On the separation of the information content of the Fermi and Coulomb holes and their influence on the electronic properties of molecular systems

ABSTRACT

In this paper, two information-based functions are employed as a real space measure of the Fermi and Coulomb holes for same-spin electrons. The first one is the information content of the Exchange-Correlation hole, calculated from the Kullback–Leibler divergence of the same-spin conditional pair density respect to the marginal probability (${\chi }_{XC}$). As reported previously, ${\chi }_{XC}$, can be used to reveal the regions of the space associated to the classical electron pair model. Here, correlated wave-functions, such as CISD, MP2, and CCSD, are considered for the calculation of ${\chi }_{XC}$. This is achieved by introducing an approximated method based on employing natural orbitals and their occupancy numbers. In addition to ${\chi }_{XC}$, in this work we propose a measure of the information content of the same-spin correlation hole, which is computed in terms of the Kullback–Leibler divergence of a correlated same-spin conditional pair density respect to the uncorrelated Hartree–Fock pair density (${\chi }_C$). The proposed methodology is discussed in the light of the result derived from noble gas atoms, the $F_2$ molecule and some non-covalently bonded systems.

GRAPHICAL ABSTRACT

KEYWORDS:

• Electron localisation
• Fermi hole
• Coulomb hole
• electron correlation
• Kullback–Leibler divergence

Acknowledgements

This work has been performed by employed the resources from the NCU's and USFQ's High Performance Computing systems. L.R, F.J.T. and M.B. highly appreciate the financial support from USFQ's POLIGRANTS 2017–2018.

Disclosure statement

No potential conflict of interest was reported by authors.