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.

Well-defined palladium(0) complexes bearing N-heterocyclic carbene and phosphine moieties: efficient catalytic applications in the Mizoroki-Heck reaction and direct C-H functionalization.

Two series of well-defined palladium(0) complexes with phosphine-functionalized N-heterocyclic carbene ligands were prepared. These complexes featured six- and seven-membered chelate rings in the two series. Among the seven-membered chelate complexes, those featuring the PCy2 moiety exhibited observable fluxional behavior on the NMR time scale, corresponding to the interchange between two sets of conformations. Most of these novel complexes were successfully structurally characterized by single-crystal X-ray diffraction studies. These two series of palladium(0) complexes were tested for their potential catalytic applications in two mechanistically distinct reactions, namely, Mizoroki-Heck coupling and direct C-H functionalization reactions. One of the six-membered chelate complexes was found to be an efficient pre-catalyst for mediating the coupling reactions between aryl chlorides and alkenes. The palladium(0) complex could also be effectively applied in the direct C-H functionalization reactions of aryl bromides with 1,2-dimethylimidazole.

Molecular Mechanics (MM4) Studies on Unusually Long Carbon-Carbon Bond Distances in Hydrocarbons.

The carbon-carbon single bond is of central importance in organic chemistry. When the molecular mechanics MM4 force field was developed beginning in the early 1990s, C-C bond lengths were not known very reliably for many important molecules, and bond lengths greater than 1.6 Å were quite poorly known experimentally. Quantum-mechanically computed values could not yet be obtained with useful accuracy in a general way. This paper examines structures now available from experiment and quantum-mechanical computations and extends the fit of the MM4 methodology to include new bond distances as long as 1.71 Å.

Catenanes: A molecular mechanics analysis of the (C13H26)2 Structure 13-13 D2.

Molecular mechanics (MM4) studies have been carried out on the catenane (C13H26)2, specifically 13-13D2. The structure obtained is in general agreement with second-order perturbation theory. More importantly, the MM4 structure allows a breakdown of the energy of the molecule into its component classical parts. This allows an understanding of why the structure is so distorted, in terms of C-C bonding and nonbonding interactions, van der Waals repulsion, C-C-C and C-C-H angle bending, torsional energies, stretch-bend, torsion-stretch, and bend-torsion-bend interactions. Clearly, the hole in 113-membered ring is too small for the other ring to fit through comfortably. There are too many atoms trying to fit into the limited space at the same time, leading to large van der Waals repulsions. The rings distort in such a way as to enlarge this available space, and lower the total energy of the molecule. While the distortions are spread around the rings, one of the nominally tetrahedral C-C-C bond angles in each ring is opened to 147.9° by MM4 (146.8° by MP2). The stability of the compound is discussed in terms of the strain energy.

How Small Can a Catenane Be?

Catenanes are playing an increasingly important role in supramolecular chemistry. In attempting to identify the minimum number of carbon atoms in a viable catenane, the B3LYP, BP86, M06-2X, MM3, and MM4 methods were applied to study representative [2]catenane models, which consist of two mechanically interlocked saturated n-cycloalkanes ([CnH2n]2). The structures, energy variations, and electron density differences vary nearly monotonically from n = 18 to 11. For example, the B3LYP/DZP++ dissociation energies [CnH2n]2 → 2CnH2n are 101, 121, 159, 191, 222, 252, 290, and 323 kcal/mol from n = 18 to 11, respectively. However, there is much variation among the energetic predictions with the B3LYP, BP86, M06-2X, MM3, and MM4 methods. The distances of the longest C-C single bond in each catenane are 1.593 (n = 18), 1.604 (n = 17), 1.631 (n = 16), 1.640 (n = 15), 1.667 (n = 14), 1.669 (n = 13), 1.680 (n = 12), and 1.689 Š(n = 11). These results display something of a shoulder in the vicinity of n = 14. This may suggest that [C15H30]2 is the smallest catenane that will resist fragmentation under specified laboratory conditions.

Formation of CC-type palladacycles with assistance from an apparently innocent NH(CO) functional group.

A novel cyclometalation pathway to form CC-type palladacycles is reported. Unlike common donor-assisted cyclometalation, the NH(CO) auxiliary group undergoes a deprotonation step to form a palladalactam intermediate. The coordinating nitrogen atom functions as an intramolecular base promoting selective C-H bond cleavage. Without the NH proton, the ortho-N-phenyl C-H is activated instead.

An improved theoretical approach to the empirical corrections of density functional theory.

An empirical correction to density functional theory (DFT) has been developed in this study. The approach, called correlation corrected atomization-dispersion (CCAZD), involves short- and long-range terms. Short-range correction consists of bond (1,2-) and angle (1,3-) interactions, which remedies the deficiency of DFT in describing the proto-branching stabilization effects. Long-range correction includes a Buckingham potential function aiming to account for the dispersion interactions. The empirical corrections of DFT were parameterized to reproduce reported ΔH ( f ) values of the training set containing alkane, alcohol and ether molecules. The ΔH ( f ) of the training set molecules predicted by the CCAZD method combined with two different DFT methods, B3LYP and MPWB1K, with a 6-31G* basis set agreed well with the experimental data. For 106 alkane, alcohol and ether compounds, the average absolute deviations (AADs) in ΔH ( f ) were 0.45 and 0.51 kcal/mol for B3LYP- and MPWB1K-CCAZD, respectively. Calculations of isomerization energies, rotational barriers and conformational energies further validated the CCAZD approach. The isomerization energies improved significantly with the CCAZD treatment. The AADs for 22 energies of isomerization reactions were decreased from 3.55 and 2.44 to 0.55 and 0.82 kcal/mol for B3LYP and MPWB1K, respectively. This study also provided predictions of MM4, G3, CBS-QB3 and B2PLYP-D for comparison. The final test of the CCAZD approach on the calculation of the cellobiose analog potential surface also showed promising results. This study demonstrated that DFT calculations with CCAZD empirical corrections achieved very good agreement with reported values for various chemical reactions with a small basis set as 6-31G*.

Accurate prediction of the enthalpies of formation for xanthophylls.

This study investigates the applications of computational approaches in the prediction of enthalpies of formation (ΔH(f)) for C-, H-, and O-containing compounds. Molecular mechanics (MM4) molecular mechanics method, density functional theory (DFT) combined with the atomic equivalent (AE) and group equivalent (GE) schemes, and DFT-based correlation corrected atomization (CCAZ) were used. We emphasized on the application to xanthophylls, C-, H-, and O-containing carotenoids which consist of ∼ 100 atoms and extended π-delocaization systems. Within the training set, MM4 predictions are more accurate than those obtained using AE and GE; however a systematic underestimation was observed in the extended systems. ΔH(f) for the training set molecules predicted by CCAZ combined with DFT are in very good agreement with the G3 results. The average absolute deviations (AADs) of CCAZ combined with B3LYP and MPWB1K are 0.38 and 0.53 kcal/mol compared with the G3 data, and are 0.74 and 0.69 kcal/mol compared with the available experimental data, respectively. Consistency of the CCAZ approach for the selected xanthophylls is revealed by the AAD of 2.68 kcal/mol between B3LYP-CCAZ and MPWB1K-CCAZ.

A theoretical approach for accurate predictions of the enthalpies of formation of carotenes.

A computational approach has been designed for accurately determining enthalpies of formation (ΔH(f)) for the carotene species. This approach, named correlation corrected atomization (CCAZ), is based on the concept of bond and group additivity, and is applied along with density functional theory (DFT). Corrections to the deficiencies in DFT were divided into 1,2-, 1,3-, and 1,4- atomic interactions, which were determined by comparisons with the G3 data of the training set. When comparing predictions from CCAZ combined with two different DFT methods (B3LYP and MPWB1K), fairly accurate prediction is expected. In contrast, DFT using the atomization and isodesmic schemes resulted in poor predictions of ΔH(f). The equivalent methods, atomic equivalent (AEQ) and group equivalent (GEQ) provide improved predictions; however, the accuracies are lower than that of CCAZ.

Selenoglycosides in silico: ab initio-derived reparameterization of MM4, conformational analysis using histo-blood group ABH antigens and lectin docking as indication for potential of bioactivity.

The identification of glycan epitopes such as the histo-blood group ABH determinants as docking sites for bacterial/viral infections and signals in growth regulation fuels the interest to develop non-hydrolysable mimetics for therapeutic applications. Inevitably, the required substitution of the linkage oxygen atom will alter the derivative's topology. Our study addresses the question of the impact of substitution of oxygen by selenium. In order to characterize spatial parameters and flexibility of selenoglycosides, we first performed ab initio calculations on model compounds to refine the MM4 force field. The following application of the resulting MM4R version appears to reduce the difference to ab initio data when compared to using the MM4 estimator. Systematic conformational searches on the derivatives of histo-blood group ABH antigens revealed increased flexibility with acquisition of additional low-energy conformer(s), akin to the behavior of S-glycosides. Docking analysis using the Glide program for eight test cases indicated potential for bioactivity, giving further experimental investigation a clear direction to testing Se-glycosides as lectin ligands.

Conformational analysis of thioglycoside derivatives of histo-blood group ABH antigens using an ab initio-derived reparameterization of MM4: implications for design of non-hydrolysable mimetics.

Histo-blood group ABH antigens serve as recognition sites for infectious microorganisms and tissue lectins in intercellular communication, e.g. in tumor progression. Thus, they are of interest as a starting point for drug design. In this respect, potent non-hydrolysable derivatives such as thioglycosides are of special interest. As prerequisite to enable estimations of ligand properties relative to their natural counterparts, conformational properties of the thioglycosidic derivatives of ABH trisaccharides and their disaccharide units were calculated using systematic and filtered systematic searches with the MM4 force field. Parameters for the glycosidic torsions of thioglycosides were independently derived from ab initio calculations. The resulting energy deviations required a reparameterization of MM4 to a new parameter set called MM4R. The data sets obtained using MM4R reveal that the thioglycosides have somewhat increased levels of flexibility about the major low-energy conformations shared with the corresponding O-glycosides. In the trisaccharides, the thiosubstitution of the Gal[NAc]alpha1-3Gal linkage leads to a preference for a conformation which is the secondary minimum of the natural counterparts. This conformation also generates contacts between the N-acetyl group and the fucose moiety in the blood group A derivative. Calculations further indicate that thiosubstitution of only the Fucalpha1-2Gal linkage does not affect the conformational preferences compared to the natural trisaccharide. Thiosubstitution of both linkages in the trisaccharide results in increased flexibility but the favored conformation of the natural trisaccharides is preferred. The study suggests that thioglycoside derivatives of ABH antigens could have pharmaceutical interest as ligands of lectins and other carbohydrate-binding proteins.

The important role of lone-pairs in force field (MM4) calculations on hydrogen bonding in alcohols.

An expanded treatment of hydrogen bonding has been developed for MM4 force field calculations, which is an extension from the traditional van der Waals-electrostatic model. It adds explicit hydrogen-bond angularity by the inclusion of lone-pair directionality. The vectors that account for this directionality are placed along the hydrogen acceptor and its chemically intuitive electron pairs. No physical lone-pairs are used in the calculations. Instead, an H-bond angularity function, and a lone-pair directionality function, are incorporated into the hydrogen-bond term. The inclusion of the lone-pair directionality results in improved accuracy in hydrogen-bonded geometries and interaction energies. In this work is described hydrogen bonding in alcohols, and also in water and hydrogen fluoride dimer. The extension to other compounds such as aldehydes, ketones, amides, and so on is straightforward and will be discussed in future work. The conformational energies of ethylene glycol are discussed.

Molecular mechanics (MM4) study of amines.

The MM4 force field has been extended to include aliphatic amines. About 20 amines have been examined to obtain a set of useful molecular mechanics parameters for this class. The vibrational spectra of seven amines (172 frequencies) calculated by MM4 have an overall rms error of 27 cm(-1), compared with corresponding MM4 value of 24 cm(-1) for alkanes. The rms and signed average errors of the moments of inertia of nine simple amines compared with the experimental data were 0.18% and -0.004%, respectively. The heats of formation of 30 amines were also studied. The MM4 weighted standard deviation is 0.41 kcal/mol, compared with experiment. Electronegativity effects occur in the hydrocarbon portion of an amine from the nitrogen, and are accounted for by including electronegativity induced changes in bond lengths and angles, and induced dipole-dipole interactions in the molecule. Negative hyperconjugation results from the presence of the lone pair of electrons on nitrogen, and leads to the Bohlmann bands in the infrared, and also to strong and unusual geometric changes in the molecules (Bohlmann effect), all of which are fairly well accounted for. The conformational energies in amines appear to be less straightforward than those for most other classes of molecules, apparently because of the Bohlmann effect, and these are probably not yet completely understood. In general, the agreement between the MM4 calculated results and the available data is reasonably good.

Molecular mechanics (MM4) study of fluorinated hydrocarbons.

A molecular mechanics study of small saturated hydrocarbons (up to C-6) substituted by up to six fluorines has been carried out with the MM4 force field. A parameter set has been developed for use in the calculation of bond lengths, bond angles, torsion angles, conformational energies, barriers to rotation, dipole moments, moments of inertia, and vibrational frequencies for these compounds. The results are mostly in fair to good agreement with experiment and ab initio calculations. The high electronegativity of fluorine leads to serious geometric consequences in these compounds, but these consequences can be dealt with adequately by suitable cross-terms in the force constant matrix, and by recognizing that some of the reference bond lengths and angles (l(0), theta(0)) and the corresponding stretching and bending constant parameters (k(s), k(theta)) that are usually thought of as constants must in fact be treated as functions of the electronegativity of the substituents. Additionally, the heavy mass of the fluorine (relative to the mass of hydrogen in alkanes) leads to large values for other cross-terms that were found to be unimportant in hydrocarbons. Conformational equilibria for polyfluorinated compounds are affected by the delta-two effect well-known in carbohydrates. A few larger fluorinated and polyfluorinated alkanes, including perfluoropropane, perfluorobutane, and Teflon, have also been studied.

The external-anomeric torsional effect.

The rotational barrier for a methyl group at the end of an anomeric system is sometimes lower than we might have anticipated. Thus, in the trans-trans conformation of dimethoxymethane, the barrier to methyl rotation is calculated (B3LYP/6-311++G(2d,2p)) to be 2.22 kcal/mol, just slightly smaller than the corresponding barrier to rotation of the methyl group in methyl propyl ether of 2.32 kcal/mol. However, if the methyl being rotated in dimethoxymethane is placed into a gauche conformation, that rotational barrier is reduced to 1.52 kcal/mol. This substantial (0.80 kcal/mol relative to methyl propyl ether) reduction in barrier height in the latter case is attributed mainly to the change in the bond order of the C-O bond to which the methyl is attached, as a function of conformation, which in turn is a result of the anomeric effect. We have called this barrier lowering the external-anomeric torsional effect. This effect is apparently widespread in carbohydrates, and it results in the changing of conformational energies by up to about 2 kcal/mol. If polysaccharide potential surfaces are to be accurately mapped by molecular mechanics, this effect clearly needs to be accounted for.

Alcohols, ethers, carbohydrates, and related compounds. I. The MM4 force field for simple compounds.

Simple alcohols and ethers have been studied with the MM4 force field. The structures of 13 molecules have been well fit using the MM4 force field. Moments of inertia have been fit with rms percentage errors as indicated: 18 moments for ethers, 0.28%; 21 moments for alcohols, 0.22%. Rotational barriers and conformational equilibria have also been examined, and the experimental and ab initio results are reproduced substantially better with MM4 than they were with MM3. Much of the improvement comes from the use of additional interaction terms in the force constant matrix, of which the torsion-bend and torsion-torsion are particularly important. Induced dipoles are included in the calculation, and dipole moments are reasonably well fit. It has been possible for the first time to fit conformational energetic data for both open chain and cyclic alcohols (e.g., propanol and cyclohexanol) with the same parameter set. For vibrational spectra, over a total of 82 frequencies, the rms error is 27 cm(-1), as opposed to 38 cm(-1) with MM3. Both the alpha and beta bond shortening resulting from the presence of the electronegative oxygen atom in the molecule are well reproduced. The electronegativity of the oxygen is sufficient that one must also include not only the alpha and beta electronegativity effects on bond lengths, but also on angle distortions, if structures are to be well reproduced. The heats of formation of 32 alcohols and ethers were fit overall to within experimental error (weighted standard deviation error 0.26 kcal/mol).

Alcohols, ethers, carbohydrates, and related compounds. III. The 1,2-dimethoxyethane system.

Ethylene glycol, its dimethyl ether, and some related compounds have been studied using the MM4 molecular mechanics force field. The MM4 calculated structural and energetic results have been brought into satisfactory agreement with a considerable number of experimental data and MP2/6-311++G(2d,2p) ab initio calculations. The heats of formation of these compounds are also well calculated. The MM4 ethylene glycol conformations in particular are in good agreement, both geometrically and in terms of energy, with those from the ab initio calculations. The corresponding dimethyl ether is of special interest, because it has been suggested that the trans-gauche conformation is unusually stable due to the hydrogen bonding of a hydrogen on a methyl group with the more distant oxygen. It is shown in the present work that while this conformation is more stable than might have been expected, the energy is adequately calculated by MM4 without using any hydrogen bonding between the Cbond;H bond and the oxygen. If such hydrogen bonding occurs, it amounts to no more than about 0.5 kcal/mol in energy, and is too small to detect with certainty. Additionally, energetic relationships in trans-1,2-dimethoxycyclohexane, 1,3,5,7-tetraoxadecalin, and 3-methoxytetrahydropyran have been studied, and the calculated results are compared with experimental information, which is adequately reproduced.

Alcohols, ethers, carbohydrates, and related compounds. II. The anomeric effect.

The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6-311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion-stretch elements. The angle changes are accounted for with torsion-bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion-torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol.

Alcohols, ethers, carbohydrates, and related compounds. IV. Carbohydrates.

Ab initio calculations [B3LYP/6-311++G(2d,2p)] have been carried out on 84 conformations of 12 different sugars (hexoses), in both pyranose and furanose forms, with the idea of generating a data base for carbohydrate structural energies that may be used for developing the predictive value of molecular mechanics calculations for carbohydrates. The average value for the apparent gas phase anomeric effect for a series of 31 pairs of pyranose conformations was found to be 1.83 kcal/mol (vs. 2.67 kcal/mol with a smaller basis set used in earlier calculations). In developing MM4 to reproduce these data, it was necessary first to have good energies for simple alcohols and ethers, together with an adequate treatment of hydrogen bonding, and then to include the anomeric effect, and the ethylene glycol type system, as was previously recognized. It was also found that the so-called delta-2 effect, long recognized in carbohydrates, must be explicitly included, in order to obtain acceptable results. When a force field that included all of these items as developed from the small molecules based on the MM4 hydrocarbon force field was applied without any parameter adjustment to the set of hexopyranose and furanose conformations mentioned earlier, the E(beta) - E(alpha) was found to have an average value of 1.88 kcal/mol, versus 1.74 for the quantum calculations. The signed average and RMS deviations of the MM4 from the QM results were +0.15 and 0.87 kcal/mol.