Potential Functional Embedding Theory with an Improved Kohn-Sham Inversion Algorithm.

Potential functional embedding theory (PFET) is a rigorous theory that can yield a unique, self-consistent embedding potential shared by different subsystems treated at different levels of theory. Application of PFET has been limited by the time-consuming and sometimes unstable optimized effective potential (OEP) procedure. Here, we improve the performance of PFET by replacing the OEP algorithm with a new method to reconstruct the effective Kohn-Sham (KS) potential. We propose a direct, efficient KS inversion algorithm to solve for the effective KS potential and then employ the resulting algorithm in PFET. We benchmark our KS inversion algorithm against the recently reported modified Ryabinkin-Kohut-Staroverov (mRKS) procedure. Numerical examples show that, with sufficiently large basis sets, our KS inversion algorithm generates almost as accurate results as the mRKS procedure does, except in the vicinity of atomic nuclei, and that it requires less computational time. Three types of chemical interactions then were tested using the new KS inversion algorithm in PFET; the energetics computed from the updated formalism compare well to benchmarks.