analytical rSE gradients are crucial for accurate molecular geometry predictions using RPA+rSE.
• RPA+rSE with optimized geometries shows improved accuracy, particularly for systems dominated by dispersion forces.
• This work paves the way for advanced computational studies using RPA+rSE.