Electron localization and delocalization indices for solids

Abstract

The electron localization and delocalization indices obtained by the integration of exchange-correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices.

Designing 3D topological insulators by 2D-Xene (X = Ge, Sn) sheet functionalization in GaGeTe-type structures

“…The DI value between the nextnearest Ge atoms (2NN) from the same Ge layer is d(Ge,Ge) = 0.046 (at the distance of 4.048 Å). The DI value between two 3NN 82,83 These findings highlight the similarity between the buckled germanium layer in GaGeTe and GeH and are consistent with the semiconducting behavior of GaGeTe.…”

“…77 The same code was used to compute the delocalization indices [78][79][80][81] between the QTAIM basins from the (L)APW and PAW results. 82,83 Delocalization indices characterize the degree of electron pair exchange between the basins (two atoms) and can be interpreted as the covalent-bond order. 81 For spinor wave functions employed in the calculations including spin-orbit coupling, the delocalization indices were computed according to the method reported in ref.…”

Extracting chemical information from plane wave calculations by a 3D ‘fuzzy atoms’ analysis

“…The analysis of the results of plane wave calculations discussed here -in full accord with those in [5,8,9] -indicates that plane wave calculations are not only capable to give accurate energies and structural information for molecular systems, but they can also provide connections between the physical and chemical pictures of molecules, quite similar to those one can obtain from calculations using conventional atom-centered basis sets. It is important to stress that the analysis can be done without introducing externally (i.e., artificially) any atom-centered functions, simply by using the numerical representation of the molecular orbitals; in all other aspects the analysis is performed exactly in the same manner as in the case of conventional "LCAO-type" quantum chemical calculations.…”

“…This success inspired us to consider another aspects of the 3D "fuzzy atoms" analysis-the possibility of obtaining chemically relevant quantities, such as bond orders and valences, following the scheme used for atom-centered basis sets [7]. That approach has much in common with recent studies employing Bader's topological theory of "Atoms in Molecules" (AIM) [8,9]. Owing to the complexity of the AIM domains, the "fuzzy atoms" scheme should be simpler (cheaper) and applicable for larger systems.…”

Identification of mixed bromidochloridotellurate anions in disordered crystal structures of (bdmim)2[TeX2Y4] (X, Y=Br, Cl; bdmim=1-butyl-2,3-dimethylimidazolium) by combined application of Raman spectroscopy and solid-state DFT calculations

“…[11][12][13][14]. The introduction of periodic boundary conditions for ab initio and DFT calculations has facilitated modeling of crystal structures in the solid state [15][16][17]. The method has recently also proven powerful for the computation of fundamental vibrations [15,18,19].…”