Conformational properties of permethylcyclohexane as compared to cyclohexane: A force field study

The conformational properties of the recently synthesized highly strained permethylcyclohexane molecule 2 have been studied by empirical force field calculations using three different potentials (CFF, MM2, MM2′) and second-derivative optimization methods. A comparison of the results with the conformational behavior of parent cyclohexane 1 leads to the following conclusions: The best conformation of 2 is a chair minimum whose six-membered ring is flatter than that of 1 , due to the strong H…H repulsions introduced by the methyl groups. The twist minimum of 2 is energetically less favorable than the chair by an amount similar to 1 . A potential energy barrier Δ V^# for the chair inversion of 2 of 15.32 kcal/mol results with the CFF, only about three kcal/mol higher than for 1 . The free energy of activation ΔG^# for this process obtained with the CFF is 16.96 kcal/mol (at 333 K) and agrees well with the experimental value of 16.7(2) kcal/mol.¹ MM2 and MM2′ give substantially lower and higher potential energy inversion barriers Δ V^# of 9.03 and 20.29 kcal/mol, respectively, which is attributed to inappropriate torsional energy terms in these force fields. The characteristic difference in the conformational behavior of 2 and 1 concerns the boat forms which are substantially less favorable in the per-methyl compound than in 1 . Expectedly, strong H…H repulsions between the 1,4 diaxial flagpole–bowsprit methyl groups in 2 are responsible for this difference. The particularly high strain of the boat forms of 2 leads to flexibility differences as compared to 1 which in turn affect the relative entropies of the various statiomers (stationary point conformations); e.g., the chair ring inversion activation entropies of 2 and 1 are predicted by the CFF calculations to have opposite signs (?4.82 and 3.41 cal/mol K, respectively, at 298 K). The twist and half-twist statiomers of 2 are much more rigid than those of 1 , which is a consequence of the substantially larger boat barriers along their pseudorotational interconversion paths. The boat transition state separating two enantiomeric twist minima represents a barrier calculated to be more than tenfold higher for 2 than for 1 (CFF Δ V^# values 11.14 and 0.92 kcal/mol, respectively); likewise the half-boat chair inversion barrier of 2 is calculated 5.07 kcal/mol less favorable than the respective half-twist barrier. These statiomers are practically equienergetic in the case of 1 . Except for the axial flagpole–bowsprit CH₃ substituents of the boat forms, the methyl groups of all the relevant calculated statiomers of 2 are more or less staggered. The rotational barrier of the equatorial methyl groups of the chair minimum of 2 is computationally predicted to be 5.78 kcal/mol (ΔG^#), i.e., unusually high. Interesting vibrational effects are brought about by the strong H…H repulsions in 2 ; thus the chair minimum has a largest C? H stretching frequency estimated to be 3050 cm^?1 and involves several particularly low frequencies which have a substantial influence on its entropy. CFF calculations for the lower homologue permethylcyclopentane 5 indicate that its pseudorotational properties are similar to those of cyclopentane 4 , in contradistinction to the pair 2/1 .     

<Emphasis Type="Italic">Ab initio</Emphasis> Study of Structural and Conformational Properties of Five- to Nine-Membered Cyclic 1,2,3-Trienes

Summary.  The structures and relative energies of fundamental conformations of cyclopenta-1,2,3-triene, cyclohexa-1,2,3-triene, cylohepta-1,2,3-triene, cycloocta-1,2,3-triene, and cyclonona-1,2,3-triene were calculated by the HF/6-31G^* and MP2/6-31G^*//HF/6-31G^* methods. Only a C _2v symmetric planar conformation is available to cyclopenta-1,2,3-triene and cyclohexa-1,2,3-triene. The calculated energy barrier for ring inversion of the C _S symmetric puckerd conformation of cyclohepta-1,2,3-triene via the planar geometry is 62.2 kJ·mol⁻¹. The C ₂ symmetric twist conformation of cycloocta-1,2,3-triene was calculated to be the most stable one. Conformational racemization of the twist form takes place via the C _S symmetric half-chair geometry, which is by 60.8 kJ·mol⁻¹ less stable than the twist conformer. The C _S symmetric chair and unsymmetrical twist-boat conformations of cyclonona-1,2,3-triene were calculated to have similar energies; their interconversion takes place via an unsymmetrical low-energy (18.4 kJ·mol⁻¹) transition state. The twist (C ₂) and boat (C _S) geometries of cyclonona-1,2,3-triene are higher in energy by 13.2 and 33.9 kJ·mol⁻¹, respectively. Ring inversion in chair and twist-boat conformations takes place via a twist form as intermediate and requires 33.6 kJ·mol⁻¹. Corresponding author. E-mail: isayavar@yahoo.com Received March 25, 2002; accepted April 4, 2002     

An ab initio study of the geometries and rotational barriers of 1-, 2-, and 5-phenylimidazole

The torsional barrier was calculated in the 3-21G basis set for 1-, 2-, and 5-phenylimidazole. Full geometry optimization was carried out at inter-ring torsional angles of 0°, 30°, 60°, 90°, 120°, 150°, 180°, and additional intermediate angles. All torsional potential energies were found to be symmetric with respect to the 90° conformation. The 2-phenylimidazole torsional energy exhibits a minimum at 0° (and 180°) and a maximum at 90° with a barrier height of 5.83 kcal/mol relative to the 0° conformation. The minima in the 1- and 5-phenylimidazole torsional potential energies correspond to non-planar conformations, resulting in a double-well potential with maxima at 0° (180°) and 90°. The 1-phenylimidazole minima are located at 46.5 and 133.5°; the 5-phenylimidazole minima, at 35.3 and 144.7°. In the 0° (180°) and 90° conformations, 1-phenylimidazole exhibits torsional barriers of 1.84 and 0.75 kcal/mol, respectively, relative to the energy of the 46.5° conformation. For 5-phenylimidazole, these barriers are 0.94 and 1.89 kcal/mol, relative to the energy of the 35.3° conformation. The energy of 5-phenylimidazole in the 35.3° conformation corresponds to a relative tautomeric energy difference of 1.80 kcal/mol compared to the 0° conformer of the 4-phenylimidazole tautomer.     

Conformational pathways of saturated six-membered rings. A static and dynamical density functional study

The conformation of the six-membered ring of pyranosyl sugars has pronounced effects on the physical and chemical properties of carbohydrates. We present a method to determine key features of the potential energy surfaces, such as transition states associated with the inversion pathways of the model compounds cyclohexane, tetrahydropyran, p-dioxane, m-dioxane, s-trioxane, and 2-oxanol. Finally, we make the first determination of the pathways for inversion of penta-O-methyl-alpha-D-glucopyranose and penta-O-methyl-beta-D-glucopyranose. For both anomers, a transition state with five coplanar atoms with appreciable (O)E character was found. The method is based on constrained Car-Parrinello ab initio molecular dynamics, as implemented in the projector augmented-wave (PAW) method. The constraints are derived from the normal modes of six-membered rings and are described in terms of the canonical conformations (1)C(4) chair, (1,4)B boat, and (O)S(2) skew-boat. The PAW derived trajectories are in agreement with previous suggestions in the literature that pseudorotation is an important feature of such conformational interconversions. The dynamic nature as well as the internal coordinate-based constraints provide a method which can reliably accommodate pseudorotation. To determine semiquantitative energies, we recalculate key conformations using standard quantum mechanical calculations while keeping the ring dihedral angles frozen at their values found in the dynamics. In all cases where experimental barriers are known, our results are in excellent agreement.     

A Conformational Study on Silacyclohexane. Comparison of ab initio (HF,MP2), DFT,and Molecular Mechanics Calculations. Conformational Energy Surface of Silacyclohexane

The structures and relative energies for the basic conformations of silacyclohexane 1 have been calculated using HF, RI‐MP2, RI‐DFT and MM3 methods. All methods predict the chair form to be the dominant conformation and all of them predict structures which are in good agreement with experimental data. The conformational energy surface of 1 has been calculated using MM3. It is found that there are two symmetric lowest energy pathways for the chair‐to‐chair inversion. Each of them consists of two sofa‐like transition states, two twist forms with C₁ symmetry (twist‐C₁), two boat forms with Si in a gunnel position (C₁ symmetry), and one twist form with C₂ symmetry (twist‐C₂). All methods calculate the relative energy to increase in the order chair < twist‐C₂ < twist‐C₁ < boat. At the MP2 level of theory and using TZVP and TZVPP (Si atoms) basis sets the relative energies are calculated to be 3.76, 4.80, and 5.47 kcal mol^–1 for the twist‐C₂, twist‐C₁, and boat conformations, respectively. The energy barrier from the chair to the twisted conformations of 1 is found to be 6.6 and 5.7 kcal mol^–1 from MM3 and RI‐DFT calculations, respectively. The boat form with Si at the prow (C_s symmetry) does not correspond to a local minimum nor a saddle point on the MM3 energy surface, whereas a RI‐DFT optimization under C_s symmetry constraint resulted in a local minimum. In both cases its energy is above that of the chair‐to‐twist‐C₁ transition state, however, and it is clearly not a part of the chair‐to‐chair inversion.     

Structural and Conformational Aspects of Equatorial and Axial Trifluoromethyl,Difluoromethyl, and Monofluoromethyl Groups

The X‐ray crystal structures of cis‐ and trans‐1‐(indol‐3‐yl)‐4‐methyl cyclohexane and its congeners with stepwise fluorination of the methyl group are reported. The trans‐configured compounds adopted diequatorial conformations, whereas the cis analogues adopted regular cyclohexane chair conformations with the methyl group preferentially assuming the axial position, even in the case of the CF₃ group. Surprisingly, although the axial CF₃ derivative displayed distinct valence deformations in the cyclohexane moiety, the observed structural changes were relatively modest. The cis derivatives with axial mono‐ and difluorinated methyl groups exhibited conformational disorder in the crystals with significant population levels for the staggered conformations that had one fluorine atom in the endo position; their respective trans counterparts adopted unique conformations, but again with one fluorine atom in the endo position. Theoretical calculations for a series of cis‐ and trans‐1,4‐dimethyl cyclohexane model compounds with stepwise fluorination of one equatorial or axial methyl group reproduced the experimentally observed structural response patterns very well, reproduced the experimentally determined nonlinear correlation of the axial–equatorial energy difference with the degree of methyl fluorination in a satisfactory manner, and provided further insights into important conformational aspects of partially fluorinated methyl groups.     

An NMR study of the conformational equilibrium of 5-fluoro-1,3-dioxan in solution. Dependence on solvent

The ¹H and ¹⁹F NMR parameters of 5-fluoro-1,3-dioxan ( 1 ) dissolved in a number of solvent systems are interpreted on the basis of fast inversion between two chair conformations. In cyclohexane solution the two chair conformations are almost equally populated, whereas in more polar solvents, such as chloroform, the conformation having the fluorine substituent in an axial position is strongly preferred. Addition of acetic acid to a solution of 1 in cyclohexane increases the preference of the fluorine substituent for the axial orientation. Possible reasons for these observations are discussed.     

Synthetic and structural studies on macrocyclic amino cyclitols--conformational chameleons

Starting from quinic acid the synthesis of 1,4-butanediol-linked macrocyclic aminocyclitols 30, 32, 34, 36 and 38 is described. Assembly was achieved by olefin cross-metathesis of appropriate cyclohexyl allyl ethers followed by ring-closing metathesis of bis-O-allyl homodimers. In all five cases studied, the only products that were formed were those resulting from direct ring-closing metathesis; the formation of larger rings was not detected. These macrocycles exhibited diverse conformational behaviour which included formation of stable separable conformers 31a and 31b as well as conformationally dynamic macrocycles 35 in which a ring flip in one cyclohexane chair conformer induces a ring flip of the other cyclohexane ring through the linking chains of the macrocycles. The activation energy for the inversion of the chair conformation in this process was determined to be about 38 kJ mol(-1), which is about 7 kJ mol(-1) lower than the activation energy for the ring flip of the unsubstituted cyclohexane ring. In all cases, the conformational studies strongly suggest that intramolecular H-bonding between 1,3-diaxially oriented amido and alcohol or ether groups exerts a decisive contribution to the overall stabilisation of the preferred cyclohexane chair conformation.     

X‐ray investigations of bicyclic α‐methylene‐δ‐valerolactones. V. (4aS,7R,8aR)‐7‐Isopropenyl‐4a‐methyl‐3‐methyleneperhydrochromen‐2‐one

The title compound, C₁₄H₂₀O₂, adopts a conformation in which the δ‐valerolactone and cyclohexane rings are almost coplanar with one another. The γ‐methyl substituent occupies an axial position with respect to the cyclohexane ring. The δ‐valerolactone moiety adopts an envelope arrangement, while the cyclohexane ring exists in a chair conformation.     

Steerochemistry of heterocycles.

The stereochemical peculiarities of substituted 1,3-dioxanes and 1,3-dithianes are discussed. The high probability of the existence of flexible conformations in these series, the considerable energy preference of the 5-C-axial position in the chair conformation of 1,3-dioxanes and 1,3-dithianes, and the definite preference of the 2-C-axial position in the chair conformation of 1,3-dithianes as compared with the axial conformations of the cyclohexane type are noted. The PMR spectra of stereoisomeric 2,5-dimethyl-5-isopropyl-1,3-dioxanes, 2-methy-l5-isopropyl-1,3-dithianes, and 2,2,5-trimethyl-1,3-dithiane are described, and their configurations and preferred conformations are proved. The results of a study of the epimerization of stereoisomers of substituted 1,3-dioxanes and 1,3-dithianes are examined, and the conformational energies of individual substituents in the 5-position of these cyclic systems are calculated on the basis of this examination.See [48] for communication IV.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 582–592, May, 1971.     

Substituentenabhängigkeit der Ringinversion des Ungesättigten Siebenringes bei Benzocycloheptenderivaten. Konformative Beweglichkeit flexibler Ringsysteme—XIV: Untersuchungen mit Hilfe der Protonenresonanzspektroskopie

NMR spectroscopy has been used to investigate the ring inversions of the unsaturated seven membered ring system in a total of 20 benzocycloheptene derivatives with 1, 2 and 3 pairs of geminal substituents. For all compounds the inversion of the ring at ? 80°C is ‘frozen’ and at this temperature only one conformation is present in detectable quantity, presumably that of the chair form. The free activation enthalpies ΔG^≠ for the chair inversions lie between 9·9 and 13·7 kcal/mole. For disubstituted and tetrasubstituted benzocycloheptenes the ΔG^≠ values vary according to the positions of the ligands: for disubstituted derivatives ΔG^≠ is largest for the 5-position and smallest for the 3-position. For the tetrasubstituted derivatives the inversion of the ring—compared to that in the comparable dimethyl derivatives—is made more difficult when the ligands are in the 3,6- or 3,7- positions, but is facilitated when in the 3,5- or 4,6- positions. The effect observed in the 3,5- and 4,6- substituted rings is due to transanular repulsion of synaxial substituents, which leads to a flattening of the ring. Such a repulsion does not occur when the ligands are in the 3,6- positions. On the other hand, when the ligands are in 3,7- positions the transanular repulsion leads to a stronger puckering of the chair; the inversion could be hindered by this. For benzocycloheptene the activation energies for the inversions between chair, boat and twist (S, W, T) conformations were determined from model calculations. The best route for the inversion of the chair is the version way S → W via the transitional conformation V₄₅ and V₅₆. The calculated activation energy for this (14·6 kcal/mole) agrees well with the experimentally determined value (13 ± 1·5 kcal/mole). For the pseudorotation W → T a slightly lower calculated value of 11·1 kcal/mole was found.     

Mechanisms of conformational chirality inversion in bicyclo[4.2.1]nonan-9-one and bicyclo[4.2.2]decane as studied in two-parametric torsional energy surfaces

With the purpose of deciphering conformational inversion processes of typical mobile bicyclic molecules, torsional energy surfaces near the enantiomers of bicyclo[4.2.1]nonan-9-one ( 1 ) and bicyclo-[4.2.2]decane ( 2 ) were prepared using molecular mechanics with an improved two-bond drive technique. Inversion of 1 takes place most favorably via a C_s transition state with the tetramethylene chain over the ethano bridge [ 1B , ΔH^± 6.1 (calculated) vs. 6.8 (observed) kcal/mol]. An alternative pathway involving a C_s local energy minimum ( 1C ), in which the tetramethylene chain is bent over the carbonyl, has a barrier 2.4 kcal higher than 1B . The global energy minimum conformation of 2 has boat–chair cyclooctane and twist–boat cyclohexane rings (BCTB ), and enantiomerizes into its mirror image (BCTB ') via three intermediates: TCTB , CB , and TCTB '. The highest point in the proposed pathway, a saddlepoint CB , is calculated to lie 8.0 kcal/mol above BCTB (observed ΔH^± 7.8 kcal/mol). The advantage of the two-parametric over the one-parametric torsional energy surface is discussed.     

Conformational analysis—CXXIII: Carboxylic acids and esters in force field calculations

Force field calculations have been extended to include carboxylic acids and esters. Necessary parameters were chosen mainly by fitting to available experimental data on small molecules. A few key facts are not known experimentally, and these were found by carrying out ab initio (STO-3G) calculations. Other molecules were then studied and structural predictions were made. It is predicted that in isobutyric acid a methyl group is twisted 15° from eclipsing the carbonyl oxygen in the ground state. The relative energies and torsional functions for cyclohexanecarboxylic acid are reported. Except for rather simple compounds, such as normal chains, the carboxyl is usually twisted with respect to the attached chain. Some conformations of lactones were also examined. For δ-valerolactone it is predicted that the boat conformation is more stable than the chair. Heats of formation of the compounds can be calculated with fair accuracy.     

Protein structure prediction using a combination of sequence homology and global energy minimization: II. Energy functions

A protein energy surface is constructed. Validation is through applications of global energy minimization to surface loops of protein crystal structures. For 9 of 10 predictions, the native backbone conformation is identified correctly. Electrostatic energy is modeled as a pairwise sum of interactions between anisotropic atomic charge densities. Model repulsion energy has a softness similar to that seen in ab initio data. Intrinsic torsional energy is modeled as a sum over pairs of adjacent torsion angles of 2-dimensional Fourier series. Hydrophobic energy is that of a hydration shell model. The remainder of hydration free energy is obtained as the energetic effect of a continuous dielectric medium. Parameters are adjusted to reproduce the following data: a complete set of ab initio energy surfaces, meaning one for each pair of adjacent torsion angles of each blocked amino acid; experimental crystal structures and sublimation energies for nine model compounds; ab initio energies over 1014 conformations of 15 small-molecule dimers; and experimental hydration free energies for 48 model compounds. All ab initio data is at the Hartree–Fock/6–31G* level. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 548–573, 1998     

Conformational study of cis-1,4-di-tert-butylcyclohexane by dynamic NMR spectroscopy and computational methods. Observation of chair and twist-boat conformations

[reaction: see text] Low-temperature 13C NMR spectra of cis-1,4-di-tert-butylcyclohexane (1) showed signals for the twist-boat (1a) and chair (1b) conformations. 13C NMR signals were assigned to specific carbons based on the different populations, different symmetries (time-averaged C(2v) for 1a and time-averaged C(s) for 1b), and calculated chemical shifts (GIAO, HF/6-311+G*). In addition to slow ring inversion and interconversion of the chair and twist-boat conformations, slow rotation of the tert-butyl groups was found. Most of the expected 13C peaks were observed. Free-energy barriers of 6.83 and 6.35 kcal/mol were found for interconversion of 1a (major) and 1b (minor) at -148.1 degrees C. Conformational space was searched with Allinger's MM3 and MM4 programs, and free energies were obtained for several low-energy conformations 1a-c. Calculations were repeated with ab initio methods up to the HF/6-311+G* level. Molecular symmetries, relative free energies, relative enthalpies and entropies, frequencies, and NMR chemical shifts were obtained. A boat conformation (1d; C(2v) symmetry) was generated and optimized as a transition state by ab initio, MM3, and MM4 calculations.     

Boat conformation in 2,5-substituted 1,3-dioxanes

The calculation of the energy equilibrium according to Pitzer between the chair and boat conformations in 2,5-substituted 1,3-dioxanes is presented, as well as the energies of the electrostatic dipole interactions. It is shown that the unsymmetrical boat conformation is stabilized in 2,5-dialkyl- and in 2,2-dimethyl-5-alkyl-5--alkoxyalkyl-1,3-dioxanes because of the presence of hetero atoms in the ring, because of the introduction of substituents in the 2 and 5 positions, and because of the interaction between the hybridized, unshared electron pairs of the oxygen atom at the apex of the boat with the hydrogen atom of the CH₂ group.     

First-principle studies of intermolecular and intramolecular catalysis of protonated cocaine

We have performed a series of first-principles electronic structure calculations to examine the reaction pathways and the corresponding free energy barriers for the ester hydrolysis of protonated cocaine in its chair and boat conformations. The calculated free energy barriers for the benzoyl ester hydrolysis of protonated chair cocaine are close to the corresponding barriers calculated for the benzoyl ester hydrolysis of neutral cocaine. However, the free energy barrier calculated for the methyl ester hydrolysis of protonated cocaine in its chair conformation is significantly lower than for the methyl ester hydrolysis of neutral cocaine and for the dominant pathway of the benzoyl ester hydrolysis of protonated cocaine. The significant decrease of the free energy barrier, approximately 4 kcal/mol, is attributed to the intramolecular acid catalysis of the methyl ester hydrolysis of protonated cocaine, because the transition state structure is stabilized by the strong hydrogen bond between the carbonyl oxygen of the methyl ester moiety and the protonated tropane N. The relative magnitudes of the free energy barriers calculated for different pathways of the ester hydrolysis of protonated chair cocaine are consistent with the experimental kinetic data for cocaine hydrolysis under physiologic conditions. Similar intramolecular acid catalysis also occurs for the benzoyl ester hydrolysis of (protonated) boat cocaine in the physiologic condition, although the contribution of the intramolecular hydrogen bonding to transition state stabilization is negligible. Nonetheless, the predictability of the intramolecular hydrogen bonding could be useful in generating antibody-based catalysts that recruit cocaine to the boat conformation and an analog that elicited antibodies to approximate the protonated tropane N and the benzoyl O more closely than the natural boat conformer might increase the contribution from hydrogen bonding. Such a stable analog of the transition state for intramolecular catalysis of cocaine benzoyl-ester hydrolysis was synthesized and used to successfully elicit a number of anticocaine catalytic antibodies.     

Internal dynamics of flexible molecules: Cyclohexane

Summary The international motions of a single cyclohexane molecule are studied by molecular dynamics calculations. Classical trajectories are calculated by integrating Newton's equation of motion. The potential functions used are essentially the same as in Allinger's MM2 program which is widely applied for calculations on conformational energies of organic molecules.Geometries and relative energies are reported for all stable low energy conformers and some transition states of cyclohexane. Vibrational frequencies of classical oscillations of individual bonds — computed for ethane as reference system — are close to the experimental values.Two trajectories of the molecular dynamics of cyclohexane were simulated. In the first we were able to follow the process of ring inversion: chair twisted forms inverted chair. The reaction path is analysed in detail and compared with static approaches. The second trajectory shows the correlated reorientation of the possible twisted forms alone. This process is known as pseudorotation.Dedicated to Prof. Dr. Karl Schlögl     

Ring conformations of 2-substituted 2-oxo-4-methyl-1,3,2-dioxaphosphorinanes. Evidence for a boat conformation in equilibrium with two interconverting chairs

The 220 MHz proton NMR spectra of three isomeric pairs of 2-R-2-oxo-4-methyl-1,3,2-dioxaphosphorinanes, where R = methoxy (1a, b), methyl (2a, b) and dimethylamino (3a, b) (a represents the trans and b the cis arrangement of R and the 4-methyl group) were analyzed by iterative computer techniques. Ten ring conformations, two chairs, two half-chairs and six boats were initially considered as being possible contributors to the overall solution conformations. Compounds 1a, 2a, 2b and 3b were all concluded to exist as single chair conformations with the 4-methyl group equatorially oriented (eqch). In addition to 68% of compound 3a being in that eqch conformation, however, significant concentrations of the chair form containing an axially oriented 4-methyl group (axch, 16%) and a boat conformation containing an equatorially oriented 4-methyl group with phosphorus and C-5 serving as the bow and stern (eq25, 16%) were also postulated. Similarly, it was suggested that 1b contained 60% eqch, 20% axch and 20% of the boat eq25. From the data for compounds 2a and b it was concluded that in the chair conformations of 2-oxo species the phosphorus substituent orientation has little effect upon the ³J(POCH) coupling constants.