Is the Pauli exclusion principle the origin of electron localisation?

KLD: a program to elucidate the localization of the Fermi and Coulomb holes in molecular systems

CONTEXT

The electron localization is a concept that allows scientists to better understand the physical and chemical properties of electronic systems. It is associated with the propensity of electron pairs with opposite spins to accumulate as well as with their response to external perturbations. This paper contains a detailed description of the design and implementation of the program KLD, which was primarily developed in our research group to elucidate electron localization in molecular systems by evaluating the information content of electron-pair density functions. KLD employs two information-based functions as a real space measure of the Fermi and Coulomb holes for same-spin electrons and shows a better resolution as compared to other methods (i.e., ELF). Information about the acceleration of the code is also included in the present work, being noticeable the reduction of wall-time calculation and the error calculation between versions.

METHODS

KLD was designed to be easy to use, extend, and maintain; thus, many principles of modern software development, extensive testing, and package management were adopted. The latest version of the KLD program was created utilizing the Compute Unified Device Architecture (CUDA) version, which allows it to use the computational capacity of NVIDIA Graphics Processing Units (GPUs) for processing purposes. The electron-pair conditional density was calculated from the canonical molecular orbitals obtained at the HF/6-31G(2df,p) level, or alternatively the natural orbitals in the case of explicit correlated wavefunctions computed at the MP2/6-31G(2df,p)//HF/6-31G(2df,p) level.

Electron delocalization in defect-containing graphene and its influence on tetrel bond formation

Using the advanced analyses of electron density and fermionic potential, we show how electron delocalization influences the ability of defect-containing graphene to form tetrel bonds. The Cg atoms of a vacancy defect can produce one nonpolar interaction, alongside a peculiar polar Cg⋯Cg bond. The latter stems from the presence of a localized electron pair on a vacancy defect Cg atom and the local depletion of electron localization on another Cg atom. This interaction is an example of intralayer tetrel bond. In the presence of an absorbed molecule of bisphenol A diglycidyl ether (DGEBA), graphene is able to form incipient tetrel Cg⋯O bonds with an ether group oxygen. In contrast to an epoxy group oxygen, the disposition of the ether oxygen often causes the orientation of electron-rich π-domains of graphene carbon on the weakly expressed electrophilic region of the oxygen. In the case of graphene with a point Si defect, the Si atom can form quite strong Si⋯C interactions with the DGEBA aryl carbons. In contrast to other noncovalent bonds, this interaction significantly alters the electron (de)localization on the Si atom and in the aryl ring. The reliability of the obtained results is enhanced by the use of multiple 2D periodic models with defects located at different positions along the DGEBA skeleton.

DFT potentials from a chemical perspective: Anatomy of electron (de)localization in molecules and crystals

We introduce a fermionic potential, v f $$ {v}_f $$ , as a comprehensive measure of electron (de)localization in atomic-molecular systems. Unlike other common descriptors as ELF, LOL, etc., it characterizes all physical effects responsible for (de)localization of electrons, namely: an exchange hole depth, its tendency to change, a sensitivity of an exchange correlation hidden in a pair density and kinetic potential to local variations in electron density. Wells in the v f $$ {v}_f $$ distribution correspond to the domains of maximum electron localization, while the potential's barriers prevent delocalization of electrons through them. It also estimates bond orders and successfully reveals the impact of chemical modifications or environmental effects on the delocalization of electrons in molecules and crystals. The v f $$ {v}_f $$ components provide a unique opportunity to compare the influence of the mentioned physical effects on electron (de)localization. This merges physical and chemical views of electron delocalization using functions appearing in density functional theory.

Keto-enol tautomerism from the electron delocalization perspective

The equilibrium between keto and enol forms in acetylacetone and its derivatives is studied using electron delocalization indices and delocalization tensor density. We demonstrate how electron delocalization governs the equilibrium between keto and enol forms. The less stable enols have more distinct double and single bond character in the CCC fragment, while electron delocalization in this fragment is more pronounced in more stable enols. Looking for the origin of such behavior, we considered the one-electron potentials entering the Euler equation for the electron density. We found that electron delocalization is mainly governed by the static exchange potential, which depends on the three-dimensional atomic structure. It, however, does not distinguish differences in electron delocalization in more and less stable enols, the effect arising from the kinetic exchange contribution, which reflects spin-dependent effects in the electron motion. The local depletion of kinetic exchange in the conjugated fragment yields the enhanced electron delocalization along the CCC bonds in more stable enols. Thus, a combination of considered descriptors allowed us to reveal the influence of electron delocalization on the equilibrium between keto and enol forms and showed the significant features of this phenomenon.

Theoretical Description of R-X⋯NH3 Halogen Bond Complexes: Effect of the R Group on the Complex Stability and Sigma-Hole Electron Depletion

In the present work, a number of R–X⋯NH₃ (X = Cl, Br, and I) halogen bonded systems were theoretical studied by means of DFT calculations performed at the ωB97XD/6-31+G(d,p) level of theory in order to get insights on the effect of the electron-donating or electron-withdrawing character of the different R substituent groups (R = halogen, methyl, partially fluorinated methyl, perfluoro-methyl, ethyl, vinyl, and acetyl) on the stability of the halogen bond. The results indicate that the relative stability of the halogen bond follows the Cl < Br < I trend considering the same R substituent whereas the more electron-withdrawing character of the R substituent the more stable the halogen bond. Refinement of the latter results, performed at the MP2/6-31+G(d,p) level showed that the DFT and the MP2 binding energies correlate remarkably well, suggesting that the Grimme’s type dispersion-corrected functional produces reasonable structural and energetic features of halogen bond systems. DFT results were also observed to agree with more refined calculations performed at the CCSD(T) level. In a further stage, a more thorough analysis of the R–Br⋯NH₃ complexes was performed by means of a novel electron localization/delocalization tool, defined in terms of an Information Theory, IT, based quantity obtained from the conditional pair density. For the latter, our in-house developed C++/CUDA program, called KLD (acronym of Kullback–Leibler divergence), was employed. KLD results mapped onto the one-electron density plotted at a 0.04 a.u. isovalue, showed that (i) as expected, the localized electron depletion of the Br sigma-hole is largely affected by the electron-withdrawing character of the R substituent group and (ii) the R–X bond is significantly polarized due to the presence of the NH₃ molecule in the complexes. The afore-mentioned constitutes a clear indication of the dominant character of electrostatics on the stabilization of halogen bonds in agreement with a number of studies reported in the main literature. Finally, the cooperative effects on the [Br—CN]_n system (n = 1–8) was evaluated at the MP2/6-31+G(d,p) level, where it was observed that an increase of about ~14.2% on the complex stability is obtained when going from n = 2 to n = 8. The latter results were corroborated by the analysis of the changes on the Fermi-hole localization pattern on the halogen bond zones, which suggests an also important contribution of the electron correlation in the stabilization of these systems.