Frozen Density Embedding Theory (FDET) [1-3] provides a rigorous framework for embedding quantum subsystems within an environment. In this formalism, the total electron density is constructed from two contributions: the embedded subsystem’s density, described by a wavefunction, and the environment’s density, which remains frozen. This partitioning allows for a flexible choice of computational methods, where the embedded subsystem can be treated using wave function-based approaches that are accurate for the observables of interest, while the environment’s density can be obtained from coarser, computationally efficient approximations. The embedding potential is determined by minimizing the total energy—expressed as a functional of both the embedded subsystem’s wavefunction and the environment’s density—with respect to variations in the subsystem’s density.

The accuracy of FDET-based methods hinges on reliable approximations to the non-additive kinetic energy (NAKE) bifunctional, which accounts for Pauli repulsion between the embedded system and its environment. However, for most properties of interest, it is not the NAKE itself but rather its functional derivative—the non-additive kinetic potential (NAKP)—that must be accurately described. A promising strategy for improving NAKP approximations is the bottom-up approach, which models the NAKP directly rather than deriving it from an approximate kinetic energy functional. This method offers key advantages, notably the ability to enforce exact constraints and recover correct physical limits, leading to improved accuracy and transferability. We demonstrate that incorporating these strategies enhances the applicability of FDET-based methods, enabling us to tackle challenging embedding problems in both ground and excited states. Specifically, we show that these approaches improve the description of charge transfer to the environment and covalent bonding between the embedded subsystem and its environment, where standard embedding methods often fail.

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Journal of Chemical Physics 2014, 140, 18A530.