Where the Electron Correlation Energy resides within Hartree-Fock Theory

- Itai Panas

Itai Panas

Department of Chemistry and Chemical Engineering Division of Energy and Materials, Chalmers University of Technology, Environmental Inorganic chemistry unit

Corresponding Author:itai@chalmers.se

Author Profile## Abstract

A method for accurately estimating the electron correlation energy as a 1 st order correction to the Hartree-Fock energy is presented. It succeeds by disallowing the representation of the electron repulsion operator to be more fine-grained than the corresponding representation of the two-particle density. To extract the electron correlation contribution to the molecular internal energy from the exact wavefunction, the short-range contribution to the electron repulsion operator is replaced by a corresponding correlation kinetic energy penalty. Utilizing the virial theorem, this self-interaction-free exact-exchange method becomes applicable on condition of stability of the Self-Consistent Field wave function. Laplace as well as Fourier transforms are resorted to as consistency checks. Atomic and small molecular ions are considered for validation. The latter require modelling of the screened Coulomb hole associated with 1s electrons owing to coupled short-range electron-nucleus and electron-electron interactions. For this purpose, Hooke's atom is analyzed (0.03 ≤ í µí¼ ≤ 1000) and consistency is demonstrated for 1s ! Helium-like ions (Z=1-36). While impacting core-valence interactions, the said screening is absent in the valence as confirmed by the Be-like ions (Z=3-36) 1í µí± ! 2í µí± ! systems, for LiH, BeH + , Li2 and for LiBe +. A chemistry associated exclusively with K-shell orbitals is briefly discussed based mainly on results for HeH + and H3 +. Fractional charges scaling the Coulomb hole is inferred to better represent the complex correlation hole in hydrogen clusters and high-pressure metallic hydrogen.27 Jan 2023Submitted to *IJQC Interactive Papers*