Topological Atoms Research Articles

A Hierarchical Clustering Approach for Large Compound Libraries

A modified version of the k-means clustering algorithm was developed that is able to analyze large compound libraries. A distance threshold determined by plotting the sum of radii of leaf clusters was used as a termination criterion for the clustering process. Hierarchical trees were constructed that can be used to obtain an overview of the data distribution and inherent cluster structure. The approach is also applicable to ligand-based virtual screening with the aim to generate preferred screening collections or focused compound libraries. Retrospective analysis of two activity classes was performed: inhibitors of caspase 1 [interleukin 1 (IL1) cleaving enzyme, ICE] and glucocorticoid receptor ligands. The MDL Drug Data Report (MDDR) and Collection of Bioactive Reference Analogues (COBRA) databases served as the compound pool, for which binary trees were produced. Molecules were encoded by all Molecular Operating Environment 2D descriptors and topological pharmacophore atom types. Individual clusters were assessed for their purity and enrichment of actives belonging to the two ligand classes. Significant enrichment was observed in individual branches of the cluster tree. After clustering a combined database of MDDR, COBRA, and the SPECS catalog, it was possible to retrieve MDDR ICE inhibitors with new scaffolds using COBRA ICE inhibitors as seeds. A Java implementation of the clustering method is available via the Internet (http://www.modlab.de).

Atomic properties of amino acids: computed atom types as a guide for future force-field design.

The quantum chemical topology (QCT) is able to propose atom types by direct computation rather than by chemical intuition. In previous work, molecular electron densities of 20 amino acids and smaller derived molecules were partitioned into a set of 760 topological atoms. Each atom was characterised by seven atomic properties and subjected to cluster analysis element by element, that is, C, H, O, N, and S. From the respective dendrograms, 21 carbon atom types were distinguished, 7 hydrogen, 2 nitrogen, 6 oxygen, and 6 sulfur atom types. Herein, we contrast the QCT atom types with those of the assisted model building with energy refinement (AMBER) force field. We conclude that in spite of fair agreement between QCT and AMBER atom types, the latter are sometimes underdifferentiated and sometimes overdifferentiated. In summary, we suggest that QCT is a useful guide in designing new force fields or improving existing ones. The computational origin of QCT atom types makes their determination unbiased compared to atom type determination by chemical intuition and a priori assumptions. We provide a list of specific recommendations.

The electrostatic potential generated by topological atoms: a continuous multipole method leading to larger convergence regions

The electrostatic potential generated by an atom in a molecule can be conveniently expressed by traditional multipole expansions. The disadvantage of such expansions is that they introduce a divergence sphere within which the expansion diverges. Because of their finite size, atoms defined according to quantum chemical topology (QCT) yield a small divergence sphere. However the introduction of an alternative continuous multipole expansion reduces the divergence region even further. The new method allows the electrostatic potential to be evaluated accurately at short-range, which is illustrated for a pair of simple molecules.

Atomic properties of selected biomolecules: quantum topological atom types of hydrogen, oxygen, nitrogen and sulfur occurring in natural amino acids and their derivatives.

Molecular electron densities are generated at B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for 57 molecules, including one conformation of each naturally occurring amino acid and smaller derived molecules. The electron densities are partitioned into atomic fragments according to the approach of quantum chemical topology (QCT). A set of 547 unique topological atoms is obtained, containing 421 hydrogens, 63 oxygens, 57 nitrogens and 6 sulfurs. Each atom is described by seven properties: volume, kinetic energy, monopole, dipole, quadrupole, octupole and hexadecapole moment. Cluster analysis groups atoms into atom types based on their similarity expressed in the discrete 7D space of atomic properties. Using a separation criterion we distinguish seven hydrogen, six oxygen, two nitrogen and six sulfur atom types.

Atomic properties of selected biomolecules: quantum topological atom types of carbon occurring in natural amino acids and derived molecules.

We seek to recover rigorous atom types from amino acid wave functions. The atom types emerge from a cluster analysis operating on a set of seven atomic properties, including kinetic energy, volume, population, and dipole, quadrupole, octupole, and hexadecapole moments. These properties are acquired by partitioning the molecular electron density into quantum topological atoms. Wave functions are generated at the B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for a sensible conformation of each of the 20 naturally occurring amino acids and smaller derived molecules, which together constitute a data set of 57 molecules. From this set 213 unique quantum topological carbons are obtained, which are linked according to the similarity of their properties. After introducing a statistical separation criterion, our cluster analysis proposes two representations: a cruder one with 5 atom types and a finer one with 21 atom types. The immediate coordination of the central carbon plays a major role in labeling the atom types.

Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction

We study the anisotropic electrostatic interaction with high rank multipoles (ℓ = 5) for a set of 10 van der Waals complexes and 27 DNA base pairs. Multipoles are generated by the distributed multipole analysis (DMA) and by the topological quantum theory of ‘atoms in molecules’ (AIM). The convergence of the multipolar expansion of the interaction between topological atoms is improved by distributing the moments over extra off-nuclear sites via a shifting procedure. A clear theoretical distinction is made between partitioning and distributing. A substantial improvement in the convergence of the AIM multipole expansion is observed for the smaller van der Waals molecules. An AIM representation with extra sites on the bond midpoints performs as well as DMA with just nuclear sites. However, for the larger DNA base pairs no improvement follows from the introduction of extra sites with AIM. For these larger systems AIM and DMA expansions perform equivalently, provided that now DMA allows for extra sites. This work further encourages the development of a topological intermolecular force field.

The prediction of energies and geometries of hydrogen bonded DNA base-pairs via a topological electrostatic potentialElectronic supplementary information (ESI) available: Comparison of the BSSE corrected interaction energies, geometrical parameters and total interaction energies of the 27 base-pair series. See http://www.rsc.org/suppdata/cp/b2/b204485d/

We introduce an anisotropic model of electrostatic interaction based on topological atoms obtained from the gradient vector field partitioning of the electron density. High-order electrostatic moments are computed within the compact spherical tensor formalism from ab initio wave functions of rigid geometry-optimized monomers. When combined with a simple hard-sphere or Lennard-Jones potential this topological electrostatic interaction potential correctly predicts the geometries of 27 DNA base-pairs. With the Lennard-Jones(LJ) potential internuclear distances of frontier atoms between base-pairs differ only by 0.08 Å compared to supermolecular calculations at B3LYP/6-31G(d,p) level. The discrepancy for angles involved in hydrogen bond contacts amounts to only 3.5°. The topological model globally reproduces the correct ranking in intermolecular interaction energy (6.5 ± 6.5 kJ mol−1). Subsequently we compare the interaction energy profiles of the topological model with distributed multipole analysis, Merz–Kollman charges and the natural population analysis at the B3LYP/6-311+G(2d,p) level. The convergence of the topological multipole expansion is somewhat more favorable than that based on DMA but the two models have similar basis set dependence. This work encourages the development of a topological intermolecular potential, which already predicts a reliable geometry of a DNA tetrad in its present form.

Convergence of the Electrostatic Interaction Based on Topological Atoms

An atom−atom partitioning of the electrostatic energy between unperturbed molecules is proposed on the basis of the topology of the electron density. Atom−atom contributions to the electrostatic energy are computed exactly, i.e., via a novel six-dimensional integration over two atomic basins, and by means of the spherical tensor multipole expansion, up to total interaction rank L = lA + lB + 1 = 6. The convergence behavior of the topological multipole expansion is compared with that using distributed multipole analysis (DMA) multipole moments for a set of van der Waals complexes at the B3LYP/6-311+G(2d,p) level. Within the context of the Buckingham−Fowler model it is shown that the topological and DMA multipole moments converge to a very similar interaction energy and geometry (average absolute discrepancy of 1.3 kJ/mol and 1.3°, respectively) and are both in good to excellent agreement with supermolecule calculations.

A new 3D molecular structure representation using quantum topology with application to structure–property relationships

We present a new 3D molecular structure representation based on Richard F.W. Bader's quantum topological atoms in molecules (AIM) theory for use in quantitative structure–property/activity relationship (QSPR/QSAR) modeling. Central to this structure representation using quantum topology (StruQT) are critical points located on the electron density distribution of the molecules. Other gradient fields such as the Laplacian of the electron density distribution can also be used. The type of critical point of particular interest is the bond critical point (BCP) which is here characterized by using the following three parameters: electron density ρ, the Laplacian ∇ 2 ρ and the ellipticity ϵ. This representation has the advantage that there is no need to probe a large number of lattice points in 3D space to capture the important parts of the 3D electronic structure as is necessary in, e.g. comparative field analysis (CoMFA). We tested the new structure representation by predicting the wavelength of the lowest UV transition for a system of 18 anthocyanidins. Different quantitative structure–property relationship (QSPR) models are constructed using several chemometric/machine learning methods such as standard partial least squares regression (PLS), truncated PLS variable selection, genetic algorithm-based variable selection and genetic programming (GP). These models identified bonds that either take part in decreasing or increasing the dominant excitation wavelength. The models also correctly emphasized on the involvement of the conjugated π system for predicting the wavelength through flagging the BCP ellipticity parameters as important for this particular data set.

Convergence of the multipole expansion for electrostatic potentials of finite topological atoms

The exact atomic electrostatic potential (AEP) and atomic multipole moments are calculated using the topological partitioning of the electron density. High rank (l⩽20) spherical tensor multipole moments are used to examine the convergence properties of the multipole expansion. We vary independently the maximum multipole rank, lmax, and the radius of the spherical grid around an atom in a molecule where we measure the discrepancy between the exact AEP and the one obtained via multipole expansion. The root mean square values are between 0.1 and 1.6 kJ/mol for four atoms (C, N, O, S) on a spherical grid with the ρ=0.001 a.u. convergence radius and for lmax=4. Our calculations demonstrate that this fast convergence is due to the decay of the electron density. We show that multipole moments generated by finite atoms are adequate for use in the multipole expansion of the electrostatic potential, contrary to some claims made in the literature. Moreover they can be used to model intermolecular and in principle intramolecular interactions as well.

Experimental Charge Density of α-Glycine at 23 K

The electrostatic properties of crystals of α-glycine have been obtained from extensive X-ray diffraction data collected at approximately 23 K and carefully processed, including corrections for scan truncation losses, anisotropic extinction, and multiple reflection. From a multipole parameterization of the X-ray intensities we have obtained an unusually preciseand we are confident, accuratemodel of the total electron distribution in the crystal including the topological features, atom and group charges, the dipole moment for the glycine zwitterion, electrostatic potentials, electric field gradients at the nucleii of the three hydrogen atoms of the ammonium group, and intermolecular electrostatic energies within the crystal. We have also calculated the total interaction energies involving the six distinct types of intermolecular pairings and examined these energies in terms of the molecular arrangement.

A comparative study of molecular similarity, statistical, and neural methods for predicting toxic modes of action

AbstractQuantitative structure–activity relationship (QSAR) models are routinely used in predicting toxicologic and ecotoxicologic effects of untested chemicals. One critical factor in QSAR‐based risk assessment is the proper assignment of a chemical to a mode of action and associated QSAR. In this paper, we used molecular similarity, neural networks, and discriminant analysis methods to predict acute toxic modes of action for a set of 283 chemicals. The majority of these molecules had been previously determined through toxicodynamic studies in fish to be narcotics (two classes), electrophiles/proelectrophiles, uncouplers of oxidative phosphorylation, acetylcholinesterase inhibitors, and neurotoxicants. Nonempirical parameters, such as topological indices and atom pairs, were used as structural descriptors for the development of similarity‐based, statistical, and neural network models. Rates of correct classification ranged from 65 to 95% for these 283 chemicals.

Chemical Similarity Using Geometric Atom Pair Descriptors

Similarity searches using topological descriptors have proved extremely useful in aiding large-scale screening. In this paper we describe the geometric atom pair, the 3D analog of the topological atom pair descriptor (Carhart et al. J. Chem. Inf. Comput. Sci. 1985, 25, 64−73). We show the results of geometric similarity searches using the CONCORD-build structures of typical small druglike molecules as probes. The database to be searched is a 3D version of the Derwent Standard Drug File that contains an average of 10 explicit conformations per compound. Using objective criteria for determining how good a descriptor is in selecting active compounds from large databases, we compare the results using the geometric versus the topological atom pair. We find that geometric and topological atom pairs are about equally effective in selecting active compounds from large databases. How the two types of descriptors rank active compounds is generally about the same as well, but occasionally active compounds will be se...

A local density functional investigation of the clean and the hydrogen covered Li(001) surface

A detailed density functional theory study on periodic slab models of the clean and the hydrogen covered Li(001) surface is presented to corroborate recent experiments on atomic hydrogen adsorption at lithium surfaces. Questions of model convergence as well as the bonding mechanism in the adsorption system are investigated. Several tools are employed to analyze the self-consistently determined electronic structure of the Li(001) and H Li(001) slab models, among them one-particle core level shifts, overlap populations and density difference maps. To quantify the charge separation within the ionic surface layer formed in the H Li(001) adsorption system, the topological atom approach and a recently developed technique uniquely based on the electrostatic potential above the surface are used. Lithium is found to behave to some extent like a covalent solid rather than an s electron metal, while the adsorption system H Li at full monolayer coverage is best characterized by an insulator-metal interface.

Charge separation and covalent bonding in metal oxide surfaces: A local density functional study on the MgO(001) surface

A first principles local density functional investigation on extended, two-dimensional periodic slab models of the MgO(001) surface is performed, using the linear combination of Gaussian-type orbitals (LCGTO) technique as implemented in the FILMS program package. Stimulated by recent theoretical evidence for a reduced charge separation in MgO(001), a detailed analysis of the charge distribution and its influence on the electrical field above the surface is carried out. Two different methods to quantify the charge separation in the ionic substrate are employed, a local one based on the topological atom approach and a global one derived from the Madelung field of the surface near potential adsorbates. Both procedures lead to a charge separation significantly (10%–20%) below the nominal ionic value of ±2 a.u. A variational atomic orbital analysis is utilized to discuss the origin of the Mg 3s and 3p structures discernible in the crystal orbitals of the MgO slab systems. They are identified as covalent magnesium valence orbital admixtures to the oxygen dominated valence bands in consistence with the reduced charge separation. Their influence on the cohesive energy of crystalline MgO, however, is found to be only 5% (∼0.5 eV).

Self‐returning walks and fractional electronic charges of atoms in molecules

AbstractThree hierarchically ordered topological factors, i.e., atom connectivity, centrality, and cyclicity, were found to control the number of self‐returning walks (SRWS) associated with every atom in the molecule. The reversal of their order was observed in a few cases where the central location of atoms had a stronger influence than did their connectivity on the number of SRWS. Three atomic topological indices, i.e., the Morgan extended connectivity, the Balaban, Mekenyan, and Bonchev hierarchical extended connectivity, the Randić atomic path code, were found to closely match the ordering of atoms in molecules determined by their number of SRWS. New atomic graph invariants fi = lim SRW/SRWn and ti = fi · SRW2 were specified and may find application in QSAR and QSPR. The ti indices are nonintegers close to atomic valence. The fi indices represent the limit of the number of SRWS of length n for the atom i, SRW, normalized by dividing it by the total number of SRWS for the molecule. In the case of Hückel MO considerations, these invariants were shown to be numerically equal to the partial electronic charges of the lowest occupied molecular orbital (LOMO). A new class of isocodal atoms (atoms having the same number of SRWns) was observed, i.e., atoms that become isocodal only at n ⩾ 1. A number of open questions following from these findings were formulated, including the possibility for a topological modeling of electron correlation. © 1993 John Wiley & Sons, Inc.

Residual charges on atoms in organic structures: A new algorithm for their calculation

A fast algorithm for the evaluation of residual charges in organic structures is presented. Its validity extends over single and isolated multiple bonds. The model considers only atom connectivities as the topological basis and atom electronegativities and covalent radii as physical characteristics; the use of an iterative procedure and well-defined computational rules ensures self consistency for the method which is tested through the calculation of atomic charges in several molecules and through a comparison of results obtained with other methods. The Fortran 77 source code RESCHA.FOR the PC executable RESCHA.EXE, sample input PROST.MOL, and resulting output PROST.OUT are included on disk.

The concept of the topological atom within the MO‐LCAO approach. II. On the nature of the nephelauxetic effect

AbstractA new MO‐LCAO description of the nephelauxetic effect is proposed based on the concept of the topological atom and on the method of reduced density matrices. This approach allows one to overcome some conceptual difficulties of ligand‐field theory and to derive effective parameters of d‐d electron repulsion of a bound transition‐metal in a proper way. The two ligand‐field mechanisms of the nephelauxetic effect—the central field covalency and the symmetry‐restricted covalency—are clarified and generalized. In addition, a new factor, important for the nephelauxetic effect is found: its size‐dependence on the region of the topological atom.

The concept of the topological atom within the MO‐LCAO approach. I. On the effective charge of an atom‐in‐molecule

AbstractA new definition of the MO‐LCAO effective atomic charge is proposed, based on the concept of the topo‐logical atom A general equation for the MO‐LCAO electron occupancy of a topological atom is derived. It is shown that the intuitively introduced Mulliken gross atomic population is in fact an approximation to the electron occupancy of the corresponding topological atom. An approximate semiempirical procedure for evaluating the effective charge and effective radius of the topological atom is discussed.