Orbital-free effective embedding potential at nuclear cusp

TL;DR

This paper introduces a new approximation for the effective embedding potential in orbital-free density functional theory, emphasizing the correct behavior at nuclear cusps to improve accuracy in embedded systems.

Contribution

A novel approach to approximate the kinetic-energy-dependent component of the embedding potential, enforcing the correct nuclear cusp limit for improved accuracy.

Findings

Enforcing the nuclear cusp limit significantly improves potential approximation for charged systems.

The new approximation enhances the accuracy of embedded system calculations involving charged components.

Improvements are less significant for neutral systems, indicating the method's specific benefit for charged environments.

Abstract

A new approach to approximate the kinetic-energy-functional dependent component ($v_t[\rho_A,\rho_B](\vec{r})$) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in [Wesolowski and Warshel, {\it J. Phys. Chem.} {\bf 97}, (1993) 8050]) is proposed. The exact limit for $v_t$ at $\rho_A\longrightarrow 0$ and $\int \rho_B d\vec{r}=2$ is enforced. The significance of this limit is analysed formally and numerically for model systems including a numerically solvable model and real cases where $\int \rho_B d\vec{r}=2$. A simple approximation to $v_t[\rho_A,\rho_B](\vec{r})$ is constructed which enforces the considered limit near nuclei in the environment. Numerical examples are provided to illustrate the numerical significance of the considered limit for real systems - intermolecular complexes comprising, non-polar, polar, charged constituents. Imposing the limit improves significantly the quality of the approximation to $v_t[\rho_A,\rho_B](\vec{r})$ for systems comprising charged components. For complexes comprising neutral molecules or atoms the improvement occurs as well but it is numerically insignificant.