Analytical Energy Gradients in Range-Separated Hybrid Density Functional Theory with Random Phase Approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular properties requires robust theoretical frameworks.
• Range-separated hybrid (RSH) methods offer a balance between short-range and long-range electron correlation.
• Random Phase Approximation (RPA) is a powerful method for describing electron correlation.

Purpose of the Study:

• To derive and implement analytical forces within the Lagrangian framework for RSH-based RPA correlated total energy methods.
• To enable efficient geometry optimization for molecules and complexes using these advanced computational methods.
• To investigate the impact of intermolecular interactions on monomer geometry using the developed methods.

Main Methods:

• Derivation of analytical forces in the Lagrangian framework.
• Application of range-separated hybrid (RSH) functionals for short-range exchange-correlation.
• Utilizing Hartree-Fock for long-range exchange and RPA for long-range correlation.
• Expressing RPA correlation energy using ring coupled cluster doubles (rCCD) theory.
• Implementation and testing of analytical gradients for geometry optimization.

Main Results:

• Successful derivation of analytical forces for RSH-based RPA methods.
• Implementation of analytical gradients enabling geometry optimizations.
• Validation of the methods on simple molecules and intermolecular charge transfer complexes.
• Demonstration that intermolecular interactions influence monomer geometries.

Conclusions:

• The developed analytical forces provide an efficient and accurate tool for computational chemistry.
• These methods are suitable for studying systems where intermolecular interactions are significant.
• The study advances the capability of theoretical methods for predicting molecular structures.