Analytical First-Order Molecular Properties and Forces within the Adiabatic Connection Random Phase Approximation.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Density Functional Theory

Background:

• The random phase approximation (RPA) is a powerful method for calculating molecular ground-state correlation energies.
• The adiabatic connection fluctuation-dissipation theorem (ACFDT) provides a framework for RPA calculations.
• Efficient implementation of RPA for molecular properties and forces is crucial for theoretical chemistry.

Purpose of the Study:

• To present an efficient analytical implementation of first-order random phase approximation (RPA) molecular properties and nuclear forces.
• To develop a variational RPA energy Lagrangian invariant under unitary transformations.
• To enable accurate calculations of molecular structures, dipole moments, and vibrational frequencies.

Main Methods:

• Utilizing the resolution-of-the-identity (RI) approximation and imaginary frequency integration.
• Employing a variational RPA energy Lagrangian requiring a single coupled-perturbed Kohn-Sham equation solution.
• Calculating energy gradients from partial derivatives of the Lagrangian and including derivatives of quadrature nodes and weights.

Main Results:

• The RPA energy gradient implementation scales as O(N^5) with system size N, similar to single-point RPA energy calculations.
• RPA outperforms semilocal functionals and MP2 theory for equilibrium structures, dipole moments, and vibrational frequencies.
• The method shows improved scaling compared to previous implementations and supports semilocal Kohn-Sham references for better performance in small-gap systems.

Conclusions:

• The presented analytical RPA implementation provides an efficient and accurate method for computing molecular properties and nuclear forces.
• RPA offers a significant improvement over traditional methods, particularly for transition metal complexes and polarizable systems.
• This work advances the application of RPA in computational chemistry, enabling more reliable predictions of molecular behavior.