Density-orbital embedding theory

Abstract

In the article density-orbital embedding (DOE) theory is proposed. DOE is based on the concept of density orbital (DO), which is a generalization of the square root of the density for real functions and fractional electron numbers. The basic feature of DOE is the representation of the total supermolecular density ${\ensuremath{\rho}}_{s}$ as the square of the sum of the DO ${\ensuremath{\varphi}}_{a}$, which represents the active subsystem $A$ and the square root of the frozen density ${\ensuremath{\rho}}_{f}$ of the environment $F$. The correct ${\ensuremath{\rho}}_{s}$ is obtained with ${\ensuremath{\varphi}}_{a}$ being negative in the regions in which ${\ensuremath{\rho}}_{f}$ might exceed ${\ensuremath{\rho}}_{s}$. This makes it possible to obtain the correct ${\ensuremath{\rho}}_{s}$ with a broad range of the input frozen densities ${\ensuremath{\rho}}_{f}$ so that DOE resolves the problem of the frozen-density admissibility of the current frozen-density embedding theory. The DOE Euler equation for the DO ${\ensuremath{\varphi}}_{a}$ is derived with the characteristic embedding potential representing the effect of the environment. The DO square ${\ensuremath{\varphi}}_{a}^{2}$ is determined from the orbitals of the effective Kohn-Sham (KS) system. Self-consistent solution of the corresponding one-electron KS equations yields not only ${\ensuremath{\varphi}}_{a}^{2}$, but also the DO ${\ensuremath{\varphi}}_{a}$ itself.