Non-nuclear Attractor Research Articles

Metal Cluster Electrides: A New Type of Molecular Electride with Delocalised Polyattractor Character.

Electrides are ionic substances containing isolated electrons. These confined electrons are topologically characterised by a quasi-atom, that is, a non-nuclear attractor (NNA) of the electron density. The electronic structure of the octahedral 4 A1g Li6+ and 5 A1g Be6 species shows that these species have a large number of NNAs. These NNAs have highly delocalised electron densities and, as a result, the chemical bonding pattern of these systems is reminiscent of that in solid metals, in which metal cations are surrounded by a "sea" of delocalised valence electrons. We propose the term metal cluster electrides to refer to this new class of compounds. In this study, we establish a computational protocol to identify, characterize, and design metal cluster electrides and we elucidate the intricate bonding patterns of this particular type of species.

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

In this investigation we explore the function and existence of the non-nuclear attractor (NNA) for a series of small charged lithium clusters Limq (m = 2-5, q = ±1) using QTAIM and the Ehrenfest force F(r) partitioning schemes. The NNAs were found to be present in all of the Limq (m = 2-5, q = ±1) clusters for QTAIM, in contrast none were found for F(r). We discovered that the anionic and cationic lithium dimers are limiting cases for minimal and maximal impact of the NNA related to the relative sparseness of total charge density ρ(r) distributions respectively. Evidence is found that the NNA in the anionic dimer is in the process of being annihilated by two neighboring BCPs. We provide a measure of the size of the NNA and find for Limq (m = 2-5, q = ±1) that larger NNAs correlate with increased Li-Li separations. The NNA was determined to be a persistent feature by varying the Li separations for the cationic and anionic dimers. Very large Li separations failed to induce an NNA in the F(r) anionic dimer and therefore we conclude that F(r) is unable to detect NNAs. The metallicity ξ(rb) was also used to measure the sparseness of the distribution of ρ(r) and significant metallic character, on the basis of ξ(rb) > 1, was present for QTAIM but not for F(r), providing further evidence that F(r) cannot detect NNAs. Advantages of the use of Ehrenfest force F(r) partitioning scheme are discussed that include the design of nano-devices through tuning of the Ehrenfest potential VF(b) by the application of external forces such as a constant electric or strain field.

The topology of the Coulomb potential density. A comparison with the electron density, the virial energy density, and the Ehrenfest force density.

The topology of the Coulomb potential density has been studied within the context of the theory of Atoms in Molecules and has been compared with the topologies of the electron density, the virial energy density and the Ehrenfest force density. The Coulomb potential density is found to be mainly structurally homeomorphic with the electron density. The Coulomb potential density reproduces the non-nuclear attractor which is observed experimentally in the molecular graph of the electron density of a Mg dimer, thus, for the first time ever providing an alternative and energetic foundation for the existence of this critical point. © 2017 Wiley Periodicals, Inc.

Helium Shows New Chemistry Not Seen Anywhere Else

Work by Dong et al., recently published in Nature Chemistry , shows that the chemistry of noble gases, far from being restricted to a few instances of covalent bonding with highly electronegative elements, is more interesting than we thought—more interesting than that of most elements, even.

Dimeric nature of N-coordinated Mg and Ca ions in metaloorganic compounds. The topological analysis of ELF functions for Mg–Mg and Ca–Ca bonds

The local electronic structure of the Mg–Mg and Ca–Ca bonds have been investigated in the model dimeric magnesium(I) and calcium(I) molecules: [C10H18Mg2N4], and [C10H18Ca2N4] using the topological analysis of Electron Localisation Function (ELF). The wave function has been approximated by the DFT method and PBE, B3LYP, M052X, M062X, ωB97XD, CAM-B3LYP, LC-ωPBE and B2PLYP functionals. The investigated bonds are covalent, and are represented by disynaptic bonding attractors V(Mg,Mg) and V(Ca,Ca). The basin population of the Ca–Ca bond (1.84–1.89e) is about 0.1e smaller than population of the Mg–Mg bond (1.95–1.98e). The results of ELF-analysis support classical Lewis representation of the 2c–2e bonds (single bond). The topological analysis of electron density field, ρ(r) shows that both the Mg–Mg and Ca–Ca bonds are characterised by the non-nuclear attractor (NNA) and pseudo-basin localised in midpoint of the bond. However, in the case of the Ca–Ca bond its localisation depends on the used functional. The median ELF-basin population of the Mg–Mg bond (1.96e) is about 2.5 larger than the population (0.79e) of pseudo-atomic basin associated with NNA of the ρ(r) field. The analysis performed for the nitrogen – magnesium and nitrogen–calcium bonds showed the dative bonds N→Mg and N→Ca with very large values of the polarity index, pNMg, pNCa, 0.96 and median ELF-basin population 3.40e.

Molecular partitioning based on the kinetic energy density

Molecular partitioning based on the kinetic energy density is performed to a number of chemical species, which show non-nuclear attractors (NNA) in their gradient maps of the electron density. It is found that NNAs are removed using this molecular partitioning and although the virial theorem is not valid for all of the basins obtained in the being used AIM, all of the atoms obtained using the new approach obey this theorem. A comparison is also made between some atomic topological parameters which are obtained from the new partitioning approach and those calculated based on the electron density partitioning.

A QTAIM and stress tensor perspective of large-amplitude motions of the tetrasulfur tetranitride S4N4molecular graph

The nature of the bonding interactions including the intramolecular SS interactions in tetrasulfur tetranitride, S4N4 are probed by performing very large amplitude vibrations of all of the 18 normal modes of vibration. The QTAIM and stress tensor point properties are -then investigated and found to be highly dependent on the mode of vibration. A considerable degree of metallicity ξ(rb) is found for the SS and SN bonding interactions. A unique bonding feature is found for a small amplitude vibration of the most anharmonic mode of this investigation, mode 2, where the SS bond critical point (BCP) transforms from a closed-shell SS BCP to a shared-shell SS BCP. We find 17 new unique QTAIM topologies for the molecular graphs corresponding to the 18 modes of vibration along with seven “missing” topologies that are mapped onto a spanning 2-D Quantum topology Phase Diagram (QTPD). In addition, eleven unique topologies existing on 3-D QTPDs are found due to the presence of non-nuclear attractors (NNAs). We use the stress tensor eigenvalues to explain the invariance of the numbers and types of QTAIM critical points. The applicability of both the stiffness S and stress tensor stiffness Sσ are also explored. Two new bond measures are introduced, a polarizability P and the stress tensor polarizability Pσ which are derived from the stiffness S and stress tensor stiffness Sσ, respectively. © 2016 Wiley Periodicals, Inc.

Nonnuclear Attractors in Heteronuclear Diatomic Systems.

Nonnuclear attractors (NNAs) are observed in the electron density of a variety of systems, but the factors governing their appearance and their contribution to the system's properties remain a mystery. The NNA occurring in homo- and heteronuclear diatomics of main group elements with atomic numbers up to Z = 38 is investigated computationally (at the UCCSD/cc-pVQZ level of theory) by varying internuclear separations. This was done to determine the NNA occurrence window along with the evolution of the respective pseudoatomic basin properties. Two distinct categories of NNAs were detected in the data analyzed by means of catastrophe theory. Type "a" implies electronic charge transfer between atoms mediated by a pseudoatom. Type "b" shows an initial relocation of some electronic charge to a pseudoatom, which posteriorly returns to the same atom that donated this charge in the first place. A small difference of polarizability between the atoms that compose these heteronuclear diatomics seems to favor NNA formation. We also show that the NNA arising tends to result in some perceptible effects on molecular dipole and/or quadrupole moment curves against internuclear distance. Finally, successive cationic ionization results in the fast disappearance of the NNA in Li2 indicating that its formation is mainly governed by the field generated by the quantum mechanical electronic density and only depends parametrically on the bare nuclear field/potential at a given molecular geometry.

Non‐Nuclear Attractor in a Molecular Compound under External Pressure

AbstractThe dimeric magnesium(I) compound [{(DipNacnac)Mg}2] [1, DipNacnac = (DipNCMe)2CH, Dip = 2,6‐diisopropylphenyl] has previously been shown to exhibit a non‐nuclear attractor (NNA) between the two Mg atoms in the molecular ground state by both experimental and theoretical electron‐density studies. To study the stability and characteristics of this topological entity, we have determined the molecular structure of 1 in the pressure range from 0.4 to 1.9 GPa by high‐pressure single‐crystal X‐ray diffraction. The central Mg–Mg bond contracts significantly in this range to 97 % of the value at ambient pressure and a temperature of 100 K. High‐level single‐point theoretical calculations with the resulting atomic coordinates show that the NNA is persistently present in the topology at all pressures and that the difference between the value of the electron density at the NNA and the Mg–NNA bond critical point (bcp) is close to a maximum at the Mg–Mg separation that is found experimentally.

Stable Compound of Helium and Sodium at High Pressure

Helium (He) is, on par with Neon, the most inert element in the Periodic Table. Indeed, no conclusive proofs about stable compounds containing chemical bonds with He at ambient conditions have been reported so far. However, pressure significantly affects chemical properties of elements. By using USPEX [1], a software which has been successfully used in the past to predict unexpected high pressure crystal structure [1], we found that above 160 GPa He and Sodium exothermically combine to form the compound Na2He, whose structure is reported in Fig. 1. Quasiharmonic free energy calculations based on computed phonon spectra indicate that the free energy of formation of Na2He is negative and that the latter is barely affected by the temperature (0-800 K range was considered). In order to understand the cause of stability of Na2He, we carried out a thorough study of its electronic structure at various pressures by means of several different approaches including the examination of the band structure and the analysis of real-space descriptors such as the electron density in the framework of the Quantum Theory of Atoms in Molecules [2], the Electron Localization Function [3] and the deformation density. By examining the band structure, we found that such compound is an insulator whose band-gap increases with pressure. Regarding real-space descriptors, two remarkable features of Na2He are the negative charge on He (obtained both using Mulliken and Bader partitioning) and the presence of interstitially localized electrons (i.e. Non-Nuclear Attractors), the latter being detectable in all the analyses above mentioned. In the range 160-350 GPa, the exothermicity associated to the formation of Na2He is mainly due to the volume reduction, while at higher pressures the electronic energy plays a prominent role in the stabilization of this compound. In this contribution we present the results of our study with particular emphasis on the role played by He in the stabilization of Na2He.

A QTAIM perspective of the Si6Li6 potential energy surface using quantum topology phase diagrams

We explore and expand the known potential energy surface of Si6Li6 using quantum topology within the QTAIM formalism to include seventeen new unique topologies. To accommodate the non-nuclear attractors (NNAs) that exist for some isomers of Si6Li6, two types of 3-D quantum topology phase diagram are created to ensure unique solutions of the Poincaré–Hopf relation. The position of the most energetically stable isomer on the quantum topology phase diagram contrasts strongly with earlier work on a range of isomer sets. A cage critical point (CCP) violating the condition of enclosing topological features is discovered for a topologically unstable molecular graph.

Communication: An approximation to Bader's topological atom

A new, more flexible definition of fuzzy Voronoi cells is proposed as a computationally efficient alternative to Bader's Quantum Theory of Atoms in Molecules (QTAIM) partitioning of the physical space for large-scale routine calculations. The new fuzzy scheme provides atomic charges, delocalization indices, and molecular energy components very close to those obtained using QTAIM. The method is flexible enough to either ignore the presence of spurious non-nuclear attractors or to readily incorporate them by introducing additional fuzzy Voronoi cells.

Metal–Metal and Metal–Ligand Bonds in (η5-C5H5)2M2 (M = Be, Mg, Ca, Ni, Cu, Zn)

The metal–metal and metal–ligand bonds in a series of binuclear metallocenes (η5-C5H5)2M2 (M = Be, Mg, Ca, Ni, Cu, Zn) have been characterized within the framework of the atoms in molecules (AIM) theory, electron localization function (ELF), and molecular formation density difference (MFDD). The calculated results show that the metal–metal bonds in the binuclear main-group-metal metallocenes are different from those in binuclear transition-metal metallocenes. In binuclear main-group-metal metallocenes, the metal–metal bonds are linked by two metal–“non-nuclear attractor (NNA)” bonds, while such NNAs do not exist in the binuclear transition-metal metallocenes. In addition, the transition-metal–transition-metal bonds are more delocalized than those of the main-group-metal–main-group-metal bonds. The main-group-metal–main-group-metal bonds show covalent characteristics while the transition-metal–transition-metal bonds display “closed shell” ionic characteristics. The metal–ligand bonds are mainly ionic. There are both σ and π characteristics in the metal–ligand interactions, and the π interaction is predominant.

Structures, energies and bonding in neutral and charged Li microclusters

Structural and chemical properties of charged and neutral Lithium microclusters are investigated for [Formula: see text]. A total of 18 quantum conformational spaces are randomly walked to produce candidate structures for local minima. Very rich potential energy surfaces are produced, with the largest structural complexity predicted for anionic clusters. Analysis of the electron charge distributions using the quantum theory of atoms in molecules (QTAIM) predicts major stabilizing roles of Non-nuclear attractors (NNAs) via NNA···Li interactions with virtually no direct Li···Li interactions, except in the least stable configurations. A transition in behavior for clusters containing more than seven nuclei is observed by using the recently introduced quantum topology to determine in a quantum mechanically consistent fashion the number of spatial dimensions each cluster has. We experiment with a novel scheme for extracting persistent structural motifs with increase in cluster size. The new structural motifs correlate well with the energetic stability, particularly in highlighting the least stable structures. Quantifying the degree of covalent character in Lithium bonding independently agrees with the observation in the transition in cluster behavior for lithium clusters containing more than seven nuclei. Good correlation with available experimental data is obtained for all properties reported in this work.

Can a Dipole-Bound Electron Form a Pseudo-Atom? An Atoms-In-Molecules Study of the Hydrated Electron

Non-nuclear local maxima, or attractors, of electron density are a rare but very interesting feature of the electron density distribution in molecules and solids. Recently, non-nuclear attractors (NNAs) and the corresponding pseudoatoms of electron density have been identified with the quantum theory of atoms in molecules for some anionic clusters formed by several polar solvent molecules and an excess electron bound in either a solvated-electron or dipole-bound fashion. This contribution reports a detailed study of the topology of the electron density for a series of dipole-bound water cluster anions, as calculated with Hartree-Fock, Møller-Plesset perturbation theory, and coupled-cluster methods together with basis sets augmented with extra diffuse basis functions to accommodate the excess electron. For dipole-bound clusters, electron densities obtained with insufficient inclusion of electron correlation effects and tight basis sets feature a well-pronounced pseudoatom due to the excess electron, which ultimately disappears when a higher level of electronic structure theory and a more diffuse basis set are used. On the other hand, for solvated-electron clusters, where the excess electron is surrounded by solvent molecules, the existence of NNAs does not seem to be an artifact of the method employed, but rather a genuine feature of the electron density distribution. Pseudoatoms of electron density thus appear to be an exclusive feature of confined environments and are unlikely to be found on the tip of a cluster dipole or on solid surfaces.

Relativistic-Consistent Electron Densities of the Coinage Metal Clusters M2, M4, M42–, and M4Na2(M = Cu, Ag, Au): A QTAIM Study

We employ second-order Møller-Plesset perturbation theory level in combination with recently developed pseudopotential-based correlation consistent basis sets to obtain accurate relativistic-consistent electron densities for small coinage metal clusters. Using calculated electron densities, we employ Bader's quantum theory of atoms in molecules (QTAIM) to gain insights into the nature of metal-metal bonding in the clusters M(2), M(4), M(4)(2-), and M(4)Na(2) (M = Cu, Ag, Au). For the simplest case of the metal dimer, M(2), we correlate the strength of the metal-metal bond with the value of the electron density at the bond critical point, the total energy density at the bond critical point, the sharing (delocalization) index, and the values of the two principle negative curvatures. We then consider changes to the metal-metal bonding and charge density distribution upon the addition of two metal atoms to form the metal tetramer, M(4), and then followed by the addition of an electron pair to form M(4)(2-) and finally followed by the addition of two alkali metal (sodium) ions to form M(4)Na(2). Using topological properties of the electron density, we present evidence for the existence of σ-aromaticity in Au(4)(2-). We also report the existence of two non-nuclear attractors in the molecular graph of Cu(4)(2-) and large negative charge accumulation in the nonbonded Cu basins of this cluster.

First Experimental Characterization of a Non-nuclear Attractor in a Dimeric Magnesium(I) Compound

High-resolution X-ray diffraction data, coupled with theoretical calculations, are used to demonstrate the presence of a non-nuclear local maximum in the electron density of a dimeric Mg(I) molecule. This is the first time such a non-nuclear attractor (NNA) has been observed in a stable molecular species. Multipole modeling of the Mg(I) centers requires use of expansion/contraction (κ) coefficients taken from density functional theory (DFT), since accurate scattering factors for Mg(I) are not available. The model developed accurately accounts for the electron density in the Mg-Mg region and is in excellent agreement with directly calculated DFT data. Within the quantum theory of atoms in molecules (QTAIM), this molecule is not bound by a Mg-Mg bond but rather by two Mg-"pseudo-atom" bonds. The NNA is associated with a large region of negative Laplacian in the Mg-Mg internuclear region and arises from the overlap of 3s orbitals in this long, nonpolar "bond". The pseudoatomic basin associated with the NNA contains 0.8 electrons, which are highly delocalized and hence weakly bound. Possible implications of this unusual electronic structure for the chemistry of such molecules, including their use as excellent reducing agents, are discussed.

Characterization of a non-nuclear attractor in a dimeric magnesium(I) compound

Characterization of a non-nuclear attractor in a dimeric magnesium(I) compound

An efficient grid‐based scheme to compute QTAIM atomic properties without explicit calculation of zero‐flux surfaces

We introduce a method to compute atomic properties according to the "quantum theory of atoms in molecules." An integration grid in real space is partitioned into subsets, omega(i). The subset, omega(i), is composed of all grid points contained in the atomic basin, Omega(i), so that integration over Omega(i) is reduced to simple quadrature over the points in omega(i). The partition is constructed from deMon2k's atomic center grids by following the steepest ascent path of the density starting from each point in the grid. We also introduce a technique that exploits the cellular nature of the grid to make the algorithm faster. The performance of the method is tested by computing properties of atoms and nonnuclear attractors (energies, charges, dipole, and quadrupole moments) for a set of representative molecules.

Characterization of the bond between hydrogen and the non-nuclear attractor in anionic water clusters

The bonding interaction between non-hydrogen-bonded (NHB) hydrogen atoms and the non-nuclear attractor (NNA) observed in cavity-bound anionic water clusters has been investigated using ab initio methods. The clusters range in size from four to ten water molecules and generally consist of several water molecules hydrogen-bonded in a ring, with two of these rings stacked such that the NHB hydrogen atoms are directed towards a central cavity. Analysis of the electron density using the theory of atoms in molecules yields information about the bonding interaction that cannot be obtained with conventional computational techniques. The results indicate that this novel interaction, Ha...NNA, is a weak, closed-shell interaction. Further analysis of the atomic properties of the NHB hydrogen atoms indicate that this novel bond cannot be classified as a hydrogen bond. On the basis of the results from the current investigation, this interaction is best described as a weak dipole-ion interaction between the positively charged NHB hydrogen atoms and the negatively charged NNA.