The topology of the Ehrenfest force density revisited. A different perspective based on Slater‐type orbitals

The topology of the Ehrenfest force density was studied with Slater‐type orbitals (STO). At larger distances from the nuclei, STOs generate similar artefacts as noticed before with Gaussian‐type orbitals. The topology of the Ehrenfest force density was found to be mainly homeomorphic with the topology of the electron density. For the first time, reliable integrations of several properties over force density atomic basins were performed successfully. Integration of the electron density of a number of hydrides, fluorides, and chlorides of first row elements over force density basins indicate substantial differences between the partial charges of the atoms as compared with those obtained from electron density basins. Calculations on saturated hydrocarbons confirm that the electronegativity of carbon atoms increases with increasing geometrical strain. Atomic interaction lines are observed to exist in the Ehrenfest force density between the hydrogen atoms of several so‐called “congested” molecules, and also in some inclusion complexes of alkanes with helium. However, interaction lines are lacking in several other controversial cases. © 2015 Wiley Periodicals, Inc.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

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.     

A theoretical study of the bonding capabilities of the zinc-zinc double bond

The theoretical knowledge about the zinc-zinc bond has been recently expanded after the proposal of a zinc-zinc double bond in several [Zn₂(L)₄] compounds (Angew. Chem. Int. Ed. 2017 , 56, 10151-10155). Prompted by these results, we have selected the [Zn₂(CO)₄] species, isolobally related to ethylene, and theoretically investigated the possible η²-Zn₂-coordination to several first-row transition metal fragments. The [Zn₂(CO)₄] coordination to the metal fragment produces an elongation of the dizinc bond and a concomitant pyramidalization of the [Zn(CO)₂] unit. These structural parameters are indicative of π-backdonation from the metal to the coordinated dizinc moiety, as occurred with ethylene ligand. A quantum theory of atoms in molecules study of the Zn Zn bond shows a decrease of ρ_BCP, ∇²ρ_BCP ∫_Zn∩Znρ and delocalization indexes δ(Zn,Zn), relative to corresponding values in the parent [Zn₂(CO)₄] molecule. The Zn Zn and M Zn bonds in these [(η²-Zn₂(CO)₄)M(L)_n] complexes can be described as shared interactions with an important covalent component where the Zn Zn bond is preserved, albeit weakened, upon coordination.     

The localized electrons detector as an ab initio representation of molecular structures

The local single particle momentum is proposed as a localized‐electrons detector (LED) that provides a direct three‐dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient. We show that the graphical representation of bonding interactions given by LED is consistent with the local curvatures of the electron density as given by the eigenvalues of the Hessian matrix, according to a local symmetry classification of the critical points here introduced. LED consistently complements the topological analysis of the electron density given by the quantum theory of atoms in molecules, by providing a graphical representation of the symmetry of the bonding interactions in molecular systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2418–2425, 2010     

Testing theory beyond molecular structure: Electron density distributions of complex molecules

The electron density distribution (EDD) of a molecular system can be determined experimentally from elaborate X‐ray diffraction measurements or calculated with quantum mechanical methods: This provides a unique opportunity for mutual validation of the experimental and theoretical methods—a validation that goes far beyond comparison of molecular structures. Two examples of complex molecular systems of biologic relevance are presented. The first is the cocrystallized complex of betaine, imidazole, and picric acid, 1, which is a 75‐atom molecular complex serving as a model for the active site in the serine proteases class of enzymes, the so‐called catalytic triad. For 1 the experimental charge density was determined by combined modeling of single crystal synchrotron X‐ray and neutron diffraction data measured at 28(1) K, and it is compared with ab initio theoretical calculations at the B3LYP/6‐311G(d,p) level of theory. Overall, the agreement is good, but in one strong N? H? O hydrogen bond clear differences are observed. The second example concerns the EDD of the mixed valence trinuclear oxo‐centered iron carboxylate, [Fe₃O(OOCC(CH₃)₃)₆(NC₅H₅)₃], 2. This molecule contains 133 atoms (542 electrons) including three open‐shell iron atoms, and the experimental investigation is based on synchrotron X‐ray diffraction data. Calculations in the experimental geometry at the commonly used UB3LYP/LanL2DZ level of theory are not able to reproduce a number of experimentally observed electron density features. In particular, the sp³‐like distribution on the central oxygen atom and the electron deformations on the iron centers are at variance with experiment. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

QTAIM and stress tensor interpretation of the (H2O)5 potential energy surface

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H₂O)₅ reaction‐pathways and five unique Poincaré–Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H₂O)₅ conformer with a 3‐D_QT quantum topology. The stress tensor Poincaré–Hopf relation indicated a preference for 2‐D_QT (H₂O)₅ topologies as well as the presence of coupling between shared‐shell O? H BCPs to the hydrogen‐bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O…O bonding interactions that were found in six of the nine (H₂O)₅ reaction‐pathways and for all points of the combined QTPD. The stabilizing role of the O…O bonding interactions from the values of the total local energy density was explored. © 2016 Wiley Periodicals, Inc.     

Relativistic and non-relativistic local-density functional, benchmark results and investigation on the dimers

Using two spinor minimax method combined with finite element methods accompanied with extrapolation and counterpoise techniques enable us to obtain relativistic highly accurate results for two atomic molecules. Like in our previous work for the (Hartree-) Dirac–Fock–Slater (DFS) functional we investigate in this work the density functional approximations of the relativistic and non-relativistic local-density functional, presenting highly accurate benchmark results of chemical properties on the dimers of the group 11 (Ib) of the periodic table of elements. The comparison with experimental values and literature’s results shows that DFS is better behaved than the other two local functionals.     

A Full Topological Analysis of Unstable and Metastable Bond Critical Points

Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to certain properties. Here we report on our efforts to identify features within the charge density that are indicative of instability and metastability. Towards this, we use our extensions to the quantum theory of atoms in molecules that capitalize on a molecule’s ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0‐, 1‐, and 2‐skeleton (dependent sets of points, lines, and surfaces). We show that the geometry of these n‐skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. As an example, we use our methods to uncover the fingerprints of instability and metastability in two much‐discussed systems, that is, the di‐benzene complex and the He and adamantane inclusion complex.     

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter‐free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add‐On” named Rhorix for the state‐of‐the‐art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Mechanistic insights on how hydroquinone disarms OH and OOH radicals

Phenol derivatives are distinguished as successful free radical scavengers. We present a detailed analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radical with emphasis on changes that take place in the vicinity of the transition state. Quantum theory of atoms in molecules is employed to elucidate the sequence of positive and negative charge transfer by studying selected properties of the three key atoms (the transferring hydrogen, the donor atom, and the acceptor atom) along intrinsic reaction path. The presented results imply that in both reactions, which are examples of proton coupled electron transfer, proton, and electron get simultaneously transferred to the radical oxygen atom. The fact that the hydrogen's charge and volume do not monotonously change in the vicinity of the transition state in the product valley results from the adjacency of the proton and the electron to the donor and the acceptor oxygen atoms. Obtaining a detailed understanding of mechanisms by which free radicals are disarmed is of paramount importance given the effects of those highly reactive species on biological systems. A comprehensive analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radicals, based on changes of selected electronic properties of the three most relevant atoms (hydrogen donor, hydrogen acceptor, and the hydrogen itself), along the reaction coordinate, can be obtained by first‐principles calculations.     

GenLocDip: A Generalized Program to Calculate and Visualize Local Electric Dipole Moments

Local dipole moments (i.e., dipole moments of atomic or molecular subsystems) are essential for understanding various phenomena in nanoscience, such as solvent effects on the conductance of single molecules in break junctions or the interaction between the tip and the adsorbate in atomic force microscopy. We introduce Gen Loc Dip , a program for calculating and visualizing local dipole moments of molecular subsystems. Gen Loc Dip currently uses the Atoms‐In‐Molecules (AIM) partitioning scheme and is interfaced to various AIM programs. This enables postprocessing of a variety of electronic structure output formats including cube and wavefunction files, and, in general, output from any other code capable of writing the electron density on a three‐dimensional grid. It uses a modified version of Bader's and Laidig's approach for achieving origin‐independence of local dipoles by referring to internal reference points which can (but do not need to be) bond critical points (BCPs). Furthermore, the code allows the export of critical points and local dipole moments into a POVray readable input format. It is particularly designed for fragments of large systems, for which no BCPs have been calculated for computational efficiency reasons, because large interfragment distances prevent their identification, or because a local partitioning scheme different from AIM was used. The program requires only minimal user input and is written in the Fortran 90 programming language. To demonstrate the capabilities of the program, examples are given for covalently and non‐covalently bound systems, in particular molecular adsorbates. © 2016 Wiley Periodicals, Inc.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ together with (ii) the anions F⁻, Cl⁻, Br⁻, NO₃⁻ and SO₄²⁻ with water clusters (H₂O)_n, n=1–8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.     

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra‐atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom‐of‐interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Evolution of chemical bonding and electron density rearrangements during D3h → D3d reaction in monolayered TiS2: A QTAIM and ELF study

Monolayered titanium disulfide TiS₂, a prospective nanoelectronic material, was previously shown to be subject to an exothermic solid‐state D_3h–D_3d reaction that proceeds via a newly discovered transition state. Here, we study the reaction in detail using topological methods of quantum chemistry (quantum theory of atoms in molecules and electron localization function analysis) and show how electron density and chemical bonding between the atoms change in the course of the reaction. The reaction is shown to undergo a series of topological catastrophes, associated with elementary chemical events such as break and formation of bonds (including the unexpected formation of S? S bonding between sulfur layers), and rearrangement of electron density of outer valence and core shells. © 2014 Wiley Periodicals, Inc.     

Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

Perturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities H_b( r _c) are plotted versus H_b( r _c) – V_b( r _c)/2 at bond critical points (BCPs) of interactions in question, where V_b( r _c) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θ_p, κ_p), where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ_p values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θ_p, κ_p) with CIV is called “intrinsic dynamic nature of interactions.”