Similarity searching in databases of three-dimensional molecules and macromolecules.

This paper discusses algorithmic techniques for measuring the degree of similarity between pairs of three-dimensional (3-D) chemical molecules represented by interatomic distance matrices. A comparison of four methods for the calculation of 3-D structural similarity suggests that the most effective one is a procedure that identifies pairs of atoms, one from each of the molecules that are being compared, that lie at the center of geometrically-related volumes of 3-D space. This atom mapping method enables the calculation of a wide range of types of intermolecular similarity coefficient, including measures that are based on physicochemical data. Massively-parallel implementations of the method are discussed, using the AMT Distributed Array Processor, that achieve a substantial increase in performance when compared with a sequential implementation on a UNIX workstation. Current work involves the use of angular information and the extension of the method to field-based similarity searching. Similarity searching in 3-D macromolecules is effected by the use of a maximal common subgraph (MCS) isomorphism algorithm with a novel, graph-based representation of the tertiary structures of proteins. This algorithm is being used to identify similarities between the 3-D structures of proteins in the Brookhaven Protein Data Bank; its use is exemplified by searches involving the NAD-binding fold motif.     

Efficient algorithm for quantitative assessment of similarities among atoms in molecules

A new algorithm for quantitative assessment of similarity between two atoms in molecules is presented. Both the atomic similarity index and its derivatives with respect to the three Euler angles that describe the mutual orientation of the atoms under comparison are computed efficiently by taking advantage of the recently developed analytical representations for atomic zero-flux surfaces. The use of such representations makes it possible to substantially enhance the accuracy of the computed similarity indices without increasing the cost of their evaluation. Numerical tests involving oxygen atoms in several carbonyl compounds demonstrate the ability of the new algorithm to discern small changes in atomic similarity that are brought about by second-neighbor effects. Comparisons among hydrogen atoms in the acrolein molecule reveal the usefulness of the similarity index in detection and quantification of the effects of steric interactions on atomic shapes. © 1996 by John Wiley & Sons, Inc.     

Density functional theory and atoms-in-molecules investigation of intramolecular hydrogen bonding in derivatives of malonaldehyde and implications for resonance-assisted hydrogen bonding

A density functional theory (DFT) and atoms-in-molecules (AIM) analysis has been applied to the intramolecular hydrogen bonding in the enol conformers of malonaldehyde and its fluoro-, chloro-, cyano-, and nitro-substituted derivatives. With the B3LYP/6-311++G(2d,p) method, good agreement between the DFT geometries and published experimental structures has been found. The donor-acceptor distance was also varied in a series of constrained optimizations in order to determine if energetic, structural, and topological trends associated with intermolecular hydrogen bonding remain valid in the intramolecular case. At very short donor-acceptor distances (<2.24 A), the hydrogen is symmetrically located between donor and acceptor; at distances longer than this, the hydrogen bonding is no longer symmetric. The AIM methodology has been applied to explore the topology of the electron density in the intramolecular hydrogen bonds of the chosen model systems. Most AIM properties for intramolecular hydrogen bond distances longer than 2.24 A show smooth trends, consistent with intermolecular hydrogen bonds. Integrated AIM properties have also been used to explore the phenomenon of resonance-assisted hydrogen bonding (RAHB). It is shown that as the donor-acceptor distance is varied, pi-electron density is redistributed among the carbon atoms in the intramolecular hydrogen bond ring; however, contrary to prior studies, the integrated atomic charges on the donor-acceptor atoms were found to be insensitive to variation of hydrogen-bonding distance.     

Similarity searching in files of three-dimensional chemical structures: Representation and searching of molecular electrostatic potentials using field-graphs

This paper reports a method for the identification of those molecules in a database of rigid 3D structures with molecular electrostatic potential (MEP) grids that are most similar to that of a user-defined target molecule. The most important features of an MEP grid are encoded in field-graphs, and a target molecule is matched against a database molecule by a comparison of the corresponding field-graphs. The matching is effected using a maximal common subgraph isomorphism algorithm, which provides an alignment of the target molecule's field- graph with those of each of the database molecules in turn. These alignments are used in the second stage of the search algorithm to calculate the intermolecular MEP similarities. Several different ways of generating field-graphs are evaluated, in terms of the effectiveness of the resulting similarity measures and of the associated computational costs. The most appropriate procedure has been implemented in an operational system that searches a corporate database, containing ca. 173,000 3D structures.     

Upperbound procedures for the identification of similar three-dimensional chemical structures

Summary This paper describes techniques for calculating the degree of similarity between an input query molecule and each of the molecules in a database of 3-D chemical structures. The inter-molecular similarity measure used is the number of atoms in the 3-D common substructure (CS) between the two molecules which are being compared. The identification of 3-D CSs is very demanding of computational resources, even when an efficient clique detection algorithm is used for this purpose. Two types of upperbound calculation are described which allow reductions in the number of exact CS searches which need to be carried out to identify those molecules from a database which are similar to a 3-D target molecule.     

Similarity searching in databases of flexible 3D structures using smoothed bounded distance matrices

This paper describes a method for calculating the similarity between pairs of chemical structures represented by 3D molecular graphs. The method is based on a graph matching procedure that accommodates conformational flexibility by using distance ranges between pairs of atoms, rather than fixing the atom pair distances. These distance ranges are generated using triangle and tetrangle bound smoothing techniques from distance geometry. The effectiveness of the proposed method in retrieving other compounds of like biological activity is evaluated, and the results are compared with those obtained from other, 2D-based methods for similarity searching.     

Examination of stabilty of molecular agglomerates in molecular crystals

We report an examination algorithm of stability of molecular aggregates based on the estimation of rigidity of intermolecular contacts in a crystal structure. The algorithm includes the intermolecular interaction energy calculation (in the atom-atom potential approximation) of a pair of molecules selected in the crystal structure. Further, the energy is minimized using a least-squares technique by varying the position and orientation of one of the molecules. The contact rigidity is quantitatively assessed by the minimized rms difference between the positions of the atoms in the original and optimized structures (Zorkii’s criterion). Every rigid contact revealed in the structure determines finite or infinite stable agglomerates. The paper presents the results of testing the computer program based on this algorithm with a number of real crystal structures previously determined by single crystal X-ray diffraction, and also the examples of the most common stable molecular agglomerates found with the aid of the program.     

Improved intermolecular force field for molecules containing H,C, N,and O atoms,with application to nucleoside and peptide crystals

A new intermolecular force field for nitrogen atoms in organic molecules was derived from a training dataset of 76 observed azahydrocarbon crystal structures and 11 observed heats of sublimation. The previously published W99 force field for hydrogen, carbon, and oxygen was thus extended to include nitrogen atoms. Nitrogen atoms were divided into four classes: N(1) for triply bonded nitrogen, N(2) for nitrogen with no bonded hydrogen (except the triple bonded case), N(3) for nitrogen with one bonded hydrogen, and N(4) for nitrogen with two or more bonded hydrogens. H(4) designated hydrogen bonded to nitrogen. Wavefunctions of 6‐31g** quality were calculated for each molecule and the molecular electric potential (MEP) was modeled with net atomic and supplementary site charges. Lone pair electron charge sites were included for nitrogen atoms where appropriate, and methylene bisector charges were used for CH₂ and CH₃ groups when fitting the MEP. X? H bond distances were set to standard values for the wave function calculation and then foreshortened by 0.1 Å for the MEP and force field fitting. Using the force field optimized to the training dataset, each azahydrocarbon crystal structure was relaxed by intermolecular energy minimization. Predicted maximum changes in unit cell edge lengths for each crystal were 3% or less. The complete force field for H, C, N, and O atoms was tested by intermolecular energy relaxation of nucleoside and peptide molecular crystals. Even though these molecules were not included in any of the training datasets for the force field, agreement with their observed crystal structures was very good, with predicted unit cell edge shifts usually less than 2%. These tests included crystal structures of representatives of all eight common nucleosides found in DNA and RNA, 15 dipeptides, four tripeptides, two tetrapeptides, and a pentapeptide with two molecules in the asymmetric unit. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1154–1166, 2001     

Molecular Structure of 1-Germatrahol and its Complex With Chloroform

The crystal structures of anhydrous 1-germatranol and its complex with HCCl₃ are centrosymmetrical dimers because of their intermolecular hydrogen bonds. In the germatranol crystal, the axial and equatorial oxygen atoms of its two molecules are hydrogen bonded into an eight-membered coordination cycle. In the complex with HCCl₃, the two molecules of germatranol are likewise linked in dimers, and both axial oxygen atoms are H bonded with HCCl₃. In the investigated structures, the axial Ge—O bond is shorter than the equatorial ones. Depending on the number and strength of the hydrogen bonds, the interatomic Ge—O and Ge ← N distances change markedly. The quantitative estimates of the H bond energy are obtained from quantum chemical calculations of the model systems containing 1-germatranol and HCCl₃ molecules.     

Van der Waals and Polar Intermolecular Contact Distances: Quantifying Supramolecular Synthons

Crystal structures are viewed as being determined by ranges and constraints on interatomic contact distances between neighboring molecules. These distances are considered to arise from environment‐dependent atomic sizes, that is, larger sizes for isotropic, van der Waals type contacts and smaller sizes for more‐polar, possibly ionic contacts. Although the idea of different, or anisotropic, radii for atoms is not new, we developed a method of obtaining atomic sizes that is based on a theoretical framework. Using different atomic sizes for the same atom in different environments, we were able to rationalize some structural observations and anomalies. For example, benzene with the Pbca structure may be described in terms of two types of C???H interactions: a longer contact largely of the van der Waals type, and a shorter, structure‐determining type (C^δ????H^δ+), which we term “n‐polar”. Our approach is illustrated with three examples: 1) the equivalence in crystal packing of fluorobenzene, benzonitrile, pyridine N‐oxide, and pyridine/HF 1:1 molecular complex, all of which take the not‐so‐common tetragonal P4₁2₁2 space group and are practically isomorphous; 2) the similarity of the Pa3 acetylene and Pbca benzene crystal structures; and 3) the equivalence between an increase in pressure and an increase in the “n‐polar” contacts in Pbca benzene; in other words, the equivalence between hydrostatic pressure and chemical pressure. In the context of crystal engineering, we describe a method whereby the topological information conveyed in a supramolecular synthon is recast in a more quantitative manner. A particular synthon, and in turn the crystal structure to which it leads, is viable within small ranges of distances of its constituent atoms, and these distances are determined by chemical factors.     

Development of a spectral clustering method for the analysis of molecular data sets

A spectral clustering method is presented and applied to two-dimensional molecular structures, where it has been found particularly useful in the analysis of screening data. The method provides a means to quantify (1) the degree of intermolecular similarity within a cluster and (2) the contribution that the features of a molecule make to a cluster. In an application of the spectral clustering method to an example data set of 125 COX-2 inhibitors, these two criteria were used to place the molecules into clusters of chemically related two-dimensional structures.     

“Crystal” conformations of 2-methyl-2,4-pentanediol: Dipole moment calculations and molecular structure optimizations

The structures of eight symmetrically independent molecules of 2-methyl-2,4-pentanediol (MPD) in six crystal substances are studied based on the data retrieved from the Cambridge Structural Database (CSD). Coordinates of the most part of hydrogen atoms in MPD molecules were not determined experimentally or not presented in CSD, however, O...O distances provide the conclusion about the formation of intramolecular hydrogen bonds in four molecules. To perform quantum chemical calculations the absent hydrogen atoms were added. The choice of H atomic positions in hydroxyl groups are based on the analysis of possible formation of intra- and intermolecular hydrogen bonds by MPD molecules in the respective crystals. The DFT method with the B3PW91 functional and the 6-31G(d,p) basis set is used to carry out for the first time: 1) the calculation of dipole moments and energies for MPD molecules in “crystal” conformations; 2) the optimization of the structure of these molecules with the calculation of dipole moments for the conformations corresponding to the local energy minima. It is found that among the molecules with the experimental geometric parameters one of the conformations without intramolecular hydrogen bonds is most favorable (μ = 0.56 D). As a result of the energy minimization of eight “crystal” conformations in vacuum, five energetically different conformers are obtained. Among them the conformer with the intramolecular hydrogen bond has the lowest energy (μ = 3.53 D). Four variants of the molecular structure correspond to it in the considered crystals, out of which two are R-enantiomers and two S-enantiomers.     

1,1-Dichloroethane: a molecular crystal structure without van der Waals contacts?

Isochoric and isobaric freezing of 1,1-dichloroethane, CH3CHCl2, mp=176.19 K, yielded the orthorhombic structure, space group Pnma, with the fully ordered molecules, in the staggered conformation, located on mirror planes. The CH3CHCl2 ambient-pressure (0.1 MPa) structures were determined at 160 and 100 K, whereas the 295 K high-pressure structures were determined at 0.59 and 1.51 GPa. At 0.1 MPa, all intermolecular distances are considerably longer than the sums of the van der Waals radii, and only a pressure of about 1.5 GPa squeezed the Cl...Cl and Cl...H contacts to distances commensurate with these sums. The exceptionally large difference between the melting points of isomeric 1,1- and 1,2-dichloroethane can be rationalized in terms of their molecular-packing efficiency. It has been shown that the location of atoms in molecules affects their intermolecular interactions, and hence their van der Waals radii are the function of molecular structures.     

General trends in atomic and nuclear quantum similarity measures

Simple and accurate relationships between atomic and nuclear quantum similarity measures and their constituent elements were found. These results complement findings in previous studies in which quantum self‐similarity measures in atoms and nuclei were linked to the atomic and mass numbers, respectively. The models were validated on a large test set, and the general trends in the behavior of the quantum similarity measures for these quantum objects were made clear. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 685–692, 2000