Developing orbital-free quantum crystallography: the local potentials and associated partial charge densities

Abstract

This work extends the orbital-free density functional theory to the field of quantum crystallography. The total electronic energy is decomposed into electrostatic, exchange, Weizsacker and Pauli components on the basis of physically grounded arguments. Then, the one-electron Euler equation is re-written through corresponding potentials, which have clear physical and chemical meaning. Partial electron densities related with these potentials by the Poisson equation are also defined. All these functions were analyzed from viewpoint of their physical content and limits of applicability. Then, they were expressed in terms of experimental electron density and its derivatives using the orbital-free density functional theory approximations, and applied to the study of chemical bonding in a heteromolecular crystal of ammonium hydrooxalate oxalic acid dihydrate. It is demonstrated that this approach allows the electron density to be decomposed into physically meaningful components associated with electrostatics, exchange, and spin-independent wave properties of electrons or with their combinations in a crystal. Therefore, the bonding information about a crystal that was previously unavailable for X-ray diffraction analysis can be now obtained.

Keto‐enol tautomerism from the electron delocalization perspective

“…We should note, that despite the features of the kinetic exchange play important role in the electron delocalization patterns in the CCC fragment of more and less stable enols (see Section 3), the use of the fermionic potential, , appear to be less informative in studying electronic delocalization in broader regions of the enol molecules (which include heteropolar bonds such as C=O) and the considered model systems. This is caused by the positive values of in heteropolar bonds 76 . In other words, overall fermionic contribution to the electronic energy in these areas is repulsive (destabilizing) and does not provide a necessary information.…”

“…In other words, it contains information about the effects of exchange correlation related with the electron motion (kinetic exchange correlation). It is a spin‐dependent part of the kinetic potential , while the remaining part is the Weizsäcker potential 74–76 . The Pauli potential can be written via gradient of the Fermi hole calculated with respect to the coordinate .…”

“…One of the advantages of the exchange and Pauli potentials is that they can be directly compared. Moreover, their combination yields a fermionic potential, 76 which measures electron delocalization arising from both static and kinetic exchange correlation effects: Its local negative values correspond to the predominant contribution to the electronic energy of the static exchange (the Fermi hole mobility is small) and reveal the areas of electron localization, such as electron lone pairs 76 . On the contrary, positive values of the indicate the regions of the predominant contribution of the kinetic electron exchange on the energy.…”

“…One of the advantages of the exchange and Pauli potentials is that they can be directly compared. Moreover, their combination yields a fermionic potential, 76 which measures electron delocalization arising from both static and kinetic exchange correlation effects:…”

“…Its local negative values correspond to the predominant contribution to the electronic energy of the static exchange (the Fermi hole mobility is small) and reveal the areas of electron localization, such as electron lone pairs. 76 On the contrary, positive values of the v f indicate the regions of the predominant contribution of the kinetic electron exchange on the energy. They show areas of abrupt changes in electronic localization, which have a destabilizing (positive) contribution to the electronic energy of a system.…”