Topology of the Effectively Paired and Unpaired Electron Densities for Complex Bonding Patterns: The Three-Center Two-Electron Bonding Case

Abstract

Our previously reported local formalism of the electron density decomposition into effectively paired and unpaired densities is applied to electron deficient molecular systems possessing complex bonding patterns. It is shown that the unpaired density is not only near the nuclear positions, like in classical bonds, but also spills out over the bonding regions, to compensate the electron deficiency. Topological information obtained from the effectively unpaired density, which may not be directly observed from the total density, allows us to establish a procedure to detect complex interactions. This study is complemented with results arising from nonlocal formalism of topological population analyses. The conclusions from both formalisms are in complete agreement and permit to interpret the well-known structural information from Lipscomb styx numbers going beyond it in cases where the electronic description becomes ambiguous, pointing out the subtle information contained in the unpaired density. Numerical results for three-center two-electron bondings in the boranes B2H6, B4H10, B5H9, and B5H11 are reported.

Donor‐acceptor interactions: Transition metal carbonyl group ligand [TM(CO)6]qcomplexes. A case study at correlated level from the topological density point of view

“…The fundamental local topological indicators reside in the determination of the critical points of the densities ( cp ), its localization (first spatial derivatives) in physical space, the local accumulation or depletion in their surroundings by evaluation of the Laplacian function and the breakdown of the symmetries along the cartesian axis (ellipticity) for each of the density fields . These magnitudes for both density fields, pairing and unpairing ones, contain enough information to define the nature of atomic interactions . The set of cp s of the total density field is defined by the condition of vanishing gradient evaluated by the relation , where is the complete set of cp s of ρ ( r ).…”

“…This topological methodology, applied to different types of electron distribution leads to identify and classify the bonding interactions regarding the determination of localization and type of cp s and the electronic populations in the domains . This methodology exposed above has been successfully applied to classical as well as complex molecular structures ranging for instance, from electron deficient compounds like boron hydrides, closoboranes, molecular organic ions, simple organo‐metallic systems, metalloid clusters, and simple one‐ligand one‐metal systems …”

“…For an adequate understanding of the physico‐mathematical information obtained from the calculations, this is transferred to the language of the fundamental chemical concepts that determine the classical magnitudes (descriptors) of chemistry, such as atomic charges, covalent bond orders, valences among others and their extensions to the case of nonclassical populations 2e‐3c and 4e‐3c . In addition, the values of the electron density fields, that is, total, pairing and unpairing ones, their cp s and the values of their Laplacian fields are considered as being the local descriptors . They are complementary to nonlocal or integrated ones in order to provide a qualitative and also quantitative density description, out of the traditional chemical information aforementioned.…”

Pairing and unpairing electron densities in organic systems: Two-electron three center through space and through bonds interactions

“…Electron deficient compounds like boron hydrids give rise to important complex patterns of bonding which has been associated to two-electron three-center interaction mechanisms. [1][2][3][4][5] These multi-center interactions are known to appear in a wide variety of molecular systems as organic ions, [6][7][8] metallic and non-metallic clusters among others. 9 Nevertheless, the different types of molecular systems, i.e., the boron hydrids and the carbonium ions show different patterns within this type of interactions characterizing the bonding interactions and thus constitute a landmark for comparative detailed studies about them.…”

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix

“…2,3 Their influence on the electron distribution reveals through their relationships with the chemical descriptors and the topology of the distribution 4,5 and it is crucial in the understanding of the nature of the chemical bond. [6][7][8][9][10][11][12][13][14][15][16][17][18][19] The fundamental chemical concepts are the summary of the physical information contained in the pth-order reduced density matrices ͑p-RDMs͒ of an N-electron molecular system ͑p Ͻ N͒ which are directly derived from the wave function. 2,3,10 Most of the attempts to describe the electron distribution in molecular systems have been concentrated on the spin blocks of the first-order reduced density matrices ͑spin up or ␣ and spin down or ␤ 1-RDMs͒, which determine electron and spin densities and provide intuitive interpretations of chemical data.…”