Non-nuclear attractors in small charged lithium clusters, Limq (m = 2-5, q = ±1), with QTAIM and the Ehrenfest force partitioning

The Ehrenfest force field: A perspective based on electron density functions

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen-hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

Bonding in the high spin lithium clusters: Non-nuclear attractors play a crucial role

The bonding in lithium high-spin clusters contradicts the usual chemical bonding concept since there are no electron pairs between the atoms, and they are bound with parallel spin electrons. Quantum theory of atoms in molecules and interacting quantum atom analysis (IQA) were used to investigate the nature of bonding in the high-spin Li n n + 1 n = 2 - 5 clusters. Our findings demonstrate that the non-nuclear attractors (NNAs) are an essential component of the high-spin lithium clusters and play a key role in keeping them stable. Based on IQA energy terms, an electrostatic destabilizing interaction between the lithium atoms works against the cluster formation. On the other hand, the interactions between lithium atoms and NNA basins are stabilizing and outweigh the lithium-lithium destabilizing effects. In fact, NNAs tend to draw lithium atoms together and stabilize the resulting cluster. The high-spin clusters of lithium can be regarded as electrostatically driven compounds since the electrostatic components are primarily responsible for the stabilizing interactions between NNAs and Li atoms. The only exception is ³ Li₂ , which lacks NNA and has a non-repellent lithium-lithium interaction. Indeed, in the ³ Li₂ , the interatomic electrostatic component is negligibly small, and the exchange-correlation term leads to a weak bonding interaction.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

New insights of QTAIM and stress tensor to finding non-competitive/competitive torquoselectivity of cyclobutene

This study aims to investigate the phenomenon of torquoselectivity through three thermal cyclobutene ring-opening reactions (N1-N3). This research focuses on the nature of the chemical bond, electronic reorganization, predicting non-competitive or competitive reactions, and torquoselectivity preference within Quantum Theory of Atoms in Molecules (QTAIM) and stress tensor frameworks. Various theoretical analyses for these reactions, such as metallicity ξ(r_b), ellipticity ε, total local energy density H(r_b), stress tensor polarizability ℙ_σ, stress tensor eigenvalue λ_3σ, and bond-path length, display differently for non-competitive and competitive reactions as well as for the conrotatory preferences either it is the transition state outward conrotatory (TS_out) or transition state inward conrotatory (TS_in) directions by presenting degeneracy or non-degeneracy in their results. The ellipticity profile provides the motion of the bond critical point locations due to the different substituents of cyclobutene. In agreement with experimental results, examinations demonstrated that N1 is a competitive reaction and N2-N3 are non-competitive reactions with TS_out and TS_in preference directions, respectively. The concordant results of QTAIM and stress tensor scalar and vectors with experimental results provide a better understanding of reaction mechanisms.

Application of a quantum genetic algorithm and QTAIM analysis in the study of structural and electronic properties of neutral bimetallic clusters NaxLiy (4 ≤ x + y ≤ 10)

Alloy clusters of Na_xLi_y (4 ≤ x + y ≤ 10) are studied by exploring the potential energy surface in the ab initio MP2 level with the support of a quantum genetic algorithm (QGA). In some cases, the structures have been also refined with DFT and coupled-cluster methods. The general trends of sodium-lithium structures are in line with previous studies. The ionization potentials and polarizabilities to all structures were calculated with MP2 method and the average error between these two properties compared with experimental data was 6% and 13%, respectively. The topological analysis based on quantum theory of atoms in molecules (QTAIM) showed that by increasing the cluster size of the diatomic system there was a decrease of atomic interaction energies. The degree of degeneracy from D3BIA aromaticity index and the analysis of the atomic charges showed the influence (by charge transfer) of the chemical element in lower quantity in the cluster with respect to the other atoms. Our achievements of comparing our theoretical results with available experimental data have demonstrated that our approach can also predict satisfactorily quantum atomic and alloy clusters properties, at least, for low nuclearities.

Orbital-free quantum crystallography: view on forces in crystals

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

3-D bond-paths of QTAIM and the stress tensor in neutral lithium clusters, Lim (m = 2-5), presented on the Ehrenfest force molecular graph

In this investigation we set out to understand the origins of non-nuclear attractors (NNAs) found for neutral lithium clusters Lim (m = 2-5) on the QTAIM molecular graph but not on the Ehrenfest force F(r) molecular graph. Therefore, we pursued the stress tensor σ(r) without using the dependency on the QTAIM partitioning, since previously σ(r) was only calculated within the QTAIM partitioning, to see if any indication of NNA character can be determined. Because the stress tensor σ(r) lacks an associated scalar- or vector-field as is the case for QTAIM and the Ehrenfest F(r) partitioning schemes respectively, a stress tensor σ(r) partitioning scheme cannot be constructed. Therefore, to overcome this difficulty we use next generation QTAIM, constructed from the most preferred directions of electronic charge density accumulation, to calculate the stress tensor σ(r) 3-D bond-paths on the Ehrenfest force F(r) molecular graph. Using next generation 3-D bond-paths within the Ehrenfest force F(r) partitioning, we can classify the degree of NNA character in the absence of NNAs. A much higher degree of NNA character is found to be present for the stress tensor σ(r) 3-D bond-paths than for the corresponding QTAIM or Ehrenfest force F(r) 3-D bond-paths. The stabilizing effect of the NNA is demonstrated by undertaking Li2 bond-path compression and stretching distortions sufficient to cause the annihilation of the NNA. The compression and stretching distortions also lead to a large increase in the 3-D bond-path asymmetry and persistent bond-path torsion respectively.

Li and Na Adsorption on Graphene and Graphene Oxide Examined by Density Functional Theory, Quantum Theory of Atoms in Molecules, and Electron Localization Function

Adsorption of Li and Na on pristine and defective graphene and graphene oxide (GO) is studied using density functional theory (DFT) structural and electronic calculations, quantum theory of atoms in molecules (QTAIM), and electron localization function (ELF) analyses. DFT calculations show that Li and Na adsorptions on pristine graphene are not stable at all metal coverages examined here. However, the presence of defects on graphene support stabilizes both Li and Na adsorptions. Increased Li and Na coverages cause metal nucleation and weaken adsorption. Defective graphene is associated with the presence of band gaps and, thus, Li and Na adsorptions can be used to tune these gaps. Electronic calculations show that Li⁻ and Na⁻graphene interactions are Coulombic: as Li and Na coverages increase, the metal valences partially hybridize with the graphene bands and weaken metal⁻graphene support interactions. However, for Li adsorption on single vacancy graphene, QTAIM, ELF, and overlap populations calculations show that the Li-C bond has some covalent character. The Li and Na adsorptions on GO are significantly stronger than on graphene and strengthen upon increased coverages. This is due to Li and Na forming bonds with both carbon and oxygen GO atoms. QTAIM and ELF are used to analyze the metal⁻C and metal⁻metal bonds (when metal nucleation is present). The Li and Na clusters may contain both covalent and metallic intra metal⁻metal bonds: This effect is related to the adsorption support selection. ELF bifurcation diagrams show individual metal⁻C and metal⁻metal interactions, as Li and Na are adsorbed on graphene and GO, at the metal coverages examined here.