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.     

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.     

The quantum divided basins: A new class of quantum subsystems

The rigorous theory of the quantum divided basins (QDB), the quantum subsystems emerging from the net zero‐flux equation, is considered in this article. This framework, the quantum theory of proper open subsystems, is derived from the extension of the quantum theory of atoms in molecules to encompass the new class of quantum subsystems. It is demonstrated that the regional hypervirial theorem and the associated regional observables as well as the subsystem variational procedure are all expressible for the QDB. The history of QDB is briefly reviewed and the bundles, which were introduced by other researchers, are offered as typical examples whereas new examples of QDB (not yet mentioned in literature) are also presented. Based on some model systems as well as the nitrogen molecule, the regional properties and the morphologies of typical QDB are scrutinized. It is also demonstrated that the QDB may be used to study the fine structure of the electron localization and delocalization. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra‐atomic and inter‐atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra‐atomic and inter‐atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange‐correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange‐correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.     

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.     

Visualization and integration of quantum topological atoms by spatial discretization into finite elements

We present a novel algorithm to integrate property densities over the volume of a quantum topological atom. Atoms are grown outward, starting from a sphere centered on the nucleus, by means of a finite element meshing algorithm. Bond critical points and ring critical points require special treatment. The overall philosophy as well as intricate features of this meshing algorithm are given, followed by details of the quadrature over the finite elements. An effort has been made to design a streamlined and compact algorithm, focusing on the core of challenges arising in tracing the electron density's gradient vector field. The current algorithm also generates a new type of pictures that can be a Graphical User Interface. Excellent integration errors, L(Omega), are obtained, even for atoms with (narrow) tails or sharp corners.     

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.     

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011 , 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi‐component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013 , 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi‐component version.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A vector‐based representation of the chemical bond for the normal modes of benzene

We introduce a vector‐based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond‐path framework set B = {p, q, r}, to follow variations in the 3D morphology of all bonds for the four infrared active normal modes of benzene. The bond‐path framework set B comprises three unique paths p, q, and r where r is the familiar QTAIM bond concept of bond‐path (r) while the two new paths p and q are formulated from the least and most preferred directions of electron density accumulation, respectively. We find 3D distortions including bond stretching/compression, torsion, and curving. We introduce two fractional measures to quantify these variations away from linearity of the bond.     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

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     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Prediction of conformationally dependent atomic multipole moments in carbohydrates

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol^?1 for open chains and just over 90% an error of maximum 4 kJ mol^?1 for rings. © 2015 Wiley Periodicals, Inc.     

The quantum theory of atoms in positronic molecules: A case study on diatomic species

This article presents the first systematic study of a series of diatomic positronic species using the recently proposed regional approach: the quantum theory of atoms in positronic molecules (QTAIPM). This survey includes the LiH,e⁺, NaH,e⁺, LiF,e⁺, NaF,e⁺, BeO,e⁺, MgO,e⁺, CN^?,e⁺, and OH^?,e⁺ species as typical examples. The computational algorithm of the whole analysis is communicated and reviewed in detail. The topological analysis of the joint density distribution reveals topological structures similar to those observed for the purely electronic systems; that is, each system decomposes into two quantum atoms. By considering some of the regional properties of these quantum atoms, it is demonstrated that the positron affects them seriously through two different mechanisms: direct and indirect contributions, the latter refers to electronic and geometric relaxations. The computational results clearly reveal the fact that the regional properties of the quantum atoms of positronic molecules are not deducible from their purely electronic counterparts; thus, an independent analysis is required for each positronic molecule. The positronic population is considered as a typical regional property showing that the attachment of a positron to a purely electronic system enhances the polarization of the electronic distribution. The concept of regional positron affinities is also introduced and discussed as a nonroutine application of the QTAIPM. The results of this article set the stage for further study on the quantum atoms of polyatomic positronic species. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011