From Energies to Structures: PNO-F12 Geometry Optimization of Large Molecules for Near-Spectroscopic Accuracy

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Molecular Modeling

Background:

• Geometry optimization at the coupled-cluster (CC) level is computationally expensive.
• Analytical gradients are unavailable for explicitly correlated and local-correlation CC methods, hindering accurate structure determination.
• Existing methods face bottlenecks for high-accuracy quantum chemistry calculations.

Purpose of the Study:

• To present a general and scalable framework for routine geometry optimizations at the PNO-F12 (Pair-Natural-Orbital explicitly Correlated F12) level.
• To enable high-accuracy structural refinements for medium-to-large molecular systems.
• To overcome limitations in current quantum chemistry computational methods.

Main Methods:

• Combined numerical gradients with a dual-coordinate strategy for geometry optimization.
• Evaluated gradients via finite differences along normal modes while performing updates in generalized internal coordinates.
• Optimized mode-dependent displacement step sizes to control numerical errors and effects from explicit correlation.

Main Results:

• Achieved submilliangstrom structural refinements with high precision.
• Delivered equilibrium geometries of near-spectroscopic accuracy for benchmark and large systems (e.g., cytosine tautomers, corannulene, coronene).
• Maintained affordable computational times and excellent parallel scalability.

Conclusions:

• The developed protocol makes geometry optimization a non-limiting factor for explicitly correlated CC accuracy.
• Enables routine high-accuracy structural and spectroscopic studies for medium-to-large molecular systems.
• Numerical gradients at the PNO-F12 level preserve coupled-cluster structural accuracy compared to composite schemes.