Towards density functional approximations from coupled cluster correlation energy densities.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Density functional approximations (DFAs) are crucial for electronic structure calculations in condensed matter physics and surface science.
• The correlation energy density, ϵc(r), is key to DFAs but is not uniquely defined, posing a challenge for constructing accurate functionals.
• Existing DFAs rely on finding suitable connections between ϵc(r) and electron density, ρ.

Purpose of the Study:

• To present a novel approach for deriving correlation energy density (ϵc(r)) directly from coupled-cluster (CC) energy expressions.
• To construct a semilocal functional that approximates CC correlation energy densities.
• To demonstrate the potential of using energy densities to guide the development of accurate correlation functionals.

Main Methods:

• Derivation of ϵc(r) from coupled-cluster (CC) energy expressions.
• Analysis of derived energy densities for two-electron systems.
• Construction of a semilocal functional based on CC correlation energy densities.

Main Results:

• A new method for deriving ϵc(r) from CC theory was established.
• The derived energy densities were analyzed for prototypical two-electron systems.
• A simple and accurate semilocal correlation functional was developed for the helium isoelectronic series, guided by CC energy densities.

Conclusions:

• The study presents a promising approach for developing DFAs by directly using CC energy densities.
• The developed functional shows high accuracy for the helium isoelectronic series.
• While not directly transferable to many-electron systems, the methodology highlights the potential of energy density-guided functional construction.