Topological Atoms Research Articles

Quantitative structure-activity relationship studies of boron-containing dipeptide proteasome inhibitors using calculated mathematical descriptors

Topological indices (TIs) and atom pairs (APs) were used to develop quantitative structure-activity relationship (QSAR) models of a set of 58 dipeptide boronic acids which are potent inhibitors of proteasome and have found applications in the treatment of various types of cancers. Of the three linear regression methods used for QSAR development, viz., principal components regression (PCR), partial least square (PLS), and ridge regression (RR), the last method gave the most satisfactory models whereas the remaining two methods yielded poor models. RR results obtained in this paper using TIs and APs are comparable to the CoMFA and CoMSIA results reported in the literature with the same set of compounds.

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

AbstractThis 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

Toward a fuzzy atom view within the context of the quantum theory of atoms in molecules: quasi-atoms

The notion of quasi-atoms is introduced within the context of the quantum theory of atoms in molecules. Being a subset of the quantum divided basins that were introduced previously, quasi-atoms are the quantum subsystems that are practically indistinguishable from the topological atoms; thus, revealing the continuous evolution of quantum divided basins into topological atoms. This indistinguishability is rooted in the limited accuracy of chemical observations; they are not sensitive to discriminate a topological atom from its associated quasi-atoms. In this regard, it is disclosed that the set of quantum atoms is in a wide-range including members other than topological atoms; the quasi-atoms are concrete examples. Finally, the idea of the fuzzy set of atoms that is foreign to the disjoint partitioning schemes for which the orthodox QTAIM is a classic example is extended employing the set of quasi-atoms.

The quantum‐chemical study of organic octupolar chromophore triaminotrinitrobenzene and the dimer: Topological analysis and nonlinear optical characteristics

AbstractThe nonempirical calculations of the structure and molecular polarizabilities of octupolar 1,3,5‐triamino‐2,4,6‐trinitrobenzene (TATB) molecule and 2TATB dimer, formed of two chromophores through H‐bonding between Oxygens of nitro groups and hydrogens of amino groups of the neighboring molecule, were calculated by TDHF/aug‐cc‐pVDZ′ method. The characterization of 2TATB formation is carried out in the framework of topological Atoms in Molecules approach. The analysis of electron charge density distribution has given evidence to the existence of two equivalent intermolecular NH…O bonds with the bond length of 2.458 Å; the intramolecular H‐bonds between oxygens and hydrogens of alternating nitro‐ and amino groups are also detected. The study of the solvent effect on the TATB electric properties, performed in the framework of conventional polarizable continuum model, demonstrated weak dependence of molecular polarizabilities on the solvent polarity. The polarizability of 2TATB dimer is nearly twice as large as that of TATB, whereas the modulus of the first hyperpolarizability of 2TATB is ∼2.3 times greater than that of TATB, thus exhibiting the cooperative effect. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Graph kernels for chemical compounds using topological and three-dimensional local atom pair environments

Approaches that can predict the biological activity or properties of a chemical compound are an important application of machine learning. In this paper, we introduce a new kernel function for measuring the similarity between chemical compounds and for learning their related properties and activities. The method is based on local atom pair environments which can be rapidly computed by using the topological all-shortest paths matrix and the geometrical distance matrix of a molecular graph as lookup tables. The local atom pair environments are stored in prefix search trees, so called tries, for an efficient comparison. The kernel can be either computed as an optimal assignment kernel or as a corresponding convolution kernel over all local atom similarities. We implemented the Tanimoto kernel, min kernel, minmax kernel and the dot product kernel as local kernels, which are computed recursively by traversing the tries. We tested the approach on eight structure-activity and structure-property molecule benchmark data sets from the literature. The models were trained with ε - support vector regression and support vector classification. The local atom pair kernels showed to be at least competitive to state-of-the-art kernels in seven out of eight cases in a direct comparison. A comparison against literature results using similar experimental setups as in the original works confirmed these findings. The method is easy to implement and has robust default parameters.

Revisiting the foundations of the quantum theory of atoms in molecules: The subsystem variational procedure and the finite nuclear models

AbstractThe role of finite nuclear models (FNMs) is scrutinized within the context of the quantum theory of atoms in molecules (QTAIMs). It is demonstrated that the newly proposed analytic‐algebraic definition of the topological atoms is consistently extendable to the cases where a FNM is employed to construct the molecular hamiltonian. The whole variational procedure is reconsidered, and the insensitivity of final results relative to the employed FNMs is explicitly demonstrated. The analysis once again clearly demonstrates that the analytic‐algebraic condition is an independent axiom that must be added to the subsystem variational procedure to construct the QTAIMs. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Explicit Solvent Effect on Cation−π Interactions: A First Principle Investigation

Sequential attachment of water molecules to cation-pi (Li+-benzene, K+-benzene, and Mg2+-benzene) systems reveals that the cation-pi interaction strength varies in opposite direction depending on the site of solvation of the cation-pi system. Solvation of the metal ion decreases its interaction energy with the pi system, while the solvation of the pi system increases its interaction energy with the metal ion. The cation binding to benzene clearly enhances the ability of aromatic protons to participate in hydrogen bonding with water molecules. The distance between the metal ion and centroid of the benzene inherently varies with the position of water molecules in the vicinity of cation-pi complex. Reduced variational space (RVS) analysis on bare and solvated cation-pi complexes indicates that the major contributions to the total interaction energy are coming from the polarization and charge transfer energy terms of the pi system. Topological atoms in molecules (AIM) analysis is performed to evaluate the nature of the cation-pi interaction. Good correlations are observed between interaction energies and charge density at the cage critical point of the cation-pi complexes.

Energetic and electron density analysis of hydrogen dissociation of protonated benzene

The electronic structure of the benzenium cation, [C6H7]+, the simplest intermediate of electrophilic aromatic substitution reactions, was analyzed in terms of the properties of electron densities obtained from multiconfigurational quantum theoretical methods. The indirect C-H coupling constants and the physical contributions to their values were calculated and rationalized in terms of the electron delocalization between the quantum topological atoms in the molecule. The evolution of the electronic structure for the intramolecular proton migration and for the dissociation into [C6H6]+ + H, or [C6H5]+ + H2 was also studied. The potential energy surface for intramolecular H migration has six equivalent transition states and two equivalent two-fold saddles, whereas each dissociation process occurs without the presence of any transition state. The calculated energy barriers of 9.5, 80.3 and 72.4 kcal mol(-1) for the intramolecular proton migration, H and H2 eliminations, respectively, agree with experimental reports. The quantitative chemical descriptors based on the electron density of the benzenium cation provide insight on the nature of the chemical bond, including electron delocalization, and its evolution during chemical transformations of the molecule.

Revisiting the foundations of the quantum theory of atoms in molecules: Toward a rigorous definition of topological atoms

AbstractAn explicit classification of consistent variational constraints within the context of the “quantum theory of proper open subsystems” as well as the “quantum theory of atoms in molecules” (QTAIM) it presented. It is demonstrated that the general variational procedure is not sensitive enough to discriminate between different mathematically consistent variational conditions. The uniqueness of the regional kinetic energy is employed to derive the net zero‐flux condition and the regions satisfying this condition are named asquantum divided basins. A modified form of the local zero‐flux is proposed in order to define topological atoms within the context of the orthodox QTAIM. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Non-nuclear attractor of electron density as a manifestation of the solvated electron

Two or more polar molecules can trap an excess electron either in a dipole-bound fashion where it is located outside of the cluster (dipole-bound electron) or inside the cluster (solvated electron). The topology of the electron density in dipole-bound and solvated-electron clusters has been examined for the paradigm (HF)3- cluster. As spatial confinement of the excess electron increases, a non-nuclear maximum (or attractor) of the electron density eventually forms, which suggests that the solvated electron can be described as a topological atom with its own set of physicochemical properties.

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.

On Three-Electron Bonds and Hydrogen Bonds in the Open-Shell Complexes [H2X2]+ for X = F, Cl, and Br†

The [H2X2]+ (X = Cl, Br) formula could refer to two possible stable structures, namely, the hydrogen-bonded complex and the three-electron-bonded one. In contrary to the results published by other authors, we claim that for the F-type structures the hydrogen-bonded form is the only possible one and the [HFFH]+ complex is an artifact as its wave function is unstable. For all analyzed molecules, the IR anharmonic spectra have been simulated, which enabled a deeper analysis of other authors' published results of IR low-temperature matrix experiments. Topological atoms in molecules and electron localization function investigations have revealed that the nature of the bond in three-electron-bonded structures is similar to the covalent-depleted one in F2 or HOO molecules, but the effect of removing electrons from the bond area is stronger.

Molecular Characterization ofp-Alkyl Phenol−n-Heptane Interactions and Their Implication as Asphaltene Dispersants

The interaction between a series of p-alkyl phenols with the solvent n-heptane (n-C7) is studied by means of theoretical methods. The solvation energies of these molecules are computed using quantum mechanical methods in which the solvent is considered as a dielectric medium. Accordingly, the interaction of a solute molecule with the reaction field of the solvent yields a solvation free energy. The electrostatic, dispersion, and repulsion contributions to the solvation energies are analyzed as a function of the alkyl chain length and the relationship with the electronic structure of the molecules, as accounted for by the properties of the quantum topological atoms defined within the formalism of the atoms in molecules theory, is also discussed. Implications of the solvation energies, computed at the microscopic level, on the efficiency of p-alkyl phenols as asphaltene dispersants are discussed. The quantitative aspects of the solubility of these amphiphiles are correlated with their experimentally reporte...

Transferability of Quantum Topological Atoms in Terms of Electrostatic Interaction Energy

Understanding atomic transferability is important to guide the design of a force field. Atoms in molecules are defined and computed according to the theory of quantum chemical topology (QCT). The electron density associated with such topological atoms is conveniently described by high-rank multipole moments. Here, we assess the transferability of atoms by means of their electrostatic interaction energy, using a convergent multipole expansion. The test systems are (H2O)3 and serine...(H2O)5. The effect of a varying electron density cutoff (i.e., truncating the atoms) is discussed and the effect of polarization is quantified.

Minerals at high pressure. Mechanics of compression from quantum mechanical calculations in a case study: the beryl (Al4Be6Si12O36)

The Bader topological analysis has been applied to ab initio computed electron densities of beryl, in order to clarify its mechanism of compression. Full structural optimization and total energy (E) calculations were performed at different cell volumes (Vc). The pressure at each volume and the equation of state were estimated from the first and second derivatives of the resultant E(Vc) curve. The total (negative) potential energy of the crystal, sum of both attractive and repulsive electrostatic terms, was found to systematically decrease (i.e., it moved to more negative values) up to the highest pressure considered (28.4 GPa), indicating that interelectronic and internuclear repulsions are not the only terms controlling the compressibility, at least in the pressure range investigated. Electronic kinetic energy increases as the cell volume is reduced, leading to a parallel increase of the total energy. Both structure at equilibrium and compressibility are therefore due to the balance between the opposing kinetic and potential energy terms. The Bader theory has been used to identify the topological atoms within the structure and to calculate their properties, with particular attention to the forces driving the structural relaxation at high pressure. On a qualitative basis, the obtained results are expected to be transferable to the discussion of compressibility of other mineral phases.

Representation of molecular structure using quantum topology with inductive logic programming in structure–activity relationships

The requirement of aligning each individual molecule in a data set severely limits the type of molecules which can be analysed with traditional structure activity relationship (SAR) methods. A method which solves this problem by using relations between objects is inductive logic programming (ILP). Another advantage of this methodology is its ability to include background knowledge as 1st-order logic. However, previous molecular ILP representations have not been effective in describing the electronic structure of molecules. We present a more unified and comprehensive representation based on Richard Bader's quantum topological atoms in molecules (AIM) theory where critical points in the electron density are connected through a network. AIM theory provides a wealth of chemical information about individual atoms and their bond connections enabling a more flexible and chemically relevant representation. To obtain even more relevant rules with higher coverage, we apply manual postprocessing and interpretation of ILP rules. We have tested the usefulness of the new representation in SAR modelling on classifying compounds of low/high mutagenicity and on a set of factor Xa inhibitors of high and low affinity.

The nature of benzene–cation interactions from the topology of the electron distribution

A theoretical analysis of complex formation of benzene with alkaline and alkaline-earth cations is presented. Two types of molecular structures are found from the topology of the electron density, ρ( r). Charge redistribution upon complex formation is accounted for by the properties of ρ( r) and the quantum topological atoms, revealing the differences between alkaline and alkaline-earth complexes. The long-range energy, calculated with multipoles of the atoms in a complex, allows to conclude that polarization plus charge transfer are essential to recover the ab initio interaction energies for alkaline cations, whereas for the other complexes additional effects such as covalent bonding are also relevant.

The hydroperoxy radical as a hydrogen bond acceptor. HOOHCl complexes—Ab initio study

Protonacceptor properties of the HOO radical were investigated previously by means of ab initio as well as topological Atoms in Molecules (AIM) and Electron Localization Function (ELF) methods. It was pointed out that in the radical there are three nonequivalent positions most susceptible to protonation, and on this basis three structures of possible hydrogen bonded complexes were proposed. Results reported in the present article concern all possible 1:1 complexes formed by HCl and HOO molecules, and fully confirm suppositions given on the basis of the above-mentioned investigations. There are three various complexes referring to the local minima, and the transition structure predicted by topological methods has been found as well. The cyclic structure appeared to be the most stable one, which confirms conclusions given in the experimental article. Apart from structure optimization, harmonic as well as anharmonic spectra of the complexes have been simulated. Anharmonicity of H-Cl stretching vibration was of special interest, as the frequency of this vibration characterizes the Cl-H...O hydrogen bond in these complexes. To obtain values of these frequencies the one-dimensional Hamiltonian has been diagonalized numerically. The potential for this Hamiltonian has been taken from a set of single-point scanning of the part of the Potential Energy Surface (PES) connected with this vibration. The potential calculated on the MP2 level leads to the result close to the experimental value, whereas the B3LYP method is inappropriate for the purpose of PES investigation of these complexes.

The electrostatic potential generated by topological atoms. II. Inverse multipole moments

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.

Rendering of quantum topological atoms and bonds

In this article, we describe and apply an algorithm that visualizes atoms and bonds in molecules and van der Waals complexes, based on the topology of the electron density. The theory of quantum chemical topology defines both atoms and bonds via a single consistent procedure, and enables the association of an atomic shape with an atomic property (charge, dipole moment, volume, …). Special attention is paid to the bridging of gaps arising in interatomic surfaces, in the presence of ring critical points or high ellipticity. This algorithm, in conjunction with the graphical user interface of the computer program MORPHY enables robust and efficient rendering of complicated interatomic surfaces, as found in larger systems.