Quantum similarity study of atoms: a bridge between hardness and similarity indices

A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev's table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3相似文献   

An analytical method for computing atomic contact areas in biomolecules

We propose a new analytical method for detecting and computing contacts between atoms in biomolecules. It is based on the alpha shape theory and proceeds in three steps. First, we compute the weighted Delaunay triangulation of the union of spheres representing the molecule. In the second step, the Delaunay complex is filtered to derive the dual complex. Finally, contacts between spheres are collected. In this approach, two atoms i and j are defined to be in contact if their centers are connected by an edge in the dual complex. The contact areas between atom i and its neighbors are computed based on the caps formed by these neighbors on the surface of i; the total area of all these caps is partitioned according to their spherical Laguerre Voronoi diagram on the surface of i. This method is analytical and its implementation in a new program BallContact is fast and robust. We have used BallContact to study contacts in a database of 1551 high resolution protein structures. We show that with this new definition of atomic contacts, we generate realistic representations of the environments of atoms and residues within a protein. In particular, we establish the importance of nonpolar contact areas that complement the information represented by the accessible surface areas. This new method bears similarity to the tessellation methods used to quantify atomic volumes and contacts, with the advantage that it does not require the presence of explicit solvent molecules if the surface of the protein is to be considered. © 2012 Wiley Periodicals, Inc.     

Similarity recognition of molecular structures by optimal atomic matching and rotational superposition

An algorithm for similarity recognition of molecules and molecular clusters is presented which also establishes the optimum matching among atoms of different structures. In the first step of the algorithm, a set of molecules are coarsely superimposed by transforming them into a common reference coordinate system. The optimum atomic matching among structures is then found with the help of the Hungarian algorithm. For this, pairs of structures are represented as complete bipartite graphs with a weight function that uses intermolecular atomic distances. In the final step, a rotational superposition method is applied using the optimum atomic matching found. This yields the minimum root mean square deviation of intermolecular atomic distances with respect to arbitrary rotation and translation of the molecules. Combined with an effective similarity prescreening method, our algorithm shows robustness and an effective quadratic scaling of computational time with the number of atoms.     

Quantum similarity study of atomic density functions: insights from information theory and the role of relativistic effects

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev's table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge.     

Rapid evaluation of molecular shape similarity index using pairwise calculation of the nearest atomic distances

Rapid evaluation method for obtaining molecular shape similarity index using pairwise calculation of the nearest atomic distance respected to the template atoms was investigated. This method for calculations of similarity indices remarkably reduced required time compared with hitherto methods (especially 2 or 3 orders of magnitude faster than the previous grid-based evaluation technique) and gave without clear loss of preciseness. The potential of these improvements and possible further enhancements are discussed.     

Radial behavior of gradient expansion approximation to atomic Fukui function and shell structure of atoms

An approximation to the Fukui function in atoms recently proposed in the form of a gradient correction to the local density approximation expression is here investigated. The spatial behavior of this function is analyzed, focusing on the gradient correction term. Physical information on the shell structure of atoms is shown to be conveyed by the radial distribution of that term. The analytically modeled densities (AMD) procedure is also implemented, and global atomic hardnesses are calculated with Hartree-Fock and AMD representations of atomic electron densities. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 488–503, 1998     

An inertial model of atoms: atomic spectra as a resonance problem

A new model of atoms based on the theory of material waves is proposed. Atoms are characterized by an inertial aggregation of negative charge within the atomic shell, the calculation yields, for hydrogen atoms, an atomic radius of 0.470 nm. Atomic spectra result from radial material waves, quantization being the consequence of boundary conditions imposed on the fundamental wave equation. Stark effects and Zeeman effects are treated in detail, they are referred to deformations and rotations of the atomic shell. An analysis of Stern--Gerlach experiments bases subsequent deflections of single atoms on rotations and interactions of magnetic fields.     

SCF Deformation densities and electrostatic potentials of purines and pyrimidines

4-31G wave functions have been computed for five purines and pyrimidines. The calculated deformation densities have been partitioned into atomic fragments, which were integrated to yield atomic multipole moments. The transferability of atomic fragments between related molecules was verified by constructing model maps for uracil and guanine from appropriate fragments of cytosine and adenine. Model electrostatic potentials calculated from the moments of model atoms are similar to the corresponding 4-31G potentials. Comparison of 4-31G and 4-31G** deformation densities of cytosine provides simple rules for estimating the effects of polarization functions on the atomic multipole moments of most atom types occurring in the purines and pyrimidines. These rules were applied to the other molecules and yielded reasonable approximations for their molecular dipole moments. Substituting CH₃ for H has little effect on the deformation density beyond the substitution center.     

The W algorithm and the D transformation for the numerical evaluation of three‐center nuclear attraction integrals

Three‐center nuclear attraction integrals over exponential‐type functions are required for ab initio molecular structure calculations and density functional theory (DFT). These integrals occur in many millions of terms, even for small molecules, and they require rapid and accurate numerical evaluation. The use of a basis set of B functions to represent atomic orbitals, combined with the Fourier transform method, led to the development of analytic expressions for these molecular integrals. Unfortunately, the numerical evaluation of the analytic expressions obtained turned out to be extremely difficult due to the presence of two‐dimensional integral representations, involving spherical Bessel integral functions. % The present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of these spherical Bessel integrals. This algorithm, which is based on the nonlinear D transformation and the W algorithm of Sidi, can be computed recursively, allowing the control of the degree of accuracy. Numerical analysis tests were performed to further improve the efficiency of our algorithm. The numerical results section demonstrates the efficiency of this new algorithm for the numerical evaluation of three‐center nuclear attraction integrals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Further evaluation and development of charge similarity indices for choosing molecular analogues

Two molecular charge similarity index (CSI ) methods are further evaluated for practical application: one method based on a simple CNDO -type approximation to the electron density function and the other based on an ab initio pseudo total charge density function. The test system consists of isosteric analogues of dimethyl ether and methoxy acetic acid. The effects of differences in skeletal structure on the CSI measure of electron density similarity about corresponding atoms is estimated, and two new developments are presented for application of the ab initio-based method: (1) an INDO -type approximation which improves the efficiency of the CSI calculation; and (2) a FOCUS feature which enables comparisons of local molecule regions.     

About using the approximate fields to calculate the electrostatic potential distribution of membrane channels

By the example of gramicidine channel, a comparative analysis of different approximate representations (heavy atoms, polar protons, near-by atoms) of AMBER force field has been carried out to calculate the electrostatic potential distribution of ionic channels in biological membranes. The results obtained are compared with the potential computed in a full-atom representation. The use of approximate representations is shown to lead to estimated errors of the potential.     

Fast and accurate methods for predicting short-range constraints in protein models

Protein modeling tools utilize many kinds of structural information that may be predicted from amino acid sequence of a target protein or obtained from experiments. Such data provide geometrical constraints in a modeling process. The main aim is to generate the best possible consensus structure. The quality of models strictly depends on the imposed conditions. In this work we present an algorithm, which predicts short-range distances between Cα atoms as well as a set of short structural fragments that possibly share structural similarity with a query sequence. The only input of the method is a query sequence profile. The algorithm searches for short protein fragments with high sequence similarity. As a result a statistics of distances observed in the similar fragments is returned. The method can be used also as a scoring function or a short-range knowledge-based potential based on the computed statistics.     

An Orbital-Overlap Complement to Atomic Partial Charge

Atomic partial charges are widely used to predict reactivity. Partial charge alone is often insufficient: the carbons of benzene and cyclobutadiene, or those of diamond, graphene, and C₆₀, possess nearly identical partial charges and very different reactivities. Our atomic overlap distance complements computed partial charges by measuring the size of orbital lobes that best overlap with the wavefunction around an atom. Compact, chemically stable atoms tend to have overlap distances smaller than chemically soft, unstable atoms. We show here how combining atomic charges and overlap distances captures trends in aromaticity, nucleophilicity, allotrope stability, and substituent effects. Applications to recent experiments in organic chemistry (counterintuitive Lewis base stabilization of alkenyl anions in anionic cyclization) and nanomaterials chemistry (facile doping of the central atom in Au₇ hexagons) illustrate this combination's predictive power.     

An Orbital‐Overlap Complement to Atomic Partial Charge

Atomic partial charges are widely used to predict reactivity. Partial charge alone is often insufficient: the carbons of benzene and cyclobutadiene, or those of diamond, graphene, and C₆₀, possess nearly identical partial charges and very different reactivities. Our atomic overlap distance complements computed partial charges by measuring the size of orbital lobes that best overlap with the wavefunction around an atom. Compact, chemically stable atoms tend to have overlap distances smaller than chemically soft, unstable atoms. We show here how combining atomic charges and overlap distances captures trends in aromaticity, nucleophilicity, allotrope stability, and substituent effects. Applications to recent experiments in organic chemistry (counterintuitive Lewis base stabilization of alkenyl anions in anionic cyclization) and nanomaterials chemistry (facile doping of the central atom in Au₇ hexagons) illustrate this combination's predictive power.     

A fast and accurate algorithm for QTAIM integration in solids

A new algorithm is presented for the calculation of atomic properties, in the sense of the quantum theory of atoms in molecules. This new method, named QTREE , applies to solid‐state densities and allows the computation of the atomic properties of all the atoms in the crystal in seconds to minutes. The basis of the method is the recursive subdivision of a symmetry‐reduced wedge of the Wigner‐Seitz cell, which in turn is expressed as a union of tetrahedra, plus the use of β‐spheres to improve the performance. A considerable speedup is thus achieved compared with traditional quadrature‐based schemes, justified by the poor performance of the latter because of the particular features of atomic basins in solids. QTREE can use both analytical or interpolated densities, calculates all the atomic properties available, and converges to the correct values in the limit of infinite precision. Several gradient path tracing and integration techniques are tested. Basin volumes and charges for a selected set of 11 crystals are determined as a test of the new method. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011