Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). I. Algorithms for finding graph orbits and canonical numbering of atoms

An iterative algorithm is described for finding topological equivalence, ordering, and canonical numbering of vertexes (atoms) in molecular graphs. Like the Morgan algorithm, it is based on extended connectivities but: (i) the latter are used hierarchically, i. e., the discrimination in the next iteration is carried out only for the vertices having the same extended connectivities (ranks) at the previous iteration; (ii) at equal extended connectivities, additional discrimination is introduced by the ranks of adjacent vertices; (iii) there is no “best name” search; (iv) three levels of complexity of chemical structures are distinguished and handled by different procedures. Two schemes of application of HOC procedures are presented: one directed towards a fast canonical numbering for coding systems, and another one yielding levels of topological equivalence allowing a unique topological representation of the molecule with possible applications to similarity search, structure-activity correlations, etc.     

Chain numbering and encoding of cyclic hydrocarbons

The numbering of carbon atoms in organic molecules is called chain numbering. It is suggested that bonds be classified as chain bonds (between atoms with consecutive indices) and nonchain bonds. Among atoms we distinguish the first atom (No. 1) and the last atom (having the largest index) as well as initial and final atoms (starting and finishing unbranched sections of atomic chains). Also, internal numbering of elements within these classes is proposed. For condensed cyclic hydrocarbons, formulas for deriving the number of cycles are given, and a linear-chain encoding system is worked out; in this system, nonchain bonds are assigned the indices of their atoms. Rules for unique numbering (canonical chain numbering) are developed; they involve maximization of the indices of the initial atoms and nonchain bonds. The linear-chain encoding of cyclic hydrocarbon structures ensures unification and systematization of their names. Tambov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 731–736, July–August, 1995. Translated by L. Smolina     

Linear notations and molecular graph similarity

Two simple linear notation systems are suggested to encode molecular structure including stereochemical elements. Both systems give rise to a unique numbering of the molecular graph, and thus also lead to a unique linear notation. Both linear notation systems are extremely compact and require only standard chemical symbols. A string comparison technique is developed to measure the similarity of two molecular linear notations. This procedure allows one to define a molecular similarity index with values that range from zero to unity, the zero value characterizing complete dissimilarity and the value of unity denoting identity. The notation and similarity index procedures are applied to several small molecular structures.     

The azine bridge as a conjugation stopper: an NMR spectroscopic study of electron delocalization in acetophenone azines

Dipole parallel-alignment of organic molecular crystals of azines has been achieved with a design that was based on the hypothesis that the azine bridge is a conjugation stopper. This hypothesis has now been tested in detail, and (1)H and (13)C NMR spectroscopic data of symmetric and asymmetric acetophenone azines are presented in support of this design concept. Previous structural, ab initio, and electrochemical studies have shown that the azine bridge largely inhibits through-conjugation in molecules with the general structure DPhC(Me) [double bond] N [bond] N [double bond] C(Me)PhA, where D is a donor group and A is an acceptor group. NMR spectroscopy is an excellent tool to probe the degree of conjugation through the azine bridge. The NMR results reported here for nine symmetrical and 18 asymmetrical azines show in a compelling fashion that the hypothesis holds. Varying the donor group does not change the chemical shifts of the aromatic hydrogen and carbon atoms on the acceptor-substituted phenyl ring. Likewise, varying the acceptor group does not change the chemical shifts of the atoms in the donor-substituted phenyl ring.     

Novel canonical coding method for representation of three-dimensional structures

A new canonical coding method for representation of three-dimensional structures, CAST (CAnonical representation of STereochemistry), is described. CAST canonically codes stereochemistry around an atom in a molecule. The same CAST notations are given for atoms of molecules in the same conformation. The CAST code is based on the dihedral angles of four atoms that are uniquely defined by a molecular tree structure. CAST has successfully represented similarities and differences between several conformers.     

Efficient enumeration of stereoisomers of outerplanar chemical graphs using dynamic programming

Exhaustive and nonredundant generation of stereoisomers of a chemical compound with a specified constitution is an important tool for molecular structure elucidation and molecular design. It is known that many chemical compounds have outerplanar graph structures. In this paper we deal with chemical compounds composed of carbon, hydrogen, oxygen, and nitrogen atoms whose graphical structures are outerplanar and consider stereoisomers caused only by asymmetry around carbon atoms. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given outerplanar graph as a graph rooted at its structural center. Our algorithm first recursively computes the number of stereoisomers of the subgraph induced by the descendants of each vertex and then constructs each stereoisomer by backtracking the process of computing the numbers of stereoisomers. Our algorithm correctly counts the number of stereoisomers in O(n) time and space and correctly enumerates all of the stereoisomers in O(n3) time per stereoisomer on average and in O(n) space, where n is the number of atoms in a given structure.     

3D structure determination of the Crh protein from highly ambiguous solid-state NMR restraints

In a wide variety of proteins, insolubility presents a challenge to structural biology, as X-ray crystallography and liquid-state NMR are unsuitable. Indeed, no general approach is available as of today for studying the three-dimensional structures of membrane proteins and protein fibrils. We here demonstrate, at the example of the microcrystalline model protein Crh, how high-resolution 3D structures can be derived from magic-angle spinning solid-state NMR distance restraints for fully labeled protein samples. First, we show that proton-mediated rare-spin correlation spectra, as well as carbon-13 spin diffusion experiments, provide enough short, medium, and long-range structural restraints to obtain high-resolution structures of this 2 x 10.4 kDa dimeric protein. Nevertheless, the large number of 13C/15N spins present in this protein, combined with solid-state NMR line widths of about 0.5-1 ppm, induces substantial ambiguities in resonance assignments, preventing 3D structure determination by using distance restraints uniquely assigned on the basis of their chemical shifts. In the second part, we thus demonstrate that an automated iterative assignment algorithm implemented in a dedicated solid-state NMR version of the program ARIA permits to resolve the majority of ambiguities and to calculate a de novo 3D structure from highly ambiguous solid-state NMR data, using a unique fully labeled protein sample. We present, using distance restraints obtained through the iterative assignment process, as well as dihedral angle restraints predicted from chemical shifts, the 3D structure of the fully labeled Crh dimer refined at a root-mean-square deviation of 1.33 A.     

Structure validation of natural products by quantum-mechanical GIAO calculations of 13C NMR chemical shifts

Geometry optimization and GIAO (gauge including atomic orbitals) (13)C NMR chemical shift calculations at Hartree-Fock level, using the 6-31G(d) basis set, are proposed as a tool to be applied in the structural characterization of new organic compounds, thus providing useful support in the interpretation of experimental NMR data. Parameters related to linear correlation plots of computed versus experimental (13)C NMR chemical shifts for fourteen low-polar natural products, containing 10-20 carbon atoms, were employed to assess the reliability of the proposed structures. A comparison with the hybrid B3LYP method was carried out to evaluate electron correlation contributions to the calculation of (13)C NMR chemical shifts and, eventually, to extend the applicability of such computational methods to the interpretation of NMR spectra in apolar solutions. The method was tested by studying three examples of revised structure assignments, analyzing how the theoretical (13)C chemical shifts of both correct and incorrect structures matched the experimental data.     

The atom assignment problem in automated de novo drug design. 2. A method for molecular graph and fragment perception

Summary If atom assignment onto 3D molecular graphs is to be optimized, an efficient scheme for placement must be developed. The strategy adopted in this paper is to analyze the molecular graphs in terms of cyclical and non-cyclical nodes; the latter are further divided into terminal and non-terminal nodes. Molecular fragments, from a fragments database, are described in a similar way. A canonical numbering scheme for the fragments and the local subgraph of the molecular graph enables fragments to be placed efficiently onto the molecular graph. Further optimization is achieved by placing similar fragments into bins using a hashing scheme based on the canonical numbering. The graph perception algorithm is illustrated in detail.     

CAST/CNMR: highly accurate C NMR chemical shift prediction system considering stereochemistry

Accurate, practical prediction of ¹³C NMR chemical shifts has been achieved with a new system, CAST/CNMR, taking account of stereochemistry. The CAST/CNMR system has solved the critical problem of the accurate distinction of differences and similarities in stereochemical structures around a specific carbon, which has not yet been achieved by any other database-oriented system for prediction of ¹³C NMR chemical shifts. CAST/CNMR uses a three-dimensional structural database together with a ¹³C NMR spectral database. Absolute/relative configurational and conformational structural information are described by the CAST (CAnonical-representation of STereochemistry) coding method. This paper provides an overview of the CAST/CNMR system, and describes its application to two natural products as examples.     

NMR characterisation of structure in solvates and polymorphs of formoterol fumarate

The solid‐state structures of two polymorphs and two alcoholates (ethanol and isopropanol) of formoterol fumarate have been investigated by a combination of NMR techniques. First‐principles shielding computations are combined with NMR data to successfully relate peaks to their crystallographic positions for the solvates, including atoms that are in equivalent molecular positions. The uncharacterised structure of the asolvate form C is found to contain a single formoterol ion and half a fumarate ion in its asymmetric unit. HETCOR experiments for the ethanolate and form C allow proton chemical shifts to be determined and give improved ¹³C resolution for the former compound. Desolvation of the solvates to form C has been monitored under the conditions of the NMR experiment. Differential rates of phenylene ring flipping are observed in the different forms. Carbon‐13 relaxation times and ²H NMR are used to probe dynamics of the fumarate ion. Copyright © 2012 John Wiley & Sons, Ltd.     

Symmetry properties of chemical graphs. IV. Rearrangement of tetragonal-pyramidal complexes

Using a canonical numbering of vertices for the graph corresponding to a particular rearrangement of tetragonal–pyramidal complexes, all 120 permutations defining the symmetry for the rearrangement are derived. An examination of the permutations points to the symmetric group S₅, which has previously been found for isomerizations of trigonal–bipyramidal complexes and in the rearrangement of homotetrahedryl cations.     

Structure and energetics of equiatomic K-Cs and Rb-Cs binary clusters

The basin-hopping algorithm combined with the Gupta many-body potential is used to study the structural and energetic properties of (KCs)(n) and (RbCs)(n) bimetallic clusters with N=2n up to 50 atoms. Each binary structure is compared to those of the pure clusters of the same size. For the cluster size N=28 and for the size range of N=34-50, the introduction of K and Rb atoms in the Cs alkali metal cluster results in new ground state structures different from those of the pure elements. In the size range N>/=38 the binary and pure clusters show not only structural differences, but they also display different magic numbers. Most of the magic Rb-Cs and K-Cs clusters possess highly symmetric structures. They belong to a family of pIh structures, where a fivefold pancake is a dominant structural motif. Such geometries have not been reported for alkali binary clusters so far, but have been found for series of binary transition metal clusters with large size mismatch. Moreover, tendency to phase separation (shell-like segregation) is predicted for both K-Cs and Rb-Cs clusters with up to 1000 atoms. Our finding of a surface segregation in Rb-Cs clusters is different from that of theoretical and experimental studies on bulk Rb-Cs alloys where phase separation does not occur.     

Prevision des spectres de résonance magnétique nucléaire de 13C par intelligence artificielle: le problème de la codificationPrediction of 13C-nuclear magnetic resonance spectra by artificial intelligence: the problem of coding structures

Possible errors in earlier methods of coding structures are discussed, particularly with regard to α- and β-conformation and double bonds. The proposed method of coding is based on the absolute interatomic distances and the relative orientations of atoms. The coding system agrees with previous theoretical equations, except for density matrices; the usual classification of α, β and δ effects is obviously not included. An advantage of the method is that neighbouring atoms which have negligible effect are not included in the coding, so that the number of plausible structures is reduced. Another advantage is that similar structures can be tested, atom by atom, to a level at which complete structural equivalence no longer exists. The program developed on this basis is applicable with personal computers and provides options which enable the theoretical spectrum to be predicted, the signals to be interpreted if the experimental spectrum is known, and the influence of each neighbouring atom on the carbon signal to be studied.     

Festkörper‐NMR‐Untersuchungen an Natriumoxothiophosphaten(V)

Solid State NMR Investigations on Sodium Oxothiophosphates(V) Sodium monothiophosphate(V) Na₃PO₃S is dimorphic. The metastable high temperature modification β‐Na₃PO₃S crystallizes hexagonal with a = 8.996(4) and c = 5.216(2)Å. According to ³¹P solid state NMR experiments, α‐Na₃PO₃S exhibits at 20 °C a non‐axial‐symmetric environment for the phosphorus nuclei in contrast to the results of the refined crystal structure. This discrepancy is discussed assuming ordered and disordered structural models. However, at 490 °C the chemical shift tensor of the phosphorus nuclei in α‐Na₃PO₃S is axial‐symmetric. So, the distortion of the phosphorus environment is abolished by the thermal motion of the atoms. The number of crystallographically distinguishable positions for phosphorus and for sodium in Na₃PO₂S₂ and Na₃POS₃ can be confirmed in good agreement with their crystal structures using solid state NMR spectroscopy.     

Effective consideration of ring structures in CAST/CNMR for highly accurate C NMR chemical shift prediction

A new function that effectively takes into account ring structural environments achieves extensive highly accurate prediction of ¹³C NMR chemical shift in the CAST/CNMR system. The approach adapts a fast and flexible ring perception algorithm and a new CAST coding method for the ring information. ¹³C NMR chemical shift prediction is performed for complicated polycyclic natural products and their synthetic intermediates as the demonstration, which shows the reliability of the function in extending the scope of the practically accurate ¹³C NMR prediction for wide range of organic compounds.     

Hypercarbons in polyhedral structures

Though carbon is mostly tetravalent and tetracoordinated, there are several examples where the coordination number exceeds four. Structural varieties that exhibit hypercarbons in polyhedral structures such as polyhedral carboranes, sandwich complexes, encapsulated polyhedral structures and novel planar aromatic systems with atoms embedded in the middle are reviewed here. The structural variety anticipated with hypercoordinate carbon among carboranes is large as there are many modes of condensation that could lead to large number of new patterns. The relative stabilities of positional isomers of polyhedral carboranes, sandwich structures, and endohedral carboranes are briefly described. The mno rule accounts for the variety of structural patterns. Wheel-shaped and planar hypercoordinated molecules are recent theoretical developments in this area.     

Automated structure elucidation of organic molecules from (13)c NMR spectra using genetic algorithms and neural networks.

The automated structure elucidation of organic molecules from experimentally obtained properties is extended by an entirely new approach. A genetic algorithm is implemented that uses molecular constitution structures as individuals. With this approach, the structure of organic molecules can be optimized to meet experimental criteria, if in addition a fast and accurate method for the prediction of the used physical or chemical features is available. This is demonstrated using (13)C NMR spectrum as readily obtainable information. (13)C NMR chemical shift, intensity, and multiplicity information is available from (13)C NMR DEPT spectra. By means of artificial neural networks a fast and accurate method for calculating the (13)C NMR spectrum of the generated structures exists. The approach is limited by the size of the constitutional space that has to be searched and by the accuracy of the shift prediction for the unknown substance. The method is implemented and tested successfully for organic molecules with up to 20 non-hydrogen atoms.     

锂离子电池电极材料固体核磁共振研究进展

对于研究材料的结构变化和考察原子所处的化学环境，固体核磁共振技术是一种有效的手段。通过⁶Li和⁷Li核磁共振谱的变化，可以清楚地了解锂离子电池电极材料中Li与邻近金属或碳原子的配位情况及在充放电过程中对应于锂离子嵌/脱过程中材料的结构变化，对于研究电极材料的电化学性能有重要的意义。本文综述了固体NMR技术在研究锂离子电池电极材料的结构及嵌锂机理方面的一些进展。