Quality of approximate electron densities and internal consistency of molecular alignment algorithms in molecular quantum similarity

The calculation of molecular quantum similarity measures using the molecular electron density requires the electron density and molecular alignment between two molecules. To obtain meaningful quantum similarity matrices, the electron density should be calculated efficiently and accurately and the alignment should be internally consistent. The internal consistency of the alignment for a series of molecules is investigated through distance geometry concepts. The calculation of the quantum similarity matrix requires the calculation of a quadratic number of similarity integrals, and a scheme to obtain these efficiently is developed. Both the alignment procedure and the ASA method for approximate molecular electron densities are tested for a set of steroid molecules.     

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring.     

Quantum similarity superposition algorithm (QSSA): a consistent scheme for molecular alignment and molecular similarity based on quantum chemistry

The use of the molecular quantum similarity overlap measure for molecular alignment is investigated. A new algorithm is presented, the quantum similarity superposition algorithm (QSSA), expressing the relative positions of two molecules in terms of mutual translation in three Cartesian directions and three Euler angles. The quantum similarity overlap is then used to optimize the mutual positions of the molecules. A comparison is made with TGSA, a topogeometrical approach, and the influence of differences on molecular clustering is discussed.     

X-ray and neutron diffraction studies of the crystal and molecular structure of the predominant monocarboxylic acid obtained by mild acid hydrolysis of cyanocobalamin. Part II. X-ray diffraction studies of wet crystals

The crystal and molecular structure of wet crystals of the O-monocarboxylic acid of cyanocobalamin has been determined. The molecule crystallizes in a monoclinic cell ofa = 14.845,b = 17.435,c = 16.243 A, β = 103.54°, space group P2₁,. Intensity data were collected by diffractometry and the structure solved by Patterson and Fourier methods. Refinement, initially by a least-squares process and latterly by Fourier methods, led to anR of 0.140. Disordered sites were found for the terminal atoms of side chaine; the identification of the acid grouping was not made with certainty. Sites for sixteen water molecules were determined.     

Orientational order of guest molecules in aligned liquid crystal as measured by EPR and UV–vis techniques

Orientational order of guest molecules in aligned liquid crystal 4-cyano-4′-pentylbiphenyl (5CB) is studied via optical dichroism and electron paramagnetic resonance (EPR) spectra measurements. The guest molecules used are bifunctional molecules bearing paramagnetic nitroxide group and photochromic azobenzene moiety. The bifunctional probe with rigidly bonded nitroxide and azobenzene moieties was found to align as a whole, while flexible long spacer between the moieties provides independent alignment for the nitroxide and azobenzene parts. Intermolecular interactions responsible for the alignment of azobenzene and nitroxide moieties of the probe molecules are discussed. The molecules with cis-configuration of azobenzene moiety are able to align in the liquid-crystalline medium, but to a lesser extent than the molecules with trans-configuration. Directions of orientational axes and characteristics of rotational mobility of spin probes are determined. Second, fourth and, in some cases, sixth rank order parameter values are found.     

Alignment of molecules by the Monte Carlo optimization of molecular similarity indices

3D-QSAR uses statistical techniques to correlate calculated structural properties with target properties like biological activity. The comparison of calculated structural properties is dependent upon the relative orientations of molecules in a given data set. Typically molecules are aligned by performing an overlap of common structural units. This “alignment rule” is adequate for a data set, that is closely related structurally, but is far more difficult to apply to either a diverse data set or on the basis of some structural property other than shape, even for sterically similar molecules. In this work we describe a new algorithm for molecular alignment based upon optimization of molecular similarity indices. We show that this Monte Carlo based algorithm is more effective and robust than other optimizers applied previously to the similarity based alignment problem. We show that QSARs derived using the alignments generated by our algorithm are superior to QSARs derived using the more common alignment of fitting of common structural units. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1344–1353, 1997     

X-Ray Diffraction Study of 2-Aminopropenenitrile at 97 K

2-Aminopropenenitrile crystallizes in the space group P2₁2₁2₁ with two molecules in the asymmetric unit. Both molecules show appreciable pyramidalization at the amino group. The crystal structure is built from approximately centrosymmetric dimers stabilized by hydrogen bonding between the amino group of each molecule and the nitrile group of its partner. The dimers are linked into chains by further hydrogen bonds in which the amino group of one molecule acts as donor, the amino group of the other as acceptor. The two types of molecule thus play different roles in the crystal structure. Electron density difference maps for the two independent molecules show characteristic bonding density features. The molecular structure as obtained by the low-temperature X-ray analysis is closely similar to that derived from ab initio molecular orbital calculations and leads to rotational constants close to those obtained from a microwave spectroscopic study.     

Graph-based molecular alignment (GMA)

We describe a combined 2D/3D approach for the superposition of flexible chemical structures, which is based on recent progress in the efficient identification of common subgraphs and a gradient-based torsion space optimization algorithm. The simplicity of the approach is reflected in its generality and computational efficiency: the suggested approach neither requires precalculated statistics on the conformations of the molecules nor does it make simplifying assumptions on the topology of the molecules being compared. Furthermore, graph-based molecular alignment produces alignments that are consistent with the chemistry of the molecules as well as their general structure, as it depends on both the local connectivities between atoms and the overall topology of the molecules. We validate this approach on benchmark sets taken from the literature and show that it leads to good results compared to computationally and algorithmically more involved methods. The results suggest that, for most practical purposes, graph-based molecular alignment is a viable alternative to molecular field alignment with respect to structural superposition and leads to structures of comparable quality in a fraction of the time.     

Second-order quantum similarity measures from intracule and extracule densities

The calculation of quantum similarity measures from second-order density functions contracted to intracule and extracule densities obtained at the Hartree-Fock level is presented and applied to a series of atoms, (He, Li, Be, and Ne), isoelectronic molecules (C₂H₂, HCN, CNH, CO, and N₂), and model hydrogen-transfer processes (H₂/H⁺, H₂/Hot, H₂/H⁻). Second-order quantum similarity measures and indices are found to be suitable measures for quantitatively analyzing electron-pair density reorganizations in atoms, molecules, and chemical processes. For the molecular series, a comparative analysis between the topology of pairwise similarity functions as computed from one-electron, intracule, and extracule densities is carried out and the assignment of each particular local similarity maximum to a molecular alignment discussed. In the comparative study of the three hydrogen-transfer reactions considered, second-order quantum similarity indices are found to be more sensitive than first-order indices for analyzing the electron-density reorganization between the reactant complex and the transition state, thus providing additional insights for a better understanding of the mechanistic aspects of each process. Received: 7 July 1997 / Accepted: 29 October 1997     

Enhanced alignment and orientation of polar molecules by vibrational resonant adiabatic passage

The authors show that polar molecules can be adiabatically aligned and oriented by laser pulses more efficiently when the laser frequencies are vibrationally resonant. The aligned molecules are found in a superposition of vibrational pendular states, each associated with the alignment of the rotor in one vibrational state. The authors construct the dressed potential associated with this mechanism. Values of detunings and field amplitudes are given to optimize the degree of alignment and orientation for the CO molecule.     

Measurement of the field-free alignment of diatomic molecules

An apparatus was constructed to experimentally quantify the field-free alignment of diatomic molecules irradiated by strong femtosecond laser pulses. In this apparatus, both homodyne and pure heterodyne detections were realized. The alignment signal is proportional to [ - 1/3](2) for homodyne detection and ( - 1/3) for pure heterodyne detection, where theta is the polar angle between the molecular axis and the laser polarization direction. Fourier transform spectra of the homodyne signal and the pure heterodyne signal were also studied. By comparing the alignment signal and its Fourier transform spectrum with the numerical calculation of the time-dependent Schr?dinger equation, we demonstrated that the pure heterodyne signal directly reproduced the alignment parameter , and its Fourier transform spectrum provided information regarding the populations of different J states in the rotational wavepacket.     

Similarity measures based on Gaussian-type promolecular electron density models: alignment of small rigid molecules

Various molecular similarity measures (overlap, Coulomb, kinetic, electrostatic energy) and similarity indices (Carbó, Hodgkin-Richards, Kulczynski, Shape Tanimoto) are applied to the superposition of 3D promolecular electron density (PED) distributions. The original aspect of the paper lies in the consideration of smoothed PEDs, which allow to decrease the number of local solutions to a superposition problem, together with the use of the less common kinetic and electrostatic energy similarity measures. Results are obtained for a family of five rigid endothiapepsin ligands that were already considered in previous applications, based on graph representations of their PED. In the present work, it is observed that the use of smoothed PED and the kinetic similarity measure, together with the Kulczynski or Shape Tanimoto index, performed the best to align molecules of different sizes.     

Nonpolar second‐order nonlinear and electrooptic materials: Axially ordered chiral polymers and liquid crystals

This article reviews our work on the development and optimization of chiral, nonpolar media with large second‐order nonlinear optical responses. We show how molecular engineering, theory, and measurements can be used to optimize this promising class of nonlinear optical materials. We describe how supramolecular alignment into easily processable materials takes advantage of the relevant molecular hyperpolarizabilities. A wide variety of techniques can be used to fabricate bulk materials belonging to the chiral nonpolar symmetry groups, D_∞ and D₂. The microscopic chromophore alignment schemes that optimize the nonlinear optical response in such materials are deduced from general symmetry considerations for both molecules and bulk. We also speculate on the possible applications of such materials as image‐plane modulators. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2744–2754, 2003     

Computational methods for the structural alignment of molecules

In drug design, often enough, no structural information on a particular receptor protein is available. However, frequently a considerable number of different ligands is known together with their measured binding affinities towards a receptor under consideration. In such a situation, a set of plausible relative superpositions of different ligands, hopefully approximating their putative binding geometry, is usually the method of choice for preparing data for the subsequent application of 3D methods that analyze the similarity or diversity of the ligands. Examples are 3D-QSAR studies, pharmacophore elucidation, and receptor modeling. An aggravating fact is that ligands are usually quite flexible and a rigorous analysis has to incorporate molecular flexibility. We review the past six years of scientific publishing on molecular superposition. Our focus lies on automatic procedures to be performed on arbitrary molecular structures. Methodical aspects are our main concern here. Accordingly, plain application studies with few methodical elements are omitted in this presentation. While this review cannot mention every contribution to this actively developing field, we intend to provide pointers to the recent literature providing important contributions to computational methods for the structural alignment of molecules. Finally we provide a perspective on how superposition methods can effectively be used for the purpose of virtual database screening. In our opinion it is the ultimate goal to detect analogues in structure databases of nontrivial size in order to narrow down the search space for subsequent experiments.     

Toward similarity measures for macromolecular bodies: Medla test calculations for substituted benzene systems

A new method is proposed for the evaluation of numerical similarity measures for large molecules, defined in terms of their electron density (ED) distributions. The technique is based on the Molecular Electron Density Lego Assembler (MEDLA) approach, proposed earlier for the generation of ab initio quality electron densities for proteins and other macromolecules. The reliability of the approach is tested using a family of 13 substituted aromatic systems for which both standard ab initio electron density computations and the MEDLA technique are applicable. These tests also provide additional examples for evaluating the accuracy of the MEDLA technique. Electron densities for a series of 13 substituted benzenes were calculated using the standard ab initio method with STO-3G, 3-21G, and 6-31G** basis sets as well as the MEDLA approach with a 6-31G** database of electron density fragments. For each type of calculation, pairwise similarity measures of these compounds were calculated using a point-by-point numerical comparison of the EDs. From these results, 2D similarity maps were constructed, serving as an aid for quick visual comparisons for the entire molecular family. The MEDLA approach is shown to give virtually equivalent numerical similarity measures and similarity maps as the standard ab initio method using a 6-31G** basis set. By contrast, significant differences are found between the standard ab initio 6-31G** results and the standard ab initio results obtained with smaller STO-3G and 3-21G basis sets. These tests indicate that the MEDLA-based similarity measures faithfully mimic the actual, standard ab initio 6-31G** similarity measures, suggesting the MEDLA method as a reliable technique to assess the shape similarities of proteins and other macromolecules. The speed of the MEDLA computations allows rapid, pairwise comparisons of the actual EDs for a series of molecules, requiring no more computer time than other simplified, less detailed representations of molecular shape. The MEDLA method also reduces the need to store large volumes of numerical density data on disk, as these densities can be quickly recomputed when needed. For these reasons, the proposed MEDLA similarity analysis technique is likely to become a useful tool in computational drug design. © 1995 John Wiley & Sons, Inc.     

Chemical bonding descriptors based on electron density inhomogeneity measure: a comparison with ELI-D

The electron localizability indicator (ELI-D) is suitable to describe certain aspects of the bonding situation of molecules and solids. ELI-D is based on integrals of electron pair density over very small regions. Recently proposed functional C _p , derived from the electron population in regions of fixed amount of electron density inhomogeneity, is based on the same approach as ELI-D, that is, ω-restricted space partitioning. The electron density inhomogeneity is given by the distance of electron density values to the averaged density within chosen region. Thus, in contrast to ELI-D, C _p is a single-electron property. The distance measure depends on a parameter that can be optimized in such way that C _p mimics the topology of the ELI-D distribution for atoms. Such an optimization was performed for the atoms Li to Xe. The optimal parameter p = 0.6 yields the functional C _0.6 that was exemplary applied to a few chosen molecules. In case of molecules the topology of the inner shell and lone-pair regions as given by C _0.6 is comparable with that of the ELI-D representation. However, in the bonding region between the atoms the topology of C _0.6 is dominated by the low density gradient close to the bond critical point. This may result in rather different topologies when comparing C _0.6 and ELI-D.     

Looking at orbitals in the laboratory: The experimental investigation of molecular wavefunctions and binding energies by electron momentum spectroscopy

The experimental technique of electron momentum spectroscopy (EMS ) (i.e., binary (e, 2e) spectroscopy) is discussed together with typical examples of its applications over the past decade in the area of experimental quantum chemistry. Results interpreted within the framework of the plane wave impulse and the target Hartree—Fock approximations provide direct measurements of, spherically averaged, orbital electron momentum distributions. Results for a variety of atoms and small molecules are compared with calculations using a range of Fourier transformed SCF position space wavefunctions of varying sophistication. Measured momentum distributions (MD ) provide a “direct” view of orbitals. In addition to offering a sensitive experimental diagnostic for semiempirical molecular wavefunctions, the MD's provide a chemically significant, additional experimental constraint to the usual variational optimization of wavefunctions. The measured MD's clearly reflect well known characteristics of various chemical and physical properties. It appears that EMS and momentum space chemistry offer the promise of supplementary perspectives and new vistas in quantum chemistry, as suggested by Coulson more than 40 years ago. Binding energy spectra in the inner valence region reveal, in many cases, a major breakdown of the simple MO model for ionization in accord with the predictions of many-body calculations. Results are considered for atomic targets, including H and the noble gases. The measured momentum distribution for H₂ is also compared with results from Compton scattering. Results for H₂ and H are combined to provide a direct experimental assessment of the bond density in H₂, which is compared with calculations. The behavior of the outer valence MD ''s for small row two and row three hydride molecules such as H₂O and H₂S, NH₃, HF, and HCl are consistent with well known differences in chemical and physical behavior such as ligand-donor activity and hydrogen bonding. MD measurements for the outermost valence orbitals of HF, H₂O and NH₃ show significant differences from those calculated using even very high-quality wavefunctions. Measurements of MD's for outer σ_g orbitals of small polyatomic molecules such as CO₂, COS, CS₂, and CF₄ show clear evidence of mixed s and p character. It is apparent that EMS is a sensitive probe of details of electronic structure and electron motion in atoms and molecules.     

Improved 3D-QSAR prediction by multiple-conformational alignment: A case study on PTP1B inhibitors

Three-dimension quantitative structure activity relationship (3D-QSAR) was one of the major statistical techniques to investigate the correlation of biological activity with structural properties of candidate molecules, and the accuracy of statistic greatly depended on molecular alignment methodology. Exhaustive conformational search and successful conformational superposition could extremely improve the predictive accuracy of QSAR modeling. In this work, we proposed a solution to optimize QSAR prediction by multiple-conformational alignment methods, with a set of 40 flexible PTP1B inhibitors as case study. Three different molecular alignment methods were used for the development of 3D-QSAR models listed as following: (1) docking-based alignment (DBA); (2) pharmacophore-based alignment (PBA) and (3) co-crystallized conformer-based alignment (CCBA). Among these three alignments, it was indicated that the CCBA was the best and the fastest strategy in 3D-QSAR development, with the square correlation coefficient (r²) and cross-validated squared correlation coefficient (q²) of comparative molecular field analysis (CoMFA) were 0.992 and 0.694; the r² and q² of comparative molecular similarity indices analysis (CoMSIA) were 0.972 and 0.603, respectively. The alignment methodologies used here not only generated a robust QSAR model with useful molecular field contour maps for designing novel PTP1B inhibitors, but also provided a solution for constructing accurate 3D-QSAR model for various disease targets. Undoubtedly, such attempt in QSAR analysis would greatly help us to understand essential structural features of inhibitors required by its target, and so as to discover more promising chemical derivatives.     

ELECT++: Faster conformational search method for docking flexible molecules using molecular similarity

We have developed a program, ELECT++ (Effective LEssening of Conformations by Template molecules in C++), to speed up the conformational search for small flexible molecules using the similar property principle. We apply this principle to molecular shape and, importantly, to molecular flexibility. After molecules in a database are clustered according to flexibility and shape (FCLUST++), additional reagents are generated to screen the conformational space of molecules in each cluster (TEMPLATE++). We call these representative reagents of each cluster template reagents. Template reagents and clustered reagents produce, after reaction, template molecules and clustered molecules, respectively (tREACT++). The conformations of a template molecule are searched in the context of a macromolecular target. Acceptable conformational choices are then applied to all molecules in its cluster, thus effectively biasing conformational space to speed up conformational searches (tSEARCH++). In our incremental search method, it is necessary to calculate the root-mean-square deviations (RMSD) matrix of distances between different conformations of the same molecule to reduce the number of conformations. Instead of calculating the RMSD matrix for all molecules in a cluster, the RMSD matrix of a template molecule is chosen as a reference and applied to all the molecules in its cluster. We demonstrate that FCLUST++ clusters the primary amine reagents from the Available Chemicals Directory (ACD) successfully. The program tSEARCH++ was applied to dihydrofolate reductase with virtual molecules generated by tREACT++ using clustered primary amine reagents. The conformational search by the program tSEARCH++ was about 4.8 times faster than by SEARCH++, with an acceptable range of errors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1834–1852, 1998