Low-frequency Raman spectrum and asymmetric potential function for internal rotation of gaseous n-butane

Conformational energies of reference organic molecules: benchmarking of common efficient computational methods against coupled cluster theory

We selected 145 reference organic molecules that include model fragments used in computer-aided drug design. We calculated 158 conformational energies and barriers using force fields, with wide applicability in commercial and free softwares and extensive application on the calculation of conformational energies of organic molecules, e.g. the UFF and DREIDING force fields, the Allinger's force fields MM3-96, MM3-00, MM4-8, the MM2-91 clones MMX and MM+, the MMFF94 force field, MM4, ab initio Hartree-Fock (HF) theory with different basis sets, the standard density functional theory B3LYP, the second-order post-HF MP2 theory and the Domain-based Local Pair Natural Orbital Coupled Cluster DLPNO-CCSD(T) theory, with the latter used for accurate reference values. The data set of the organic molecules includes hydrocarbons, haloalkanes, conjugated compounds, and oxygen-, nitrogen-, phosphorus- and sulphur-containing compounds. We reviewed in detail the conformational aspects of these model organic molecules providing the current understanding of the steric and electronic factors that determine the stability of low energy conformers and the literature including previous experimental observations and calculated findings. While progress on the computer hardware allows the calculations of thousands of conformations for later use in drug design projects, this study is an update from previous classical studies that used, as reference values, experimental ones using a variety of methods and different environments. The lowest mean error against the DLPNO-CCSD(T) reference was calculated for MP2 (0.35 kcal mol-1), followed by B3LYP (0.69 kcal mol-1) and the HF theories (0.81-1.0 kcal mol-1). As regards the force fields, the lowest errors were observed for the Allinger's force fields MM3-00 (1.28 kcal mol-1), ΜΜ3-96 (1.40 kcal mol-1) and the Halgren's MMFF94 force field (1.30 kcal mol-1) and then for the MM2-91 clones MMX (1.77 kcal mol-1) and MM+ (2.01 kcal mol-1) and MM4 (2.05 kcal mol-1). The DREIDING (3.63 kcal mol-1) and UFF (3.77 kcal mol-1) force fields have the lowest performance. These model organic molecules we used are often present as fragments in drug-like molecules. The values calculated using DLPNO-CCSD(T) make up a valuable data set for further comparisons and for improved force field parameterization.

Multi-slit-type interference in carbon 2s photoionization of polyatomic molecules: from a fundamental effect to structural parameters

In molecular photoemission, the analogue of the celebrated Young's double slit experiment is coherent electron emission from two equivalent atomic centers, giving rise to an interference pattern. Here multi-slit interference is investigated in inner-valence photoionization of propane, n-butane, isobutane and methyl peroxide. A more complex pattern is observed due to molecular orbital delocalization in polyatomic molecules, blurring the distinction between interference and diffraction. The potential to extract geometrical information is emphasized, as a more powerful extension of the EXAFS technique. Accurate reproduction of experimental features is obtained by simulations at the static Density Functional Theory level.

Isomerization kinetics of flexible molecules in the gas phase: Atomistic versus coarse-grained sampling

Isomerization kinetics of molecules in the gas phase naturally falls on the microcanonical ensemble of statistical mechanics, which for small systems might significantly differ from the more traditional canonical ensemble. In this work, we explore the examples of cis-trans isomerization in butane and bibenzyl and to what extent the fully atomistic rate constants in isolated molecules can be reproduced by coarse-graining the system into a lower dimensional potential of mean force (PMF) along a reaction coordinate of interest, the orthogonal degrees of freedom acting as a canonical bath in a Langevin description. Time independent microcanonical rate constants can be properly defined from appropriate state residence time correlation functions; however, the resulting rate constants acquire some time dependence upon canonical averaging of initial conditions. Stationary rate constants are recovered once the molecule is placed into a real condensed environment pertaining to the canonical ensemble. The effective one-dimensional kinetics along the PMF, based on appropriately chosen inertia and damping parameters, quantitatively reproduces the atomistic rate constants at short times but deviates systematically over long times owing to the neglect of some couplings between the system and the bath that are all intrinsically present in the atomistic treatment. In bibenzyl, where stronger temperature effects are noted than in butane, the effective Langevin dynamics along the PMF still performs well at short times, indicating the potential interest of this extremely simplified approach for sampling high-dimensional energy surfaces and evaluating reaction rate constants.

Optimization of the GAFF force field to describe liquid crystal molecules: the path to a dramatic improvement in transition temperature predictions

Systematic optimization of the General Amber Force Field (GAFF) for mesogenic fragments leads to a dramatic improvement in the modelling of liquid crystal clearing points.

Conformational problem of alkanes in liquid crystals by NMR spectroscopy: a mini-review

Recent discoveries of the role of alkane flexibility in determining liquid-crystal behaviour are surveyed. With the impetus for understanding the alkane conformational problem established, recent model dependent (1)H NMR work on the topic will be reviewed where progress is made but the need to circumvent models eventually becomes evident. A closer look at the rigid basic units of alkanes will provide the way forward where it is shown that the orientational ordering and anisotropic potentials of these molecules dissolved in liquid crystals scale with each other. Once this relationship is established, a series of works using anisotropic and isotropic (1)H NMR spectroscopy to study alkane conformational statistics will be covered, wherein the influence of the gas, isotropic condensed and anisotropic condensed phases will be described.

(1) H NMR spectral analysis and conformational behavior of n-alkanes in different chemical environments

Alkyl chains are common structural units, for example in lipids, and their (1) H NMR spectral parameters offer valuable information about their conformational behavior in solvent environment. Even the spectra of short n-alkanes are complex, which is obviously a reason why their accurate spectral analyses have not been reported before. The present study reports the quantum mechanical analysis of (1) H NMR spectra of n-butane, n-pentane, n-hexane, and n-heptane. The spectral parameters were used to characterize the conformational behavior of n-alkanes. The temperature dependence analysis of coupling constants suggests that the enthalpy difference between the gauche (g) and trans (t) conformations (ΔH(g) ) of n-butane in chloroform is 2.55-2.85 kJ mol(-1) . The difference between the trans-gauche (tg) and all-trans (tt) conformers of n-pentane (ΔH(tg) ) seems to be 0.1-0.2 kJ mol(-1) higher. The coupling constant information shows that the t(n) conformations become more favored with longer chains, although not only for energetic reasons but also partly because the g(+) g(-) arrangements become sterically unfavorable, which decreases the number of favorable g(n) -type conformations. The analysis of the (1) H NMR spectra of n-pentane and n-hexane in solvents representing different chemical environments indicates that polar and spherical dimethyl sulfoxide favors clearly the g conformations, whereas n-hexane-d(14) favors slightly the extended t(n) conformation. In addition to the intrinsic scientific importance for NMR spectral parameter prediction and molecular modeling in solution, the results provide some insights to behavior of hydrocarbon chains and their spectra in different chemical environments.

Benchmarking Experimental and Computational Thermochemical Data: A Case Study of the Butane Conformers

Due to its crucial importance, numerous studies have been conducted to determine the enthalpy difference between the conformers of butane. However, it is shown here that the most reliable experimental values are biased due to the statistical model utilized during the evaluation of the raw experimental data. In this study, using the appropriate statistical model, both the experimental expectation values and the associated uncertainties are revised. For the 133-196 and 223-297 K temperature ranges, 668 ± 20 and 653 ± 125 cal mol(-1), respectively, are recommended as reference values. Furthermore, to show that present-day quantum chemistry is a favorable alternative to experimental techniques in the determination of enthalpy differences of conformers, a focal-point analysis, based on coupled-cluster electronic structure computations, has been performed that included contributions of up to perturbative quadruple excitations as well as small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. For the 133-196 and 223-297 K temperature ranges, in exceptional agreement with the corresponding revised experimental data, our computations yielded 668 ± 3 and 650 ± 6 cal mol(-1), respectively. The most reliable enthalpy difference values for 0 and 298.15 K are also provided by the computational approach, 680.9 ± 2.5 and 647.4 ± 7.0 cal mol(-1), respectively.

Conformational and configurational analysis in the study and synthesis of chlorinated natural products

The first detailed study of the J-based configuration analysis method in chlorinated hydrocarbons and chlorohydrins is presented along with the development of a spectroscopic database that facilitates configurational assignment of these structures. The data are generated through the investigation of model structures in solution by NMR spectroscopic methods and in the solid state by X-ray crystallography. Consequently, complete conformational analysis of trichlorinated hexane-1,2- and -1,3-diols is presented. The investigations in chlorinated systems for the first time attest to the relevance, reliability, and accuracy of the spectroscopic approach in configurational assignment, which had been otherwise developed for polyketides. During the synthesis of the various molecules that constitute the database and exemplify the various possible stereochemical patterns, a number of observations were made that underscore the unique features of these chlorinated systems. Thus, certain diastereomeric subclasses of 4,5-dichloro-2,3-epoxyhexane-1-ols display a propensity to undergo ring-opening reactions at C-3 with concomitant inversion of configuration at the neighboring C-Cl at C4, implicating the intermediacy of chloronium ions. The observations of positional and stereochemical scrambling in polychlorinated hydrocarbons underscore the necessity of a spectroscopic database that enables rapid, reliable configurational assignment of chlorinated natural products and intermediates en route to these.

Efforts toward developing probes of protein dynamics: vibrational dephasing and relaxation of carbon-deuterium stretching modes in deuterated leucine

The spectral position of C-D stretching absorptions in the so-called "transparent window" of protein absorption (1800-2300 cm(-1)) makes them well suited as probes of protein dynamics with high temporal and structural resolution. We have previously incorporated single deuterated amino acids into proteins to site-selectively follow protein folding and ligand binding by steady-state FT IR spectroscopy. Ultimately, our goal is to use C-D bonds as probes in time-resolved IR spectroscopy to study dynamics and intramolecular vibrational energy redistribution (IVR) in proteins. As a step toward this goal, we now present the first time-resolved experiments characterizing the population and dephasing dynamics of selectively excited C-D bonds in a deuterated amino acid. Three differently deuterated, Boc-protected leucines were selected to systematically alter the number of additional C-D bonds that may mediate IVR out of the initially populated bright C-D stretching mode. Three-pulse photon echo experiments show that the steady-state C-D absorption linewidths are broadened by both homogeneous and inhomogeneous effects, and transient grating experiments reveal that IVR occurs on a subpicosecond time scale and is nonstatistical. The results have important implications for the interpretation of steady-state C-D spectra and demonstrate the potential utility of C-D bonds as probes of dynamics and IVR within a protein.

Conformations and coherences in structure determination by ultrafast electron diffraction

In this article we consider consequences of spatial coherences and conformations in diffraction of (macro)molecules with different potential energy landscapes. The emphasis is on using this understanding to extract structural and temporal information from diffraction experiments. The theoretical analysis of structural interconversions spans an increased range of complexity, from small hydrocarbons to proteins. For each molecule considered, we construct the potential energy landscape and assess the characteristic conformational states available. For molecules that are quasiharmonic in the vicinity of energy minima, we find that the distinct conformer model is sufficient even at high temperatures. If, however, the energy surface is either locally flat around the minima or the molecule includes many degrees of conformational freedom, a Boltzmann ensemble must be used, in what we define as the pseudoconformer approach, to reproduce the diffraction. For macromolecules with numerous energy minima, the ensemble of hundreds of structures is considered, but we also utilize the concept of the persistence length to provide information on orientational coherence and its use to assess the degree of resonance contribution to diffraction. It is shown that the erosion of the resonant features in diffraction which are characteristic of some quasiperiodic structural motifs can be exploited in experimental studies of conformational interconversions triggered by a laser-induced temperature jump.

Computational study of ligand binding to protein receptors

We have determined, for the first time, the enthalpic contributions to the energy change associated with ligand reorganization (LR) upon the binding of the same ligand to multiple sites within human serum albumine (HSA). Quantum mechanics based density functional theory (DFT) has been used for the LR calculations, which provides much better accuracy than previously used molecular mechanics methods (MM). Our findings show that for some ligands these enthalpic contributions can be attributed to specific structural and conformational changes.

GLYCAM06: a generalizable biomolecular force field. Carbohydrates

A new derivation of the GLYCAM06 force field, which removes its previous specificity for carbohydrates, and its dependency on the AMBER force field and parameters, is presented. All pertinent force field terms have been explicitly specified and so no default or generic parameters are employed. The new GLYCAM is no longer limited to any particular class of biomolecules, but is extendible to all molecular classes in the spirit of a small-molecule force field. The torsion terms in the present work were all derived from quantum mechanical data from a collection of minimal molecular fragments and related small molecules. For carbohydrates, there is now a single parameter set applicable to both alpha- and beta-anomers and to all monosaccharide ring sizes and conformations. We demonstrate that deriving dihedral parameters by fitting to QM data for internal rotational energy curves for representative small molecules generally leads to correct rotamer populations in molecular dynamics simulations, and that this approach removes the need for phase corrections in the dihedral terms. However, we note that there are cases where this approach is inadequate. Reported here are the basic components of the new force field as well as an illustration of its extension to carbohydrates. In addition to reproducing the gas-phase properties of an array of small test molecules, condensed-phase simulations employing GLYCAM06 are shown to reproduce rotamer populations for key small molecules and representative biopolymer building blocks in explicit water, as well as crystalline lattice properties, such as unit cell dimensions, and vibrational frequencies.

The Substituted Alkyne 3-Heptyne is Eclipsed

Although butane exists in staggered anti and gauche conformations, when the ethyl groups are separated by a C[triple bond]C triple bond (3-hexyne), the stable conformation changes to eclipsed, (1)C(2v). Using rotational microwave spectroscopy, we have studied another example, 3-heptyne, the C[triple bond]C elongated analogue of pentane. The most stable conformer of pentane has anti-anti (AA) conformations about the central C-C bonds (C(2v)) and the next most stable has a gauche dihedral angle (GA, C1). This microwave study determines that the extended analogue of the AA form is not staggered about the C[triple bond]C axis but eclipsed (Cs). Also, the elongated analogue of the GA conformer is also not staggered but nearly eclipsed. The conformations of low-polarity substituted acetylenes is determined by dispersion attractions between the end groups. A microwave study of the AA and GA conformers of pentane is also reported.

Conformational Equilibrium of 1,2-Dichloroethane in Water: Comparison of PCM and RISM-SCF Methods

The RISM-SCF and polarizable continuum model (PCM) approaches have been applied to study the conformational equilibrium of 1,2-dichloroethane (DCE) in water. Both the electron correlation effect and basis sets play an important role in the relative energies of the gauche and trans conformers in gas and solution phases. Both PCM and RISM-MP2 methods resulted in a consistent trend with the previous experimental and theoretical studies that the population of the gauche conformer increases in going from the gas phase to the aqueous solution. However, the PCM treatment could not describe the solvent effect completely in that the sign of the relative free energy of the gauche and trans forms is opposite to the most recent experimental and theoretical data, while the RISM-MP2 gives the right sign in the free energy difference. We found that the larger excess chemical potential gain (by ca. -4.1 kcal/mol) for the gauche conformer is large enough to result in the gauche preference of DCE in water, though it has to compensate for more solute reorganization energy (approximately 1.6 kcal/mol) and overcome the energy difference (approximately 1.6 kcal/mol) in the gas phase. The radial distribution functions between DCE and the nearest water shows that the electrostatic repulsion between chlorine and oxygen atoms is higher in the trans conformer than in the gauche one, while the attractive interaction between chlorine and hydrogen of water is higher in the gauche conformer.

Parametrization and validation of a force field for liquid-crystal forming molecules

First principles density functional calculations have been carried out to determine the structures and conformational energies of a series of liquid-crystal fragment molecules. The calculations have been used to derive a molecular mechanics force field that describes a subset of commonly occurring liquid-crystal molecules. The force field has been used to carry out molecular dynamics simulations of the bulk phase for these fragment molecules. Computed densities and heats of vaporization are in good agreement with experimental data. These results should be useful in future molecular dynamics simulations of liquid-crystal systems.

The energetics of off-rotamer protein side-chain conformations

Non-rotameric ("off-rotamer") conformations are commonly observed for the side-chains of protein crystal structures. This study examines whether such conformations are real or artifactual by comparing the energetics of on and off-rotamer side-chain conformations calculated with the CHARMM energy function. Energy-based predictions of side-chain orientation are carried out by rigid-geometry mapping in the presence of the fixed protein environment for 1709 non-polar side-chains in 24 proteins for which high-resolution (2.0 A or better) structures are available. For on-rotamer conformations, 97.6 % are correctly predicted; i.e. they correspond to the absolute minima of their local side-chain energy maps (generally to within 10 degrees or less). By contrast, for the observed off-rotamer side-chain conformations, 63.8 % are predicted correctly. This difference is statistically significant (P<0.001) and suggests that while most of the observed off-rotamer conformations are real, many of the erroneously predicted ones are likely to be artifacts of the X-ray refinements. Probabilities for off-rotamer conformations of the non-polar side-chains are calculated to be 5.0-6.1 % by adaptive umbrella-sampled molecular dynamics trajectories of individual amino acid residues in vacuum and in the presence of an average protein or aqueous dielectric environment. These results correspond closely to the 5.7 % off-rotamer fraction predicted by the rigid-geometry mapping studies. Since these values are about one-half of the 10.2 % off-rotamer fraction observed in the X-ray structures, they support the conclusion that many of the latter are artifacts. In both the rigid-geometry mapping and the molecular dynamics studies, the discrepancies between the predicted and observed fractions of off-rotamer conformations are largest for leucine residues (approximately 6 % versus 16.6 %). The simulations for the isolated amino acid residues indicate that the real off-rotamer frequency of 5-6 % is consistent with the internal side-chain and local side-chain-backbone energetics and does not originate from shifts due to the protein. The present results suggest that energy-based rotation maps can be used to find side-chain positional artifacts that appear in crystal structures based on refinements in the 2 A resolution range.

Probing molecular conformations with electron momentum spectroscopy: the case of n-butane

High-resolution (e,2e) measurements of the valence electronic structure and momentum-space electron density distributions of n-butane have been exhaustively reanalyzed in order to cope with the presence of two stable structures in the gas phase, namely the all-staggered and gauche conformers. The measurements are compared to a series of Boltzmann-weighted simulations based on the momentum-space form of Kohn-Sham (B3LYP) orbital densities, and to ionization spectra obtained from high-level [ADC(3)] one-particle Green's Function calculations. Indubitable improvements in the quality of the simulated (e,2e) ionization spectra and electron momentum profiles are seen when the contributions of the gauche form of n-butane are included. Both the one-electron binding energies and momentum distributions consistently image the distortions and topological changes that molecular orbitals undergo due to torsion of the carbon backbone, and thereby exhibit variations which can be traced experimentally. With regard to the intimate relation of (e,2e) cross sections with orbital densities, electron momentum spectroscopy can therefore be viewed as a very powerful, but up to now largely unexploited, conformational probe. The study also emphasizes the influence of thermal agitation in photoionization experiments of all kind.

Conformational study of asialo-GM1 (GA1) ganglioside

In order to investigate the significance of preferred conformations of the saccharide for the steric orientation and recognition of glycosphingolipids at the membrane surface, the conformational free energy calculations were carried out on the asialo-GM1 [GA1; beta-D-Gal (1-->3) beta-D-GalNac(1-->4) beta-D-Gal(1-->4) beta-D-Glc-O-ceramide) using a new program CONCARB (CONformational study program for CARBohydrate) in the unhydrated and hydrated states. The overall backbone conformational of GA1 appears to be extended with a little bent at the glycosidic II-III linkage, in which two pyranose rings of Gal(IV)-GalNAc-(III) moiety orient approximately perpendicular to those of Gal(II)-Glc(I) moiety. This is consistent with the structures deduced from high-sensitivity differential scanning calorimetry experiments and the nmr study on GA1. The calculated glycosidic torsion angles of the lowest free energy conformation of GA1 in the hydrated state are in accord with the structures of relevant oligosaccharides deduced from nmr experiments and hard sphere exoanomeric calculations. A comparison of the values of glycosidic torsion angles phi and psi of GA1 and its constituent oligosaccharides indicates that the overall backbone conformation of each oligosaccharide is retained when the oligosaccharide chain becomes longer. This implies that the short-range interactions between the nearest-neighbored saccharides are of significant importance in stabilizing the overall backbone conformation of GA1 in both the unhydrated and hydrated states. The different orientation and hydrogen bonds of hydroxymethyl and hydroxyl groups from one oligosaccharide to another suggest that the medium- and long-range interactions are also of consequence. Hydration seems to affect significantly the confirmation of these groups, but not to perturb remarkably the overall backbone conformation of GA1.

Bayesian statistical analysis of protein side-chain rotamer preferences

We present a Bayesian statistical analysis of the conformations of side chains in proteins from the Protein Data Bank. This is an extension of the backbone-dependent rotamer library, and includes rotamer populations and average chi angles for a full range of phi, psi values. The Bayesian analysis used here provides a rigorous statistical method for taking account of varying amounts of data. Bayesian statistics requires the assumption of a prior distribution for parameters over their range of possible values. This prior distribution can be derived from previous data or from pooling some of the present data. The prior distribution is combined with the data to form the posterior distribution, which is a compromise between the prior distribution and the data. For the chi 2, chi 3, and chi 4 rotamer prior distributions, we assume that the probability of each rotamer type is dependent only on the previous chi rotamer in the chain. For the backbone-dependence of the chi 1 rotamers, we derive prior distributions from the product of the phi-dependent and psi-dependent probabilities. Molecular mechanics calculations with the CHARMM22 potential show a strong similarity with the experimental distributions, indicating that proteins attain their lowest energy rotamers with respect to local backbone-side-chain interactions. The new library is suitable for use in homology modeling, protein folding simulations, and the refinement of X-ray and NMR structures.

Prediction of protein side-chain rotamers from a backbone-dependent rotamer library: a new homology modeling tool

Modeling by homology is the most accurate computational method for translating an amino acid sequence into a protein structure. Homology modeling can be divided into two sub-problems, placing the polypeptide backbone and adding side-chains. We present a method for rapidly predicting the conformations of protein side-chains, starting from main-chain coordinates alone. The method involves using fewer than ten rotamers per residue from a backbone-dependent rotamer library and a search to remove steric conflicts. The method is initially tested on 299 high resolution crystal structures by rebuilding side-chains onto the experimentally determined backbone structures. A total of 77% of chi1 and 66% of chi(1 + 2) dihedral angles are predicted within 40 degrees of their crystal structure values. We then tested the method on the entire database of known structures in the Protein Data Bank. The predictive accuracy of the algorithm was strongly correlated with the resolution of the structures. In an effort to simulate a realistic homology modeling problem, 9424 homology models were created using three different modeling strategies. For prediction purposes, pairs of structures were identified which shared between 30% and 90% sequence identity. One strategy results in 82% of chi1 and 72% chi(1 + 2) dihedral angles predicted within 40 degrees of the target crystal structure values, suggesting that movements of the backbone associated with this degree of sequence identity are not large enough to disrupt the predictive ability of our method for non-native backbones. These results compared favorably with existing methods over a comprehensive data set.