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.     

Biphenyl: A stress tensor and vector‐based perspective explored within the quantum theory of atoms in molecules

We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion φ of the C‐C bond linking the two phenyl rings of the biphenyl molecule on a bond‐by‐bond basis using both a scalar and vector‐based analysis. Using the total local energy density H( r _b), we show the favorable conditions for the formation of the controversial H–H bonding interactions for a planar biphenyl geometry. This bond‐by‐bond QTAIM analysis is found to be agreement with an earlier alternative QTAIM atom‐by‐atom approach that indicated that the H–H bonding interaction provided a locally stabilizing effect that is overwhelmed by the destabilizing role of the C‐C bond. This leads to a global destabilization of the planar biphenyl conformation compared with the twisted global minimum. In addition, the H( r _b) analysis showed that only the central torsional C‐C bond indicated a minimum for a torsion φ value coinciding with that of the conventional global energy minimum. The H–H bonding interactions are found to be topologically unstable for any torsion of the central C‐C bond away from the planar biphenyl geometry. Conversely, we demonstrate that for 0.0° < φ < 39.95° there is a resultant increase in the topological stability of the C nuclei comprising the central torsional C‐C bond. Evidence is found of the effect of the H–H bonding interactions on the torsion φ of the central C‐C bond of the biphenyl molecule in the form of the QTAIM response β of the total electronic charge density ρ( r _b). Using a vector‐based treatment of QTAIM we confirm the presence of the sharing of chemical character between adjacent bonds. In addition, we present a QTAIM interpretation of hyperconjugation and conjugation effects, the former was quantified as larger in agreement with molecular orbital (MO) theory. The stress tensor and the QTAIM H atomic basin path set areas are independently found to be new tools relevant for the incommensurate gas to solid phase transition occurring in biphenyl for a value of the torsion reaction coordinate φ ≈ 5°. © 2015 Wiley Periodicals, Inc.     

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.     

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.     

A reference‐free stockholder partitioning method based on the force on electrons

We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc.     

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.     

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.     

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.     

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     

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     

Grid‐based algorithm to search critical points,in the electron density,accelerated by graphics processing units

Using a grid‐based method to search the critical points in electron density, we show how to accelerate such a method with graphics processing units (GPUs). When the GPU implementation is contrasted with that used on central processing units (CPUs), we found a large difference between the time elapsed by both implementations: the smallest time is observed when GPUs are used. We tested two GPUs, one related with video games and other used for high‐performance computing (HPC). By the side of the CPUs, two processors were tested, one used in common personal computers and other used for HPC, both of last generation. Although our parallel algorithm scales quite well on CPUs, the same implementation on GPUs runs around 10× faster than 16 CPUs, with any of the tested GPUs and CPUs. We have found what one GPU dedicated for video games can be used without any problem for our application, delivering a remarkable performance, in fact; this GPU competes against one HPC GPU, in particular when single‐precision is used. © 2014 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.     

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.     

Tetrel bonds,penta‐ and hexa‐coordinated tin and lead centres

A tetrel bond – an interaction between a Group 14 element acting as Lewis acid centre and an electron‐donating moiety – is analysed for ZF₄ (Z = Sn, Pb) complexes with NH₃ and HCN species. MP2/aug‐cc‐pVTZ calculations were performed and supported by results of the quantum theory of atoms in molecules. The results of calculations show that the tetrel centre may be considered as a pentavalent one if ZF₄ interacts with one NH₃ or HCN ligand or even as a hexavalent centre if it interacts with two ligands; thus the hypervalency phenomenon is discussed for the complexes analysed here. The theoretical analysis is supported by a discussion of the crystal structures containing the SnF₄ fragment; these structures are characterized by a hexa‐coordinated tin centre.