Evaluating and interpreting the exchange correlation contributions to the total static and interelectron interaction force densities, with a force-field perspective on the exchange charge density

A crucial aspect of the conservative exchange force <b>F</b>_<i>x</i>(<b>r</b>) is the possible existence of nonnuclear basins in the corresponding vector field, which encompass internuclear binding regions for various covalent bonds. The intricate behavior of <b>F</b>_<i>x</i>(<b>r</b>) can be evaluated through its component contributions to the total static force density and the interelectron interaction force density <b>F</b>_ee(<b>r</b>). The sought-after contributions are expressed as the scalar projection of the partial force (SPPF) onto the corresponding cumulative force. The resulting scalar component distribution permits the differentiation of the regions of physical space, exhibiting directional divergence or convergence between the two considered force fields. The scalar projections of <b>F</b>_<i>x</i>(<b>r</b>) onto and <b>F</b>_ee(<b>r</b>) enable the identification of shared electrons and lone electron pairs. Concurrently, the SPPF discloses the counteracting mechanism for the charge-transfer-induced quantum chemical response, which is implicated in a negative contribution of <b>F</b>_<i>x</i>(<b>r</b>) to for the interatomic transferred density. Furthermore, <b>F</b>_<i>x</i>(<b>r</b>) typically positively contributes to <b>F</b>_ee(<b>r</b>) within a part of each binding region, thereby facilitating the retention of electron "glue" between nuclei. Its negative contribution outside the binding regions highlights the role of <b>F</b>_<i>x</i>(<b>r</b>) in mitigating interelectron repulsion. These findings demonstrate the mechanical role of the exchange correlation in chemical bonding and the interatomic electron transfer in many-electron multinuclear systems. Additionally, the exchange charge density ∇·<b>F</b>_<i>x</i>(<b>r</b>)/(4π), which signifies the effective electron density distribution that arises from the influence of <b>F</b>_<i>x</i>(<b>r</b>), has been shown to accurately reproduce the details of subatomic structure, with negative values indicating electron cloud thickening. The underlying procedures are readily implementable and offer reliable chemical structure descriptors.