Analytical nuclear second derivatives for frozen-density embedding employing self-consistent field methods.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Materials Science

Background:

• Accurate calculation of molecular vibrations is crucial for understanding chemical reactions and material properties.
• Frozen-Density Embedding (FDE) offers a computationally efficient way to study large systems by embedding a subsystem in a larger environment.
• Analytical gradients and Hessians are essential for geometry optimization and vibrational analysis.

Purpose of the Study:

• To derive and implement analytical nuclear ground-state second derivatives for uncoupled Frozen-Density Embedding (FDEu).
• To assess the accuracy of the developed method for both weakly and strongly coupled subsystems.
• To demonstrate the applicability of the FDEu approach to extended molecular systems for vibrational frequency calculations.

Main Methods:

• Derivation and implementation of analytical nuclear second derivatives for FDEu within Hartree-Fock and Kohn-Sham density functional theory.
• Evaluation of exchange integrals using the chain-of-spheres exchange approach with exact and approximate nuclear second derivatives.
• Assessment of FDEu Hessian accuracy by comparison with supermolecule calculations.

Main Results:

• Successful derivation and implementation of analytical nuclear second derivatives for FDEu.
• Demonstrated accuracy of the FDEu Hessian for various coupled subsystems.
• Calculated vibrational frequencies for a large naphthalene dimer system (792 atoms) embedded in a crystalline environment.

Conclusions:

• The developed FDEu method provides an accurate and efficient approach for calculating vibrational frequencies in large molecular systems.
• This method holds significant potential for analyzing intermolecular vibrations relevant to charge transport phenomena.
• The study validates the strengths and limitations of FDEu for diverse chemical environments.