Approximate versus Exact Embedding for Chiroptical Properties: Reconsidering Failures in Potential and Response

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Accurate calculation of chiroptical properties is crucial in chemistry and biology.
• Frozen-density embedding (FDE) offers a computationally efficient approach for large molecular systems.
• Previous FDE methods struggled with response properties, particularly for covalently bound systems.

Purpose of the Study:

• To implement and validate subsystem time-dependent density-functional theory (sTDDFT) using a projection-based coupled FDE (FDEc) framework.
• To assess the impact of common approximations in FDE calculations for chiroptical response properties.
• To improve the accuracy and applicability of FDE for describing optical rotation and electronic circular dichroism (ECD).

Main Methods:

• Developed a new implementation of the projection-based, coupled frozen-density embedding (FDEc) framework.
• Adapted the generalized, non-Hermitian formulation of TDDFT for subsystem calculations.
• Derived expressions for regular and damped response properties within sTDDFT.
• Systematically tested approximations: nonadditive kinetic-energy (NAKE) functionals, monomer basis sets, and uncoupled FDE (FDEu).

Main Results:

• The implemented "exact" sTDDFT formulation accurately reproduces supermolecular results for ECD spectra, optical rotatory dispersion, and polarizabilities.
• Errors from approximate NAKE functionals can be significant, but basis set choice and intersubsystem coupling are often more critical.
• Neglecting intersubsystem response coupling (FDEu) is a major source of error, as demonstrated by comparison to fully coupled calculations.
• Good agreement with reference data is achievable even with standard NAKE approximations and efficient monomer basis sets when coupling is properly handled.

Conclusions:

• Coupled FDE with sTDDFT is a suitable and accurate method for calculating chiroptical properties, including optical rotation.
• The choice of basis set and the inclusion of intersubsystem response coupling are crucial for accurate FDE calculations of response properties.
• This work makes FDE a more accessible and reliable tool for studying larger systems with complex electronic structures and chiroptical behavior.