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.

On the Heats of Formation of Alkanes

A broad diverse test set of alkanes and cycloalkanes previously studied with MM4 calculations has had the heats of formation calculated by several different quantum mechanical methods: HartreeFock, MP2, and MP4, and also by B3LYP and B3LYP + dispersion energy. Overall, three computational methods (MM4, MP4, and B3LYP + dispersion) yield results that are generally of experimental accuracy. These results are analyzed and compared in some detail.

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 Å (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.

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. 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. 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.

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. 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.

Molecular mechanics (MM3) calculations on lithium amide compounds

The MM3 force field has been extended to deal with the lithium amide molecules that are widely used as efficient catalysts for stereoselective asymmetric synthesis. The MM3 force field parameters have been determined on the basis of the ab initio MP2/6-31G* and/or DFT (B3LYP/6-31G*, B3-PW91/6-31G*) geometry optimization calculations. To evaluate the electronic interactions specific to the lithium amides derived from the diamine molecules properly, the Lewis bonding potential term for the interaction between the lithium atom and the nonbonded adjacent electronegative atom such as nitrogen was introduced into the MM3 force field. The bond dipoles were evaluated correctly from the electronic charges on the atoms calculated by fitting to the electrostatic potential at points selected. The MM3 results on the molecular structures, conformational energies, and vibrational spectra show good agreement with those from the quantum mechanical calculations.

MM3(96) parameterization for camptothecin analogs: an ab initio and molecular mechanics study

Torsional parameters for MM3(96) were derived for the missing atom types present in the natural product camptothecin (CPT). Potential energy curves were calculated via ab initio calculations on representative compounds for dihedral angles containing these missing parameters. Gaussian 92 at the restricted Hartree-Fock level of theory using the standard 6-31G** and 4-31G** basis sets, was used for all the quantum-mechanics calculations. Missing MM3 torsional terms were obtained by optimizing the V1, V2 and V3 parameters such that MM3 could reproduce the ab initio torsional profile. MM3 calculated molecular structures that compare well with the ab initio results. Using the newly developed parameters, conformational analyses and QSAR studies of camptothecin analogs were undertaken. MM3 predicts two distinct 'boatlike' conformations for the alpha-hydroxy lactone moiety. The low-energy lactone conformation predicted by MM3 is in general agreement with reported X-ray crystal structures of CPT iodoacetate and 7-ethyl-10-(4-piperidino)piperidinylcarbonyloxy CPT HCl as well as the ab initio structure of a CPT-like alpha-hydroxy lactone.

The dopaminergic moiety of the ergots: a controversial topic studied with molecular mechanics

Conformational analyses of the side chain of model compounds of the in vivo active dopamine receptor agonist 4-[2-(di-n-propylamino)ethyl]indole (DPAI) were performed with molecular mechanics calculations. The results from these calculations, together with the possibility of meta hydroxylation of indoles in vivo, led to the proposal of fitting 6-hydroxy-4-[2-(di-n-propylamino)ethyl]indole (6-OH-DPAI), (S)-5-hydroxy-N,N-dialkyl-6,7,8,9-tetrahydro-3H-benzo[e]indol-8-ylami nes and (S)-5-hydroxy-2-(dialkylamino)tetralins in a common concept, considering both stereochemistry and hydrogen-bond function in such an overlap. This study emphasizes the importance of considering both conformational analysis and the possibilities of metabolic activation when performing structure-activity studies based on flexible compounds and in vivo data. The answer to the question as to which part of the ergot molecule is responsible for its dopaminergic effect is thus ambiguous. It is possible that the pyrrolylethylamine moiety of the ergots contributes to both in vitro and in vivo effects, and that their 13-OH metabolites contribute, possibly significantly, to their in vivo effects.

Conformational analysis of 2-aminoindans and 2-(aminomethyl)indans in relation to their central dopaminergic effects and a dynamic dopamine receptor concept

Conformational analyses on differently substituted 2-aminoindans of significant pharmacological interest were carried out by the molecular mechanics method (MM2). An X-ray structure of (R)-4-methoxy-2-aminoindan has shown the ammonium nitrogen [-)-D-tartaric acid salt) in an axial position. From comparison with other, highly potent, centrally acting dopamine (DA) receptor agonists, it can be predicted that the active enantiomer (R)-4-hydroxy-2-(di-n-propylamino)indan should have its nitrogen atom in an equatorial position. This places it close to the aromatic ring plane, which is one of several prerequisites for potent DA receptor agonism. MM2 correctly calculates (R)-4-methoxy-2-aminoindan and (R)-4-hydroxy-2-(dialkylamino)indan to be more stable in the N-axial and N-equatorial conformations, respectively. Conformational analysis of the dimethyl model compound of the moderately potent dopaminergic phenylpropylamine analogue 4-hydroxy-2-[(di-n-propylamino)methyl]indan was also carried out, in order to see if any conformations of this compound satisfy the requirements for dopaminergic agonism. Two such stable conformations were found.