Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.     

Searching for conformers of nine- to twelve-ring hydrocarbons on the MM2 and MM3 energy surfaces: Stochastic search for interconversion pathways

The stochastic search method was employed to find as many conformers on the MM2 and MM3 energy surfaces as possible for cyclic saturated hydrocarbons with ring sizes from 9 through 12. The number found was 8 MM2 (8 MM3) for 9 rings, 18 MM2 (16 MM3) for 10 rings, 40 MM2 (29 MM3) for 11 rings, and 111 MM2 (90 MM3) for 12 rings. A measure of similarity between pairs of conformers of a compound, called conformational distance, is described. It was used to correlate similar MM2 and MM3 conformers. It was discovered that some conformers on each energy surface are not close to minima on the other surface in rings larger than 9. On refinement with the other optimizer, they changed considerably—going downhill to other previously found minima on the other energy surface or (in a few cases) going to minima which had not been found by direct searches. Conformational distance was also employed as an indication of which pairs of MM2 (or MM3) conformers are likely to interconvert rapidly. A new stochastic procedure of using small kicks was used to search for the most likely interconversion processes among the conformers. There is fairly good agreement between the most facile pathways located by it and unusually short conformational distances. Several additional 12-ring conformers (not found with previous methods) were located through application of this small kick procedure.     

CAESAR: a new conformer generation algorithm based on recursive buildup and local rotational symmetry consideration

A highly efficient conformer search algorithm based on a divide-and-conquer and recursive conformer build-up approach is presented in this paper. This approach is combined with consideration of local rotational symmetry so that conformer duplicates due to topological symmetry in the systematic search can be efficiently eliminated. This new algorithm, termed CAESAR (Conformer Algorithm based on Energy Screening and Recursive Buildup), has been implemented in Discovery Studio 1.7 as part of the Catalyst Component Collection. CAESAR has been validated by comparing the conformer models generated by the new method and Catalyst/FAST. CAESAR is consistently 5-20 times faster than Catalyst/FAST for all data sets investigated. The speedup is even more dramatic for molecules with high topological symmetry or for molecules that require a large number of conformers to be sampled. The quality of the conformer models generated by CAESAR has been validated by assessing the ability to reproduce the receptor-bound X-ray conformation of ligands extracted for the Protein Data Bank (PDB) and assessing the ability to adequately cover the pharmacophore space. It is shown that CAESAR is able to reproduce the receptor-bound conformation slightly better than the Catalyst/FAST method for a data set of 918 ligands retrieved from the PDB. In addition, it is shown that CEASAR covers the pharmacophore space as well or better than Catalyst/FAST.     

Gas Phase Conformations of Tetrapeptide Glycine-Phenylalanine-Glycine-Glycine

Systematic search of the potential energy surface of tetrapeptide glycine-phenylalanine-glycine-glycine (GFGG) in gas phase is conducted by a combination of PM3, HF and BHandHLYP methods. The conformational search method is described in detail. The rela-tive electronic energies, zero point vibrational energies, dipole moments, rotational constants, vertical ionization energies and the temperature dependent conformational distributions for a number of important conformers are obtained. The structural characteristics of these conformers are analyzed and it is found that the entropic effect is a dominating factor in determining the relative stabilities of the conformers. The measurements of dipole moments and some characteristic IR mode are shown to be effective approaches to verify the theoreti-cal prediction. The structures of the low energy GFGG conformers are also analyzed in their connection with the secondary structures of proteins. Similarity between the local structures of low energy GFGG conformers and the α-helix is discussed and many β- and γ-turn local structures in GFGG conformers are found.     

Conformational analysis of arginine in gas phase--a strategy for scanning the potential energy surface effectively

The determination of all possible low-lying energy conformers of flexible molecules is of fundamental interest for various applications. It necessitates a reliable conformational search that is able to detect all important minimum structures and calculates the energies on an adequate level of theory. This work presents a strategy to identify low-energy conformers using arginine as an example by means of a force-field based conformational search in combination with high-level geometry optimizations (RI-MP2/TZVPP+). The methods used for various stages in the conformational search strategy are shown and various pitfalls are discussed. We can show that electronic energies calculated on a DFT level of theory with standard exchange-correlation functionals strongly underestimate the intramolecular stabilization resulting from stacked orientations of the guanidine and carbonyl moiety of arginine due to the deficiency of DFT to describe dispersion effects. In this case by usage of electron correlation methods, low energy conformers comprising stacked arrangements that are counterintuitive become favorable.     

Poling: Promoting conformational variation

This article introduces several methods of assessing the extent to which a collection of conformations represents or covers conformational space. It also describes poling: a novel technique for promoting conformational variation that can be applied to any method of conformational analysis that locally minimizes a penalty or energy function. The function being minimized is modified to force similar conformers away from each other. The method is independent of the origin of the initial conformers and of the particular minimization method used. It is found that, with the modification of the penalty function, clustering of the resulting conformers is generally unnecessary because the conformers are forced to be dissimilar. The functional form of the poling function is presented, and the merits are discussed with reference to (1) efficacy at promoting variation and (2) perturbation of the unmodified function. Results will be presented using conformers obtained from distance geometry with and without poling. It will be shown that the addition of poling eliminates much redundancy in conformer generation and improves the coverage of the conformational space. © 1995 by John Wiley & Sons, Inc.     

Inhibitors of prolyl endopeptidase: Characterization of the pharmacophoric pattern using conformational analysis and 3D-QSAR

Summary A structure-activity study has been carried out on several compounds known as inhibitors of the serine protease prolyl endopeptidase. Conformational analysis has been done using different molecular mechanics methods such as molecular dynamics, or a randomized conformational search method. The conformers obtained were classified using geometric and energetic criteria. A pattern recognition analysis was done in order to divide conformers according to families. The resulting dominant families, for all compounds investigated, showed very similar geometric features. Based on the lowest energy conformers obtained after randomized conformational analysis, a 3D-QSAR model was established using the CoMFA approach. The validity of this model was verified by prediciting correctly the activity of other molecules not used in the construction of this model.     

A Robust and Cost-Efficient Scheme for Accurate Conformational Energies of Organic Molecules

Several standard semiempirical methods as well as the MMFF94 force field approximation have been tested in reproducing 8 DLPNO-CCSD(T)/cc-pVTZ level conformational energies and spatial structures for 37 organic molecules representing pharmaceuticals, drugs, catalysts, synthetic precursors, industry-related chemicals (37conf8 database). All contemporary semiempirical methods surpass their standard counterparts resulting in more reliable conformational energies and spatial structures, even though at significantly higher computational costs. However, even these methods show unexpected failures in reproducing energy differences between several conformers of the crown ether 1,4,7,10,13,16-hexaoxacyclooctadecane (18-crown-6). Inexpensive force field MMFF94 approximation groups with contemporary semiempirical methods in reproducing the correct order of conformational energies and spatial structures, although the performance in predicting absolute conformational energies compares to standard semiempirical methods. Based on these findings, we suggest a two-step strategy for reliable yet feasible conformational search and sampling in realistic-size flexible organic molecules: i) geometry optimization/preselection of relevant conformers using the MMFF94 force field; ii) single-point energy evaluations using a contemporary semiempirical method. We expect that developed database 37conf8 is going to be useful for development of semiempirical methods.     

A comparison of a direct search method and a genetic algorithm for conformational searching

We present results from the application of two conformational searching methods: genetic algorithms (GA) and direct search methods for finding low energy conformations of organic molecules. GAs are in a class of biologically motivated optimization methods that evolve a population of individuals in which individuals who are more “fit” have a higher probability of surviving into subsequent generations. The parallel direct search method (PDS) is a type of pattern search method that uses an adaptive grid to search for minima. Both methods found energies equal to or lower than the energy of the relaxed crystal structure in all cases, at a relatively small cost in CPU time. We suggest that either method would be a good candidate to find 3-D conformations in a large scale screening application. © 1996 by John Wiley & Sons, Inc.     

THEORETICAL APPROACHES TO PROTEIN STRUCTURE-FUNCTION ANALYSIS (Ⅰ)——DIRECTED PERTURBATION CONFORMATIONAL ANALYSIS

A new computational technique called directed perturbation conformational analysis has been developed for use in protein model building and structure-function studies. Designed to perform an efficient local search of a macromolecular potential energy surface, the algorithm can be used to locate multiple energy minimum conformers via low energy transition state structures from a single starting or trial structure. The algorithm contains developments to stabilize transition state optimizations for systems described by many degrees of freedom displaying anharmonic potential energy surfaces. It has been found to be efficient in the generation of alternative equilibrium structures from a given trial structure when compared with those generated from a standard molecular dynamics simulation of N-acetyl, N'-methyl-deca-L-alaninamide.     

Self-consistent combination of the three-dimensional RISM theory of molecular solvation with analytical gradients and the Amsterdam density functional package

The three-dimensional reference interaction site model with the closure relation by Kovalenko and Hirata (3D-RISM-KH) in combination with the density functional theory (DFT) method has been implemented in the Amsterdam density functional (ADF) software package. The analytical first derivatives of the free energy with respect to displacements of the solute nuclear coordinates have also been developed. This enables study of chemical reactions, including reaction coordinates and transition state search, with the molecular solvation described from the first principles. The method yields all of the features available by using other solvation approaches, for instance infrared spectra of solvated molecules. To evaluate the accuracy of the present method, test calculations have been carried out for a number of small molecules, including four glycine conformers, a set of small organic compounds, and carbon nanotubes of various lengths in aqueous solution. Our predictions for the solvation free energy agree well with other approaches as well as experiment. This new development makes it possible to calculate at modest computational cost the electronic properties and molecular solvation structure of a solute molecule in a given molecular liquid or mixture from the first principles.     

A theoretical investigation of the low energy conformers of the isomers glycine and methylcarbamic acid and their role in the interstellar medium

We have theoretically investigated the low energy conformers of neutral glycine (NH(2)CH(2)COOH) and its isomer methylcarbamic acid (CH(3)NHCOOH) in the gas phase. A total of 16 different levels of the theory, including CCSD(T), MP2 and B3LYP methods with various Pople and Dunning type basis sets with and without polarization and diffuse functions were used. We found eight low energy glycine conformers, where the heavy atoms in three have a planar backbone, and four low energy methylcarbamic acid conformers all with non-planar backbones. Interestingly at all levels of theory, we found that the most stable methylcarbamic acid conformer is significantly lower in energy than the lowest energy glycine conformer. The MP2 level and single point CCSD(T) calculations show the lowest energy methylcarbamic acid conformer to be between 31 to 37 kJ mol(-1) lower in energy than the lowest energy glycine conformer. These calculations suggest that methylcarbamic acid might serve as a precursor to glycine formation in the Interstellar Medium (ISM). We also report the theoretical harmonic vibrational frequencies, infrared intensities, moment of inertia, rotational constants and dipole moments for all of the conformers. In order to understand how glycine or methylcarbamic acid might be formed in the ISM, larger calculations which model glycine or its isomer interacting with several surrounding molecules, such as water, are needed. We demonstrate that B3LYP method should provide a reliable and computationally practical approach to modeling these larger systems.     

Conformational analysis and flexibility of carbohydrates using the CICADA approach with MM3

The potential energy hypersurfaces (PES) of several carbohydrate molecules were studied with a new algorithm for conformational searches, CICADA (Channels in Conformational Space Analyzed by Driver Approach) interfaced with the molecular mechanics program MM3(92). The method requires (1) one or a few low-energy conformations as starting points; and (2) designation of the torsion angles important for understanding the conformational behavior of the molecule. The PES is explored by driving separately each selected torsion angle (in both directions) with a concomitant full-geometry optimization at each increment (except for the driven angle). When a minimum has been detected, the molecule is freely optimized, and the minima so detected are then stored if not encountered previously. The new minima serve as starting structures for further explorations. The results from CICADA permit prediction of relative and absolute flexibility and conformational softness for both the entire molecule as well as for individual group rotations and local minima. The carbohydrates analyzed were Me-α-D -glucopyranoside, β-D -GlcNAc(1-2)α-D -Man, and α-D -GalNAc(1-3)[α-L -Fuc(1-2)]Gal-O-Me. All the low-energy conformers along with the transition states and flexibilities features were characterized. CICADA found all minima and low-energy conversion pathways for the disaccharide that were found by a traditional grid search. In contrast to the grid search method, CICADA concentrates mostly on the exploration of the low-energy regions of the PES, thereby saving a significant amount of computational time. The performance of the method opens new routes for exploring conformational space of larger molecules, such as oligosaccharides. © 1995 by John Wiley & Sons, Inc.     

Experimental IR and Raman spectra and quantum chemical studies of molecular structures, conformers and vibrational characteristics of nicotinic acid and its N-oxide

FTIR and Raman spectra of nicotinic acid and its N-oxide have been recorded and analyzed. The stabilities, optimized molecular geometries, APT charges and vibrational characteristics for the two possible conformers of nicotinic acid and its N-oxide have been computed using DFT method. The E (trans) conformers of both the molecules are found to be more stable and less polar than their respective Z (cis) conformers. Due to addition of an O atom at the N1 site in nicotinic acid the magnitudes of atomic charges on all the H atomic sites of the nicotinic acid N-oxide molecule are found to increase. Most of the vibrational frequencies have nearly the same magnitude for the two conformers of both the molecules. However, significant changes are noticed in their IR intensities, Raman activities and depolarization ratios of the Raman bands. The calculated frequencies have been correlated with the experimental frequencies.     

Accurate predictions of water cluster formation, (H₂O)(n=2-10)

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2-10 water molecules. This approach reveals new low energy conformers for (H(2)O)(n=7,9,10). The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.     

A fast and efficient method to generate biologically relevant conformations

Summary Mutual binding between a ligand of low molecular weight and its macromolecular receptor demands structural complementarity of both species at the recognition site. To predict binding properties of new molecules before synthesis, information about possible conformations of drug molecules at the active site is required, especially if the 3D structure of the receptor is not known. The statistical analysis of small-molecule crystal data allows one to elucidate conformational preferences of molecular fragments and accordingly to compile libraries of putative ligand conformations. A comparison of geometries adopted by corresponding fragments in ligands bound to proteins shows similar distributions in conformation space. We have developed an automatic procedure that generates different conformers of a given ligand. The entire molecule is decomposed into its individual ring and open-chain torsional fragments, each used in a variety of favorable conformations. The latter ones are produced according to the library information about conformational preferences. During this building process, an extensive energy ranking is applied. Conformers ranked as energetically favorable are subjected to an optimization in torsion angle space. During minimization, unfavorable van der Waals interactions are removed while keeping the open-chain torsion angles as close as possible to the experimentally most frequently observed values. In order to assess how well the generated conformers map conformation space, a comparison with experimental data has been performed. This comparison gives some confidence in the efficiency and completeness of this approach. For some ligands that had been structurally characterized by protein crystallography, the program was used to generate sets of some 10 to 100 conformers. Among these, geometries are found that fall convincingly close to the conformations actually adopted by these ligands at the binding site.     

On the conformation of the propranolol molecule

The structure of the propranolol molecule has been optimized within the AM1 and PM3 semiempirical framework followed by ab initio HF/6-31G^* refinement. On each calculation level the conformational space was sampled to search for the lowest-energy conformer(s) from among a few hundreds of conformers at the semiempirical step and next from among a few dozens of conformers at the ab initio level. Finally, five stable conformers were found; each stabilized by one or two of the three possible hydrogen bonds. The geometrical and electronic parameters were established and found to differ only slightly in the structures with the hydrogen bond either present or not.     

A complementary mobile phase approach based on the peak count concept oriented to the full resolution of complex mixtures

Situations of minimal resolution are often found in liquid chromatography, when samples that contain a large number of compounds, or highly similar in terms of structure and/or polarity, are analysed. This makes full resolution with a single separation condition (e.g., mobile phase, gradient or column) unfeasible. In this work, the optimisation of the resolution of such samples in reversed-phase liquid chromatography is approached using two or more isocratic mobile phases with a complementary resolution behaviour (complementary mobile phases, CMPs). Each mobile phase is dedicated to the separation of a group of compounds. The CMPs are selected in such a way that, when the separation is considered globally, all the compounds in the sample are satisfactorily resolved. The search of optimal CMPs can be carried out through a comprehensive examination of the mobile phases in a selected domain. The computation time of this search has been reported to be substantially reduced by application of a genetic algorithm with local search (LOGA). A much simpler approach is here described, which is accessible to non-experts in programming, and offers solutions of the same quality as LOGA, with a similar computation time. The approach makes a sequential search of CMPs based on the peak count concept, which is the number of peaks exceeding a pre-established resolution threshold. The new approach is described using as test sample a mixture of 30 probe compounds, 23 of them with an ionisable character, and the pH and organic solvent contents as experimental factors.     

Atomic Level Characterization Based on Focus Modulation Electron Microscopy

Defocus image modulation processing and three-dimensional Fourier filtering methods are compared from the viewpoint of application to high-resolution phase transmission electron microscopy. Both methods can successfully correct the spherical aberration in TEM by image processing using through-focus images resulting in resolution improvement from the Scherzer resolution limit to the information limit. Comparing the processed images demonstrates that the potential to determine localized atomic structures between the two methods is at the same level when the sample thickness is thin. However, the achieved signal-to-noise ratio is better in images processed by the three-dimensional Fourier filtering method because the filtering process in Fourier space effectively reduces quantum noises involved in the original images. Spherical aberration-free phase observation by the latter method clearly shows the existence of individual gadolinium atoms in C₈₂ molecules encapsulated in single wall carbon nanotubes. It is demonstrated that the three-dimensional Fourier filtering method works effectively for atomic level characterization even when a sample consisting of light atoms is observed under the condition of a low electron dose.     

How Accurate Are Approximate Methods for Evaluating Partition Functions for Hindered Internal Rotations?

The accuracy of several low-cost methods (harmonic oscillator approximation, CT-Comega, SR-TDPPI-HS, and TDPPI-HS) for calculating one-dimensional hindered rotor (1D-HR) partition functions is assessed for a test set of 644 rotations in 104 organic molecules, using full torsional eigenvalue summation (TES) as a benchmark. For methods requiring full rotational potentials, the effect of the resolution at which the rotational potential was calculated was also assessed. Although lower-cost methods such as Pitzer's Tables are appropriate when potentials can be adequately described by simple cosine curves, these were found to show large errors (as much as 3 orders of magnitude) for non-cosine curve potentials. In those cases, it is found that the TDPPI-HS method in conjunction with a potential compiled at a resolution of 60 degrees offers the best compromise between accuracy and computational expense. It can reproduce the benchmark values of the partition functions for an individual mode to within a factor of 2; its average error is just of a factor of 1.08. The corresponding error in the overall internal rotational partition functions of the molecules studied is less than a factor of 4 in all cases. Excellent cost-effective performance is also offered by CT-Comega, which requires only the geometries, energies, and frequencies of the distinguishable minima in the potential. With this method the geometric mean error in individual partition functions is 1.14, the maximum error is a modest 2.98 and the resulting error in the total 1D-HR partition function of a molecule is less than a factor of 5 in all cases.